Improve documentation on functions

Remove bad panic in coordinator
It expected ConfirmationShare to be n-of-n, not t-of-n.
2025-12-13 06:29:25 +00:00 · 2024-08-06 00:27:54 -04:00 · 2024-08-06 00:27:19 -04:00 · 2024-08-06 00:27:07 -04:00 · 2024-08-05 23:50:23 -04:00 · 2024-08-05 23:43:38 -04:00
118 changed files with 10270 additions and 2433 deletions
--- a/.github/workflows/crypto-tests.yml
+++ b/.github/workflows/crypto-tests.yml
@@ -35,6 +35,10 @@ jobs:
            -p multiexp \
            -p schnorr-signatures \
            -p dleq \
+            -p generalized-bulletproofs \
+            -p generalized-bulletproofs-circuit-abstraction \
+            -p ec-divisors \
+            -p generalized-bulletproofs-ec-gadgets \
            -p dkg \
            -p modular-frost \
            -p frost-schnorrkel
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1069,6 +1069,7 @@ checksum = "1bc2832c24239b0141d5674bb9174f9d68a8b5b3f2753311927c172ca46f7e9c"
 dependencies = [
 "funty",
 "radium",
+ "serde",
 "tap",
 "wyz",
 ]
@@ -2128,15 +2129,27 @@ dependencies = [
 name = "dkg"
 version = "0.5.1"
 dependencies = [
+ "blake2",
 "borsh",
 "chacha20",
 "ciphersuite",
 "dleq",
+ "ec-divisors",
+ "embedwards25519",
 "flexible-transcript",
+ "generalized-bulletproofs",
+ "generalized-bulletproofs-circuit-abstraction",
+ "generalized-bulletproofs-ec-gadgets",
+ "generic-array 1.1.0",
 "multiexp",
+ "pasta_curves",
+ "rand",
+ "rand_chacha",
 "rand_core",
 "schnorr-signatures",
+ "secq256k1",
 "std-shims",
+ "subtle",
 "thiserror",
 "zeroize",
 ]
@@ -2226,6 +2239,18 @@ version = "1.0.17"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "0d6ef0072f8a535281e4876be788938b528e9a1d43900b82c2569af7da799125"

+[[package]]
+name = "ec-divisors"
+version = "0.1.0"
+dependencies = [
+ "dalek-ff-group",
+ "group",
+ "hex",
+ "pasta_curves",
+ "rand_core",
+ "zeroize",
+]
+
 [[package]]
 name = "ecdsa"
 version = "0.16.9"
@@ -2306,6 +2331,26 @@ dependencies = [
 "zeroize",
 ]

+[[package]]
+name = "embedwards25519"
+version = "0.1.0"
+dependencies = [
+ "blake2",
+ "ciphersuite",
+ "crypto-bigint",
+ "dalek-ff-group",
+ "ec-divisors",
+ "ff-group-tests",
+ "generalized-bulletproofs-ec-gadgets",
+ "generic-array 0.14.7",
+ "hex",
+ "hex-literal",
+ "rand_core",
+ "rustversion",
+ "subtle",
+ "zeroize",
+]
+
 [[package]]
 name = "enum-as-inner"
 version = "0.5.1"
@@ -2977,6 +3022,36 @@ dependencies = [
 "serde_json",
 ]

+[[package]]
+name = "generalized-bulletproofs"
+version = "0.1.0"
+dependencies = [
+ "blake2",
+ "ciphersuite",
+ "flexible-transcript",
+ "multiexp",
+ "rand_core",
+ "zeroize",
+]
+
+[[package]]
+name = "generalized-bulletproofs-circuit-abstraction"
+version = "0.1.0"
+dependencies = [
+ "ciphersuite",
+ "generalized-bulletproofs",
+ "zeroize",
+]
+
+[[package]]
+name = "generalized-bulletproofs-ec-gadgets"
+version = "0.1.0"
+dependencies = [
+ "ciphersuite",
+ "generalized-bulletproofs-circuit-abstraction",
+ "generic-array 1.1.0",
+]
+
 [[package]]
 name = "generator"
 version = "0.8.1"
@@ -3337,7 +3412,7 @@ dependencies = [
 "httpdate",
 "itoa",
 "pin-project-lite",
- "socket2 0.4.10",
+ "socket2 0.5.7",
 "tokio",
 "tower-service",
 "tracing",
@@ -3867,7 +3942,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "4979f22fdb869068da03c9f7528f8297c6fd2606bc3a4affe42e6a823fdb8da4"
 dependencies = [
 "cfg-if",
- "windows-targets 0.48.5",
+ "windows-targets 0.52.6",
 ]

 [[package]]
@@ -5702,8 +5777,7 @@ dependencies = [
 [[package]]
 name = "pasta_curves"
 version = "0.5.1"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d3e57598f73cc7e1b2ac63c79c517b31a0877cd7c402cdcaa311b5208de7a095"
+source = "git+https://github.com/kayabaNerve/pasta_curves?rev=a46b5be95cacbff54d06aad8d3bbcba42e05d616#a46b5be95cacbff54d06aad8d3bbcba42e05d616"
 dependencies = [
 "blake2b_simd",
 "ff",
@@ -5712,6 +5786,7 @@ dependencies = [
 "rand",
 "static_assertions",
 "subtle",
+ "zeroize",
 ]

 [[package]]
@@ -7841,6 +7916,26 @@ dependencies = [
 "cc",
 ]

+[[package]]
+name = "secq256k1"
+version = "0.1.0"
+dependencies = [
+ "blake2",
+ "ciphersuite",
+ "crypto-bigint",
+ "ec-divisors",
+ "ff-group-tests",
+ "generalized-bulletproofs-ec-gadgets",
+ "generic-array 0.14.7",
+ "hex",
+ "hex-literal",
+ "k256",
+ "rand_core",
+ "rustversion",
+ "subtle",
+ "zeroize",
+]
+
 [[package]]
 name = "secrecy"
 version = "0.8.0"
@@ -7925,6 +8020,7 @@ checksum = "cd0b0ec5f1c1ca621c432a25813d8d60c88abe6d3e08a3eb9cf37d97a0fe3d73"
 name = "serai-abi"
 version = "0.1.0"
 dependencies = [
+ "bitvec",
 "borsh",
 "frame-support",
 "parity-scale-codec",
@@ -7948,6 +8044,7 @@ version = "0.1.0"
 dependencies = [
 "async-lock",
 "bitcoin",
+ "bitvec",
 "blake2",
 "ciphersuite",
 "dockertest",
@@ -8005,6 +8102,7 @@ name = "serai-coordinator"
 version = "0.1.0"
 dependencies = [
 "async-trait",
+ "bitvec",
 "blake2",
 "borsh",
 "ciphersuite",
@@ -8042,10 +8140,12 @@ dependencies = [
 "ciphersuite",
 "dkg",
 "dockertest",
+ "embedwards25519",
 "hex",
 "parity-scale-codec",
 "rand_core",
 "schnorrkel",
+ "secq256k1",
 "serai-client",
 "serai-docker-tests",
 "serai-message-queue",
@@ -8256,7 +8356,9 @@ dependencies = [
 name = "serai-node"
 version = "0.1.0"
 dependencies = [
+ "ciphersuite",
 "clap",
+ "embedwards25519",
 "frame-benchmarking",
 "futures-util",
 "hex",
@@ -8282,6 +8384,7 @@ dependencies = [
 "sc-transaction-pool",
 "sc-transaction-pool-api",
 "schnorrkel",
+ "secq256k1",
 "serai-env",
 "serai-runtime",
 "sp-api",
@@ -8303,11 +8406,13 @@ name = "serai-orchestrator"
 version = "0.0.1"
 dependencies = [
 "ciphersuite",
+ "embedwards25519",
 "flexible-transcript",
 "hex",
 "home",
 "rand_chacha",
 "rand_core",
+ "secq256k1",
 "zalloc",
 "zeroize",
 ]
@@ -8317,6 +8422,7 @@ name = "serai-primitives"
 version = "0.1.0"
 dependencies = [
 "borsh",
+ "ciphersuite",
 "frame-support",
 "parity-scale-codec",
 "rand_core",
@@ -8335,11 +8441,14 @@ version = "0.1.0"
 dependencies = [
 "async-trait",
 "bitcoin-serai",
+ "blake2",
 "borsh",
 "ciphersuite",
 "const-hex",
 "dalek-ff-group",
+ "dkg",
 "dockertest",
+ "ec-divisors",
 "env_logger",
 "ethereum-serai",
 "flexible-transcript",
@@ -8495,9 +8604,9 @@ dependencies = [
 name = "serai-validator-sets-pallet"
 version = "0.1.0"
 dependencies = [
+ "bitvec",
 "frame-support",
 "frame-system",
- "hashbrown 0.14.5",
 "pallet-babe",
 "pallet-grandpa",
 "parity-scale-codec",
@@ -8506,6 +8615,7 @@ dependencies = [
 "serai-dex-pallet",
 "serai-primitives",
 "serai-validator-sets-primitives",
+ "serde",
 "sp-application-crypto",
 "sp-core",
 "sp-io",
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -30,9 +30,16 @@ members = [
  "crypto/ciphersuite",

  "crypto/multiexp",
-
  "crypto/schnorr",
  "crypto/dleq",
+
+  "crypto/evrf/secq256k1",
+  "crypto/evrf/embedwards25519",
+  "crypto/evrf/generalized-bulletproofs",
+  "crypto/evrf/circuit-abstraction",
+  "crypto/evrf/divisors",
+  "crypto/evrf/ec-gadgets",
+
  "crypto/dkg",
  "crypto/frost",
  "crypto/schnorrkel",
@@ -110,18 +117,32 @@ members = [
 # to the extensive operations required for Bulletproofs
 [profile.dev.package]
 subtle = { opt-level = 3 }
-curve25519-dalek = { opt-level = 3 }

 ff = { opt-level = 3 }
 group = { opt-level = 3 }

 crypto-bigint = { opt-level = 3 }
+secp256k1 = { opt-level = 3 }
+curve25519-dalek = { opt-level = 3 }
 dalek-ff-group = { opt-level = 3 }
 minimal-ed448 = { opt-level = 3 }

 multiexp = { opt-level = 3 }

-monero-serai = { opt-level = 3 }
+secq256k1 = { opt-level = 3 }
+embedwards25519 = { opt-level = 3 }
+generalized-bulletproofs = { opt-level = 3 }
+generalized-bulletproofs-circuit-abstraction = { opt-level = 3 }
+ec-divisors = { opt-level = 3 }
+generalized-bulletproofs-ec-gadgets = { opt-level = 3 }
+
+dkg = { opt-level = 3 }
+
+monero-generators = { opt-level = 3 }
+monero-borromean = { opt-level = 3 }
+monero-bulletproofs = { opt-level = 3 }
+monero-mlsag = { opt-level = 3 }
+monero-clsag = { opt-level = 3 }

 [profile.release]
 panic = "unwind"
@@ -155,6 +176,9 @@ matches = { path = "patches/matches" }
 option-ext = { path = "patches/option-ext" }
 directories-next = { path = "patches/directories-next" }

+# The official pasta_curves repo doesn't support Zeroize
+pasta_curves = { git = "https://github.com/kayabaNerve/pasta_curves", rev = "a46b5be95cacbff54d06aad8d3bbcba42e05d616" }
+
 [workspace.lints.clippy]
 unwrap_or_default = "allow"
 borrow_as_ptr = "deny"
--- a/coordinator/Cargo.toml
+++ b/coordinator/Cargo.toml
@@ -20,6 +20,7 @@ workspace = true
 async-trait = { version = "0.1", default-features = false }

 zeroize = { version = "^1.5", default-features = false, features = ["std"] }
+bitvec = { version = "1", default-features = false, features = ["std"] }
 rand_core = { version = "0.6", default-features = false, features = ["std"] }

 blake2 = { version = "0.10", default-features = false, features = ["std"] }
--- a/coordinator/src/main.rs
+++ b/coordinator/src/main.rs
@@ -16,7 +16,6 @@ use ciphersuite::{
  Ciphersuite, Ristretto,
 };
 use schnorr::SchnorrSignature;
-use frost::Participant;

 use serai_db::{DbTxn, Db};

@@ -114,16 +113,17 @@ async fn add_tributary<D: Db, Pro: Processors, P: P2p>(
  // If we're rebooting, we'll re-fire this message
  // This is safe due to the message-queue deduplicating based off the intent system
  let set = spec.set();
-  let our_i = spec
-    .i(&[], Ristretto::generator() * key.deref())
-    .expect("adding a tributary for a set we aren't in set for");
+
  processors
    .send(
      set.network,
      processor_messages::key_gen::CoordinatorMessage::GenerateKey {
-        id: processor_messages::key_gen::KeyGenId { session: set.session, attempt: 0 },
-        params: frost::ThresholdParams::new(spec.t(), spec.n(&[]), our_i.start).unwrap(),
-        shares: u16::from(our_i.end) - u16::from(our_i.start),
+        session: set.session,
+        threshold: spec.t(),
+        evrf_public_keys: spec.evrf_public_keys(),
+        // TODO
+        // params: frost::ThresholdParams::new(spec.t(), spec.n(&[]), our_i.start).unwrap(),
+        // shares: u16::from(our_i.end) - u16::from(our_i.start),
      },
    )
    .await;
@@ -166,12 +166,9 @@ async fn handle_processor_message<D: Db, P: P2p>(
    // We'll only receive these if we fired GenerateKey, which we'll only do if if we're
    // in-set, making the Tributary relevant
    ProcessorMessage::KeyGen(inner_msg) => match inner_msg {
-      key_gen::ProcessorMessage::Commitments { id, .. } |
-      key_gen::ProcessorMessage::InvalidCommitments { id, .. } |
-      key_gen::ProcessorMessage::Shares { id, .. } |
-      key_gen::ProcessorMessage::InvalidShare { id, .. } |
-      key_gen::ProcessorMessage::GeneratedKeyPair { id, .. } |
-      key_gen::ProcessorMessage::Blame { id, .. } => Some(id.session),
+      key_gen::ProcessorMessage::Participation { session, .. } |
+      key_gen::ProcessorMessage::GeneratedKeyPair { session, .. } |
+      key_gen::ProcessorMessage::Blame { session, .. } => Some(*session),
    },
    ProcessorMessage::Sign(inner_msg) => match inner_msg {
      // We'll only receive InvalidParticipant/Preprocess/Share if we're actively signing
@@ -421,125 +418,33 @@ async fn handle_processor_message<D: Db, P: P2p>(

    let txs = match msg.msg.clone() {
      ProcessorMessage::KeyGen(inner_msg) => match inner_msg {
-        key_gen::ProcessorMessage::Commitments { id, commitments } => {
-          vec![Transaction::DkgCommitments {
-            attempt: id.attempt,
-            commitments,
-            signed: Transaction::empty_signed(),
-          }]
+        key_gen::ProcessorMessage::Participation { session, participation } => {
+          assert_eq!(session, spec.set().session);
+          vec![Transaction::DkgParticipation { participation, signed: Transaction::empty_signed() }]
        }
-        key_gen::ProcessorMessage::InvalidCommitments { id, faulty } => {
-          // This doesn't have guaranteed timing
-          //
-          // While the party *should* be fatally slashed and not included in future attempts,
-          // they'll actually be fatally slashed (assuming liveness before the Tributary retires)
-          // and not included in future attempts *which begin after the latency window completes*
-          let participant = spec
-            .reverse_lookup_i(
-              &crate::tributary::removed_as_of_dkg_attempt(&txn, spec.genesis(), id.attempt)
-                .expect("participating in DKG attempt yet we didn't save who was removed"),
-              faulty,
-            )
-            .unwrap();
-          vec![Transaction::RemoveParticipantDueToDkg {
-            participant,
-            signed: Transaction::empty_signed(),
-          }]
-        }
-        key_gen::ProcessorMessage::Shares { id, mut shares } => {
-          // Create a MuSig-based machine to inform Substrate of this key generation
-          let nonces = crate::tributary::dkg_confirmation_nonces(key, spec, &mut txn, id.attempt);
-
-          let removed = crate::tributary::removed_as_of_dkg_attempt(&txn, genesis, id.attempt)
-            .expect("participating in a DKG attempt yet we didn't track who was removed yet?");
-          let our_i = spec
-            .i(&removed, pub_key)
-            .expect("processor message to DKG for an attempt we aren't a validator in");
-
-          // `tx_shares` needs to be done here as while it can be serialized from the HashMap
-          // without further context, it can't be deserialized without context
-          let mut tx_shares = Vec::with_capacity(shares.len());
-          for shares in &mut shares {
-            tx_shares.push(vec![]);
-            for i in 1 ..= spec.n(&removed) {
-              let i = Participant::new(i).unwrap();
-              if our_i.contains(&i) {
-                if shares.contains_key(&i) {
-                  panic!("processor sent us our own shares");
-                }
-                continue;
-              }
-              tx_shares.last_mut().unwrap().push(
-                shares.remove(&i).expect("processor didn't send share for another validator"),
-              );
-            }
-          }
-
-          vec![Transaction::DkgShares {
-            attempt: id.attempt,
-            shares: tx_shares,
-            confirmation_nonces: nonces,
-            signed: Transaction::empty_signed(),
-          }]
-        }
-        key_gen::ProcessorMessage::InvalidShare { id, accuser, faulty, blame } => {
-          vec![Transaction::InvalidDkgShare {
-            attempt: id.attempt,
-            accuser,
-            faulty,
-            blame,
-            signed: Transaction::empty_signed(),
-          }]
-        }
-        key_gen::ProcessorMessage::GeneratedKeyPair { id, substrate_key, network_key } => {
-          // TODO2: Check the KeyGenId fields
-
-          // Tell the Tributary the key pair, get back the share for the MuSig signature
-          let share = crate::tributary::generated_key_pair::<D>(
+        key_gen::ProcessorMessage::GeneratedKeyPair { session, substrate_key, network_key } => {
+          assert_eq!(session, spec.set().session);
+          crate::tributary::generated_key_pair::<D>(
            &mut txn,
-            key,
-            spec,
+            genesis,
            &KeyPair(Public(substrate_key), network_key.try_into().unwrap()),
-            id.attempt,
          );

-          // TODO: Move this into generated_key_pair?
-          match share {
-            Ok(share) => {
-              vec![Transaction::DkgConfirmed {
-                attempt: id.attempt,
-                confirmation_share: share,
-                signed: Transaction::empty_signed(),
-              }]
-            }
-            Err(p) => {
-              let participant = spec
-                .reverse_lookup_i(
-                  &crate::tributary::removed_as_of_dkg_attempt(&txn, spec.genesis(), id.attempt)
-                    .expect("participating in DKG attempt yet we didn't save who was removed"),
-                  p,
-                )
-                .unwrap();
-              vec![Transaction::RemoveParticipantDueToDkg {
-                participant,
-                signed: Transaction::empty_signed(),
-              }]
-            }
-          }
-        }
-        key_gen::ProcessorMessage::Blame { id, participant } => {
-          let participant = spec
-            .reverse_lookup_i(
-              &crate::tributary::removed_as_of_dkg_attempt(&txn, spec.genesis(), id.attempt)
-                .expect("participating in DKG attempt yet we didn't save who was removed"),
-              participant,
-            )
-            .unwrap();
-          vec![Transaction::RemoveParticipantDueToDkg {
-            participant,
+          // Create a MuSig-based machine to inform Substrate of this key generation
+          let confirmation_nonces =
+            crate::tributary::dkg_confirmation_nonces(key, spec, &mut txn, 0);
+
+          vec![Transaction::DkgConfirmationNonces {
+            attempt: 0,
+            confirmation_nonces,
            signed: Transaction::empty_signed(),
          }]
        }
+        key_gen::ProcessorMessage::Blame { session, participant } => {
+          assert_eq!(session, spec.set().session);
+          let participant = spec.reverse_lookup_i(participant).unwrap();
+          vec![Transaction::RemoveParticipant { participant, signed: Transaction::empty_signed() }]
+        }
      },
      ProcessorMessage::Sign(msg) => match msg {
        sign::ProcessorMessage::InvalidParticipant { .. } => {
--- a/coordinator/src/substrate/mod.rs
+++ b/coordinator/src/substrate/mod.rs
@@ -10,7 +10,7 @@ use ciphersuite::{group::GroupEncoding, Ciphersuite, Ristretto};

 use serai_client::{
  SeraiError, Block, Serai, TemporalSerai,
-  primitives::{BlockHash, NetworkId},
+  primitives::{BlockHash, EmbeddedEllipticCurve, NetworkId},
  validator_sets::{primitives::ValidatorSet, ValidatorSetsEvent},
  in_instructions::InInstructionsEvent,
  coins::CoinsEvent,
@@ -60,13 +60,46 @@ async fn handle_new_set<D: Db>(
  {
    log::info!("present in set {:?}", set);

-    let set_data = {
+    let validators;
+    let mut evrf_public_keys = vec![];
+    {
      let serai = serai.as_of(block.hash());
      let serai = serai.validator_sets();
      let set_participants =
        serai.participants(set.network).await?.expect("NewSet for set which doesn't exist");

-      set_participants.into_iter().map(|(k, w)| (k, u16::try_from(w).unwrap())).collect::<Vec<_>>()
+      validators = set_participants
+        .iter()
+        .map(|(k, w)| {
+          (
+            <Ristretto as Ciphersuite>::read_G::<&[u8]>(&mut k.0.as_ref())
+              .expect("invalid key registered as participant"),
+            u16::try_from(*w).unwrap(),
+          )
+        })
+        .collect::<Vec<_>>();
+      for (validator, _) in set_participants {
+        // This is only run for external networks which always do a DKG for Serai
+        let substrate = serai
+          .embedded_elliptic_curve_key(validator, EmbeddedEllipticCurve::Embedwards25519)
+          .await?
+          .expect("Serai called NewSet on a validator without an Embedwards25519 key");
+        // `embedded_elliptic_curves` is documented to have the second entry be the
+        // network-specific curve (if it exists and is distinct from Embedwards25519)
+        let network =
+          if let Some(embedded_elliptic_curve) = set.network.embedded_elliptic_curves().get(1) {
+            serai.embedded_elliptic_curve_key(validator, *embedded_elliptic_curve).await?.expect(
+            "Serai called NewSet on a validator without the embedded key required for the network",
+          )
+          } else {
+            substrate.clone()
+          };
+        evrf_public_keys.push((
+          <[u8; 32]>::try_from(substrate)
+            .expect("validator-sets pallet accepted a key of an invalid length"),
+          network,
+        ));
+      }
    };

    let time = if let Ok(time) = block.time() {
@@ -90,7 +123,7 @@ async fn handle_new_set<D: Db>(
    const SUBSTRATE_TO_TRIBUTARY_TIME_DELAY: u64 = 120;
    let time = time + SUBSTRATE_TO_TRIBUTARY_TIME_DELAY;

-    let spec = TributarySpec::new(block.hash(), time, set, set_data);
+    let spec = TributarySpec::new(block.hash(), time, set, validators, evrf_public_keys);

    log::info!("creating new tributary for {:?}", spec.set());

--- a/coordinator/src/tests/tributary/chain.rs
+++ b/coordinator/src/tests/tributary/chain.rs
@@ -7,12 +7,8 @@ use zeroize::Zeroizing;
 use rand_core::{RngCore, CryptoRng, OsRng};
 use futures_util::{task::Poll, poll};

-use ciphersuite::{
-  group::{ff::Field, GroupEncoding},
-  Ciphersuite, Ristretto,
-};
+use ciphersuite::{group::ff::Field, Ciphersuite, Ristretto};

-use sp_application_crypto::sr25519;
 use borsh::BorshDeserialize;
 use serai_client::{
  primitives::NetworkId,
@@ -52,12 +48,22 @@ pub fn new_spec<R: RngCore + CryptoRng>(

  let set = ValidatorSet { session: Session(0), network: NetworkId::Bitcoin };

-  let set_participants = keys
+  let validators = keys
    .iter()
-    .map(|key| (sr25519::Public((<Ristretto as Ciphersuite>::generator() * **key).to_bytes()), 1))
+    .map(|key| ((<Ristretto as Ciphersuite>::generator() * **key), 1))
    .collect::<Vec<_>>();

-  let res = TributarySpec::new(serai_block, start_time, set, set_participants);
+  // Generate random eVRF keys as none of these test rely on them to have any structure
+  let mut evrf_keys = vec![];
+  for _ in 0 .. keys.len() {
+    let mut substrate = [0; 32];
+    OsRng.fill_bytes(&mut substrate);
+    let mut network = vec![0; 64];
+    OsRng.fill_bytes(&mut network);
+    evrf_keys.push((substrate, network));
+  }
+
+  let res = TributarySpec::new(serai_block, start_time, set, validators, evrf_keys);
  assert_eq!(
    TributarySpec::deserialize_reader(&mut borsh::to_vec(&res).unwrap().as_slice()).unwrap(),
    res,
--- a/coordinator/src/tests/tributary/dkg.rs
+++ b/coordinator/src/tests/tributary/dkg.rs
@@ -1,5 +1,4 @@
 use core::time::Duration;
-use std::collections::HashMap;

 use zeroize::Zeroizing;
 use rand_core::{RngCore, OsRng};
@@ -9,7 +8,7 @@ use frost::Participant;

 use sp_runtime::traits::Verify;
 use serai_client::{
-  primitives::{SeraiAddress, Signature},
+  primitives::Signature,
  validator_sets::primitives::{ValidatorSet, KeyPair},
 };

@@ -17,10 +16,7 @@ use tokio::time::sleep;

 use serai_db::{Get, DbTxn, Db, MemDb};

-use processor_messages::{
-  key_gen::{self, KeyGenId},
-  CoordinatorMessage,
-};
+use processor_messages::{key_gen, CoordinatorMessage};

 use tributary::{TransactionTrait, Tributary};

@@ -54,44 +50,41 @@ async fn dkg_test() {
  tokio::spawn(run_tributaries(tributaries.clone()));

  let mut txs = vec![];
-  // Create DKG commitments for each key
+  // Create DKG participation for each key
  for key in &keys {
-    let attempt = 0;
-    let mut commitments = vec![0; 256];
-    OsRng.fill_bytes(&mut commitments);
+    let mut participation = vec![0; 4096];
+    OsRng.fill_bytes(&mut participation);

-    let mut tx = Transaction::DkgCommitments {
-      attempt,
-      commitments: vec![commitments],
-      signed: Transaction::empty_signed(),
-    };
+    let mut tx =
+      Transaction::DkgParticipation { participation, signed: Transaction::empty_signed() };
    tx.sign(&mut OsRng, spec.genesis(), key);
    txs.push(tx);
  }

  let block_before_tx = tributaries[0].1.tip().await;

-  // Publish all commitments but one
-  for (i, tx) in txs.iter().enumerate().skip(1) {
+  // Publish t-1 participations
+  let t = ((keys.len() * 2) / 3) + 1;
+  for (i, tx) in txs.iter().take(t - 1).enumerate() {
    assert_eq!(tributaries[i].1.add_transaction(tx.clone()).await, Ok(true));
-  }
-
-  // Wait until these are included
-  for tx in txs.iter().skip(1) {
    wait_for_tx_inclusion(&tributaries[0].1, block_before_tx, tx.hash()).await;
  }

-  let expected_commitments: HashMap<_, _> = txs
+  let expected_participations = txs
    .iter()
    .enumerate()
    .map(|(i, tx)| {
-      if let Transaction::DkgCommitments { commitments, .. } = tx {
-        (Participant::new((i + 1).try_into().unwrap()).unwrap(), commitments[0].clone())
+      if let Transaction::DkgParticipation { participation, .. } = tx {
+        CoordinatorMessage::KeyGen(key_gen::CoordinatorMessage::Participation {
+          session: spec.set().session,
+          participant: Participant::new((i + 1).try_into().unwrap()).unwrap(),
+          participation: participation.clone(),
+        })
      } else {
-        panic!("txs had non-commitments");
+        panic!("txs wasn't a DkgParticipation");
      }
    })
-    .collect();
+    .collect::<Vec<_>>();

  async fn new_processors(
    db: &mut MemDb,
@@ -120,28 +113,30 @@ async fn dkg_test() {
    processors
  }

-  // Instantiate a scanner and verify it has nothing to report
+  // Instantiate a scanner and verify it has the first two participations to report (and isn't
+  // waiting for `t`)
  let processors = new_processors(&mut dbs[0], &keys[0], &spec, &tributaries[0].1).await;
-  assert!(processors.0.read().await.is_empty());
+  assert_eq!(processors.0.read().await.get(&spec.set().network).unwrap().len(), t - 1);

-  // Publish the last commitment
+  // Publish the rest of the participations
  let block_before_tx = tributaries[0].1.tip().await;
-  assert_eq!(tributaries[0].1.add_transaction(txs[0].clone()).await, Ok(true));
-  wait_for_tx_inclusion(&tributaries[0].1, block_before_tx, txs[0].hash()).await;
-  sleep(Duration::from_secs(Tributary::<MemDb, Transaction, LocalP2p>::block_time().into())).await;
+  for tx in txs.iter().skip(t - 1) {
+    assert_eq!(tributaries[0].1.add_transaction(tx.clone()).await, Ok(true));
+    wait_for_tx_inclusion(&tributaries[0].1, block_before_tx, tx.hash()).await;
+  }

-  // Verify the scanner emits a KeyGen::Commitments message
+  // Verify the scanner emits all KeyGen::Participations messages
  handle_new_blocks::<_, _, _, _, _, LocalP2p>(
    &mut dbs[0],
    &keys[0],
    &|_, _, _, _| async {
-      panic!("provided TX caused recognized_id to be called after Commitments")
+      panic!("provided TX caused recognized_id to be called after DkgParticipation")
    },
    &processors,
    &(),
    &|_| async {
      panic!(
-        "test tried to publish a new Tributary TX from handle_application_tx after Commitments"
+        "test tried to publish a new Tributary TX from handle_application_tx after DkgParticipation"
      )
    },
    &spec,
@@ -150,17 +145,11 @@ async fn dkg_test() {
  .await;
  {
    let mut msgs = processors.0.write().await;
-    assert_eq!(msgs.len(), 1);
    let msgs = msgs.get_mut(&spec.set().network).unwrap();
-    let mut expected_commitments = expected_commitments.clone();
-    expected_commitments.remove(&Participant::new((1).try_into().unwrap()).unwrap());
-    assert_eq!(
-      msgs.pop_front().unwrap(),
-      CoordinatorMessage::KeyGen(key_gen::CoordinatorMessage::Commitments {
-        id: KeyGenId { session: spec.set().session, attempt: 0 },
-        commitments: expected_commitments
-      })
-    );
+    assert_eq!(msgs.len(), keys.len());
+    for expected in &expected_participations {
+      assert_eq!(&msgs.pop_front().unwrap(), expected);
+    }
    assert!(msgs.is_empty());
  }

@@ -168,149 +157,14 @@ async fn dkg_test() {
  for (i, key) in keys.iter().enumerate().skip(1) {
    let processors = new_processors(&mut dbs[i], key, &spec, &tributaries[i].1).await;
    let mut msgs = processors.0.write().await;
-    assert_eq!(msgs.len(), 1);
    let msgs = msgs.get_mut(&spec.set().network).unwrap();
-    let mut expected_commitments = expected_commitments.clone();
-    expected_commitments.remove(&Participant::new((i + 1).try_into().unwrap()).unwrap());
-    assert_eq!(
-      msgs.pop_front().unwrap(),
-      CoordinatorMessage::KeyGen(key_gen::CoordinatorMessage::Commitments {
-        id: KeyGenId { session: spec.set().session, attempt: 0 },
-        commitments: expected_commitments
-      })
-    );
+    assert_eq!(msgs.len(), keys.len());
+    for expected in &expected_participations {
+      assert_eq!(&msgs.pop_front().unwrap(), expected);
+    }
    assert!(msgs.is_empty());
  }

-  // Now do shares
-  let mut txs = vec![];
-  for (k, key) in keys.iter().enumerate() {
-    let attempt = 0;
-
-    let mut shares = vec![vec![]];
-    for i in 0 .. keys.len() {
-      if i != k {
-        let mut share = vec![0; 256];
-        OsRng.fill_bytes(&mut share);
-        shares.last_mut().unwrap().push(share);
-      }
-    }
-
-    let mut txn = dbs[k].txn();
-    let mut tx = Transaction::DkgShares {
-      attempt,
-      shares,
-      confirmation_nonces: crate::tributary::dkg_confirmation_nonces(key, &spec, &mut txn, 0),
-      signed: Transaction::empty_signed(),
-    };
-    txn.commit();
-    tx.sign(&mut OsRng, spec.genesis(), key);
-    txs.push(tx);
-  }
-
-  let block_before_tx = tributaries[0].1.tip().await;
-  for (i, tx) in txs.iter().enumerate().skip(1) {
-    assert_eq!(tributaries[i].1.add_transaction(tx.clone()).await, Ok(true));
-  }
-  for tx in txs.iter().skip(1) {
-    wait_for_tx_inclusion(&tributaries[0].1, block_before_tx, tx.hash()).await;
-  }
-
-  // With just 4 sets of shares, nothing should happen yet
-  handle_new_blocks::<_, _, _, _, _, LocalP2p>(
-    &mut dbs[0],
-    &keys[0],
-    &|_, _, _, _| async {
-      panic!("provided TX caused recognized_id to be called after some shares")
-    },
-    &processors,
-    &(),
-    &|_| async {
-      panic!(
-        "test tried to publish a new Tributary TX from handle_application_tx after some shares"
-      )
-    },
-    &spec,
-    &tributaries[0].1.reader(),
-  )
-  .await;
-  assert_eq!(processors.0.read().await.len(), 1);
-  assert!(processors.0.read().await[&spec.set().network].is_empty());
-
-  // Publish the final set of shares
-  let block_before_tx = tributaries[0].1.tip().await;
-  assert_eq!(tributaries[0].1.add_transaction(txs[0].clone()).await, Ok(true));
-  wait_for_tx_inclusion(&tributaries[0].1, block_before_tx, txs[0].hash()).await;
-  sleep(Duration::from_secs(Tributary::<MemDb, Transaction, LocalP2p>::block_time().into())).await;
-
-  // Each scanner should emit a distinct shares message
-  let shares_for = |i: usize| {
-    CoordinatorMessage::KeyGen(key_gen::CoordinatorMessage::Shares {
-      id: KeyGenId { session: spec.set().session, attempt: 0 },
-      shares: vec![txs
-        .iter()
-        .enumerate()
-        .filter_map(|(l, tx)| {
-          if let Transaction::DkgShares { shares, .. } = tx {
-            if i == l {
-              None
-            } else {
-              let relative_i = i - (if i > l { 1 } else { 0 });
-              Some((
-                Participant::new((l + 1).try_into().unwrap()).unwrap(),
-                shares[0][relative_i].clone(),
-              ))
-            }
-          } else {
-            panic!("txs had non-shares");
-          }
-        })
-        .collect::<HashMap<_, _>>()],
-    })
-  };
-
-  // Any scanner which has handled the prior blocks should only emit the new event
-  for (i, key) in keys.iter().enumerate() {
-    handle_new_blocks::<_, _, _, _, _, LocalP2p>(
-      &mut dbs[i],
-      key,
-      &|_, _, _, _| async { panic!("provided TX caused recognized_id to be called after shares") },
-      &processors,
-      &(),
-      &|_| async { panic!("test tried to publish a new Tributary TX from handle_application_tx") },
-      &spec,
-      &tributaries[i].1.reader(),
-    )
-    .await;
-    {
-      let mut msgs = processors.0.write().await;
-      assert_eq!(msgs.len(), 1);
-      let msgs = msgs.get_mut(&spec.set().network).unwrap();
-      assert_eq!(msgs.pop_front().unwrap(), shares_for(i));
-      assert!(msgs.is_empty());
-    }
-  }
-
-  // Yet new scanners should emit all events
-  for (i, key) in keys.iter().enumerate() {
-    let processors = new_processors(&mut MemDb::new(), key, &spec, &tributaries[i].1).await;
-    let mut msgs = processors.0.write().await;
-    assert_eq!(msgs.len(), 1);
-    let msgs = msgs.get_mut(&spec.set().network).unwrap();
-    let mut expected_commitments = expected_commitments.clone();
-    expected_commitments.remove(&Participant::new((i + 1).try_into().unwrap()).unwrap());
-    assert_eq!(
-      msgs.pop_front().unwrap(),
-      CoordinatorMessage::KeyGen(key_gen::CoordinatorMessage::Commitments {
-        id: KeyGenId { session: spec.set().session, attempt: 0 },
-        commitments: expected_commitments
-      })
-    );
-    assert_eq!(msgs.pop_front().unwrap(), shares_for(i));
-    assert!(msgs.is_empty());
-  }
-
-  // Send DkgConfirmed
  let mut substrate_key = [0; 32];
  OsRng.fill_bytes(&mut substrate_key);
  let mut network_key = vec![0; usize::try_from((OsRng.next_u64() % 32) + 32).unwrap()];
@@ -319,17 +173,19 @@ async fn dkg_test() {

  let mut txs = vec![];
  for (i, key) in keys.iter().enumerate() {
-    let attempt = 0;
    let mut txn = dbs[i].txn();
-    let share =
-      crate::tributary::generated_key_pair::<MemDb>(&mut txn, key, &spec, &key_pair, 0).unwrap();
-    txn.commit();

-    let mut tx = Transaction::DkgConfirmed {
+    // Claim we've generated the key pair
+    crate::tributary::generated_key_pair::<MemDb>(&mut txn, spec.genesis(), &key_pair);
+
+    // Publish the nonces
+    let attempt = 0;
+    let mut tx = Transaction::DkgConfirmationNonces {
      attempt,
-      confirmation_share: share,
+      confirmation_nonces: crate::tributary::dkg_confirmation_nonces(key, &spec, &mut txn, 0),
      signed: Transaction::empty_signed(),
    };
+    txn.commit();
    tx.sign(&mut OsRng, spec.genesis(), key);
    txs.push(tx);
  }
@@ -341,6 +197,35 @@ async fn dkg_test() {
    wait_for_tx_inclusion(&tributaries[0].1, block_before_tx, tx.hash()).await;
  }

+  // This should not cause any new processor event as the processor doesn't handle DKG confirming
+  for (i, key) in keys.iter().enumerate() {
+    handle_new_blocks::<_, _, _, _, _, LocalP2p>(
+      &mut dbs[i],
+      key,
+      &|_, _, _, _| async {
+        panic!("provided TX caused recognized_id to be called after DkgConfirmationNonces")
+      },
+      &processors,
+      &(),
+      // The Tributary handler should publish ConfirmationShare itself after ConfirmationNonces
+      &|tx| async { assert_eq!(tributaries[i].1.add_transaction(tx).await, Ok(true)) },
+      &spec,
+      &tributaries[i].1.reader(),
+    )
+    .await;
+    {
+      assert!(processors.0.read().await.get(&spec.set().network).unwrap().is_empty());
+    }
+  }
+
+  // Yet once these TXs are on-chain, the tributary should itself publish the confirmation shares
+  // This means in the block after the next block, the keys should be set onto Serai
+  // Sleep twice as long as two blocks, in case there's some stability issue
+  sleep(Duration::from_secs(
+    2 * 2 * u64::from(Tributary::<MemDb, Transaction, LocalP2p>::block_time()),
+  ))
+  .await;
+
  struct CheckPublishSetKeys {
    spec: TributarySpec,
    key_pair: KeyPair,
@@ -351,19 +236,24 @@ async fn dkg_test() {
      &self,
      _db: &(impl Sync + Get),
      set: ValidatorSet,
-      removed: Vec<SeraiAddress>,
      key_pair: KeyPair,
+      signature_participants: bitvec::vec::BitVec<u8, bitvec::order::Lsb0>,
      signature: Signature,
    ) {
      assert_eq!(set, self.spec.set());
-      assert!(removed.is_empty());
      assert_eq!(self.key_pair, key_pair);
      assert!(signature.verify(
-        &*serai_client::validator_sets::primitives::set_keys_message(&set, &[], &key_pair),
+        &*serai_client::validator_sets::primitives::set_keys_message(&set, &key_pair),
        &serai_client::Public(
          frost::dkg::musig::musig_key::<Ristretto>(
            &serai_client::validator_sets::primitives::musig_context(set),
-            &self.spec.validators().into_iter().map(|(validator, _)| validator).collect::<Vec<_>>()
+            &self
+              .spec
+              .validators()
+              .into_iter()
+              .zip(signature_participants)
+              .filter_map(|((validator, _), included)| included.then_some(validator))
+              .collect::<Vec<_>>()
          )
          .unwrap()
          .to_bytes()
--- a/coordinator/src/tests/tributary/mod.rs
+++ b/coordinator/src/tests/tributary/mod.rs
@@ -6,7 +6,7 @@ use ciphersuite::{group::Group, Ciphersuite, Ristretto};

 use scale::{Encode, Decode};
 use serai_client::{
-  primitives::{SeraiAddress, Signature},
+  primitives::Signature,
  validator_sets::primitives::{MAX_KEY_SHARES_PER_SET, ValidatorSet, KeyPair},
 };
 use processor_messages::coordinator::SubstrateSignableId;
@@ -32,8 +32,8 @@ impl PublishSeraiTransaction for () {
    &self,
    _db: &(impl Sync + serai_db::Get),
    _set: ValidatorSet,
-    _removed: Vec<SeraiAddress>,
    _key_pair: KeyPair,
+    _signature_participants: bitvec::vec::BitVec<u8, bitvec::order::Lsb0>,
    _signature: Signature,
  ) {
    panic!("publish_set_keys was called in test")
@@ -143,84 +143,34 @@ fn serialize_sign_data() {

 #[test]
 fn serialize_transaction() {
-  test_read_write(&Transaction::RemoveParticipantDueToDkg {
+  test_read_write(&Transaction::RemoveParticipant {
    participant: <Ristretto as Ciphersuite>::G::random(&mut OsRng),
    signed: random_signed_with_nonce(&mut OsRng, 0),
  });

-  {
-    let mut commitments = vec![random_vec(&mut OsRng, 512)];
-    for _ in 0 .. (OsRng.next_u64() % 100) {
-      let mut temp = commitments[0].clone();
-      OsRng.fill_bytes(&mut temp);
-      commitments.push(temp);
-    }
-    test_read_write(&Transaction::DkgCommitments {
-      attempt: random_u32(&mut OsRng),
-      commitments,
-      signed: random_signed_with_nonce(&mut OsRng, 0),
-    });
-  }
+  test_read_write(&Transaction::DkgParticipation {
+    participation: random_vec(&mut OsRng, 4096),
+    signed: random_signed_with_nonce(&mut OsRng, 0),
+  });

-  {
-    // This supports a variable share length, and variable amount of sent shares, yet share length
-    // and sent shares is expected to be constant among recipients
-    let share_len = usize::try_from((OsRng.next_u64() % 512) + 1).unwrap();
-    let amount_of_shares = usize::try_from((OsRng.next_u64() % 3) + 1).unwrap();
-    // Create a valid vec of shares
-    let mut shares = vec![];
-    // Create up to 150 participants
-    for _ in 0 ..= (OsRng.next_u64() % 150) {
-      // Give each sender multiple shares
-      let mut sender_shares = vec![];
-      for _ in 0 .. amount_of_shares {
-        let mut share = vec![0; share_len];
-        OsRng.fill_bytes(&mut share);
-        sender_shares.push(share);
-      }
-      shares.push(sender_shares);
-    }
+  test_read_write(&Transaction::DkgConfirmationNonces {
+    attempt: random_u32(&mut OsRng),
+    confirmation_nonces: {
+      let mut nonces = [0; 64];
+      OsRng.fill_bytes(&mut nonces);
+      nonces
+    },
+    signed: random_signed_with_nonce(&mut OsRng, 0),
+  });

-    test_read_write(&Transaction::DkgShares {
-      attempt: random_u32(&mut OsRng),
-      shares,
-      confirmation_nonces: {
-        let mut nonces = [0; 64];
-        OsRng.fill_bytes(&mut nonces);
-        nonces
-      },
-      signed: random_signed_with_nonce(&mut OsRng, 1),
-    });
-  }
-
-  for i in 0 .. 2 {
-    test_read_write(&Transaction::InvalidDkgShare {
-      attempt: random_u32(&mut OsRng),
-      accuser: frost::Participant::new(
-        u16::try_from(OsRng.next_u64() >> 48).unwrap().saturating_add(1),
-      )
-      .unwrap(),
-      faulty: frost::Participant::new(
-        u16::try_from(OsRng.next_u64() >> 48).unwrap().saturating_add(1),
-      )
-      .unwrap(),
-      blame: if i == 0 {
-        None
-      } else {
-        Some(random_vec(&mut OsRng, 500)).filter(|blame| !blame.is_empty())
-      },
-      signed: random_signed_with_nonce(&mut OsRng, 2),
-    });
-  }
-
-  test_read_write(&Transaction::DkgConfirmed {
+  test_read_write(&Transaction::DkgConfirmationShare {
    attempt: random_u32(&mut OsRng),
    confirmation_share: {
      let mut share = [0; 32];
      OsRng.fill_bytes(&mut share);
      share
    },
-    signed: random_signed_with_nonce(&mut OsRng, 2),
+    signed: random_signed_with_nonce(&mut OsRng, 1),
  });

  {
--- a/coordinator/src/tests/tributary/sync.rs
+++ b/coordinator/src/tests/tributary/sync.rs
@@ -29,7 +29,7 @@ async fn sync_test() {
  let mut keys = new_keys(&mut OsRng);
  let spec = new_spec(&mut OsRng, &keys);
  // Ensure this can have a node fail
-  assert!(spec.n(&[]) > spec.t());
+  assert!(spec.n() > spec.t());

  let mut tributaries = new_tributaries(&keys, &spec)
    .await
@@ -142,7 +142,7 @@ async fn sync_test() {
  // Because only `t` validators are used in a commit, take n - t nodes offline
  // leaving only `t` nodes. Which should force it to participate in the consensus
  // of next blocks.
-  let spares = usize::from(spec.n(&[]) - spec.t());
+  let spares = usize::from(spec.n() - spec.t());
  for thread in p2p_threads.iter().take(spares) {
    thread.abort();
  }
--- a/coordinator/src/tests/tributary/tx.rs
+++ b/coordinator/src/tests/tributary/tx.rs
@@ -37,15 +37,14 @@ async fn tx_test() {
    usize::try_from(OsRng.next_u64() % u64::try_from(tributaries.len()).unwrap()).unwrap();
  let key = keys[sender].clone();

-  let attempt = 0;
-  let mut commitments = vec![0; 256];
-  OsRng.fill_bytes(&mut commitments);
-
-  // Create the TX with a null signature so we can get its sig hash
  let block_before_tx = tributaries[sender].1.tip().await;
-  let mut tx = Transaction::DkgCommitments {
-    attempt,
-    commitments: vec![commitments.clone()],
+  // Create the TX with a null signature so we can get its sig hash
+  let mut tx = Transaction::DkgParticipation {
+    participation: {
+      let mut participation = vec![0; 4096];
+      OsRng.fill_bytes(&mut participation);
+      participation
+    },
    signed: Transaction::empty_signed(),
  };
  tx.sign(&mut OsRng, spec.genesis(), &key);
--- a/coordinator/src/tributary/db.rs
+++ b/coordinator/src/tributary/db.rs
@@ -18,7 +18,6 @@ use crate::tributary::{Label, Transaction};

 #[derive(Clone, Copy, PartialEq, Eq, Debug, Encode, BorshSerialize, BorshDeserialize)]
 pub enum Topic {
-  Dkg,
  DkgConfirmation,
  SubstrateSign(SubstrateSignableId),
  Sign([u8; 32]),
@@ -46,15 +45,13 @@ pub enum Accumulation {
 create_db!(
  Tributary {
    SeraiBlockNumber: (hash: [u8; 32]) -> u64,
-    SeraiDkgCompleted: (spec: ValidatorSet) -> [u8; 32],
+    SeraiDkgCompleted: (set: ValidatorSet) -> [u8; 32],

    TributaryBlockNumber: (block: [u8; 32]) -> u32,
    LastHandledBlock: (genesis: [u8; 32]) -> [u8; 32],

    // TODO: Revisit the point of this
    FatalSlashes: (genesis: [u8; 32]) -> Vec<[u8; 32]>,
-    RemovedAsOfDkgAttempt: (genesis: [u8; 32], attempt: u32) -> Vec<[u8; 32]>,
-    OfflineDuringDkg: (genesis: [u8; 32]) -> Vec<[u8; 32]>,
    // TODO: Combine these two
    FatallySlashed: (genesis: [u8; 32], account: [u8; 32]) -> (),
    SlashPoints: (genesis: [u8; 32], account: [u8; 32]) -> u32,
@@ -67,11 +64,9 @@ create_db!(
    DataReceived: (genesis: [u8; 32], data_spec: &DataSpecification) -> u16,
    DataDb: (genesis: [u8; 32], data_spec: &DataSpecification, signer_bytes: &[u8; 32]) -> Vec<u8>,

-    DkgShare: (genesis: [u8; 32], from: u16, to: u16) -> Vec<u8>,
+    DkgParticipation: (genesis: [u8; 32], from: u16) -> Vec<u8>,
    ConfirmationNonces: (genesis: [u8; 32], attempt: u32) -> HashMap<Participant, Vec<u8>>,
-    DkgKeyPair: (genesis: [u8; 32], attempt: u32) -> KeyPair,
-    KeyToDkgAttempt: (key: [u8; 32]) -> u32,
-    DkgLocallyCompleted: (genesis: [u8; 32]) -> (),
+    DkgKeyPair: (genesis: [u8; 32]) -> KeyPair,

    PlanIds: (genesis: &[u8], block: u64) -> Vec<[u8; 32]>,

@@ -123,12 +118,12 @@ impl AttemptDb {

  pub fn attempt(getter: &impl Get, genesis: [u8; 32], topic: Topic) -> Option<u32> {
    let attempt = Self::get(getter, genesis, &topic);
-    // Don't require explicit recognition of the Dkg topic as it starts when the chain does
+    // Don't require explicit recognition of the DkgConfirmation topic as it starts when the chain
+    // does
    // Don't require explicit recognition of the SlashReport topic as it isn't a DoS risk and it
    // should always happen (eventually)
    if attempt.is_none() &&
-      ((topic == Topic::Dkg) ||
-        (topic == Topic::DkgConfirmation) ||
+      ((topic == Topic::DkgConfirmation) ||
        (topic == Topic::SubstrateSign(SubstrateSignableId::SlashReport)))
    {
      return Some(0);
@@ -155,16 +150,12 @@ impl ReattemptDb {
    // 5 minutes for attempts 0 ..= 2, 10 minutes for attempts 3 ..= 5, 15 minutes for attempts > 5
    // Assumes no event will take longer than 15 minutes, yet grows the time in case there are
    // network bandwidth issues
-    let mut reattempt_delay = BASE_REATTEMPT_DELAY *
+    let reattempt_delay = BASE_REATTEMPT_DELAY *
      ((AttemptDb::attempt(txn, genesis, topic)
        .expect("scheduling re-attempt for unknown topic") /
        3) +
        1)
      .min(3);
-    // Allow more time for DKGs since they have an extra round and much more data
-    if matches!(topic, Topic::Dkg) {
-      reattempt_delay *= 4;
-    }
    let upon_block = current_block_number + reattempt_delay;

    let mut reattempts = Self::get(txn, genesis, upon_block).unwrap_or(vec![]);
--- a/coordinator/src/tributary/handle.rs
+++ b/coordinator/src/tributary/handle.rs
@@ -13,7 +13,7 @@ use serai_client::{Signature, validator_sets::primitives::KeyPair};
 use tributary::{Signed, TransactionKind, TransactionTrait};

 use processor_messages::{
-  key_gen::{self, KeyGenId},
+  key_gen::self,
  coordinator::{self, SubstrateSignableId, SubstrateSignId},
  sign::{self, SignId},
 };
@@ -38,33 +38,20 @@ pub fn dkg_confirmation_nonces(
  txn: &mut impl DbTxn,
  attempt: u32,
 ) -> [u8; 64] {
-  DkgConfirmer::new(key, spec, txn, attempt)
-    .expect("getting DKG confirmation nonces for unknown attempt")
-    .preprocess()
+  DkgConfirmer::new(key, spec, txn, attempt).preprocess()
 }

 pub fn generated_key_pair<D: Db>(
  txn: &mut D::Transaction<'_>,
-  key: &Zeroizing<<Ristretto as Ciphersuite>::F>,
-  spec: &TributarySpec,
+  genesis: [u8; 32],
  key_pair: &KeyPair,
-  attempt: u32,
-) -> Result<[u8; 32], Participant> {
-  DkgKeyPair::set(txn, spec.genesis(), attempt, key_pair);
-  KeyToDkgAttempt::set(txn, key_pair.0 .0, &attempt);
-  let preprocesses = ConfirmationNonces::get(txn, spec.genesis(), attempt).unwrap();
-  DkgConfirmer::new(key, spec, txn, attempt)
-    .expect("claiming to have generated a key pair for an unrecognized attempt")
-    .share(preprocesses, key_pair)
+) {
+  DkgKeyPair::set(txn, genesis, key_pair);
 }

-fn unflatten(
-  spec: &TributarySpec,
-  removed: &[<Ristretto as Ciphersuite>::G],
-  data: &mut HashMap<Participant, Vec<u8>>,
-) {
+fn unflatten(spec: &TributarySpec, data: &mut HashMap<Participant, Vec<u8>>) {
  for (validator, _) in spec.validators() {
-    let Some(range) = spec.i(removed, validator) else { continue };
+    let Some(range) = spec.i(validator) else { continue };
    let Some(all_segments) = data.remove(&range.start) else {
      continue;
    };
@@ -88,7 +75,6 @@ impl<
 {
  fn accumulate(
    &mut self,
-    removed: &[<Ristretto as Ciphersuite>::G],
    data_spec: &DataSpecification,
    signer: <Ristretto as Ciphersuite>::G,
    data: &Vec<u8>,
@@ -99,10 +85,7 @@ impl<
      panic!("accumulating data for a participant multiple times");
    }
    let signer_shares = {
-      let Some(signer_i) = self.spec.i(removed, signer) else {
-        log::warn!("accumulating data from {} who was removed", hex::encode(signer.to_bytes()));
-        return Accumulation::NotReady;
-      };
+      let signer_i = self.spec.i(signer).expect("transaction signer wasn't a member of the set");
      u16::from(signer_i.end) - u16::from(signer_i.start)
    };

@@ -115,11 +98,7 @@ impl<

    // If 2/3rds of the network participated in this preprocess, queue it for an automatic
    // re-attempt
-    // DkgConfirmation doesn't have a re-attempt as it's just an extension for Dkg
-    if (data_spec.label == Label::Preprocess) &&
-      received_range.contains(&self.spec.t()) &&
-      (data_spec.topic != Topic::DkgConfirmation)
-    {
+    if (data_spec.label == Label::Preprocess) && received_range.contains(&self.spec.t()) {
      // Double check the attempt on this entry, as we don't want to schedule a re-attempt if this
      // is an old entry
      // This is an assert, not part of the if check, as old data shouldn't be here in the first
@@ -129,10 +108,7 @@ impl<
    }

    // If we have all the needed commitments/preprocesses/shares, tell the processor
-    let needs_everyone =
-      (data_spec.topic == Topic::Dkg) || (data_spec.topic == Topic::DkgConfirmation);
-    let needed = if needs_everyone { self.spec.n(removed) } else { self.spec.t() };
-    if received_range.contains(&needed) {
+    if received_range.contains(&self.spec.t()) {
      log::debug!(
        "accumulation for entry {:?} attempt #{} is ready",
        &data_spec.topic,
@@ -141,7 +117,7 @@ impl<

      let mut data = HashMap::new();
      for validator in self.spec.validators().iter().map(|validator| validator.0) {
-        let Some(i) = self.spec.i(removed, validator) else { continue };
+        let Some(i) = self.spec.i(validator) else { continue };
        data.insert(
          i.start,
          if let Some(data) = DataDb::get(self.txn, genesis, data_spec, &validator.to_bytes()) {
@@ -152,10 +128,10 @@ impl<
        );
      }

-      assert_eq!(data.len(), usize::from(needed));
+      assert_eq!(data.len(), usize::from(self.spec.t()));

      // Remove our own piece of data, if we were involved
-      if let Some(i) = self.spec.i(removed, Ristretto::generator() * self.our_key.deref()) {
+      if let Some(i) = self.spec.i(Ristretto::generator() * self.our_key.deref()) {
        if data.remove(&i.start).is_some() {
          return Accumulation::Ready(DataSet::Participating(data));
        }
@@ -167,7 +143,6 @@ impl<

  fn handle_data(
    &mut self,
-    removed: &[<Ristretto as Ciphersuite>::G],
    data_spec: &DataSpecification,
    bytes: &Vec<u8>,
    signed: &Signed,
@@ -213,21 +188,15 @@ impl<
    // TODO: If this is shares, we need to check they are part of the selected signing set

    // Accumulate this data
-    self.accumulate(removed, data_spec, signed.signer, bytes)
+    self.accumulate(data_spec, signed.signer, bytes)
  }

  fn check_sign_data_len(
    &mut self,
-    removed: &[<Ristretto as Ciphersuite>::G],
    signer: <Ristretto as Ciphersuite>::G,
    len: usize,
  ) -> Result<(), ()> {
-    let Some(signer_i) = self.spec.i(removed, signer) else {
-      // TODO: Ensure processor doesn't so participate/check how it handles removals for being
-      // offline
-      self.fatal_slash(signer.to_bytes(), "signer participated despite being removed");
-      Err(())?
-    };
+    let signer_i = self.spec.i(signer).expect("signer wasn't a member of the set");
    if len != usize::from(u16::from(signer_i.end) - u16::from(signer_i.start)) {
      self.fatal_slash(
        signer.to_bytes(),
@@ -254,12 +223,9 @@ impl<
    }

    match tx {
-      Transaction::RemoveParticipantDueToDkg { participant, signed } => {
-        if self.spec.i(&[], participant).is_none() {
-          self.fatal_slash(
-            participant.to_bytes(),
-            "RemoveParticipantDueToDkg vote for non-validator",
-          );
+      Transaction::RemoveParticipant { participant, signed } => {
+        if self.spec.i(participant).is_none() {
+          self.fatal_slash(participant.to_bytes(), "RemoveParticipant vote for non-validator");
          return;
        }

@@ -274,268 +240,106 @@ impl<

        let prior_votes = VotesToRemove::get(self.txn, genesis, participant).unwrap_or(0);
        let signer_votes =
-          self.spec.i(&[], signed.signer).expect("signer wasn't a validator for this network?");
+          self.spec.i(signed.signer).expect("signer wasn't a validator for this network?");
        let new_votes = prior_votes + u16::from(signer_votes.end) - u16::from(signer_votes.start);
        VotesToRemove::set(self.txn, genesis, participant, &new_votes);
        if ((prior_votes + 1) ..= new_votes).contains(&self.spec.t()) {
-          self.fatal_slash(participant, "RemoveParticipantDueToDkg vote")
+          self.fatal_slash(participant, "RemoveParticipant vote")
        }
      }

-      Transaction::DkgCommitments { attempt, commitments, signed } => {
-        let Some(removed) = removed_as_of_dkg_attempt(self.txn, genesis, attempt) else {
-          self.fatal_slash(signed.signer.to_bytes(), "DkgCommitments with an unrecognized attempt");
-          return;
-        };
-        let Ok(()) = self.check_sign_data_len(&removed, signed.signer, commitments.len()) else {
-          return;
-        };
-        let data_spec = DataSpecification { topic: Topic::Dkg, label: Label::Preprocess, attempt };
-        match self.handle_data(&removed, &data_spec, &commitments.encode(), &signed) {
-          Accumulation::Ready(DataSet::Participating(mut commitments)) => {
-            log::info!("got all DkgCommitments for {}", hex::encode(genesis));
-            unflatten(self.spec, &removed, &mut commitments);
-            self
-              .processors
-              .send(
-                self.spec.set().network,
-                key_gen::CoordinatorMessage::Commitments {
-                  id: KeyGenId { session: self.spec.set().session, attempt },
-                  commitments,
-                },
-              )
-              .await;
-          }
-          Accumulation::Ready(DataSet::NotParticipating) => {
-            assert!(
-              removed.contains(&(Ristretto::generator() * self.our_key.deref())),
-              "NotParticipating in a DkgCommitments we weren't removed for"
-            );
-          }
-          Accumulation::NotReady => {}
-        }
-      }
-
-      Transaction::DkgShares { attempt, mut shares, confirmation_nonces, signed } => {
-        let Some(removed) = removed_as_of_dkg_attempt(self.txn, genesis, attempt) else {
-          self.fatal_slash(signed.signer.to_bytes(), "DkgShares with an unrecognized attempt");
-          return;
-        };
-        let not_participating = removed.contains(&(Ristretto::generator() * self.our_key.deref()));
-
-        let Ok(()) = self.check_sign_data_len(&removed, signed.signer, shares.len()) else {
-          return;
-        };
-
-        let Some(sender_i) = self.spec.i(&removed, signed.signer) else {
-          self.fatal_slash(
-            signed.signer.to_bytes(),
-            "DkgShares for a DKG they aren't participating in",
-          );
-          return;
-        };
-        let sender_is_len = u16::from(sender_i.end) - u16::from(sender_i.start);
-        for shares in &shares {
-          if shares.len() != (usize::from(self.spec.n(&removed) - sender_is_len)) {
-            self.fatal_slash(signed.signer.to_bytes(), "invalid amount of DKG shares");
-            return;
-          }
-        }
-
-        // Save each share as needed for blame
-        for (from_offset, shares) in shares.iter().enumerate() {
-          let from =
-            Participant::new(u16::from(sender_i.start) + u16::try_from(from_offset).unwrap())
-              .unwrap();
-
-          for (to_offset, share) in shares.iter().enumerate() {
-            // 0-indexed (the enumeration) to 1-indexed (Participant)
-            let mut to = u16::try_from(to_offset).unwrap() + 1;
-            // Adjust for the omission of the sender's own shares
-            if to >= u16::from(sender_i.start) {
-              to += u16::from(sender_i.end) - u16::from(sender_i.start);
-            }
-            let to = Participant::new(to).unwrap();
-
-            DkgShare::set(self.txn, genesis, from.into(), to.into(), share);
-          }
-        }
-
-        // Filter down to only our share's bytes for handle
-        let our_shares = if let Some(our_i) =
-          self.spec.i(&removed, Ristretto::generator() * self.our_key.deref())
-        {
-          if sender_i == our_i {
-            vec![]
-          } else {
-            // 1-indexed to 0-indexed
-            let mut our_i_pos = u16::from(our_i.start) - 1;
-            // Handle the omission of the sender's own data
-            if u16::from(our_i.start) > u16::from(sender_i.start) {
-              our_i_pos -= sender_is_len;
-            }
-            let our_i_pos = usize::from(our_i_pos);
-            shares
-              .iter_mut()
-              .map(|shares| {
-                shares
-                  .drain(
-                    our_i_pos ..
-                      (our_i_pos + usize::from(u16::from(our_i.end) - u16::from(our_i.start))),
-                  )
-                  .collect::<Vec<_>>()
-              })
-              .collect()
-          }
-        } else {
-          assert!(
-            not_participating,
-            "we didn't have an i while handling DkgShares we weren't removed for"
-          );
-          // Since we're not participating, simply save vec![] for our shares
-          vec![]
-        };
-        // Drop shares as it's presumably been mutated into invalidity
-        drop(shares);
-
-        let data_spec = DataSpecification { topic: Topic::Dkg, label: Label::Share, attempt };
-        let encoded_data = (confirmation_nonces.to_vec(), our_shares.encode()).encode();
-        match self.handle_data(&removed, &data_spec, &encoded_data, &signed) {
-          Accumulation::Ready(DataSet::Participating(confirmation_nonces_and_shares)) => {
-            log::info!("got all DkgShares for {}", hex::encode(genesis));
-
-            let mut confirmation_nonces = HashMap::new();
-            let mut shares = HashMap::new();
-            for (participant, confirmation_nonces_and_shares) in confirmation_nonces_and_shares {
-              let (these_confirmation_nonces, these_shares) =
-                <(Vec<u8>, Vec<u8>)>::decode(&mut confirmation_nonces_and_shares.as_slice())
-                  .unwrap();
-              confirmation_nonces.insert(participant, these_confirmation_nonces);
-              shares.insert(participant, these_shares);
-            }
-            ConfirmationNonces::set(self.txn, genesis, attempt, &confirmation_nonces);
-
-            // shares is a HashMap<Participant, Vec<Vec<Vec<u8>>>>, with the values representing:
-            // - Each of the sender's shares
-            // - Each of the our shares
-            // - Each share
-            // We need a Vec<HashMap<Participant, Vec<u8>>>, with the outer being each of ours
-            let mut expanded_shares = vec![];
-            for (sender_start_i, shares) in shares {
-              let shares: Vec<Vec<Vec<u8>>> = Vec::<_>::decode(&mut shares.as_slice()).unwrap();
-              for (sender_i_offset, our_shares) in shares.into_iter().enumerate() {
-                for (our_share_i, our_share) in our_shares.into_iter().enumerate() {
-                  if expanded_shares.len() <= our_share_i {
-                    expanded_shares.push(HashMap::new());
-                  }
-                  expanded_shares[our_share_i].insert(
-                    Participant::new(
-                      u16::from(sender_start_i) + u16::try_from(sender_i_offset).unwrap(),
-                    )
-                    .unwrap(),
-                    our_share,
-                  );
-                }
-              }
-            }
-
-            self
-              .processors
-              .send(
-                self.spec.set().network,
-                key_gen::CoordinatorMessage::Shares {
-                  id: KeyGenId { session: self.spec.set().session, attempt },
-                  shares: expanded_shares,
-                },
-              )
-              .await;
-          }
-          Accumulation::Ready(DataSet::NotParticipating) => {
-            assert!(not_participating, "NotParticipating in a DkgShares we weren't removed for");
-          }
-          Accumulation::NotReady => {}
-        }
-      }
-
-      Transaction::InvalidDkgShare { attempt, accuser, faulty, blame, signed } => {
-        let Some(removed) = removed_as_of_dkg_attempt(self.txn, genesis, attempt) else {
-          self
-            .fatal_slash(signed.signer.to_bytes(), "InvalidDkgShare with an unrecognized attempt");
-          return;
-        };
-        let Some(range) = self.spec.i(&removed, signed.signer) else {
-          self.fatal_slash(
-            signed.signer.to_bytes(),
-            "InvalidDkgShare for a DKG they aren't participating in",
-          );
-          return;
-        };
-        if !range.contains(&accuser) {
-          self.fatal_slash(
-            signed.signer.to_bytes(),
-            "accused with a Participant index which wasn't theirs",
-          );
-          return;
-        }
-        if range.contains(&faulty) {
-          self.fatal_slash(signed.signer.to_bytes(), "accused self of having an InvalidDkgShare");
-          return;
-        }
-
-        let Some(share) = DkgShare::get(self.txn, genesis, accuser.into(), faulty.into()) else {
-          self.fatal_slash(
-            signed.signer.to_bytes(),
-            "InvalidDkgShare had a non-existent faulty participant",
-          );
-          return;
-        };
+      Transaction::DkgParticipation { participation, signed } => {
+        // Send the participation to the processor
        self
          .processors
          .send(
            self.spec.set().network,
-            key_gen::CoordinatorMessage::VerifyBlame {
-              id: KeyGenId { session: self.spec.set().session, attempt },
-              accuser,
-              accused: faulty,
-              share,
-              blame,
+            key_gen::CoordinatorMessage::Participation {
+              session: self.spec.set().session,
+              participant: self
+                .spec
+                .i(signed.signer)
+                .expect("signer wasn't a validator for this network?")
+                .start,
+              participation,
            },
          )
          .await;
      }

-      Transaction::DkgConfirmed { attempt, confirmation_share, signed } => {
-        let Some(removed) = removed_as_of_dkg_attempt(self.txn, genesis, attempt) else {
-          self.fatal_slash(signed.signer.to_bytes(), "DkgConfirmed with an unrecognized attempt");
-          return;
-        };
+      Transaction::DkgConfirmationNonces { attempt, confirmation_nonces, signed } => {
+        let data_spec =
+          DataSpecification { topic: Topic::DkgConfirmation, label: Label::Preprocess, attempt };
+        match self.handle_data(&data_spec, &confirmation_nonces.to_vec(), &signed) {
+          Accumulation::Ready(DataSet::Participating(confirmation_nonces)) => {
+            log::info!(
+              "got all DkgConfirmationNonces for {}, attempt {attempt}",
+              hex::encode(genesis)
+            );

+            ConfirmationNonces::set(self.txn, genesis, attempt, &confirmation_nonces);
+
+            // Send the expected DkgConfirmationShare
+            // TODO: Slight race condition here due to set, publish tx, then commit txn
+            let key_pair = DkgKeyPair::get(self.txn, genesis)
+              .expect("participating in confirming key we don't have");
+            let mut tx = match DkgConfirmer::new(self.our_key, self.spec, self.txn, attempt)
+              .share(confirmation_nonces, &key_pair)
+            {
+              Ok(confirmation_share) => Transaction::DkgConfirmationShare {
+                attempt,
+                confirmation_share,
+                signed: Transaction::empty_signed(),
+              },
+              Err(participant) => Transaction::RemoveParticipant {
+                participant: self.spec.reverse_lookup_i(participant).unwrap(),
+                signed: Transaction::empty_signed(),
+              },
+            };
+            tx.sign(&mut OsRng, genesis, self.our_key);
+            self.publish_tributary_tx.publish_tributary_tx(tx).await;
+          }
+          Accumulation::Ready(DataSet::NotParticipating) | Accumulation::NotReady => {}
+        }
+      }
+
+      Transaction::DkgConfirmationShare { attempt, confirmation_share, signed } => {
        let data_spec =
          DataSpecification { topic: Topic::DkgConfirmation, label: Label::Share, attempt };
-        match self.handle_data(&removed, &data_spec, &confirmation_share.to_vec(), &signed) {
+        match self.handle_data(&data_spec, &confirmation_share.to_vec(), &signed) {
          Accumulation::Ready(DataSet::Participating(shares)) => {
-            log::info!("got all DkgConfirmed for {}", hex::encode(genesis));
-
-            let Some(removed) = removed_as_of_dkg_attempt(self.txn, genesis, attempt) else {
-              panic!(
-                "DkgConfirmed for everyone yet didn't have the removed parties for this attempt",
-              );
-            };
+            log::info!(
+              "got all DkgConfirmationShare for {}, attempt {attempt}",
+              hex::encode(genesis)
+            );

            let preprocesses = ConfirmationNonces::get(self.txn, genesis, attempt).unwrap();
+
            // TODO: This can technically happen under very very very specific timing as the txn
-            // put happens before DkgConfirmed, yet the txn commit isn't guaranteed to
-            let key_pair = DkgKeyPair::get(self.txn, genesis, attempt).expect(
-              "in DkgConfirmed handling, which happens after everyone \
-              (including us) fires DkgConfirmed, yet no confirming key pair",
+            // put happens before DkgConfirmationShare, yet the txn isn't guaranteed to be
+            // committed
+            let key_pair = DkgKeyPair::get(self.txn, genesis).expect(
+              "in DkgConfirmationShare handling, which happens after everyone \
+              (including us) fires DkgConfirmationShare, yet no confirming key pair",
            );
-            let mut confirmer = DkgConfirmer::new(self.our_key, self.spec, self.txn, attempt)
-              .expect("confirming DKG for unrecognized attempt");
+
+            // Determine the bitstring representing who participated before we move `shares`
+            let validators = self.spec.validators();
+            let mut signature_participants = bitvec::vec::BitVec::with_capacity(validators.len());
+            for (participant, _) in validators {
+              signature_participants.push(
+                (participant == (<Ristretto as Ciphersuite>::generator() * self.our_key.deref())) ||
+                  shares.contains_key(&self.spec.i(participant).unwrap().start),
+              );
+            }
+
+            // Produce the final signature
+            let mut confirmer = DkgConfirmer::new(self.our_key, self.spec, self.txn, attempt);
            let sig = match confirmer.complete(preprocesses, &key_pair, shares) {
              Ok(sig) => sig,
              Err(p) => {
-                let mut tx = Transaction::RemoveParticipantDueToDkg {
-                  participant: self.spec.reverse_lookup_i(&removed, p).unwrap(),
+                let mut tx = Transaction::RemoveParticipant {
+                  participant: self.spec.reverse_lookup_i(p).unwrap(),
                  signed: Transaction::empty_signed(),
                };
                tx.sign(&mut OsRng, genesis, self.our_key);
@@ -544,23 +348,18 @@ impl<
              }
            };

-            DkgLocallyCompleted::set(self.txn, genesis, &());
-
            self
              .publish_serai_tx
              .publish_set_keys(
                self.db,
                self.spec.set(),
-                removed.into_iter().map(|key| key.to_bytes().into()).collect(),
                key_pair,
+                signature_participants,
                Signature(sig),
              )
              .await;
          }
-          Accumulation::Ready(DataSet::NotParticipating) => {
-            panic!("wasn't a participant in DKG confirmination shares")
-          }
-          Accumulation::NotReady => {}
+          Accumulation::Ready(DataSet::NotParticipating) | Accumulation::NotReady => {}
        }
      }

@@ -618,19 +417,8 @@ impl<
      }

      Transaction::SubstrateSign(data) => {
-        // Provided transactions ensure synchrony on any signing protocol, and we won't start
-        // signing with threshold keys before we've confirmed them on-chain
-        let Some(removed) =
-          crate::tributary::removed_as_of_set_keys(self.txn, self.spec.set(), genesis)
-        else {
-          self.fatal_slash(
-            data.signed.signer.to_bytes(),
-            "signing despite not having set keys on substrate",
-          );
-          return;
-        };
        let signer = data.signed.signer;
-        let Ok(()) = self.check_sign_data_len(&removed, signer, data.data.len()) else {
+        let Ok(()) = self.check_sign_data_len(signer, data.data.len()) else {
          return;
        };
        let expected_len = match data.label {
@@ -653,11 +441,11 @@ impl<
          attempt: data.attempt,
        };
        let Accumulation::Ready(DataSet::Participating(mut results)) =
-          self.handle_data(&removed, &data_spec, &data.data.encode(), &data.signed)
+          self.handle_data(&data_spec, &data.data.encode(), &data.signed)
        else {
          return;
        };
-        unflatten(self.spec, &removed, &mut results);
+        unflatten(self.spec, &mut results);

        let id = SubstrateSignId {
          session: self.spec.set().session,
@@ -678,16 +466,7 @@ impl<
      }

      Transaction::Sign(data) => {
-        let Some(removed) =
-          crate::tributary::removed_as_of_set_keys(self.txn, self.spec.set(), genesis)
-        else {
-          self.fatal_slash(
-            data.signed.signer.to_bytes(),
-            "signing despite not having set keys on substrate",
-          );
-          return;
-        };
-        let Ok(()) = self.check_sign_data_len(&removed, data.signed.signer, data.data.len()) else {
+        let Ok(()) = self.check_sign_data_len(data.signed.signer, data.data.len()) else {
          return;
        };

@@ -697,9 +476,9 @@ impl<
          attempt: data.attempt,
        };
        if let Accumulation::Ready(DataSet::Participating(mut results)) =
-          self.handle_data(&removed, &data_spec, &data.data.encode(), &data.signed)
+          self.handle_data(&data_spec, &data.data.encode(), &data.signed)
        {
-          unflatten(self.spec, &removed, &mut results);
+          unflatten(self.spec, &mut results);
          let id =
            SignId { session: self.spec.set().session, id: data.plan, attempt: data.attempt };
          self
@@ -740,8 +519,7 @@ impl<
      }

      Transaction::SlashReport(points, signed) => {
-        // Uses &[] as we only need the length which is independent to who else was removed
-        let signer_range = self.spec.i(&[], signed.signer).unwrap();
+        let signer_range = self.spec.i(signed.signer).unwrap();
        let signer_len = u16::from(signer_range.end) - u16::from(signer_range.start);
        if points.len() != (self.spec.validators().len() - 1) {
          self.fatal_slash(
--- a/coordinator/src/tributary/mod.rs
+++ b/coordinator/src/tributary/mod.rs
@@ -1,7 +1,3 @@
-use ciphersuite::{group::GroupEncoding, Ciphersuite, Ristretto};
-
-use serai_client::validator_sets::primitives::ValidatorSet;
-
 use tributary::{
  ReadWrite,
  transaction::{TransactionError, TransactionKind, Transaction as TransactionTrait},
@@ -24,39 +20,6 @@ pub use handle::*;

 pub mod scanner;

-pub fn removed_as_of_dkg_attempt(
-  getter: &impl Get,
-  genesis: [u8; 32],
-  attempt: u32,
-) -> Option<Vec<<Ristretto as Ciphersuite>::G>> {
-  if attempt == 0 {
-    Some(vec![])
-  } else {
-    RemovedAsOfDkgAttempt::get(getter, genesis, attempt).map(|keys| {
-      keys.iter().map(|key| <Ristretto as Ciphersuite>::G::from_bytes(key).unwrap()).collect()
-    })
-  }
-}
-
-pub fn removed_as_of_set_keys(
-  getter: &impl Get,
-  set: ValidatorSet,
-  genesis: [u8; 32],
-) -> Option<Vec<<Ristretto as Ciphersuite>::G>> {
-  // SeraiDkgCompleted has the key placed on-chain.
-  // This key can be uniquely mapped to an attempt so long as one participant was honest, which we
-  // assume as a presumably honest participant.
-  // Resolve from generated key to attempt to fatally slashed as of attempt.
-
-  // This expect will trigger if this is prematurely called and Substrate has tracked the keys yet
-  // we haven't locally synced and handled the Tributary
-  // All callers of this, at the time of writing, ensure the Tributary has sufficiently synced
-  // making the panic with context more desirable than the None
-  let attempt = KeyToDkgAttempt::get(getter, SeraiDkgCompleted::get(getter, set)?)
-    .expect("key completed on-chain didn't have an attempt related");
-  removed_as_of_dkg_attempt(getter, genesis, attempt)
-}
-
 pub async fn publish_signed_transaction<D: Db, P: crate::P2p>(
  txn: &mut D::Transaction<'_>,
  tributary: &Tributary<D, Transaction, P>,
--- a/coordinator/src/tributary/scanner.rs
+++ b/coordinator/src/tributary/scanner.rs
@@ -1,15 +1,17 @@
-use core::{marker::PhantomData, ops::Deref, future::Future, time::Duration};
-use std::{sync::Arc, collections::HashSet};
+use core::{marker::PhantomData, future::Future, time::Duration};
+use std::sync::Arc;

 use zeroize::Zeroizing;

+use rand_core::OsRng;
+
 use ciphersuite::{group::GroupEncoding, Ciphersuite, Ristretto};

 use tokio::sync::broadcast;

 use scale::{Encode, Decode};
 use serai_client::{
-  primitives::{SeraiAddress, Signature},
+  primitives::Signature,
  validator_sets::primitives::{KeyPair, ValidatorSet},
  Serai,
 };
@@ -67,8 +69,8 @@ pub trait PublishSeraiTransaction {
    &self,
    db: &(impl Sync + Get),
    set: ValidatorSet,
-    removed: Vec<SeraiAddress>,
    key_pair: KeyPair,
+    signature_participants: bitvec::vec::BitVec<u8, bitvec::order::Lsb0>,
    signature: Signature,
  );
 }
@@ -129,17 +131,12 @@ mod impl_pst_for_serai {
      &self,
      db: &(impl Sync + Get),
      set: ValidatorSet,
-      removed: Vec<SeraiAddress>,
      key_pair: KeyPair,
+      signature_participants: bitvec::vec::BitVec<u8, bitvec::order::Lsb0>,
      signature: Signature,
    ) {
-      // TODO: BoundedVec as an arg to avoid this expect
-      let tx = SeraiValidatorSets::set_keys(
-        set.network,
-        removed.try_into().expect("removing more than allowed"),
-        key_pair,
-        signature,
-      );
+      let tx =
+        SeraiValidatorSets::set_keys(set.network, key_pair, signature_participants, signature);
      async fn check(serai: SeraiValidatorSets<'_>, set: ValidatorSet, (): ()) -> bool {
        if matches!(serai.keys(set).await, Ok(Some(_))) {
          log::info!("another coordinator set key pair for {:?}", set);
@@ -249,18 +246,15 @@ impl<

    let genesis = self.spec.genesis();

-    let current_fatal_slashes = FatalSlashes::get_as_keys(self.txn, genesis);
-
    // Calculate the shares still present, spinning if not enough are
-    // still_present_shares is used by a below branch, yet it's a natural byproduct of checking if
-    // we should spin, hence storing it in a variable here
-    let still_present_shares = {
+    {
      // Start with the original n value
-      let mut present_shares = self.spec.n(&[]);
+      let mut present_shares = self.spec.n();
      // Remove everyone fatally slashed
+      let current_fatal_slashes = FatalSlashes::get_as_keys(self.txn, genesis);
      for removed in &current_fatal_slashes {
        let original_i_for_removed =
-          self.spec.i(&[], *removed).expect("removed party was never present");
+          self.spec.i(*removed).expect("removed party was never present");
        let removed_shares =
          u16::from(original_i_for_removed.end) - u16::from(original_i_for_removed.start);
        present_shares -= removed_shares;
@@ -276,79 +270,17 @@ impl<
          tokio::time::sleep(core::time::Duration::from_secs(60)).await;
        }
      }
-
-      present_shares
-    };
+    }

    for topic in ReattemptDb::take(self.txn, genesis, self.block_number) {
      let attempt = AttemptDb::start_next_attempt(self.txn, genesis, topic);
-      log::info!("re-attempting {topic:?} with attempt {attempt}");
+      log::info!("potentially re-attempting {topic:?} with attempt {attempt}");

      // Slash people who failed to participate as expected in the prior attempt
      {
        let prior_attempt = attempt - 1;
-        let (removed, expected_participants) = match topic {
-          Topic::Dkg => {
-            // Every validator who wasn't removed is expected to have participated
-            let removed =
-              crate::tributary::removed_as_of_dkg_attempt(self.txn, genesis, prior_attempt)
-                .expect("prior attempt didn't have its removed saved to disk");
-            let removed_set = removed.iter().copied().collect::<HashSet<_>>();
-            (
-              removed,
-              self
-                .spec
-                .validators()
-                .into_iter()
-                .filter_map(|(validator, _)| {
-                  Some(validator).filter(|validator| !removed_set.contains(validator))
-                })
-                .collect(),
-            )
-          }
-          Topic::DkgConfirmation => {
-            panic!("TODO: re-attempting DkgConfirmation when we should be re-attempting the Dkg")
-          }
-          Topic::SubstrateSign(_) | Topic::Sign(_) => {
-            let removed =
-              crate::tributary::removed_as_of_set_keys(self.txn, self.spec.set(), genesis)
-                .expect("SubstrateSign/Sign yet have yet to set keys");
-            // TODO: If 67% sent preprocesses, this should be them. Else, this should be vec![]
-            let expected_participants = vec![];
-            (removed, expected_participants)
-          }
-        };
-
-        let (expected_topic, expected_label) = match topic {
-          Topic::Dkg => {
-            let n = self.spec.n(&removed);
-            // If we got all the DKG shares, we should be on DKG confirmation
-            let share_spec =
-              DataSpecification { topic: Topic::Dkg, label: Label::Share, attempt: prior_attempt };
-            if DataReceived::get(self.txn, genesis, &share_spec).unwrap_or(0) == n {
-              // Label::Share since there is no Label::Preprocess for DkgConfirmation since the
-              // preprocess is part of Topic::Dkg Label::Share
-              (Topic::DkgConfirmation, Label::Share)
-            } else {
-              let preprocess_spec = DataSpecification {
-                topic: Topic::Dkg,
-                label: Label::Preprocess,
-                attempt: prior_attempt,
-              };
-              // If we got all the DKG preprocesses, DKG shares
-              if DataReceived::get(self.txn, genesis, &preprocess_spec).unwrap_or(0) == n {
-                // Label::Share since there is no Label::Preprocess for DkgConfirmation since the
-                // preprocess is part of Topic::Dkg Label::Share
-                (Topic::Dkg, Label::Share)
-              } else {
-                (Topic::Dkg, Label::Preprocess)
-              }
-            }
-          }
-          Topic::DkgConfirmation => unreachable!(),
-          // If we got enough participants to move forward, then we expect shares from them all
-          Topic::SubstrateSign(_) | Topic::Sign(_) => (topic, Label::Share),
-        };
+        // TODO: If 67% sent preprocesses, this should be them. Else, this should be vec![]
+        let expected_participants: Vec<<Ristretto as Ciphersuite>::G> = vec![];

        let mut did_not_participate = vec![];
        for expected_participant in expected_participants {
@@ -356,8 +288,9 @@ impl<
            self.txn,
            genesis,
            &DataSpecification {
-              topic: expected_topic,
-              label: expected_label,
+              topic,
+              // Since we got the preprocesses, we were supposed to get the shares
+              label: Label::Share,
              attempt: prior_attempt,
            },
            &expected_participant.to_bytes(),
@@ -373,15 +306,8 @@ impl<
        // Accordingly, clear did_not_participate
        // TODO

-        // If during the DKG, explicitly mark these people as having been offline
-        // TODO: If they were offline sufficiently long ago, don't strike them off
-        if topic == Topic::Dkg {
-          let mut existing = OfflineDuringDkg::get(self.txn, genesis).unwrap_or(vec![]);
-          for did_not_participate in did_not_participate {
-            existing.push(did_not_participate.to_bytes());
-          }
-          OfflineDuringDkg::set(self.txn, genesis, &existing);
-        }
+        // TODO: Increment the slash points of people who didn't preprocess in some expected window
+        // of time

        // Slash everyone who didn't participate as expected
        // This may be overzealous as if a minority detects a completion, they'll abort yet the
@@ -411,75 +337,22 @@ impl<
        then preprocesses. This only sends preprocesses).
      */
      match topic {
-        Topic::Dkg => {
-          let mut removed = current_fatal_slashes.clone();
+        Topic::DkgConfirmation => {
+          if SeraiDkgCompleted::get(self.txn, self.spec.set()).is_none() {
+            log::info!("re-attempting DKG confirmation with attempt {attempt}");

-          let t = self.spec.t();
-          {
-            let mut present_shares = still_present_shares;
-
-            // Load the parties marked as offline across the various attempts
-            let mut offline = OfflineDuringDkg::get(self.txn, genesis)
-              .unwrap_or(vec![])
-              .iter()
-              .map(|key| <Ristretto as Ciphersuite>::G::from_bytes(key).unwrap())
-              .collect::<Vec<_>>();
-            // Pop from the list to prioritize the removal of those recently offline
-            while let Some(offline) = offline.pop() {
-              // Make sure they weren't removed already (such as due to being fatally slashed)
-              // This also may trigger if they were offline across multiple attempts
-              if removed.contains(&offline) {
-                continue;
-              }
-
-              // If we can remove them and still meet the threshold, do so
-              let original_i_for_offline =
-                self.spec.i(&[], offline).expect("offline was never present?");
-              let offline_shares =
-                u16::from(original_i_for_offline.end) - u16::from(original_i_for_offline.start);
-              if (present_shares - offline_shares) >= t {
-                present_shares -= offline_shares;
-                removed.push(offline);
-              }
-
-              // If we've removed as many people as we can, break
-              if present_shares == t {
-                break;
-              }
-            }
-          }
-
-          RemovedAsOfDkgAttempt::set(
-            self.txn,
-            genesis,
-            attempt,
-            &removed.iter().map(<Ristretto as Ciphersuite>::G::to_bytes).collect(),
-          );
-
-          if DkgLocallyCompleted::get(self.txn, genesis).is_none() {
-            let Some(our_i) = self.spec.i(&removed, Ristretto::generator() * self.our_key.deref())
-            else {
-              continue;
+            // Since it wasn't completed, publish our nonces for the next attempt
+            let confirmation_nonces =
+              crate::tributary::dkg_confirmation_nonces(self.our_key, self.spec, self.txn, attempt);
+            let mut tx = Transaction::DkgConfirmationNonces {
+              attempt,
+              confirmation_nonces,
+              signed: Transaction::empty_signed(),
            };
-
-            // Since it wasn't completed, instruct the processor to start the next attempt
-            let id =
-              processor_messages::key_gen::KeyGenId { session: self.spec.set().session, attempt };
-
-            let params =
-              frost::ThresholdParams::new(t, self.spec.n(&removed), our_i.start).unwrap();
-            let shares = u16::from(our_i.end) - u16::from(our_i.start);
-
-            self
-              .processors
-              .send(
-                self.spec.set().network,
-                processor_messages::key_gen::CoordinatorMessage::GenerateKey { id, params, shares },
-              )
-              .await;
+            tx.sign(&mut OsRng, genesis, self.our_key);
+            self.publish_tributary_tx.publish_tributary_tx(tx).await;
          }
        }
-        Topic::DkgConfirmation => unreachable!(),
        Topic::SubstrateSign(inner_id) => {
          let id = processor_messages::coordinator::SubstrateSignId {
            session: self.spec.set().session,
@@ -496,6 +369,8 @@ impl<
                crate::cosign_evaluator::LatestCosign::get(self.txn, self.spec.set().network)
                  .map_or(0, |cosign| cosign.block_number);
              if latest_cosign < block_number {
+                log::info!("re-attempting cosigning {block_number:?} with attempt {attempt}");
+
                // Instruct the processor to start the next attempt
                self
                  .processors
@@ -512,6 +387,8 @@ impl<
            SubstrateSignableId::Batch(batch) => {
              // If the Batch hasn't appeared on-chain...
              if BatchInstructionsHashDb::get(self.txn, self.spec.set().network, batch).is_none() {
+                log::info!("re-attempting signing batch {batch:?} with attempt {attempt}");
+
                // Instruct the processor to start the next attempt
                // The processor won't continue if it's already signed a Batch
                // Prior checking if the Batch is on-chain just may reduce the non-participating
@@ -529,6 +406,11 @@ impl<
              // If this Tributary hasn't been retired...
              // (published SlashReport/took too long to do so)
              if crate::RetiredTributaryDb::get(self.txn, self.spec.set()).is_none() {
+                log::info!(
+                  "re-attempting signing slash report for {:?} with attempt {attempt}",
+                  self.spec.set()
+                );
+
                let report = SlashReport::get(self.txn, self.spec.set())
                  .expect("re-attempting signing a SlashReport we don't have?");
                self
@@ -575,8 +457,7 @@ impl<
        };
        // Assign them 0 points for themselves
        report.insert(i, 0);
-        // Uses &[] as we only need the length which is independent to who else was removed
-        let signer_i = self.spec.i(&[], validator).unwrap();
+        let signer_i = self.spec.i(validator).unwrap();
        let signer_len = u16::from(signer_i.end) - u16::from(signer_i.start);
        // Push `n` copies, one for each of their shares
        for _ in 0 .. signer_len {
--- a/coordinator/src/tributary/signing_protocol.rs
+++ b/coordinator/src/tributary/signing_protocol.rs
@@ -55,7 +55,7 @@
 */

 use core::ops::Deref;
-use std::collections::HashMap;
+use std::collections::{HashSet, HashMap};

 use zeroize::{Zeroize, Zeroizing};

@@ -63,10 +63,7 @@ use rand_core::OsRng;

 use blake2::{Digest, Blake2s256};

-use ciphersuite::{
-  group::{ff::PrimeField, GroupEncoding},
-  Ciphersuite, Ristretto,
-};
+use ciphersuite::{group::ff::PrimeField, Ciphersuite, Ristretto};
 use frost::{
  FrostError,
  dkg::{Participant, musig::musig},
@@ -77,10 +74,7 @@ use frost_schnorrkel::Schnorrkel;

 use scale::Encode;

-use serai_client::{
-  Public,
-  validator_sets::primitives::{KeyPair, musig_context, set_keys_message},
-};
+use serai_client::validator_sets::primitives::{KeyPair, musig_context, set_keys_message};

 use serai_db::*;

@@ -89,6 +83,7 @@ use crate::tributary::TributarySpec;
 create_db!(
  SigningProtocolDb {
    CachedPreprocesses: (context: &impl Encode) -> [u8; 32]
+    DataSignedWith: (context: &impl Encode) -> (Vec<u8>, HashMap<Participant, Vec<u8>>),
  }
 );

@@ -117,16 +112,22 @@ impl<T: DbTxn, C: Encode> SigningProtocol<'_, T, C> {
    };
    let encryption_key_slice: &mut [u8] = encryption_key.as_mut();

-    let algorithm = Schnorrkel::new(b"substrate");
+    // Create the MuSig keys
    let keys: ThresholdKeys<Ristretto> =
      musig(&musig_context(self.spec.set()), self.key, participants)
        .expect("signing for a set we aren't in/validator present multiple times")
        .into();

+    // Define the algorithm
+    let algorithm = Schnorrkel::new(b"substrate");
+
+    // Check if we've prior preprocessed
    if CachedPreprocesses::get(self.txn, &self.context).is_none() {
+      // If we haven't, we create a machine solely to obtain the preprocess with
      let (machine, _) =
        AlgorithmMachine::new(algorithm.clone(), keys.clone()).preprocess(&mut OsRng);

+      // Cache and save the preprocess to disk
      let mut cache = machine.cache();
      assert_eq!(cache.0.len(), 32);
      #[allow(clippy::needless_range_loop)]
@@ -137,13 +138,15 @@ impl<T: DbTxn, C: Encode> SigningProtocol<'_, T, C> {
      CachedPreprocesses::set(self.txn, &self.context, &cache.0);
    }

+    // We're now guaranteed to have the preprocess, hence why this `unwrap` is safe
    let cached = CachedPreprocesses::get(self.txn, &self.context).unwrap();
-    let mut cached: Zeroizing<[u8; 32]> = Zeroizing::new(cached);
+    let mut cached = Zeroizing::new(cached);
    #[allow(clippy::needless_range_loop)]
    for b in 0 .. 32 {
      cached[b] ^= encryption_key_slice[b];
    }
    encryption_key_slice.zeroize();
+    // Create the machine from the cached preprocess
    let (machine, preprocess) =
      AlgorithmSignMachine::from_cache(algorithm, keys, CachedPreprocess(cached));

@@ -156,8 +159,29 @@ impl<T: DbTxn, C: Encode> SigningProtocol<'_, T, C> {
    mut serialized_preprocesses: HashMap<Participant, Vec<u8>>,
    msg: &[u8],
  ) -> Result<(AlgorithmSignatureMachine<Ristretto, Schnorrkel>, [u8; 32]), Participant> {
-    let machine = self.preprocess_internal(participants).0;
+    // We can't clear the preprocess as we sitll need it to accumulate all of the shares
+    // We do save the message we signed so any future calls with distinct messages panic
+    // This assumes the txn deciding this data is committed before the share is broaadcast
+    if let Some((existing_msg, existing_preprocesses)) =
+      DataSignedWith::get(self.txn, &self.context)
+    {
+      assert_eq!(msg, &existing_msg, "obtaining a signature share for a distinct message");
+      assert_eq!(
+        &serialized_preprocesses, &existing_preprocesses,
+        "obtaining a signature share with a distinct set of preprocesses"
+      );
+    } else {
+      DataSignedWith::set(
+        self.txn,
+        &self.context,
+        &(msg.to_vec(), serialized_preprocesses.clone()),
+      );
+    }

+    // Get the preprocessed machine
+    let (machine, _) = self.preprocess_internal(participants);
+
+    // Deserialize all the preprocesses
    let mut participants = serialized_preprocesses.keys().copied().collect::<Vec<_>>();
    participants.sort();
    let mut preprocesses = HashMap::new();
@@ -170,13 +194,14 @@ impl<T: DbTxn, C: Encode> SigningProtocol<'_, T, C> {
      );
    }

+    // Sign the share
    let (machine, share) = machine.sign(preprocesses, msg).map_err(|e| match e {
      FrostError::InternalError(e) => unreachable!("FrostError::InternalError {e}"),
      FrostError::InvalidParticipant(_, _) |
      FrostError::InvalidSigningSet(_) |
      FrostError::InvalidParticipantQuantity(_, _) |
      FrostError::DuplicatedParticipant(_) |
-      FrostError::MissingParticipant(_) => unreachable!("{e:?}"),
+      FrostError::MissingParticipant(_) => panic!("unexpected error during sign: {e:?}"),
      FrostError::InvalidPreprocess(p) | FrostError::InvalidShare(p) => p,
    })?;

@@ -207,24 +232,24 @@ impl<T: DbTxn, C: Encode> SigningProtocol<'_, T, C> {
 }

 // Get the keys of the participants, noted by their threshold is, and return a new map indexed by
-// the MuSig is.
+// their MuSig is.
 fn threshold_i_map_to_keys_and_musig_i_map(
  spec: &TributarySpec,
-  removed: &[<Ristretto as Ciphersuite>::G],
  our_key: &Zeroizing<<Ristretto as Ciphersuite>::F>,
  mut map: HashMap<Participant, Vec<u8>>,
 ) -> (Vec<<Ristretto as Ciphersuite>::G>, HashMap<Participant, Vec<u8>>) {
  // Insert our own index so calculations aren't offset
  let our_threshold_i = spec
-    .i(removed, <Ristretto as Ciphersuite>::generator() * our_key.deref())
-    .expect("MuSig t-of-n signing a for a protocol we were removed from")
+    .i(<Ristretto as Ciphersuite>::generator() * our_key.deref())
+    .expect("not in a set we're signing for")
    .start;
+  // Asserts we weren't unexpectedly already present
  assert!(map.insert(our_threshold_i, vec![]).is_none());

  let spec_validators = spec.validators();
  let key_from_threshold_i = |threshold_i| {
    for (key, _) in &spec_validators {
-      if threshold_i == spec.i(removed, *key).expect("MuSig t-of-n participant was removed").start {
+      if threshold_i == spec.i(*key).expect("validator wasn't in a set they're in").start {
        return *key;
      }
    }
@@ -235,19 +260,27 @@ fn threshold_i_map_to_keys_and_musig_i_map(
  let mut threshold_is = map.keys().copied().collect::<Vec<_>>();
  threshold_is.sort();
  for threshold_i in threshold_is {
-    sorted.push((key_from_threshold_i(threshold_i), map.remove(&threshold_i).unwrap()));
+    sorted.push((
+      threshold_i,
+      key_from_threshold_i(threshold_i),
+      map.remove(&threshold_i).unwrap(),
+    ));
  }

  // Now that signers are sorted, with their shares, create a map with the is needed for MuSig
  let mut participants = vec![];
  let mut map = HashMap::new();
-  for (raw_i, (key, share)) in sorted.into_iter().enumerate() {
-    let musig_i = u16::try_from(raw_i).unwrap() + 1;
+  let mut our_musig_i = None;
+  for (raw_i, (threshold_i, key, share)) in sorted.into_iter().enumerate() {
+    let musig_i = Participant::new(u16::try_from(raw_i).unwrap() + 1).unwrap();
+    if threshold_i == our_threshold_i {
+      our_musig_i = Some(musig_i);
+    }
    participants.push(key);
-    map.insert(Participant::new(musig_i).unwrap(), share);
+    map.insert(musig_i, share);
  }

-  map.remove(&our_threshold_i).unwrap();
+  map.remove(&our_musig_i.unwrap()).unwrap();

  (participants, map)
 }
@@ -257,7 +290,6 @@ type DkgConfirmerSigningProtocol<'a, T> = SigningProtocol<'a, T, (&'static [u8;
 pub(crate) struct DkgConfirmer<'a, T: DbTxn> {
  key: &'a Zeroizing<<Ristretto as Ciphersuite>::F>,
  spec: &'a TributarySpec,
-  removed: Vec<<Ristretto as Ciphersuite>::G>,
  txn: &'a mut T,
  attempt: u32,
 }
@@ -268,19 +300,19 @@ impl<T: DbTxn> DkgConfirmer<'_, T> {
    spec: &'a TributarySpec,
    txn: &'a mut T,
    attempt: u32,
-  ) -> Option<DkgConfirmer<'a, T>> {
-    // This relies on how confirmations are inlined into the DKG protocol and they accordingly
-    // share attempts
-    let removed = crate::tributary::removed_as_of_dkg_attempt(txn, spec.genesis(), attempt)?;
-    Some(DkgConfirmer { key, spec, removed, txn, attempt })
+  ) -> DkgConfirmer<'a, T> {
+    DkgConfirmer { key, spec, txn, attempt }
  }
+
  fn signing_protocol(&mut self) -> DkgConfirmerSigningProtocol<'_, T> {
    let context = (b"DkgConfirmer", self.attempt);
    SigningProtocol { key: self.key, spec: self.spec, txn: self.txn, context }
  }

  fn preprocess_internal(&mut self) -> (AlgorithmSignMachine<Ristretto, Schnorrkel>, [u8; 64]) {
-    let participants = self.spec.validators().iter().map(|val| val.0).collect::<Vec<_>>();
+    // This preprocesses with just us as we only decide the participants after obtaining
+    // preprocesses
+    let participants = vec![<Ristretto as Ciphersuite>::generator() * self.key.deref()];
    self.signing_protocol().preprocess_internal(&participants)
  }
  // Get the preprocess for this confirmation.
@@ -293,14 +325,9 @@ impl<T: DbTxn> DkgConfirmer<'_, T> {
    preprocesses: HashMap<Participant, Vec<u8>>,
    key_pair: &KeyPair,
  ) -> Result<(AlgorithmSignatureMachine<Ristretto, Schnorrkel>, [u8; 32]), Participant> {
-    let participants = self.spec.validators().iter().map(|val| val.0).collect::<Vec<_>>();
-    let preprocesses =
-      threshold_i_map_to_keys_and_musig_i_map(self.spec, &self.removed, self.key, preprocesses).1;
-    let msg = set_keys_message(
-      &self.spec.set(),
-      &self.removed.iter().map(|key| Public(key.to_bytes())).collect::<Vec<_>>(),
-      key_pair,
-    );
+    let (participants, preprocesses) =
+      threshold_i_map_to_keys_and_musig_i_map(self.spec, self.key, preprocesses);
+    let msg = set_keys_message(&self.spec.set(), key_pair);
    self.signing_protocol().share_internal(&participants, preprocesses, &msg)
  }
  // Get the share for this confirmation, if the preprocesses are valid.
@@ -318,8 +345,9 @@ impl<T: DbTxn> DkgConfirmer<'_, T> {
    key_pair: &KeyPair,
    shares: HashMap<Participant, Vec<u8>>,
  ) -> Result<[u8; 64], Participant> {
-    let shares =
-      threshold_i_map_to_keys_and_musig_i_map(self.spec, &self.removed, self.key, shares).1;
+    assert_eq!(preprocesses.keys().collect::<HashSet<_>>(), shares.keys().collect::<HashSet<_>>());
+
+    let shares = threshold_i_map_to_keys_and_musig_i_map(self.spec, self.key, shares).1;

    let machine = self
      .share_internal(preprocesses, key_pair)
--- a/coordinator/src/tributary/spec.rs
+++ b/coordinator/src/tributary/spec.rs
@@ -9,7 +9,7 @@ use frost::Participant;
 use scale::Encode;
 use borsh::{BorshSerialize, BorshDeserialize};

-use serai_client::{primitives::PublicKey, validator_sets::primitives::ValidatorSet};
+use serai_client::validator_sets::primitives::ValidatorSet;

 fn borsh_serialize_validators<W: io::Write>(
  validators: &Vec<(<Ristretto as Ciphersuite>::G, u16)>,
@@ -49,6 +49,7 @@ pub struct TributarySpec {
    deserialize_with = "borsh_deserialize_validators"
  )]
  validators: Vec<(<Ristretto as Ciphersuite>::G, u16)>,
+  evrf_public_keys: Vec<([u8; 32], Vec<u8>)>,
 }

 impl TributarySpec {
@@ -56,16 +57,10 @@ impl TributarySpec {
    serai_block: [u8; 32],
    start_time: u64,
    set: ValidatorSet,
-    set_participants: Vec<(PublicKey, u16)>,
+    validators: Vec<(<Ristretto as Ciphersuite>::G, u16)>,
+    evrf_public_keys: Vec<([u8; 32], Vec<u8>)>,
  ) -> TributarySpec {
-    let mut validators = vec![];
-    for (participant, shares) in set_participants {
-      let participant = <Ristretto as Ciphersuite>::read_G::<&[u8]>(&mut participant.0.as_ref())
-        .expect("invalid key registered as participant");
-      validators.push((participant, shares));
-    }
-
-    Self { serai_block, start_time, set, validators }
+    Self { serai_block, start_time, set, validators, evrf_public_keys }
  }

  pub fn set(&self) -> ValidatorSet {
@@ -88,24 +83,15 @@ impl TributarySpec {
    self.start_time
  }

-  pub fn n(&self, removed_validators: &[<Ristretto as Ciphersuite>::G]) -> u16 {
-    self
-      .validators
-      .iter()
-      .map(|(validator, weight)| if removed_validators.contains(validator) { 0 } else { *weight })
-      .sum()
+  pub fn n(&self) -> u16 {
+    self.validators.iter().map(|(_, weight)| *weight).sum()
  }

  pub fn t(&self) -> u16 {
-    // t doesn't change with regards to the amount of removed validators
-    ((2 * self.n(&[])) / 3) + 1
+    ((2 * self.n()) / 3) + 1
  }

-  pub fn i(
-    &self,
-    removed_validators: &[<Ristretto as Ciphersuite>::G],
-    key: <Ristretto as Ciphersuite>::G,
-  ) -> Option<Range<Participant>> {
+  pub fn i(&self, key: <Ristretto as Ciphersuite>::G) -> Option<Range<Participant>> {
    let mut all_is = HashMap::new();
    let mut i = 1;
    for (validator, weight) in &self.validators {
@@ -116,34 +102,12 @@ impl TributarySpec {
      i += weight;
    }

-    let original_i = all_is.get(&key)?.clone();
-    let mut result_i = original_i.clone();
-    for removed_validator in removed_validators {
-      let removed_i = all_is
-        .get(removed_validator)
-        .expect("removed validator wasn't present in set to begin with");
-      // If the queried key was removed, return None
-      if &original_i == removed_i {
-        return None;
-      }
-
-      // If the removed was before the queried, shift the queried down accordingly
-      if removed_i.start < original_i.start {
-        let removed_shares = u16::from(removed_i.end) - u16::from(removed_i.start);
-        result_i.start = Participant::new(u16::from(original_i.start) - removed_shares).unwrap();
-        result_i.end = Participant::new(u16::from(original_i.end) - removed_shares).unwrap();
-      }
-    }
-    Some(result_i)
+    Some(all_is.get(&key)?.clone())
  }

-  pub fn reverse_lookup_i(
-    &self,
-    removed_validators: &[<Ristretto as Ciphersuite>::G],
-    i: Participant,
-  ) -> Option<<Ristretto as Ciphersuite>::G> {
+  pub fn reverse_lookup_i(&self, i: Participant) -> Option<<Ristretto as Ciphersuite>::G> {
    for (validator, _) in &self.validators {
-      if self.i(removed_validators, *validator).map_or(false, |range| range.contains(&i)) {
+      if self.i(*validator).map_or(false, |range| range.contains(&i)) {
        return Some(*validator);
      }
    }
@@ -153,4 +117,8 @@ impl TributarySpec {
  pub fn validators(&self) -> Vec<(<Ristretto as Ciphersuite>::G, u64)> {
    self.validators.iter().map(|(validator, weight)| (*validator, u64::from(*weight))).collect()
  }
+
+  pub fn evrf_public_keys(&self) -> Vec<([u8; 32], Vec<u8>)> {
+    self.evrf_public_keys.clone()
+  }
 }
--- a/coordinator/src/tributary/transaction.rs
+++ b/coordinator/src/tributary/transaction.rs
@@ -12,7 +12,6 @@ use ciphersuite::{
  Ciphersuite, Ristretto,
 };
 use schnorr::SchnorrSignature;
-use frost::Participant;

 use scale::{Encode, Decode};
 use processor_messages::coordinator::SubstrateSignableId;
@@ -130,32 +129,26 @@ impl<Id: Clone + PartialEq + Eq + Debug + Encode + Decode> SignData<Id> {

 #[derive(Clone, PartialEq, Eq)]
 pub enum Transaction {
-  RemoveParticipantDueToDkg {
+  RemoveParticipant {
    participant: <Ristretto as Ciphersuite>::G,
    signed: Signed,
  },

-  DkgCommitments {
-    attempt: u32,
-    commitments: Vec<Vec<u8>>,
+  DkgParticipation {
+    participation: Vec<u8>,
    signed: Signed,
  },
-  DkgShares {
+  DkgConfirmationNonces {
+    // The confirmation attempt
    attempt: u32,
-    // Sending Participant, Receiving Participant, Share
-    shares: Vec<Vec<Vec<u8>>>,
+    // The nonces for DKG confirmation attempt #attempt
    confirmation_nonces: [u8; 64],
    signed: Signed,
  },
-  InvalidDkgShare {
-    attempt: u32,
-    accuser: Participant,
-    faulty: Participant,
-    blame: Option<Vec<u8>>,
-    signed: Signed,
-  },
-  DkgConfirmed {
+  DkgConfirmationShare {
+    // The confirmation attempt
    attempt: u32,
+    // The share for DKG confirmation attempt #attempt
    confirmation_share: [u8; 32],
    signed: Signed,
  },
@@ -197,29 +190,22 @@ pub enum Transaction {
 impl Debug for Transaction {
  fn fmt(&self, fmt: &mut core::fmt::Formatter<'_>) -> Result<(), core::fmt::Error> {
    match self {
-      Transaction::RemoveParticipantDueToDkg { participant, signed } => fmt
-        .debug_struct("Transaction::RemoveParticipantDueToDkg")
+      Transaction::RemoveParticipant { participant, signed } => fmt
+        .debug_struct("Transaction::RemoveParticipant")
        .field("participant", &hex::encode(participant.to_bytes()))
        .field("signer", &hex::encode(signed.signer.to_bytes()))
        .finish_non_exhaustive(),
-      Transaction::DkgCommitments { attempt, commitments: _, signed } => fmt
-        .debug_struct("Transaction::DkgCommitments")
+      Transaction::DkgParticipation { signed, .. } => fmt
+        .debug_struct("Transaction::DkgParticipation")
+        .field("signer", &hex::encode(signed.signer.to_bytes()))
+        .finish_non_exhaustive(),
+      Transaction::DkgConfirmationNonces { attempt, signed, .. } => fmt
+        .debug_struct("Transaction::DkgConfirmationNonces")
        .field("attempt", attempt)
        .field("signer", &hex::encode(signed.signer.to_bytes()))
        .finish_non_exhaustive(),
-      Transaction::DkgShares { attempt, signed, .. } => fmt
-        .debug_struct("Transaction::DkgShares")
-        .field("attempt", attempt)
-        .field("signer", &hex::encode(signed.signer.to_bytes()))
-        .finish_non_exhaustive(),
-      Transaction::InvalidDkgShare { attempt, accuser, faulty, .. } => fmt
-        .debug_struct("Transaction::InvalidDkgShare")
-        .field("attempt", attempt)
-        .field("accuser", accuser)
-        .field("faulty", faulty)
-        .finish_non_exhaustive(),
-      Transaction::DkgConfirmed { attempt, confirmation_share: _, signed } => fmt
-        .debug_struct("Transaction::DkgConfirmed")
+      Transaction::DkgConfirmationShare { attempt, signed, .. } => fmt
+        .debug_struct("Transaction::DkgConfirmationShare")
        .field("attempt", attempt)
        .field("signer", &hex::encode(signed.signer.to_bytes()))
        .finish_non_exhaustive(),
@@ -261,43 +247,32 @@ impl ReadWrite for Transaction {
    reader.read_exact(&mut kind)?;

    match kind[0] {
-      0 => Ok(Transaction::RemoveParticipantDueToDkg {
+      0 => Ok(Transaction::RemoveParticipant {
        participant: Ristretto::read_G(reader)?,
        signed: Signed::read_without_nonce(reader, 0)?,
      }),

      1 => {
-        let mut attempt = [0; 4];
-        reader.read_exact(&mut attempt)?;
-        let attempt = u32::from_le_bytes(attempt);
+        let participation = {
+          let mut participation_len = [0; 4];
+          reader.read_exact(&mut participation_len)?;
+          let participation_len = u32::from_le_bytes(participation_len);

-        let commitments = {
-          let mut commitments_len = [0; 1];
-          reader.read_exact(&mut commitments_len)?;
-          let commitments_len = usize::from(commitments_len[0]);
-          if commitments_len == 0 {
-            Err(io::Error::other("zero commitments in DkgCommitments"))?;
-          }
-
-          let mut each_commitments_len = [0; 2];
-          reader.read_exact(&mut each_commitments_len)?;
-          let each_commitments_len = usize::from(u16::from_le_bytes(each_commitments_len));
-          if (commitments_len * each_commitments_len) > TRANSACTION_SIZE_LIMIT {
+          if participation_len > u32::try_from(TRANSACTION_SIZE_LIMIT).unwrap() {
            Err(io::Error::other(
-              "commitments present in transaction exceeded transaction size limit",
+              "participation present in transaction exceeded transaction size limit",
            ))?;
          }
-          let mut commitments = vec![vec![]; commitments_len];
-          for commitments in &mut commitments {
-            *commitments = vec![0; each_commitments_len];
-            reader.read_exact(commitments)?;
-          }
-          commitments
+          let participation_len = usize::try_from(participation_len).unwrap();
+
+          let mut participation = vec![0; participation_len];
+          reader.read_exact(&mut participation)?;
+          participation
        };

        let signed = Signed::read_without_nonce(reader, 0)?;

-        Ok(Transaction::DkgCommitments { attempt, commitments, signed })
+        Ok(Transaction::DkgParticipation { participation, signed })
      }

      2 => {
@@ -305,36 +280,12 @@ impl ReadWrite for Transaction {
        reader.read_exact(&mut attempt)?;
        let attempt = u32::from_le_bytes(attempt);

-        let shares = {
-          let mut share_quantity = [0; 1];
-          reader.read_exact(&mut share_quantity)?;
-
-          let mut key_share_quantity = [0; 1];
-          reader.read_exact(&mut key_share_quantity)?;
-
-          let mut share_len = [0; 2];
-          reader.read_exact(&mut share_len)?;
-          let share_len = usize::from(u16::from_le_bytes(share_len));
-
-          let mut all_shares = vec![];
-          for _ in 0 .. share_quantity[0] {
-            let mut shares = vec![];
-            for _ in 0 .. key_share_quantity[0] {
-              let mut share = vec![0; share_len];
-              reader.read_exact(&mut share)?;
-              shares.push(share);
-            }
-            all_shares.push(shares);
-          }
-          all_shares
-        };
-
        let mut confirmation_nonces = [0; 64];
        reader.read_exact(&mut confirmation_nonces)?;

-        let signed = Signed::read_without_nonce(reader, 1)?;
+        let signed = Signed::read_without_nonce(reader, 0)?;

-        Ok(Transaction::DkgShares { attempt, shares, confirmation_nonces, signed })
+        Ok(Transaction::DkgConfirmationNonces { attempt, confirmation_nonces, signed })
      }

      3 => {
@@ -342,53 +293,21 @@ impl ReadWrite for Transaction {
        reader.read_exact(&mut attempt)?;
        let attempt = u32::from_le_bytes(attempt);

-        let mut accuser = [0; 2];
-        reader.read_exact(&mut accuser)?;
-        let accuser = Participant::new(u16::from_le_bytes(accuser))
-          .ok_or_else(|| io::Error::other("invalid participant in InvalidDkgShare"))?;
-
-        let mut faulty = [0; 2];
-        reader.read_exact(&mut faulty)?;
-        let faulty = Participant::new(u16::from_le_bytes(faulty))
-          .ok_or_else(|| io::Error::other("invalid participant in InvalidDkgShare"))?;
-
-        let mut blame_len = [0; 2];
-        reader.read_exact(&mut blame_len)?;
-        let mut blame = vec![0; u16::from_le_bytes(blame_len).into()];
-        reader.read_exact(&mut blame)?;
-
-        // This shares a nonce with DkgConfirmed as only one is expected
-        let signed = Signed::read_without_nonce(reader, 2)?;
-
-        Ok(Transaction::InvalidDkgShare {
-          attempt,
-          accuser,
-          faulty,
-          blame: Some(blame).filter(|blame| !blame.is_empty()),
-          signed,
-        })
-      }
-
-      4 => {
-        let mut attempt = [0; 4];
-        reader.read_exact(&mut attempt)?;
-        let attempt = u32::from_le_bytes(attempt);
-
        let mut confirmation_share = [0; 32];
        reader.read_exact(&mut confirmation_share)?;

-        let signed = Signed::read_without_nonce(reader, 2)?;
+        let signed = Signed::read_without_nonce(reader, 1)?;

-        Ok(Transaction::DkgConfirmed { attempt, confirmation_share, signed })
+        Ok(Transaction::DkgConfirmationShare { attempt, confirmation_share, signed })
      }

-      5 => {
+      4 => {
        let mut block = [0; 32];
        reader.read_exact(&mut block)?;
        Ok(Transaction::CosignSubstrateBlock(block))
      }

-      6 => {
+      5 => {
        let mut block = [0; 32];
        reader.read_exact(&mut block)?;
        let mut batch = [0; 4];
@@ -396,16 +315,16 @@ impl ReadWrite for Transaction {
        Ok(Transaction::Batch { block, batch: u32::from_le_bytes(batch) })
      }

-      7 => {
+      6 => {
        let mut block = [0; 8];
        reader.read_exact(&mut block)?;
        Ok(Transaction::SubstrateBlock(u64::from_le_bytes(block)))
      }

-      8 => SignData::read(reader).map(Transaction::SubstrateSign),
-      9 => SignData::read(reader).map(Transaction::Sign),
+      7 => SignData::read(reader).map(Transaction::SubstrateSign),
+      8 => SignData::read(reader).map(Transaction::Sign),

-      10 => {
+      9 => {
        let mut plan = [0; 32];
        reader.read_exact(&mut plan)?;

@@ -420,7 +339,7 @@ impl ReadWrite for Transaction {
        Ok(Transaction::SignCompleted { plan, tx_hash, first_signer, signature })
      }

-      11 => {
+      10 => {
        let mut len = [0];
        reader.read_exact(&mut len)?;
        let len = len[0];
@@ -445,109 +364,59 @@ impl ReadWrite for Transaction {

  fn write<W: io::Write>(&self, writer: &mut W) -> io::Result<()> {
    match self {
-      Transaction::RemoveParticipantDueToDkg { participant, signed } => {
+      Transaction::RemoveParticipant { participant, signed } => {
        writer.write_all(&[0])?;
        writer.write_all(&participant.to_bytes())?;
        signed.write_without_nonce(writer)
      }

-      Transaction::DkgCommitments { attempt, commitments, signed } => {
+      Transaction::DkgParticipation { participation, signed } => {
        writer.write_all(&[1])?;
-        writer.write_all(&attempt.to_le_bytes())?;
-        if commitments.is_empty() {
-          Err(io::Error::other("zero commitments in DkgCommitments"))?
-        }
-        writer.write_all(&[u8::try_from(commitments.len()).unwrap()])?;
-        for commitments_i in commitments {
-          if commitments_i.len() != commitments[0].len() {
-            Err(io::Error::other("commitments of differing sizes in DkgCommitments"))?
-          }
-        }
-        writer.write_all(&u16::try_from(commitments[0].len()).unwrap().to_le_bytes())?;
-        for commitments in commitments {
-          writer.write_all(commitments)?;
-        }
+        writer.write_all(&u32::try_from(participation.len()).unwrap().to_le_bytes())?;
+        writer.write_all(participation)?;
        signed.write_without_nonce(writer)
      }

-      Transaction::DkgShares { attempt, shares, confirmation_nonces, signed } => {
+      Transaction::DkgConfirmationNonces { attempt, confirmation_nonces, signed } => {
        writer.write_all(&[2])?;
        writer.write_all(&attempt.to_le_bytes())?;
-
-        // `shares` is a Vec which is supposed to map to a HashMap<Participant, Vec<u8>>. Since we
-        // bound participants to 150, this conversion is safe if a valid in-memory transaction.
-        writer.write_all(&[u8::try_from(shares.len()).unwrap()])?;
-        // This assumes at least one share is being sent to another party
-        writer.write_all(&[u8::try_from(shares[0].len()).unwrap()])?;
-        let share_len = shares[0][0].len();
-        // For BLS12-381 G2, this would be:
-        // - A 32-byte share
-        // - A 96-byte ephemeral key
-        // - A 128-byte signature
-        // Hence why this has to be u16
-        writer.write_all(&u16::try_from(share_len).unwrap().to_le_bytes())?;
-
-        for these_shares in shares {
-          assert_eq!(these_shares.len(), shares[0].len(), "amount of sent shares was variable");
-          for share in these_shares {
-            assert_eq!(share.len(), share_len, "sent shares were of variable length");
-            writer.write_all(share)?;
-          }
-        }
-
        writer.write_all(confirmation_nonces)?;
        signed.write_without_nonce(writer)
      }

-      Transaction::InvalidDkgShare { attempt, accuser, faulty, blame, signed } => {
+      Transaction::DkgConfirmationShare { attempt, confirmation_share, signed } => {
        writer.write_all(&[3])?;
        writer.write_all(&attempt.to_le_bytes())?;
-        writer.write_all(&u16::from(*accuser).to_le_bytes())?;
-        writer.write_all(&u16::from(*faulty).to_le_bytes())?;
-
-        // Flattens Some(vec![]) to None on the expectation no actual blame will be 0-length
-        assert!(blame.as_ref().map_or(1, Vec::len) != 0);
-        let blame_len =
-          u16::try_from(blame.as_ref().unwrap_or(&vec![]).len()).expect("blame exceeded 64 KB");
-        writer.write_all(&blame_len.to_le_bytes())?;
-        writer.write_all(blame.as_ref().unwrap_or(&vec![]))?;
-
-        signed.write_without_nonce(writer)
-      }
-
-      Transaction::DkgConfirmed { attempt, confirmation_share, signed } => {
-        writer.write_all(&[4])?;
-        writer.write_all(&attempt.to_le_bytes())?;
        writer.write_all(confirmation_share)?;
        signed.write_without_nonce(writer)
      }

      Transaction::CosignSubstrateBlock(block) => {
-        writer.write_all(&[5])?;
+        writer.write_all(&[4])?;
        writer.write_all(block)
      }

      Transaction::Batch { block, batch } => {
-        writer.write_all(&[6])?;
+        writer.write_all(&[5])?;
        writer.write_all(block)?;
        writer.write_all(&batch.to_le_bytes())
      }

      Transaction::SubstrateBlock(block) => {
-        writer.write_all(&[7])?;
+        writer.write_all(&[6])?;
        writer.write_all(&block.to_le_bytes())
      }

      Transaction::SubstrateSign(data) => {
-        writer.write_all(&[8])?;
+        writer.write_all(&[7])?;
        data.write(writer)
      }
      Transaction::Sign(data) => {
-        writer.write_all(&[9])?;
+        writer.write_all(&[8])?;
        data.write(writer)
      }
      Transaction::SignCompleted { plan, tx_hash, first_signer, signature } => {
-        writer.write_all(&[10])?;
+        writer.write_all(&[9])?;
        writer.write_all(plan)?;
        writer
          .write_all(&[u8::try_from(tx_hash.len()).expect("tx hash length exceed 255 bytes")])?;
@@ -556,7 +425,7 @@ impl ReadWrite for Transaction {
        signature.write(writer)
      }
      Transaction::SlashReport(points, signed) => {
-        writer.write_all(&[11])?;
+        writer.write_all(&[10])?;
        writer.write_all(&[u8::try_from(points.len()).unwrap()])?;
        for points in points {
          writer.write_all(&points.to_le_bytes())?;
@@ -570,15 +439,16 @@ impl ReadWrite for Transaction {
 impl TransactionTrait for Transaction {
  fn kind(&self) -> TransactionKind<'_> {
    match self {
-      Transaction::RemoveParticipantDueToDkg { participant, signed } => {
+      Transaction::RemoveParticipant { participant, signed } => {
        TransactionKind::Signed((b"remove", participant.to_bytes()).encode(), signed)
      }

-      Transaction::DkgCommitments { attempt, commitments: _, signed } |
-      Transaction::DkgShares { attempt, signed, .. } |
-      Transaction::InvalidDkgShare { attempt, signed, .. } |
-      Transaction::DkgConfirmed { attempt, signed, .. } => {
-        TransactionKind::Signed((b"dkg", attempt).encode(), signed)
+      Transaction::DkgParticipation { signed, .. } => {
+        TransactionKind::Signed(b"dkg".to_vec(), signed)
+      }
+      Transaction::DkgConfirmationNonces { attempt, signed, .. } |
+      Transaction::DkgConfirmationShare { attempt, signed, .. } => {
+        TransactionKind::Signed((b"dkg_confirmation", attempt).encode(), signed)
      }

      Transaction::CosignSubstrateBlock(_) => TransactionKind::Provided("cosign"),
@@ -645,11 +515,14 @@ impl Transaction {
    fn signed(tx: &mut Transaction) -> (u32, &mut Signed) {
      #[allow(clippy::match_same_arms)] // Doesn't make semantic sense here
      let nonce = match tx {
-        Transaction::RemoveParticipantDueToDkg { .. } => 0,
+        Transaction::RemoveParticipant { .. } => 0,

-        Transaction::DkgCommitments { .. } => 0,
-        Transaction::DkgShares { .. } => 1,
-        Transaction::InvalidDkgShare { .. } | Transaction::DkgConfirmed { .. } => 2,
+        Transaction::DkgParticipation { .. } => 0,
+        // Uses a nonce of 0 as it has an internal attempt counter we distinguish by
+        Transaction::DkgConfirmationNonces { .. } => 0,
+        // Uses a nonce of 1 due to internal attempt counter and due to following
+        // DkgConfirmationNonces
+        Transaction::DkgConfirmationShare { .. } => 1,

        Transaction::CosignSubstrateBlock(_) => panic!("signing CosignSubstrateBlock"),

@@ -668,11 +541,10 @@ impl Transaction {
        nonce,
        #[allow(clippy::match_same_arms)]
        match tx {
-          Transaction::RemoveParticipantDueToDkg { ref mut signed, .. } |
-          Transaction::DkgCommitments { ref mut signed, .. } |
-          Transaction::DkgShares { ref mut signed, .. } |
-          Transaction::InvalidDkgShare { ref mut signed, .. } |
-          Transaction::DkgConfirmed { ref mut signed, .. } => signed,
+          Transaction::RemoveParticipant { ref mut signed, .. } |
+          Transaction::DkgParticipation { ref mut signed, .. } |
+          Transaction::DkgConfirmationNonces { ref mut signed, .. } => signed,
+          Transaction::DkgConfirmationShare { ref mut signed, .. } => signed,

          Transaction::CosignSubstrateBlock(_) => panic!("signing CosignSubstrateBlock"),

--- a/crypto/dkg/Cargo.toml
+++ b/crypto/dkg/Cargo.toml
@@ -36,9 +36,26 @@ multiexp = { path = "../multiexp", version = "0.4", default-features = false }
 schnorr = { package = "schnorr-signatures", path = "../schnorr", version = "^0.5.1", default-features = false }
 dleq = { path = "../dleq", version = "^0.4.1", default-features = false }

+# eVRF DKG dependencies
+subtle = { version = "2", default-features = false, features = ["std"], optional = true }
+generic-array = { version = "1", default-features = false, features = ["alloc"], optional = true }
+blake2 = { version = "0.10", default-features = false, features = ["std"], optional = true }
+rand_chacha = { version = "0.3", default-features = false, features = ["std"], optional = true }
+generalized-bulletproofs = { path = "../evrf/generalized-bulletproofs", default-features = false, optional = true }
+ec-divisors = { path = "../evrf/divisors", default-features = false, optional = true }
+generalized-bulletproofs-circuit-abstraction = { path = "../evrf/circuit-abstraction", optional = true }
+generalized-bulletproofs-ec-gadgets = { path = "../evrf/ec-gadgets", optional = true }
+
+secq256k1 = { path = "../evrf/secq256k1", optional = true }
+embedwards25519 = { path = "../evrf/embedwards25519", optional = true }
+
 [dev-dependencies]
 rand_core = { version = "0.6", default-features = false, features = ["getrandom"] }
+rand = { version = "0.8", default-features = false, features = ["std"] }
 ciphersuite = { path = "../ciphersuite", default-features = false, features = ["ristretto"] }
+generalized-bulletproofs = { path = "../evrf/generalized-bulletproofs", features = ["tests"] }
+ec-divisors = { path = "../evrf/divisors", features = ["pasta"] }
+pasta_curves = "0.5"

 [features]
 std = [
@@ -62,5 +79,22 @@ std = [
  "dleq/serialize"
 ]
 borsh = ["dep:borsh"]
+evrf = [
+  "std",
+
+  "dep:subtle",
+  "dep:generic-array",
+
+  "dep:blake2",
+  "dep:rand_chacha",
+
+  "dep:generalized-bulletproofs",
+  "dep:ec-divisors",
+  "dep:generalized-bulletproofs-circuit-abstraction",
+  "dep:generalized-bulletproofs-ec-gadgets",
+]
+evrf-secp256k1 = ["evrf", "ciphersuite/secp256k1", "secq256k1"]
+evrf-ed25519 = ["evrf", "ciphersuite/ed25519", "embedwards25519"]
+evrf-ristretto = ["evrf", "ciphersuite/ristretto", "embedwards25519"]
 tests = ["rand_core/getrandom"]
 default = ["std"]
--- a/crypto/dkg/src/encryption.rs
+++ b/crypto/dkg/src/encryption.rs
@@ -48,8 +48,8 @@ pub(crate) use sealed::*;
 /// Wraps a message with a key to use for encryption in the future.
 #[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
 pub struct EncryptionKeyMessage<C: Ciphersuite, M: Message> {
-  msg: M,
-  enc_key: C::G,
+  pub(crate) msg: M,
+  pub(crate) enc_key: C::G,
 }

 // Doesn't impl ReadWrite so that doesn't need to be imported
@@ -98,11 +98,11 @@ fn ecdh<C: Ciphersuite>(private: &Zeroizing<C::F>, public: C::G) -> Zeroizing<C:

 // Each ecdh must be distinct. Reuse of an ecdh for multiple ciphers will cause the messages to be
 // leaked.
-fn cipher<C: Ciphersuite>(context: &str, ecdh: &Zeroizing<C::G>) -> ChaCha20 {
+fn cipher<C: Ciphersuite>(context: [u8; 32], ecdh: &Zeroizing<C::G>) -> ChaCha20 {
  // Ideally, we'd box this transcript with ZAlloc, yet that's only possible on nightly
  // TODO: https://github.com/serai-dex/serai/issues/151
  let mut transcript = RecommendedTranscript::new(b"DKG Encryption v0.2");
-  transcript.append_message(b"context", context.as_bytes());
+  transcript.append_message(b"context", context);

  transcript.domain_separate(b"encryption_key");

@@ -134,7 +134,7 @@ fn cipher<C: Ciphersuite>(context: &str, ecdh: &Zeroizing<C::G>) -> ChaCha20 {

 fn encrypt<R: RngCore + CryptoRng, C: Ciphersuite, E: Encryptable>(
  rng: &mut R,
-  context: &str,
+  context: [u8; 32],
  from: Participant,
  to: C::G,
  mut msg: Zeroizing<E>,
@@ -197,7 +197,7 @@ impl<C: Ciphersuite, E: Encryptable> EncryptedMessage<C, E> {
  pub(crate) fn invalidate_msg<R: RngCore + CryptoRng>(
    &mut self,
    rng: &mut R,
-    context: &str,
+    context: [u8; 32],
    from: Participant,
  ) {
    // Invalidate the message by specifying a new key/Schnorr PoP
@@ -219,7 +219,7 @@ impl<C: Ciphersuite, E: Encryptable> EncryptedMessage<C, E> {
  pub(crate) fn invalidate_share_serialization<R: RngCore + CryptoRng>(
    &mut self,
    rng: &mut R,
-    context: &str,
+    context: [u8; 32],
    from: Participant,
    to: C::G,
  ) {
@@ -243,7 +243,7 @@ impl<C: Ciphersuite, E: Encryptable> EncryptedMessage<C, E> {
  pub(crate) fn invalidate_share_value<R: RngCore + CryptoRng>(
    &mut self,
    rng: &mut R,
-    context: &str,
+    context: [u8; 32],
    from: Participant,
    to: C::G,
  ) {
@@ -300,14 +300,14 @@ impl<C: Ciphersuite> EncryptionKeyProof<C> {
 // This still doesn't mean the DKG offers an authenticated channel. The per-message keys have no
 // root of trust other than their existence in the assumed-to-exist external authenticated channel.
 fn pop_challenge<C: Ciphersuite>(
-  context: &str,
+  context: [u8; 32],
  nonce: C::G,
  key: C::G,
  sender: Participant,
  msg: &[u8],
 ) -> C::F {
  let mut transcript = RecommendedTranscript::new(b"DKG Encryption Key Proof of Possession v0.2");
-  transcript.append_message(b"context", context.as_bytes());
+  transcript.append_message(b"context", context);

  transcript.domain_separate(b"proof_of_possession");

@@ -323,9 +323,9 @@ fn pop_challenge<C: Ciphersuite>(
  C::hash_to_F(b"DKG-encryption-proof_of_possession", &transcript.challenge(b"schnorr"))
 }

-fn encryption_key_transcript(context: &str) -> RecommendedTranscript {
+fn encryption_key_transcript(context: [u8; 32]) -> RecommendedTranscript {
  let mut transcript = RecommendedTranscript::new(b"DKG Encryption Key Correctness Proof v0.2");
-  transcript.append_message(b"context", context.as_bytes());
+  transcript.append_message(b"context", context);
  transcript
 }

@@ -337,14 +337,69 @@ pub(crate) enum DecryptionError {
  InvalidProof,
 }

+// A simple box for managing decryption.
+#[derive(Clone, Debug)]
+pub(crate) struct Decryption<C: Ciphersuite> {
+  context: [u8; 32],
+  enc_keys: HashMap<Participant, C::G>,
+}
+
+impl<C: Ciphersuite> Decryption<C> {
+  pub(crate) fn new(context: [u8; 32]) -> Self {
+    Self { context, enc_keys: HashMap::new() }
+  }
+  pub(crate) fn register(&mut self, participant: Participant, key: C::G) {
+    assert!(
+      !self.enc_keys.contains_key(&participant),
+      "Re-registering encryption key for a participant"
+    );
+    self.enc_keys.insert(participant, key);
+  }
+
+  // Given a message, and the intended decryptor, and a proof for its key, decrypt the message.
+  // Returns None if the key was wrong.
+  pub(crate) fn decrypt_with_proof<E: Encryptable>(
+    &self,
+    from: Participant,
+    decryptor: Participant,
+    mut msg: EncryptedMessage<C, E>,
+    // There's no encryption key proof if the accusation is of an invalid signature
+    proof: Option<EncryptionKeyProof<C>>,
+  ) -> Result<Zeroizing<E>, DecryptionError> {
+    if !msg.pop.verify(
+      msg.key,
+      pop_challenge::<C>(self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
+    ) {
+      Err(DecryptionError::InvalidSignature)?;
+    }
+
+    if let Some(proof) = proof {
+      // Verify this is the decryption key for this message
+      proof
+        .dleq
+        .verify(
+          &mut encryption_key_transcript(self.context),
+          &[C::generator(), msg.key],
+          &[self.enc_keys[&decryptor], *proof.key],
+        )
+        .map_err(|_| DecryptionError::InvalidProof)?;
+
+      cipher::<C>(self.context, &proof.key).apply_keystream(msg.msg.as_mut().as_mut());
+      Ok(msg.msg)
+    } else {
+      Err(DecryptionError::InvalidProof)
+    }
+  }
+}
+
 // A simple box for managing encryption.
 #[derive(Clone)]
 pub(crate) struct Encryption<C: Ciphersuite> {
-  context: String,
-  i: Option<Participant>,
+  context: [u8; 32],
+  i: Participant,
  enc_key: Zeroizing<C::F>,
  enc_pub_key: C::G,
-  enc_keys: HashMap<Participant, C::G>,
+  decryption: Decryption<C>,
 }

 impl<C: Ciphersuite> fmt::Debug for Encryption<C> {
@@ -354,7 +409,7 @@ impl<C: Ciphersuite> fmt::Debug for Encryption<C> {
      .field("context", &self.context)
      .field("i", &self.i)
      .field("enc_pub_key", &self.enc_pub_key)
-      .field("enc_keys", &self.enc_keys)
+      .field("decryption", &self.decryption)
      .finish_non_exhaustive()
  }
 }
@@ -363,25 +418,20 @@ impl<C: Ciphersuite> Zeroize for Encryption<C> {
  fn zeroize(&mut self) {
    self.enc_key.zeroize();
    self.enc_pub_key.zeroize();
-    for (_, mut value) in self.enc_keys.drain() {
+    for (_, mut value) in self.decryption.enc_keys.drain() {
      value.zeroize();
    }
  }
 }

 impl<C: Ciphersuite> Encryption<C> {
-  pub(crate) fn new<R: RngCore + CryptoRng>(
-    context: String,
-    i: Option<Participant>,
-    rng: &mut R,
-  ) -> Self {
-    let enc_key = Zeroizing::new(C::random_nonzero_F(rng));
+  pub(crate) fn new(context: [u8; 32], i: Participant, enc_key: Zeroizing<C::F>) -> Self {
    Self {
      context,
      i,
      enc_pub_key: C::generator() * enc_key.deref(),
      enc_key,
-      enc_keys: HashMap::new(),
+      decryption: Decryption::new(context),
    }
  }

@@ -389,17 +439,8 @@ impl<C: Ciphersuite> Encryption<C> {
    EncryptionKeyMessage { msg, enc_key: self.enc_pub_key }
  }

-  pub(crate) fn register<M: Message>(
-    &mut self,
-    participant: Participant,
-    msg: EncryptionKeyMessage<C, M>,
-  ) -> M {
-    assert!(
-      !self.enc_keys.contains_key(&participant),
-      "Re-registering encryption key for a participant"
-    );
-    self.enc_keys.insert(participant, msg.enc_key);
-    msg.msg
+  pub(crate) fn register(&mut self, participant: Participant, key: C::G) {
+    self.decryption.register(participant, key)
  }

  pub(crate) fn encrypt<R: RngCore + CryptoRng, E: Encryptable>(
@@ -408,7 +449,7 @@ impl<C: Ciphersuite> Encryption<C> {
    participant: Participant,
    msg: Zeroizing<E>,
  ) -> EncryptedMessage<C, E> {
-    encrypt(rng, &self.context, self.i.unwrap(), self.enc_keys[&participant], msg)
+    encrypt(rng, self.context, self.i, self.decryption.enc_keys[&participant], msg)
  }

  pub(crate) fn decrypt<R: RngCore + CryptoRng, I: Copy + Zeroize, E: Encryptable>(
@@ -426,18 +467,18 @@ impl<C: Ciphersuite> Encryption<C> {
      batch,
      batch_id,
      msg.key,
-      pop_challenge::<C>(&self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
+      pop_challenge::<C>(self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
    );

    let key = ecdh::<C>(&self.enc_key, msg.key);
-    cipher::<C>(&self.context, &key).apply_keystream(msg.msg.as_mut().as_mut());
+    cipher::<C>(self.context, &key).apply_keystream(msg.msg.as_mut().as_mut());
    (
      msg.msg,
      EncryptionKeyProof {
        key,
        dleq: DLEqProof::prove(
          rng,
-          &mut encryption_key_transcript(&self.context),
+          &mut encryption_key_transcript(self.context),
          &[C::generator(), msg.key],
          &self.enc_key,
        ),
@@ -445,38 +486,7 @@ impl<C: Ciphersuite> Encryption<C> {
    )
  }

-  // Given a message, and the intended decryptor, and a proof for its key, decrypt the message.
-  // Returns None if the key was wrong.
-  pub(crate) fn decrypt_with_proof<E: Encryptable>(
-    &self,
-    from: Participant,
-    decryptor: Participant,
-    mut msg: EncryptedMessage<C, E>,
-    // There's no encryption key proof if the accusation is of an invalid signature
-    proof: Option<EncryptionKeyProof<C>>,
-  ) -> Result<Zeroizing<E>, DecryptionError> {
-    if !msg.pop.verify(
-      msg.key,
-      pop_challenge::<C>(&self.context, msg.pop.R, msg.key, from, msg.msg.deref().as_ref()),
-    ) {
-      Err(DecryptionError::InvalidSignature)?;
-    }
-
-    if let Some(proof) = proof {
-      // Verify this is the decryption key for this message
-      proof
-        .dleq
-        .verify(
-          &mut encryption_key_transcript(&self.context),
-          &[C::generator(), msg.key],
-          &[self.enc_keys[&decryptor], *proof.key],
-        )
-        .map_err(|_| DecryptionError::InvalidProof)?;
-
-      cipher::<C>(&self.context, &proof.key).apply_keystream(msg.msg.as_mut().as_mut());
-      Ok(msg.msg)
-    } else {
-      Err(DecryptionError::InvalidProof)
-    }
+  pub(crate) fn into_decryption(self) -> Decryption<C> {
+    self.decryption
  }
 }
--- a/crypto/dkg/src/evrf/mod.rs
+++ b/crypto/dkg/src/evrf/mod.rs
@@ -0,0 +1,584 @@
+/*
+  We implement a DKG using an eVRF, as detailed in the eVRF paper. For the eVRF itself, we do not
+  use a Paillier-based construction, nor the detailed construction premised on a Bulletproof.
+
+  For reference, the detailed construction premised on a Bulletproof involves two curves, notated
+  here as `C` and `E`, where the scalar field of `C` is the field of `E`. Accordingly, Bulletproofs
+  over `C` can efficiently perform group operations of points of curve `E`. Each participant has a
+  private point (`P_i`) on curve `E` committed to over curve `C`. The eVRF selects a pair of
+  scalars `a, b`, where the participant proves in-Bulletproof the points `A_i, B_i` are
+  `a * P_i, b * P_i`. The eVRF proceeds to commit to `A_i.x + B_i.x` in a Pedersen Commitment.
+
+  Our eVRF uses
+  [Generalized Bulletproofs](
+    https://repo.getmonero.org/monero-project/ccs-proposals
+      /uploads/a9baa50c38c6312efc0fea5c6a188bb9/gbp.pdf
+  ).
+  This allows us much larger witnesses without growing the reference string, and enables us to
+  efficiently sample challenges off in-circuit variables (via placing the variables in a vector
+  commitment, then challenging from a transcript of the commitments). We proceed to use
+  [elliptic curve divisors](
+    https://repo.getmonero.org/-/project/54/
+      uploads/eb1bf5b4d4855a3480c38abf895bd8e8/Veridise_Divisor_Proofs.pdf
+  )
+  (which require the ability to sample a challenge off in-circuit variables) to prove discrete
+  logarithms efficiently.
+
+  This is done via having a private scalar (`p_i`) on curve `E`, not a private point, and
+  publishing the public key for it (`P_i = p_i * G`, where `G` is a generator of `E`). The eVRF
+  samples two points with unknown discrete logarithms `A, B`, and the circuit proves a Pedersen
+  Commitment commits to `(p_i * A).x + (p_i * B).x`.
+
+  With the eVRF established, we now detail our other novel aspect. The eVRF paper expects secret
+  shares to be sent to the other parties yet does not detail a precise way to do so. If we
+  encrypted the secret shares with some stream cipher, each recipient would have to attest validity
+  or accuse the sender of impropriety. We want an encryption scheme where anyone can verify the
+  secret shares were encrypted properly, without additional info, efficiently.
+
+  Please note from the published commitments, it's possible to calculcate a commitment to the
+  secret share each party should receive (`V_i`).
+
+  We have the sender sample two scalars per recipient, denoted `x_i, y_i` (where `i` is the
+  recipient index). They perform the eVRF to prove a Pedersen Commitment commits to
+  `z_i = (x_i * P_i).x + (y_i * P_i).x` and `x_i, y_i` are the discrete logarithms of `X_i, Y_i`
+  over `G`. They then publish the encrypted share `s_i + z_i` and `X_i, Y_i`.
+
+  The recipient is able to decrypt the share via calculating
+  `s_i - ((p_i * X_i).x + (p_i * Y_i).x)`.
+
+  To verify the secret share, we have the `F` terms of the Pedersen Commitments revealed (where
+  `F, H` are generators of `C`, `F` is used for binding and `H` for blinding). This already needs
+  to be done for the eVRF outputs used within the DKG, in order to obtain thecommitments to the
+  coefficients. When we have the commitment `Z_i = ((p_i * A).x + (p_i * B).x) * F`, we simply
+  check `s_i * F = Z_i + V_i`.
+
+  In order to open the Pedersen Commitments to their `F` terms, we transcript the commitments and
+  the claimed openings, then assign random weights to each pair of `(commitment, opening). The
+  prover proves knowledge of the discrete logarithm of the sum weighted commitments, minus the sum
+  sum weighted openings, over `H`.
+
+  The benefit to this construction is that given an broadcast channel which is reliable and
+  ordered, only `t` messages must be broadcast from honest parties in order to create a `t`-of-`n`
+  multisig. If the encrypted secret shares were not verifiable, one would need at least `t + n`
+  messages to ensure every participant has a correct dealing and can participate in future
+  reconstructions of the secret. This would also require all `n` parties be online, whereas this is
+  robust to threshold `t`.
+*/
+
+use core::ops::Deref;
+use std::{
+  io::{self, Read, Write},
+  collections::{HashSet, HashMap},
+};
+
+use rand_core::{RngCore, CryptoRng};
+
+use zeroize::{Zeroize, Zeroizing};
+
+use blake2::{Digest, Blake2s256};
+use ciphersuite::{
+  group::{
+    ff::{Field, PrimeField},
+    Group, GroupEncoding,
+  },
+  Ciphersuite,
+};
+use multiexp::multiexp_vartime;
+
+use generalized_bulletproofs::arithmetic_circuit_proof::*;
+use ec_divisors::DivisorCurve;
+
+use crate::{Participant, ThresholdParams, Interpolation, ThresholdCore, ThresholdKeys};
+
+pub(crate) mod proof;
+use proof::*;
+pub use proof::{EvrfCurve, EvrfGenerators};
+
+/// Participation in the DKG.
+///
+/// `Participation` is meant to be broadcast to all other participants over an authenticated,
+/// reliable broadcast channel.
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct Participation<C: Ciphersuite> {
+  proof: Vec<u8>,
+  encrypted_secret_shares: HashMap<Participant, C::F>,
+}
+
+impl<C: Ciphersuite> Participation<C> {
+  pub fn read<R: Read>(reader: &mut R, n: u16) -> io::Result<Self> {
+    // TODO: Replace `len` with some calculcation deterministic to the params
+    let mut len = [0; 4];
+    reader.read_exact(&mut len)?;
+    let len = usize::try_from(u32::from_le_bytes(len)).expect("<32-bit platform?");
+
+    // Don't allocate a buffer for the claimed length
+    // Read chunks until we reach the claimed length
+    // This means if we were told to read GB, we must actually be sent GB before allocating as such
+    const CHUNK_SIZE: usize = 1024;
+    let mut proof = Vec::with_capacity(len.min(CHUNK_SIZE));
+    while proof.len() < len {
+      let next_chunk = (len - proof.len()).min(CHUNK_SIZE);
+      let old_proof_len = proof.len();
+      proof.resize(old_proof_len + next_chunk, 0);
+      reader.read_exact(&mut proof[old_proof_len ..])?;
+    }
+
+    let mut encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
+    for i in (1 ..= n).map(Participant) {
+      encrypted_secret_shares.insert(i, C::read_F(reader)?);
+    }
+
+    Ok(Self { proof, encrypted_secret_shares })
+  }
+
+  pub fn write<W: Write>(&self, writer: &mut W) -> io::Result<()> {
+    writer.write_all(&u32::try_from(self.proof.len()).unwrap().to_le_bytes())?;
+    writer.write_all(&self.proof)?;
+    for i in (1 ..= u16::try_from(self.encrypted_secret_shares.len())
+      .expect("writing a Participation which has a n > u16::MAX"))
+      .map(Participant)
+    {
+      writer.write_all(self.encrypted_secret_shares[&i].to_repr().as_ref())?;
+    }
+    Ok(())
+  }
+}
+
+fn polynomial<F: PrimeField + Zeroize>(
+  coefficients: &[Zeroizing<F>],
+  l: Participant,
+) -> Zeroizing<F> {
+  let l = F::from(u64::from(u16::from(l)));
+  // This should never be reached since Participant is explicitly non-zero
+  assert!(l != F::ZERO, "zero participant passed to polynomial");
+  let mut share = Zeroizing::new(F::ZERO);
+  for (idx, coefficient) in coefficients.iter().rev().enumerate() {
+    *share += coefficient.deref();
+    if idx != (coefficients.len() - 1) {
+      *share *= l;
+    }
+  }
+  share
+}
+
+#[allow(clippy::type_complexity)]
+fn share_verification_statements<C: Ciphersuite>(
+  rng: &mut (impl RngCore + CryptoRng),
+  commitments: &[C::G],
+  n: u16,
+  encryption_commitments: &[C::G],
+  encrypted_secret_shares: &HashMap<Participant, C::F>,
+) -> (C::F, Vec<(C::F, C::G)>) {
+  debug_assert_eq!(usize::from(n), encryption_commitments.len());
+  debug_assert_eq!(usize::from(n), encrypted_secret_shares.len());
+
+  let mut g_scalar = C::F::ZERO;
+  let mut pairs = Vec::with_capacity(commitments.len() + encryption_commitments.len());
+  for commitment in commitments {
+    pairs.push((C::F::ZERO, *commitment));
+  }
+
+  let mut weight;
+  for (i, enc_share) in encrypted_secret_shares {
+    let enc_commitment = encryption_commitments[usize::from(u16::from(*i)) - 1];
+
+    weight = C::F::random(&mut *rng);
+
+    // s_i F
+    g_scalar += weight * enc_share;
+    // - Z_i
+    let weight = -weight;
+    pairs.push((weight, enc_commitment));
+    // - V_i
+    {
+      let i = C::F::from(u64::from(u16::from(*i)));
+      // The first `commitments.len()` pairs are for the commitments
+      (0 .. commitments.len()).fold(weight, |exp, j| {
+        pairs[j].0 += exp;
+        exp * i
+      });
+    }
+  }
+
+  (g_scalar, pairs)
+}
+
+/// Errors from the eVRF DKG.
+#[derive(Clone, PartialEq, Eq, Debug, thiserror::Error)]
+pub enum EvrfError {
+  #[error("n, the amount of participants, exceeded a u16")]
+  TooManyParticipants,
+  #[error("the threshold t wasn't in range 1 <= t <= n")]
+  InvalidThreshold,
+  #[error("a public key was the identity point")]
+  PublicKeyWasIdentity,
+  #[error("participating in a DKG we aren't a participant in")]
+  NotAParticipant,
+  #[error("a participant with an unrecognized ID participated")]
+  NonExistentParticipant,
+  #[error("the passed in generators did not have enough generators for this DKG")]
+  NotEnoughGenerators,
+}
+
+/// The result of calling EvrfDkg::verify.
+pub enum VerifyResult<C: EvrfCurve> {
+  Valid(EvrfDkg<C>),
+  Invalid(Vec<Participant>),
+  NotEnoughParticipants,
+}
+
+/// Struct to perform/verify the DKG with.
+#[derive(Debug)]
+pub struct EvrfDkg<C: EvrfCurve> {
+  t: u16,
+  n: u16,
+  evrf_public_keys: Vec<<C::EmbeddedCurve as Ciphersuite>::G>,
+  group_key: C::G,
+  verification_shares: HashMap<Participant, C::G>,
+  #[allow(clippy::type_complexity)]
+  encrypted_secret_shares:
+    HashMap<Participant, HashMap<Participant, ([<C::EmbeddedCurve as Ciphersuite>::G; 2], C::F)>>,
+}
+
+impl<C: EvrfCurve> EvrfDkg<C> {
+  // Form the initial transcript for the proofs.
+  fn initial_transcript(
+    invocation: [u8; 32],
+    evrf_public_keys: &[<C::EmbeddedCurve as Ciphersuite>::G],
+    t: u16,
+  ) -> [u8; 32] {
+    let mut transcript = Blake2s256::new();
+    transcript.update(invocation);
+    for key in evrf_public_keys {
+      transcript.update(key.to_bytes().as_ref());
+    }
+    transcript.update(t.to_le_bytes());
+    transcript.finalize().into()
+  }
+
+  /// Participate in performing the DKG for the specified parameters.
+  ///
+  /// The context MUST be unique across invocations. Reuse of context will lead to sharing
+  /// prior-shared secrets.
+  ///
+  /// Public keys are not allowed to be the identity point. This will error if any are.
+  pub fn participate(
+    rng: &mut (impl RngCore + CryptoRng),
+    generators: &EvrfGenerators<C>,
+    context: [u8; 32],
+    t: u16,
+    evrf_public_keys: &[<C::EmbeddedCurve as Ciphersuite>::G],
+    evrf_private_key: &Zeroizing<<C::EmbeddedCurve as Ciphersuite>::F>,
+  ) -> Result<Participation<C>, EvrfError> {
+    let Ok(n) = u16::try_from(evrf_public_keys.len()) else { Err(EvrfError::TooManyParticipants)? };
+    if (t == 0) || (t > n) {
+      Err(EvrfError::InvalidThreshold)?;
+    }
+    if evrf_public_keys.iter().any(|key| bool::from(key.is_identity())) {
+      Err(EvrfError::PublicKeyWasIdentity)?;
+    };
+    let evrf_public_key = <C::EmbeddedCurve as Ciphersuite>::generator() * evrf_private_key.deref();
+    if !evrf_public_keys.iter().any(|key| *key == evrf_public_key) {
+      Err(EvrfError::NotAParticipant)?;
+    };
+
+    let transcript = Self::initial_transcript(context, evrf_public_keys, t);
+    // Further bind to the participant index so each index gets unique generators
+    // This allows reusing eVRF public keys as the prover
+    let mut per_proof_transcript = Blake2s256::new();
+    per_proof_transcript.update(transcript);
+    per_proof_transcript.update(evrf_public_key.to_bytes());
+
+    // The above transcript is expected to be binding to all arguments here
+    // The generators are constant to this ciphersuite's generator, and the parameters are
+    // transcripted
+    let EvrfProveResult { coefficients, encryption_masks, proof } = match Evrf::prove(
+      rng,
+      &generators.0,
+      per_proof_transcript.finalize().into(),
+      usize::from(t),
+      evrf_public_keys,
+      evrf_private_key,
+    ) {
+      Ok(res) => res,
+      Err(AcError::NotEnoughGenerators) => Err(EvrfError::NotEnoughGenerators)?,
+      Err(
+        AcError::DifferingLrLengths |
+        AcError::InconsistentAmountOfConstraints |
+        AcError::ConstrainedNonExistentTerm |
+        AcError::ConstrainedNonExistentCommitment |
+        AcError::InconsistentWitness |
+        AcError::Ip(_) |
+        AcError::IncompleteProof,
+      ) => {
+        panic!("failed to prove for the eVRF proof")
+      }
+    };
+
+    let mut encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
+    for (l, encryption_mask) in (1 ..= n).map(Participant).zip(encryption_masks) {
+      let share = polynomial::<C::F>(&coefficients, l);
+      encrypted_secret_shares.insert(l, *share + *encryption_mask);
+    }
+
+    Ok(Participation { proof, encrypted_secret_shares })
+  }
+
+  /// Check if a batch of `Participation`s are valid.
+  ///
+  /// If any `Participation` is invalid, the list of all invalid participants will be returned.
+  /// If all `Participation`s are valid and there's at least `t`, an instance of this struct
+  /// (usable to obtain a threshold share of generated key) is returned. If all are valid and
+  /// there's not at least `t`, `VerifyResult::NotEnoughParticipants` is returned.
+  ///
+  /// This DKG is unbiased if all `n` people participate. This DKG is biased if only a threshold
+  /// participate.
+  pub fn verify(
+    rng: &mut (impl RngCore + CryptoRng),
+    generators: &EvrfGenerators<C>,
+    context: [u8; 32],
+    t: u16,
+    evrf_public_keys: &[<C::EmbeddedCurve as Ciphersuite>::G],
+    participations: &HashMap<Participant, Participation<C>>,
+  ) -> Result<VerifyResult<C>, EvrfError> {
+    let Ok(n) = u16::try_from(evrf_public_keys.len()) else { Err(EvrfError::TooManyParticipants)? };
+    if (t == 0) || (t > n) {
+      Err(EvrfError::InvalidThreshold)?;
+    }
+    if evrf_public_keys.iter().any(|key| bool::from(key.is_identity())) {
+      Err(EvrfError::PublicKeyWasIdentity)?;
+    };
+    for i in participations.keys() {
+      if u16::from(*i) > n {
+        Err(EvrfError::NonExistentParticipant)?;
+      }
+    }
+
+    let mut valid = HashMap::with_capacity(participations.len());
+    let mut faulty = HashSet::new();
+
+    let transcript = Self::initial_transcript(context, evrf_public_keys, t);
+
+    let mut evrf_verifier = generators.0.batch_verifier();
+    for (i, participation) in participations {
+      let evrf_public_key = evrf_public_keys[usize::from(u16::from(*i)) - 1];
+
+      let mut per_proof_transcript = Blake2s256::new();
+      per_proof_transcript.update(transcript);
+      per_proof_transcript.update(evrf_public_key.to_bytes());
+
+      // Clone the verifier so if this proof is faulty, it doesn't corrupt the verifier
+      let mut verifier_clone = evrf_verifier.clone();
+      let Ok(data) = Evrf::<C>::verify(
+        rng,
+        &generators.0,
+        &mut verifier_clone,
+        per_proof_transcript.finalize().into(),
+        usize::from(t),
+        evrf_public_keys,
+        evrf_public_key,
+        &participation.proof,
+      ) else {
+        faulty.insert(*i);
+        continue;
+      };
+      evrf_verifier = verifier_clone;
+
+      valid.insert(*i, (participation.encrypted_secret_shares.clone(), data));
+    }
+    debug_assert_eq!(valid.len() + faulty.len(), participations.len());
+
+    // Perform the batch verification of the eVRFs
+    if !generators.0.verify(evrf_verifier) {
+      // If the batch failed, verify them each individually
+      for (i, participation) in participations {
+        if faulty.contains(i) {
+          continue;
+        }
+        let mut evrf_verifier = generators.0.batch_verifier();
+        Evrf::<C>::verify(
+          rng,
+          &generators.0,
+          &mut evrf_verifier,
+          context,
+          usize::from(t),
+          evrf_public_keys,
+          evrf_public_keys[usize::from(u16::from(*i)) - 1],
+          &participation.proof,
+        )
+        .expect("evrf failed basic checks yet prover wasn't prior marked faulty");
+        if !generators.0.verify(evrf_verifier) {
+          valid.remove(i);
+          faulty.insert(*i);
+        }
+      }
+    }
+    debug_assert_eq!(valid.len() + faulty.len(), participations.len());
+
+    // Perform the batch verification of the shares
+    let mut sum_encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
+    let mut sum_masks = HashMap::with_capacity(usize::from(n));
+    let mut all_encrypted_secret_shares = HashMap::with_capacity(usize::from(t));
+    {
+      let mut share_verification_statements_actual = HashMap::with_capacity(valid.len());
+      if !{
+        let mut g_scalar = C::F::ZERO;
+        let mut pairs = Vec::with_capacity(valid.len() * (usize::from(t) + evrf_public_keys.len()));
+        for (i, (encrypted_secret_shares, data)) in &valid {
+          let (this_g_scalar, mut these_pairs) = share_verification_statements::<C>(
+            &mut *rng,
+            &data.coefficients,
+            evrf_public_keys
+              .len()
+              .try_into()
+              .expect("n prior checked to be <= u16::MAX couldn't be converted to a u16"),
+            &data.encryption_commitments,
+            encrypted_secret_shares,
+          );
+          // Queue this into our batch
+          g_scalar += this_g_scalar;
+          pairs.extend(&these_pairs);
+
+          // Also push this g_scalar onto these_pairs so these_pairs can be verified individually
+          // upon error
+          these_pairs.push((this_g_scalar, generators.0.g()));
+          share_verification_statements_actual.insert(*i, these_pairs);
+
+          // Also format this data as we'd need it upon success
+          let mut formatted_encrypted_secret_shares = HashMap::with_capacity(usize::from(n));
+          for (j, enc_share) in encrypted_secret_shares {
+            /*
+              We calculcate verification shares as the sum of the encrypted scalars, minus their
+              masks. This only does one scalar multiplication, and `1+t` point additions (with
+              one negation), and is accordingly much cheaper than interpolating the commitments.
+              This is only possible because already interpolated the commitments to verify the
+              encrypted secret share.
+            */
+            let sum_encrypted_secret_share =
+              sum_encrypted_secret_shares.get(j).copied().unwrap_or(C::F::ZERO);
+            let sum_mask = sum_masks.get(j).copied().unwrap_or(C::G::identity());
+            sum_encrypted_secret_shares.insert(*j, sum_encrypted_secret_share + enc_share);
+
+            let j_index = usize::from(u16::from(*j)) - 1;
+            sum_masks.insert(*j, sum_mask + data.encryption_commitments[j_index]);
+
+            formatted_encrypted_secret_shares.insert(*j, (data.ecdh_keys[j_index], *enc_share));
+          }
+          all_encrypted_secret_shares.insert(*i, formatted_encrypted_secret_shares);
+        }
+        pairs.push((g_scalar, generators.0.g()));
+        bool::from(multiexp_vartime(&pairs).is_identity())
+      } {
+        // If the batch failed, verify them each individually
+        for (i, pairs) in share_verification_statements_actual {
+          if !bool::from(multiexp_vartime(&pairs).is_identity()) {
+            valid.remove(&i);
+            faulty.insert(i);
+          }
+        }
+      }
+    }
+    debug_assert_eq!(valid.len() + faulty.len(), participations.len());
+
+    let mut faulty = faulty.into_iter().collect::<Vec<_>>();
+    if !faulty.is_empty() {
+      faulty.sort_unstable();
+      return Ok(VerifyResult::Invalid(faulty));
+    }
+
+    // We check at least t key shares of people have participated in contributing entropy
+    // Since the key shares of the participants exceed t, meaning if they're malicious they can
+    // reconstruct the key regardless, this is safe to the threshold
+    {
+      let mut participating_weight = 0;
+      let mut evrf_public_keys_mut = evrf_public_keys.to_vec();
+      for i in valid.keys() {
+        let evrf_public_key = evrf_public_keys[usize::from(u16::from(*i)) - 1];
+
+        // Remove this key from the Vec to prevent double-counting
+        /*
+          Double-counting would be a risk if multiple participants shared an eVRF public key and
+          participated. This code does still allow such participants (in order to let participants
+          be weighted), and any one of them participating will count as all participating. This is
+          fine as any one such participant will be able to decrypt the shares for themselves and
+          all other participants, so this is still a key generated by an amount of participants who
+          could simply reconstruct the key.
+        */
+        let start_len = evrf_public_keys_mut.len();
+        evrf_public_keys_mut.retain(|key| *key != evrf_public_key);
+        let end_len = evrf_public_keys_mut.len();
+        let count = start_len - end_len;
+
+        participating_weight += count;
+      }
+      if participating_weight < usize::from(t) {
+        return Ok(VerifyResult::NotEnoughParticipants);
+      }
+    }
+
+    // If we now have >= t participations, calculate the group key and verification shares
+
+    // The group key is the sum of the zero coefficients
+    let group_key = valid.values().map(|(_, evrf_data)| evrf_data.coefficients[0]).sum::<C::G>();
+
+    // Calculate each user's verification share
+    let mut verification_shares = HashMap::with_capacity(usize::from(n));
+    for i in (1 ..= n).map(Participant) {
+      verification_shares
+        .insert(i, (C::generator() * sum_encrypted_secret_shares[&i]) - sum_masks[&i]);
+    }
+
+    Ok(VerifyResult::Valid(EvrfDkg {
+      t,
+      n,
+      evrf_public_keys: evrf_public_keys.to_vec(),
+      group_key,
+      verification_shares,
+      encrypted_secret_shares: all_encrypted_secret_shares,
+    }))
+  }
+
+  pub fn keys(
+    &self,
+    evrf_private_key: &Zeroizing<<C::EmbeddedCurve as Ciphersuite>::F>,
+  ) -> Vec<ThresholdKeys<C>> {
+    let evrf_public_key = <C::EmbeddedCurve as Ciphersuite>::generator() * evrf_private_key.deref();
+    let mut is = Vec::with_capacity(1);
+    for (i, evrf_key) in self.evrf_public_keys.iter().enumerate() {
+      if *evrf_key == evrf_public_key {
+        let i = u16::try_from(i).expect("n <= u16::MAX yet i > u16::MAX?");
+        let i = Participant(1 + i);
+        is.push(i);
+      }
+    }
+
+    let mut res = Vec::with_capacity(is.len());
+    for i in is {
+      let mut secret_share = Zeroizing::new(C::F::ZERO);
+      for shares in self.encrypted_secret_shares.values() {
+        let (ecdh_keys, enc_share) = shares[&i];
+
+        let mut ecdh = Zeroizing::new(C::F::ZERO);
+        for point in ecdh_keys {
+          let (mut x, mut y) =
+            <C::EmbeddedCurve as Ciphersuite>::G::to_xy(point * evrf_private_key.deref()).unwrap();
+          *ecdh += x;
+          x.zeroize();
+          y.zeroize();
+        }
+        *secret_share += enc_share - ecdh.deref();
+      }
+
+      debug_assert_eq!(self.verification_shares[&i], C::generator() * secret_share.deref());
+
+      res.push(ThresholdKeys::from(ThresholdCore {
+        params: ThresholdParams::new(self.t, self.n, i).unwrap(),
+        interpolation: Interpolation::Lagrange,
+        secret_share,
+        group_key: self.group_key,
+        verification_shares: self.verification_shares.clone(),
+      }));
+    }
+    res
+  }
+}
--- a/crypto/dkg/src/evrf/proof.rs
+++ b/crypto/dkg/src/evrf/proof.rs
@@ -0,0 +1,861 @@
+use core::{marker::PhantomData, ops::Deref, fmt};
+
+use subtle::*;
+use zeroize::{Zeroize, Zeroizing};
+
+use rand_core::{RngCore, CryptoRng, SeedableRng};
+use rand_chacha::ChaCha20Rng;
+
+use generic_array::{typenum::Unsigned, ArrayLength, GenericArray};
+
+use blake2::{Digest, Blake2s256};
+use ciphersuite::{
+  group::{
+    ff::{Field, PrimeField, PrimeFieldBits},
+    Group, GroupEncoding,
+  },
+  Ciphersuite,
+};
+
+use generalized_bulletproofs::{
+  *,
+  transcript::{Transcript as ProverTranscript, VerifierTranscript},
+  arithmetic_circuit_proof::*,
+};
+use generalized_bulletproofs_circuit_abstraction::*;
+
+use ec_divisors::{DivisorCurve, new_divisor};
+use generalized_bulletproofs_ec_gadgets::*;
+
+/// A pair of curves to perform the eVRF with.
+pub trait EvrfCurve: Ciphersuite {
+  type EmbeddedCurve: Ciphersuite<G: DivisorCurve<FieldElement = <Self as Ciphersuite>::F>>;
+  type EmbeddedCurveParameters: DiscreteLogParameters;
+}
+
+#[cfg(feature = "evrf-secp256k1")]
+impl EvrfCurve for ciphersuite::Secp256k1 {
+  type EmbeddedCurve = secq256k1::Secq256k1;
+  type EmbeddedCurveParameters = secq256k1::Secq256k1;
+}
+
+#[cfg(feature = "evrf-ed25519")]
+impl EvrfCurve for ciphersuite::Ed25519 {
+  type EmbeddedCurve = embedwards25519::Embedwards25519;
+  type EmbeddedCurveParameters = embedwards25519::Embedwards25519;
+}
+
+#[cfg(feature = "evrf-ristretto")]
+impl EvrfCurve for ciphersuite::Ristretto {
+  type EmbeddedCurve = embedwards25519::Embedwards25519;
+  type EmbeddedCurveParameters = embedwards25519::Embedwards25519;
+}
+
+fn sample_point<C: Ciphersuite>(rng: &mut (impl RngCore + CryptoRng)) -> C::G {
+  let mut repr = <C::G as GroupEncoding>::Repr::default();
+  loop {
+    rng.fill_bytes(repr.as_mut());
+    if let Ok(point) = C::read_G(&mut repr.as_ref()) {
+      if bool::from(!point.is_identity()) {
+        return point;
+      }
+    }
+  }
+}
+
+/// Generators for eVRF proof.
+#[derive(Clone, Debug)]
+pub struct EvrfGenerators<C: EvrfCurve>(pub(crate) Generators<C>);
+
+impl<C: EvrfCurve> EvrfGenerators<C> {
+  /// Create a new set of generators.
+  pub fn new(max_threshold: u16, max_participants: u16) -> EvrfGenerators<C> {
+    let g = C::generator();
+    let mut rng = ChaCha20Rng::from_seed(Blake2s256::digest(g.to_bytes()).into());
+    let h = sample_point::<C>(&mut rng);
+    let (_, generators) =
+      Evrf::<C>::muls_and_generators_to_use(max_threshold.into(), max_participants.into());
+    let mut g_bold = vec![];
+    let mut h_bold = vec![];
+    for _ in 0 .. generators {
+      g_bold.push(sample_point::<C>(&mut rng));
+      h_bold.push(sample_point::<C>(&mut rng));
+    }
+    Self(Generators::new(g, h, g_bold, h_bold).unwrap())
+  }
+}
+
+/// The result of proving for an eVRF.
+pub(crate) struct EvrfProveResult<C: Ciphersuite> {
+  /// The coefficients for use in the DKG.
+  pub(crate) coefficients: Vec<Zeroizing<C::F>>,
+  /// The masks to encrypt secret shares with.
+  pub(crate) encryption_masks: Vec<Zeroizing<C::F>>,
+  /// The proof itself.
+  pub(crate) proof: Vec<u8>,
+}
+
+/// The result of verifying an eVRF.
+pub(crate) struct EvrfVerifyResult<C: EvrfCurve> {
+  /// The commitments to the coefficients for use in the DKG.
+  pub(crate) coefficients: Vec<C::G>,
+  /// The ephemeral public keys to perform ECDHs with
+  pub(crate) ecdh_keys: Vec<[<C::EmbeddedCurve as Ciphersuite>::G; 2]>,
+  /// The commitments to the masks used to encrypt secret shares with.
+  pub(crate) encryption_commitments: Vec<C::G>,
+}
+
+impl<C: EvrfCurve> fmt::Debug for EvrfVerifyResult<C> {
+  fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
+    fmt.debug_struct("EvrfVerifyResult").finish_non_exhaustive()
+  }
+}
+
+/// A struct to prove/verify eVRFs with.
+pub(crate) struct Evrf<C: EvrfCurve>(PhantomData<C>);
+impl<C: EvrfCurve> Evrf<C> {
+  // Sample uniform points (via rejection-sampling) on the embedded elliptic curve
+  fn transcript_to_points(
+    seed: [u8; 32],
+    coefficients: usize,
+  ) -> Vec<<C::EmbeddedCurve as Ciphersuite>::G> {
+    // We need to do two Diffie-Hellman's per coefficient in order to achieve an unbiased result
+    let quantity = 2 * coefficients;
+
+    let mut rng = ChaCha20Rng::from_seed(seed);
+    let mut res = Vec::with_capacity(quantity);
+    for _ in 0 .. quantity {
+      res.push(sample_point::<C::EmbeddedCurve>(&mut rng));
+    }
+    res
+  }
+
+  /// Read a Variable from a theoretical vector commitment tape
+  fn read_one_from_tape(generators_to_use: usize, start: &mut usize) -> Variable {
+    // Each commitment has twice as many variables as generators in use
+    let commitment = *start / (2 * generators_to_use);
+    // The index will be less than the amount of generators in use, as half are left and half are
+    // right
+    let index = *start % generators_to_use;
+    let res = if (*start / generators_to_use) % 2 == 0 {
+      Variable::CG { commitment, index }
+    } else {
+      Variable::CH { commitment, index }
+    };
+    *start += 1;
+    res
+  }
+
+  /// Read a set of variables from a theoretical vector commitment tape
+  fn read_from_tape<N: ArrayLength>(
+    generators_to_use: usize,
+    start: &mut usize,
+  ) -> GenericArray<Variable, N> {
+    let mut buf = Vec::with_capacity(N::USIZE);
+    for _ in 0 .. N::USIZE {
+      buf.push(Self::read_one_from_tape(generators_to_use, start));
+    }
+    GenericArray::from_slice(&buf).clone()
+  }
+
+  /// Read `PointWithDlog`s, which share a discrete logarithm, from the theoretical vector
+  /// commitment tape.
+  fn point_with_dlogs(
+    start: &mut usize,
+    quantity: usize,
+    generators_to_use: usize,
+  ) -> Vec<PointWithDlog<C::EmbeddedCurveParameters>> {
+    // We define a serialized tape of the discrete logarithm, then for each divisor/point, we push:
+    //   zero, x**i, y x**i, y, x_coord, y_coord
+    // We then chunk that into vector commitments
+    // Here, we take the assumed layout and generate the expected `Variable`s for this layout
+
+    let dlog = Self::read_from_tape(generators_to_use, start);
+
+    let mut res = Vec::with_capacity(quantity);
+    let mut read_point_with_dlog = || {
+      let zero = Self::read_one_from_tape(generators_to_use, start);
+      let x_from_power_of_2 = Self::read_from_tape(generators_to_use, start);
+      let yx = Self::read_from_tape(generators_to_use, start);
+      let y = Self::read_one_from_tape(generators_to_use, start);
+      let divisor = Divisor { zero, x_from_power_of_2, yx, y };
+
+      let point = (
+        Self::read_one_from_tape(generators_to_use, start),
+        Self::read_one_from_tape(generators_to_use, start),
+      );
+
+      res.push(PointWithDlog { dlog: dlog.clone(), divisor, point });
+    };
+
+    for _ in 0 .. quantity {
+      read_point_with_dlog();
+    }
+    res
+  }
+
+  fn muls_and_generators_to_use(coefficients: usize, ecdhs: usize) -> (usize, usize) {
+    const MULS_PER_DH: usize = 7;
+    // 1 DH to prove the discrete logarithm corresponds to the eVRF public key
+    // 2 DHs per generated coefficient
+    // 2 DHs per generated ECDH
+    let expected_muls = MULS_PER_DH * (1 + (2 * coefficients) + (2 * 2 * ecdhs));
+    let generators_to_use = {
+      let mut padded_pow_of_2 = 1;
+      while padded_pow_of_2 < expected_muls {
+        padded_pow_of_2 <<= 1;
+      }
+      // This may as small as 16, which would create an excessive amount of vector commitments
+      // We set a floor of 1024 rows for bandwidth reasons
+      padded_pow_of_2.max(1024)
+    };
+    (expected_muls, generators_to_use)
+  }
+
+  fn circuit(
+    curve_spec: &CurveSpec<C::F>,
+    evrf_public_key: (C::F, C::F),
+    coefficients: usize,
+    ecdh_commitments: &[[(C::F, C::F); 2]],
+    generator_tables: &[GeneratorTable<C::F, C::EmbeddedCurveParameters>],
+    circuit: &mut Circuit<C>,
+    transcript: &mut impl Transcript,
+  ) {
+    let (expected_muls, generators_to_use) =
+      Self::muls_and_generators_to_use(coefficients, ecdh_commitments.len());
+    let (challenge, challenged_generators) =
+      circuit.discrete_log_challenge(transcript, curve_spec, generator_tables);
+    debug_assert_eq!(challenged_generators.len(), 1 + (2 * coefficients) + ecdh_commitments.len());
+
+    // The generators tables/challenged generators are expected to have the following layouts
+    // G, coefficients * [A, B], ecdhs * [P]
+    #[allow(non_snake_case)]
+    let challenged_G = &challenged_generators[0];
+
+    // Execute the circuit for the coefficients
+    let mut tape_pos = 0;
+    {
+      let mut point_with_dlogs =
+        Self::point_with_dlogs(&mut tape_pos, 1 + (2 * coefficients), generators_to_use)
+          .into_iter();
+
+      // Verify the discrete logarithm is in the fact the discrete logarithm of the eVRF public key
+      let point = circuit.discrete_log(
+        curve_spec,
+        point_with_dlogs.next().unwrap(),
+        &challenge,
+        challenged_G,
+      );
+      circuit.equality(LinComb::from(point.x()), &LinComb::empty().constant(evrf_public_key.0));
+      circuit.equality(LinComb::from(point.y()), &LinComb::empty().constant(evrf_public_key.1));
+
+      // Verify the DLog claims against the sampled points
+      for (i, pair) in challenged_generators[1 ..].chunks(2).take(coefficients).enumerate() {
+        let mut lincomb = LinComb::empty();
+        debug_assert_eq!(pair.len(), 2);
+        for challenged_generator in pair {
+          let point = circuit.discrete_log(
+            curve_spec,
+            point_with_dlogs.next().unwrap(),
+            &challenge,
+            challenged_generator,
+          );
+          // For each point in this pair, add its x coordinate to a lincomb
+          lincomb = lincomb.term(C::F::ONE, point.x());
+        }
+        // Constrain the sum of the two x coordinates to be equal to the value in the Pedersen
+        // commitment
+        circuit.equality(lincomb, &LinComb::from(Variable::V(i)));
+      }
+      debug_assert!(point_with_dlogs.next().is_none());
+    }
+
+    // Now execute the circuit for the ECDHs
+    let mut challenged_generators = challenged_generators.iter().skip(1 + (2 * coefficients));
+    for (i, ecdh) in ecdh_commitments.iter().enumerate() {
+      let challenged_generator = challenged_generators.next().unwrap();
+      let mut lincomb = LinComb::empty();
+      for ecdh in ecdh {
+        let mut point_with_dlogs =
+          Self::point_with_dlogs(&mut tape_pos, 2, generators_to_use).into_iter();
+
+        // One proof of the ECDH secret * G for the commitment published
+        let point = circuit.discrete_log(
+          curve_spec,
+          point_with_dlogs.next().unwrap(),
+          &challenge,
+          challenged_G,
+        );
+        circuit.equality(LinComb::from(point.x()), &LinComb::empty().constant(ecdh.0));
+        circuit.equality(LinComb::from(point.y()), &LinComb::empty().constant(ecdh.1));
+
+        // One proof of the ECDH secret * P for the ECDH
+        let point = circuit.discrete_log(
+          curve_spec,
+          point_with_dlogs.next().unwrap(),
+          &challenge,
+          challenged_generator,
+        );
+        // For each point in this pair, add its x coordinate to a lincomb
+        lincomb = lincomb.term(C::F::ONE, point.x());
+      }
+
+      // Constrain the sum of the two x coordinates to be equal to the value in the Pedersen
+      // commitment
+      circuit.equality(lincomb, &LinComb::from(Variable::V(coefficients + i)));
+    }
+
+    debug_assert_eq!(expected_muls, circuit.muls());
+    debug_assert!(challenged_generators.next().is_none());
+  }
+
+  /// Convert a scalar to a sequence of coefficients for the polynomial 2**i, where the sum of the
+  /// coefficients is F::NUM_BITS.
+  ///
+  /// Despite the name, the returned coefficients are not guaranteed to be bits (0 or 1).
+  ///
+  /// This scalar will presumably be used in a discrete log proof. That requires calculating a
+  /// divisor which is variable time to the amount of points interpolated. Since the amount of
+  /// points interpolated is equal to the sum of the coefficients in the polynomial, we need all
+  /// scalars to have a constant sum of their coefficients (instead of one variable to its bits).
+  ///
+  /// We achieve this by finding the highest non-0 coefficient, decrementing it, and increasing the
+  /// immediately less significant coefficient by 2. This increases the sum of the coefficients by
+  /// 1 (-1+2=1).
+  fn scalar_to_bits(scalar: &<C::EmbeddedCurve as Ciphersuite>::F) -> Vec<u64> {
+    let num_bits = u64::from(<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F::NUM_BITS);
+
+    // Obtain the bits of the private key
+    let num_bits_usize = usize::try_from(num_bits).unwrap();
+    let mut decomposition = vec![0; num_bits_usize];
+    for (i, bit) in scalar.to_le_bits().into_iter().take(num_bits_usize).enumerate() {
+      let bit = u64::from(u8::from(bit));
+      decomposition[i] = bit;
+    }
+
+    // The following algorithm only works if the value of the scalar exceeds num_bits
+    // If it isn't, we increase it by the modulus such that it does exceed num_bits
+    {
+      let mut less_than_num_bits = Choice::from(0);
+      for i in 0 .. num_bits {
+        less_than_num_bits |= scalar.ct_eq(&<C::EmbeddedCurve as Ciphersuite>::F::from(i));
+      }
+      let mut decomposition_of_modulus = vec![0; num_bits_usize];
+      // Decompose negative one
+      for (i, bit) in (-<C::EmbeddedCurve as Ciphersuite>::F::ONE)
+        .to_le_bits()
+        .into_iter()
+        .take(num_bits_usize)
+        .enumerate()
+      {
+        let bit = u64::from(u8::from(bit));
+        decomposition_of_modulus[i] = bit;
+      }
+      // Increment it by one
+      decomposition_of_modulus[0] += 1;
+
+      // Add the decomposition onto the decomposition of the modulus
+      for i in 0 .. num_bits_usize {
+        let new_decomposition = <_>::conditional_select(
+          &decomposition[i],
+          &(decomposition[i] + decomposition_of_modulus[i]),
+          less_than_num_bits,
+        );
+        decomposition[i] = new_decomposition;
+      }
+    }
+
+    // Calculcate the sum of the coefficients
+    let mut sum_of_coefficients: u64 = 0;
+    for decomposition in &decomposition {
+      sum_of_coefficients += *decomposition;
+    }
+
+    /*
+      Now, because we added a log2(k)-bit number to a k-bit number, we may have our sum of
+      coefficients be *too high*. We attempt to reduce the sum of the coefficients accordingly.
+
+      This algorithm is guaranteed to complete as expected. Take the sequence `222`. `222` becomes
+      `032` becomes `013`. Even if the next coefficient in the sequence is `2`, the third
+      coefficient will be reduced once and the next coefficient (`2`, increased to `3`) will only
+      be eligible for reduction once. This demonstrates, even for a worst case of log2(k) `2`s
+      followed by `1`s (as possible if the modulus is a Mersenne prime), the log2(k) `2`s can be
+      reduced as necessary so long as there is a single coefficient after (requiring the entire
+      sequence be at least of length log2(k) + 1). For a 2-bit number, log2(k) + 1 == 2, so this
+      holds for any odd prime field.
+
+      To fully type out the demonstration for the Mersenne prime 3, with scalar to encode 1 (the
+      highest value less than the number of bits):
+
+      10 - Little-endian bits of 1
+      21 - Little-endian bits of 1, plus the modulus
+      02 - After one reduction, where the sum of the coefficients does in fact equal 2 (the target)
+    */
+    {
+      let mut log2_num_bits = 0;
+      while (1 << log2_num_bits) < num_bits {
+        log2_num_bits += 1;
+      }
+
+      for _ in 0 .. log2_num_bits {
+        // If the sum of coefficients is the amount of bits, we're done
+        let mut done = sum_of_coefficients.ct_eq(&num_bits);
+
+        for i in 0 .. (num_bits_usize - 1) {
+          let should_act = (!done) & decomposition[i].ct_gt(&1);
+          // Subtract 2 from this coefficient
+          let amount_to_sub = <_>::conditional_select(&0, &2, should_act);
+          decomposition[i] -= amount_to_sub;
+          // Add 1 to the next coefficient
+          let amount_to_add = <_>::conditional_select(&0, &1, should_act);
+          decomposition[i + 1] += amount_to_add;
+
+          // Also update the sum of coefficients
+          sum_of_coefficients -= <_>::conditional_select(&0, &1, should_act);
+
+          // If we updated the coefficients this loop iter, we're done for this loop iter
+          done |= should_act;
+        }
+      }
+    }
+
+    for _ in 0 .. num_bits {
+      // If the sum of coefficients is the amount of bits, we're done
+      let mut done = sum_of_coefficients.ct_eq(&num_bits);
+
+      // Find the highest coefficient currently non-zero
+      for i in (1 .. decomposition.len()).rev() {
+        // If this is non-zero, we should decrement this coefficient if we haven't already
+        // decremented a coefficient this round
+        let is_non_zero = !(0.ct_eq(&decomposition[i]));
+        let should_act = (!done) & is_non_zero;
+
+        // Update this coefficient and the prior coefficient
+        let amount_to_sub = <_>::conditional_select(&0, &1, should_act);
+        decomposition[i] -= amount_to_sub;
+
+        let amount_to_add = <_>::conditional_select(&0, &2, should_act);
+        // i must be at least 1, so i - 1 will be at least 0 (meaning it's safe to index with)
+        decomposition[i - 1] += amount_to_add;
+
+        // Also update the sum of coefficients
+        sum_of_coefficients += <_>::conditional_select(&0, &1, should_act);
+
+        // If we updated the coefficients this loop iter, we're done for this loop iter
+        done |= should_act;
+      }
+    }
+    debug_assert!(bool::from(decomposition.iter().sum::<u64>().ct_eq(&num_bits)));
+
+    decomposition
+  }
+
+  /// Prove a point on an elliptic curve had its discrete logarithm generated via an eVRF.
+  pub(crate) fn prove(
+    rng: &mut (impl RngCore + CryptoRng),
+    generators: &Generators<C>,
+    transcript: [u8; 32],
+    coefficients: usize,
+    ecdh_public_keys: &[<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G],
+    evrf_private_key: &Zeroizing<<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F>,
+  ) -> Result<EvrfProveResult<C>, AcError> {
+    let curve_spec = CurveSpec {
+      a: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::a(),
+      b: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::b(),
+    };
+
+    // A tape of the discrete logarithm, then [zero, x**i, y x**i, y, x_coord, y_coord]
+    let mut vector_commitment_tape = vec![];
+
+    let mut generator_tables = Vec::with_capacity(1 + (2 * coefficients) + ecdh_public_keys.len());
+
+    // A function to calculate a divisor and push it onto the tape
+    // This defines a vec, divisor_points, outside of the fn to reuse its allocation
+    let mut divisor_points =
+      Vec::with_capacity((<C::EmbeddedCurve as Ciphersuite>::F::NUM_BITS as usize) + 1);
+    let mut divisor =
+      |vector_commitment_tape: &mut Vec<_>,
+       dlog: &[u64],
+       push_generator: bool,
+       generator: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G,
+       dh: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G| {
+        if push_generator {
+          let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(generator).unwrap();
+          generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
+        }
+
+        {
+          let mut generator = generator;
+          for coefficient in dlog {
+            let mut coefficient = *coefficient;
+            while coefficient != 0 {
+              coefficient -= 1;
+              divisor_points.push(generator);
+            }
+            generator = generator.double();
+          }
+          debug_assert_eq!(
+            dlog.iter().sum::<u64>(),
+            u64::from(<C::EmbeddedCurve as Ciphersuite>::F::NUM_BITS)
+          );
+        }
+        divisor_points.push(-dh);
+        let mut divisor = new_divisor(&divisor_points).unwrap().normalize_x_coefficient();
+        divisor_points.zeroize();
+
+        vector_commitment_tape.push(divisor.zero_coefficient);
+
+        for coefficient in divisor.x_coefficients.iter().skip(1) {
+          vector_commitment_tape.push(*coefficient);
+        }
+        for _ in divisor.x_coefficients.len() ..
+          <C::EmbeddedCurveParameters as DiscreteLogParameters>::XCoefficientsMinusOne::USIZE
+        {
+          vector_commitment_tape.push(<C as Ciphersuite>::F::ZERO);
+        }
+
+        for coefficient in divisor.yx_coefficients.first().unwrap_or(&vec![]) {
+          vector_commitment_tape.push(*coefficient);
+        }
+        for _ in divisor.yx_coefficients.first().unwrap_or(&vec![]).len() ..
+          <C::EmbeddedCurveParameters as DiscreteLogParameters>::YxCoefficients::USIZE
+        {
+          vector_commitment_tape.push(<C as Ciphersuite>::F::ZERO);
+        }
+
+        vector_commitment_tape
+          .push(divisor.y_coefficients.first().copied().unwrap_or(<C as Ciphersuite>::F::ZERO));
+
+        divisor.zeroize();
+        drop(divisor);
+
+        let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(dh).unwrap();
+        vector_commitment_tape.push(x);
+        vector_commitment_tape.push(y);
+
+        (x, y)
+      };
+
+    // Start with the coefficients
+    let evrf_public_key;
+    let mut actual_coefficients = Vec::with_capacity(coefficients);
+    {
+      let mut dlog = Self::scalar_to_bits(evrf_private_key);
+      let points = Self::transcript_to_points(transcript, coefficients);
+
+      // Start by pushing the discrete logarithm onto the tape
+      for coefficient in &dlog {
+        vector_commitment_tape.push(<_>::from(*coefficient));
+      }
+
+      // Push a divisor for proving that we're using the correct scalar
+      evrf_public_key = divisor(
+        &mut vector_commitment_tape,
+        &dlog,
+        true,
+        <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator(),
+        <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator() * evrf_private_key.deref(),
+      );
+
+      // Push a divisor for each point we use in the eVRF
+      for pair in points.chunks(2) {
+        let mut res = Zeroizing::new(C::F::ZERO);
+        for point in pair {
+          let (dh_x, _) = divisor(
+            &mut vector_commitment_tape,
+            &dlog,
+            true,
+            *point,
+            *point * evrf_private_key.deref(),
+          );
+          *res += dh_x;
+        }
+        actual_coefficients.push(res);
+      }
+      debug_assert_eq!(actual_coefficients.len(), coefficients);
+
+      dlog.zeroize();
+    }
+
+    // Now do the ECDHs for the encryption
+    let mut encryption_masks = Vec::with_capacity(ecdh_public_keys.len());
+    let mut ecdh_commitments = Vec::with_capacity(2 * ecdh_public_keys.len());
+    let mut ecdh_commitments_xy = Vec::with_capacity(ecdh_public_keys.len());
+    for ecdh_public_key in ecdh_public_keys {
+      ecdh_commitments_xy.push([(C::F::ZERO, C::F::ZERO); 2]);
+
+      let mut res = Zeroizing::new(C::F::ZERO);
+      for j in 0 .. 2 {
+        let mut ecdh_private_key;
+        loop {
+          ecdh_private_key = <C::EmbeddedCurve as Ciphersuite>::F::random(&mut *rng);
+          // Generate a non-0 ECDH private key, as necessary to not produce an identity output
+          // Identity isn't representable with the divisors, hence the explicit effort
+          if bool::from(!ecdh_private_key.is_zero()) {
+            break;
+          }
+        }
+        let mut dlog = Self::scalar_to_bits(&ecdh_private_key);
+        let ecdh_commitment = <C::EmbeddedCurve as Ciphersuite>::generator() * ecdh_private_key;
+        ecdh_commitments.push(ecdh_commitment);
+        ecdh_commitments_xy.last_mut().unwrap()[j] =
+          <<C::EmbeddedCurve as Ciphersuite>::G as DivisorCurve>::to_xy(ecdh_commitment).unwrap();
+
+        // Start by pushing the discrete logarithm onto the tape
+        for coefficient in &dlog {
+          vector_commitment_tape.push(<_>::from(*coefficient));
+        }
+
+        // Push a divisor for proving that we're using the correct scalar for the commitment
+        divisor(
+          &mut vector_commitment_tape,
+          &dlog,
+          false,
+          <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator(),
+          <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator() * ecdh_private_key,
+        );
+        // Push a divisor for the key we're performing the ECDH with
+        let (dh_x, _) = divisor(
+          &mut vector_commitment_tape,
+          &dlog,
+          j == 0,
+          *ecdh_public_key,
+          *ecdh_public_key * ecdh_private_key,
+        );
+        *res += dh_x;
+
+        ecdh_private_key.zeroize();
+        dlog.zeroize();
+      }
+      encryption_masks.push(res);
+    }
+    debug_assert_eq!(encryption_masks.len(), ecdh_public_keys.len());
+
+    // Now that we have the vector commitment tape, chunk it
+    let (_, generators_to_use) =
+      Self::muls_and_generators_to_use(coefficients, ecdh_public_keys.len());
+
+    let mut vector_commitments =
+      Vec::with_capacity(vector_commitment_tape.len().div_ceil(2 * generators_to_use));
+    for chunk in vector_commitment_tape.chunks(2 * generators_to_use) {
+      let g_values = chunk[.. generators_to_use.min(chunk.len())].to_vec().into();
+      let h_values = chunk[generators_to_use.min(chunk.len()) ..].to_vec().into();
+      vector_commitments.push(PedersenVectorCommitment {
+        g_values,
+        h_values,
+        mask: C::F::random(&mut *rng),
+      });
+    }
+
+    vector_commitment_tape.zeroize();
+    drop(vector_commitment_tape);
+
+    let mut commitments = Vec::with_capacity(coefficients + ecdh_public_keys.len());
+    for coefficient in &actual_coefficients {
+      commitments.push(PedersenCommitment { value: **coefficient, mask: C::F::random(&mut *rng) });
+    }
+    for enc_mask in &encryption_masks {
+      commitments.push(PedersenCommitment { value: **enc_mask, mask: C::F::random(&mut *rng) });
+    }
+
+    let mut transcript = ProverTranscript::new(transcript);
+    let commited_commitments = transcript.write_commitments(
+      vector_commitments
+        .iter()
+        .map(|commitment| {
+          commitment
+            .commit(generators.g_bold_slice(), generators.h_bold_slice(), generators.h())
+            .ok_or(AcError::NotEnoughGenerators)
+        })
+        .collect::<Result<_, _>>()?,
+      commitments
+        .iter()
+        .map(|commitment| commitment.commit(generators.g(), generators.h()))
+        .collect(),
+    );
+    for ecdh_commitment in ecdh_commitments {
+      transcript.push_point(ecdh_commitment);
+    }
+
+    let mut circuit = Circuit::prove(vector_commitments, commitments.clone());
+    Self::circuit(
+      &curve_spec,
+      evrf_public_key,
+      coefficients,
+      &ecdh_commitments_xy,
+      &generator_tables,
+      &mut circuit,
+      &mut transcript,
+    );
+
+    let (statement, Some(witness)) = circuit
+      .statement(
+        generators.reduce(generators_to_use).ok_or(AcError::NotEnoughGenerators)?,
+        commited_commitments,
+      )
+      .unwrap()
+    else {
+      panic!("proving yet wasn't yielded the witness");
+    };
+    statement.prove(&mut *rng, &mut transcript, witness).unwrap();
+
+    // Push the reveal onto the transcript
+    for commitment in &commitments {
+      transcript.push_point(generators.g() * commitment.value);
+    }
+
+    // Define a weight to aggregate the commitments with
+    let mut agg_weights = Vec::with_capacity(commitments.len());
+    agg_weights.push(C::F::ONE);
+    while agg_weights.len() < commitments.len() {
+      agg_weights.push(transcript.challenge::<C::F>());
+    }
+    let mut x = commitments
+      .iter()
+      .zip(&agg_weights)
+      .map(|(commitment, weight)| commitment.mask * *weight)
+      .sum::<C::F>();
+
+    // Do a Schnorr PoK for the randomness of the aggregated Pedersen commitment
+    let mut r = C::F::random(&mut *rng);
+    transcript.push_point(generators.h() * r);
+    let c = transcript.challenge::<C::F>();
+    transcript.push_scalar(r + (c * x));
+    r.zeroize();
+    x.zeroize();
+
+    Ok(EvrfProveResult {
+      coefficients: actual_coefficients,
+      encryption_masks,
+      proof: transcript.complete(),
+    })
+  }
+
+  /// Verify an eVRF proof, returning the commitments output.
+  #[allow(clippy::too_many_arguments)]
+  pub(crate) fn verify(
+    rng: &mut (impl RngCore + CryptoRng),
+    generators: &Generators<C>,
+    verifier: &mut BatchVerifier<C>,
+    transcript: [u8; 32],
+    coefficients: usize,
+    ecdh_public_keys: &[<<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G],
+    evrf_public_key: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G,
+    proof: &[u8],
+  ) -> Result<EvrfVerifyResult<C>, ()> {
+    let curve_spec = CurveSpec {
+      a: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::a(),
+      b: <<C as EvrfCurve>::EmbeddedCurve as Ciphersuite>::G::b(),
+    };
+
+    let mut generator_tables = Vec::with_capacity(1 + (2 * coefficients) + ecdh_public_keys.len());
+    {
+      let (x, y) =
+        <C::EmbeddedCurve as Ciphersuite>::G::to_xy(<C::EmbeddedCurve as Ciphersuite>::generator())
+          .unwrap();
+      generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
+    }
+    let points = Self::transcript_to_points(transcript, coefficients);
+    for generator in points {
+      let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(generator).unwrap();
+      generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
+    }
+    for generator in ecdh_public_keys {
+      let (x, y) = <C::EmbeddedCurve as Ciphersuite>::G::to_xy(*generator).unwrap();
+      generator_tables.push(GeneratorTable::new(&curve_spec, x, y));
+    }
+
+    let (_, generators_to_use) =
+      Self::muls_and_generators_to_use(coefficients, ecdh_public_keys.len());
+
+    let mut transcript = VerifierTranscript::new(transcript, proof);
+
+    let dlog_len = <C::EmbeddedCurveParameters as DiscreteLogParameters>::ScalarBits::USIZE;
+    let divisor_len = 1 +
+      <C::EmbeddedCurveParameters as DiscreteLogParameters>::XCoefficientsMinusOne::USIZE +
+      <C::EmbeddedCurveParameters as DiscreteLogParameters>::YxCoefficients::USIZE +
+      1;
+    let dlog_proof_len = divisor_len + 2;
+
+    let coeffs_vc_variables = dlog_len + ((1 + (2 * coefficients)) * dlog_proof_len);
+    let ecdhs_vc_variables = ((2 * ecdh_public_keys.len()) * dlog_len) +
+      ((2 * 2 * ecdh_public_keys.len()) * dlog_proof_len);
+    let vcs = (coeffs_vc_variables + ecdhs_vc_variables).div_ceil(2 * generators_to_use);
+
+    let all_commitments =
+      transcript.read_commitments(vcs, coefficients + ecdh_public_keys.len()).map_err(|_| ())?;
+    let commitments = all_commitments.V().to_vec();
+
+    let mut ecdh_keys = Vec::with_capacity(ecdh_public_keys.len());
+    let mut ecdh_keys_xy = Vec::with_capacity(ecdh_public_keys.len());
+    for _ in 0 .. ecdh_public_keys.len() {
+      let ecdh_keys_i = [
+        transcript.read_point::<C::EmbeddedCurve>().map_err(|_| ())?,
+        transcript.read_point::<C::EmbeddedCurve>().map_err(|_| ())?,
+      ];
+      ecdh_keys.push(ecdh_keys_i);
+      // This bans zero ECDH keys
+      ecdh_keys_xy.push([
+        <<C::EmbeddedCurve as Ciphersuite>::G as DivisorCurve>::to_xy(ecdh_keys_i[0]).ok_or(())?,
+        <<C::EmbeddedCurve as Ciphersuite>::G as DivisorCurve>::to_xy(ecdh_keys_i[1]).ok_or(())?,
+      ]);
+    }
+
+    let mut circuit = Circuit::verify();
+    Self::circuit(
+      &curve_spec,
+      <C::EmbeddedCurve as Ciphersuite>::G::to_xy(evrf_public_key).ok_or(())?,
+      coefficients,
+      &ecdh_keys_xy,
+      &generator_tables,
+      &mut circuit,
+      &mut transcript,
+    );
+
+    let (statement, None) =
+      circuit.statement(generators.reduce(generators_to_use).ok_or(())?, all_commitments).unwrap()
+    else {
+      panic!("verifying yet was yielded a witness");
+    };
+
+    statement.verify(rng, verifier, &mut transcript).map_err(|_| ())?;
+
+    // Read the openings for the commitments
+    let mut openings = Vec::with_capacity(commitments.len());
+    for _ in 0 .. commitments.len() {
+      openings.push(transcript.read_point::<C>().map_err(|_| ())?);
+    }
+
+    // Verify the openings of the commitments
+    let mut agg_weights = Vec::with_capacity(commitments.len());
+    agg_weights.push(C::F::ONE);
+    while agg_weights.len() < commitments.len() {
+      agg_weights.push(transcript.challenge::<C::F>());
+    }
+
+    let sum_points =
+      openings.iter().zip(&agg_weights).map(|(point, weight)| *point * *weight).sum::<C::G>();
+    let sum_commitments =
+      commitments.into_iter().zip(agg_weights).map(|(point, weight)| point * weight).sum::<C::G>();
+    #[allow(non_snake_case)]
+    let A = sum_commitments - sum_points;
+
+    #[allow(non_snake_case)]
+    let R = transcript.read_point::<C>().map_err(|_| ())?;
+    let c = transcript.challenge::<C::F>();
+    let s = transcript.read_scalar::<C>().map_err(|_| ())?;
+
+    // Doesn't batch verify this as we can't access the internals of the GBP batch verifier
+    if (R + (A * c)) != (generators.h() * s) {
+      Err(())?;
+    }
+
+    if !transcript.complete().is_empty() {
+      Err(())?
+    };
+
+    let encryption_commitments = openings[coefficients ..].to_vec();
+    let coefficients = openings[.. coefficients].to_vec();
+    Ok(EvrfVerifyResult { coefficients, ecdh_keys, encryption_commitments })
+  }
+}
--- a/crypto/dkg/src/lib.rs
+++ b/crypto/dkg/src/lib.rs
@@ -21,6 +21,10 @@ pub mod encryption;
 #[cfg(feature = "std")]
 pub mod pedpop;

+/// The one-round DKG described in the [eVRF paper](https://eprint.iacr.org/2024/397).
+#[cfg(all(feature = "std", feature = "evrf"))]
+pub mod evrf;
+
 /// Promote keys between ciphersuites.
 #[cfg(feature = "std")]
 pub mod promote;
@@ -205,25 +209,37 @@ mod lib {
    }
  }

-  /// Calculate the lagrange coefficient for a signing set.
-  pub fn lagrange<F: PrimeField>(i: Participant, included: &[Participant]) -> F {
-    let i_f = F::from(u64::from(u16::from(i)));
+  #[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+  pub(crate) enum Interpolation<F: Zeroize + PrimeField> {
+    Constant(Vec<F>),
+    Lagrange,
+  }

-    let mut num = F::ONE;
-    let mut denom = F::ONE;
-    for l in included {
-      if i == *l {
-        continue;
+  impl<F: Zeroize + PrimeField> Interpolation<F> {
+    pub(crate) fn interpolation_factor(&self, i: Participant, included: &[Participant]) -> F {
+      match self {
+        Interpolation::Constant(c) => c[usize::from(u16::from(i) - 1)],
+        Interpolation::Lagrange => {
+          let i_f = F::from(u64::from(u16::from(i)));
+
+          let mut num = F::ONE;
+          let mut denom = F::ONE;
+          for l in included {
+            if i == *l {
+              continue;
+            }
+
+            let share = F::from(u64::from(u16::from(*l)));
+            num *= share;
+            denom *= share - i_f;
+          }
+
+          // Safe as this will only be 0 if we're part of the above loop
+          // (which we have an if case to avoid)
+          num * denom.invert().unwrap()
+        }
      }
-
-      let share = F::from(u64::from(u16::from(*l)));
-      num *= share;
-      denom *= share - i_f;
    }
-
-    // Safe as this will only be 0 if we're part of the above loop
-    // (which we have an if case to avoid)
-    num * denom.invert().unwrap()
  }

  /// Keys and verification shares generated by a DKG.
@@ -232,6 +248,8 @@ mod lib {
  pub struct ThresholdCore<C: Ciphersuite> {
    /// Threshold Parameters.
    pub(crate) params: ThresholdParams,
+    /// The interpolation method used.
+    pub(crate) interpolation: Interpolation<C::F>,

    /// Secret share key.
    pub(crate) secret_share: Zeroizing<C::F>,
@@ -246,6 +264,7 @@ mod lib {
      fmt
        .debug_struct("ThresholdCore")
        .field("params", &self.params)
+        .field("interpolation", &self.interpolation)
        .field("group_key", &self.group_key)
        .field("verification_shares", &self.verification_shares)
        .finish_non_exhaustive()
@@ -255,6 +274,7 @@ mod lib {
  impl<C: Ciphersuite> Zeroize for ThresholdCore<C> {
    fn zeroize(&mut self) {
      self.params.zeroize();
+      self.interpolation.zeroize();
      self.secret_share.zeroize();
      self.group_key.zeroize();
      for share in self.verification_shares.values_mut() {
@@ -266,16 +286,14 @@ mod lib {
  impl<C: Ciphersuite> ThresholdCore<C> {
    pub(crate) fn new(
      params: ThresholdParams,
+      interpolation: Interpolation<C::F>,
      secret_share: Zeroizing<C::F>,
      verification_shares: HashMap<Participant, C::G>,
    ) -> ThresholdCore<C> {
      let t = (1 ..= params.t()).map(Participant).collect::<Vec<_>>();
-      ThresholdCore {
-        params,
-        secret_share,
-        group_key: t.iter().map(|i| verification_shares[i] * lagrange::<C::F>(*i, &t)).sum(),
-        verification_shares,
-      }
+      let group_key =
+        t.iter().map(|i| verification_shares[i] * interpolation.interpolation_factor(*i, &t)).sum();
+      ThresholdCore { params, interpolation, secret_share, group_key, verification_shares }
    }

    /// Parameters for these keys.
@@ -304,6 +322,15 @@ mod lib {
      writer.write_all(&self.params.t.to_le_bytes())?;
      writer.write_all(&self.params.n.to_le_bytes())?;
      writer.write_all(&self.params.i.to_bytes())?;
+      match &self.interpolation {
+        Interpolation::Constant(c) => {
+          writer.write_all(&[0])?;
+          for c in c {
+            writer.write_all(c.to_repr().as_ref())?;
+          }
+        }
+        Interpolation::Lagrange => writer.write_all(&[1])?,
+      };
      let mut share_bytes = self.secret_share.to_repr();
      writer.write_all(share_bytes.as_ref())?;
      share_bytes.as_mut().zeroize();
@@ -352,6 +379,20 @@ mod lib {
        )
      };

+      let mut interpolation = [0];
+      reader.read_exact(&mut interpolation)?;
+      let interpolation = match interpolation[0] {
+        0 => Interpolation::Constant({
+          let mut res = Vec::with_capacity(usize::from(n));
+          for _ in 0 .. n {
+            res.push(C::read_F(reader)?);
+          }
+          res
+        }),
+        1 => Interpolation::Lagrange,
+        _ => Err(io::Error::other("invalid interpolation method"))?,
+      };
+
      let secret_share = Zeroizing::new(C::read_F(reader)?);

      let mut verification_shares = HashMap::new();
@@ -361,6 +402,7 @@ mod lib {

      Ok(ThresholdCore::new(
        ThresholdParams::new(t, n, i).map_err(|_| io::Error::other("invalid parameters"))?,
+        interpolation,
        secret_share,
        verification_shares,
      ))
@@ -383,6 +425,7 @@ mod lib {
  /// View of keys, interpolated and offset for usage.
  #[derive(Clone)]
  pub struct ThresholdView<C: Ciphersuite> {
+    interpolation: Interpolation<C::F>,
    offset: C::F,
    group_key: C::G,
    included: Vec<Participant>,
@@ -395,6 +438,7 @@ mod lib {
    fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
      fmt
        .debug_struct("ThresholdView")
+        .field("interpolation", &self.interpolation)
        .field("offset", &self.offset)
        .field("group_key", &self.group_key)
        .field("included", &self.included)
@@ -480,12 +524,13 @@ mod lib {
      included.sort();

      let mut secret_share = Zeroizing::new(
-        lagrange::<C::F>(self.params().i(), &included) * self.secret_share().deref(),
+        self.core.interpolation.interpolation_factor(self.params().i(), &included) *
+          self.secret_share().deref(),
      );

      let mut verification_shares = self.verification_shares();
      for (i, share) in &mut verification_shares {
-        *share *= lagrange::<C::F>(*i, &included);
+        *share *= self.core.interpolation.interpolation_factor(*i, &included);
      }

      // The offset is included by adding it to the participant with the lowest ID
@@ -496,6 +541,7 @@ mod lib {
      *verification_shares.get_mut(&included[0]).unwrap() += C::generator() * offset;

      Ok(ThresholdView {
+        interpolation: self.core.interpolation.clone(),
        offset,
        group_key: self.group_key(),
        secret_share,
@@ -528,6 +574,14 @@ mod lib {
      &self.included
    }

+    /// Return the interpolation factor for a signer.
+    pub fn interpolation_factor(&self, participant: Participant) -> Option<C::F> {
+      if !self.included.contains(&participant) {
+        None?
+      }
+      Some(self.interpolation.interpolation_factor(participant, &self.included))
+    }
+
    /// Return the interpolated, offset secret share.
    pub fn secret_share(&self) -> &Zeroizing<C::F> {
      &self.secret_share
--- a/crypto/dkg/src/musig.rs
+++ b/crypto/dkg/src/musig.rs
@@ -7,8 +7,6 @@ use std_shims::collections::HashMap;
 #[cfg(feature = "std")]
 use zeroize::Zeroizing;

-#[cfg(feature = "std")]
-use ciphersuite::group::ff::Field;
 use ciphersuite::{
  group::{Group, GroupEncoding},
  Ciphersuite,
@@ -16,7 +14,7 @@ use ciphersuite::{

 use crate::DkgError;
 #[cfg(feature = "std")]
-use crate::{Participant, ThresholdParams, ThresholdCore, lagrange};
+use crate::{Participant, ThresholdParams, Interpolation, ThresholdCore};

 fn check_keys<C: Ciphersuite>(keys: &[C::G]) -> Result<u16, DkgError<()>> {
  if keys.is_empty() {
@@ -67,6 +65,7 @@ pub fn musig_key<C: Ciphersuite>(context: &[u8], keys: &[C::G]) -> Result<C::G,
  let transcript = binding_factor_transcript::<C>(context, keys)?;
  let mut res = C::G::identity();
  for i in 1 ..= keys_len {
+    // TODO: Calculate this with a multiexp
    res += keys[usize::from(i - 1)] * binding_factor::<C>(transcript.clone(), i);
  }
  Ok(res)
@@ -104,38 +103,26 @@ pub fn musig<C: Ciphersuite>(
    binding.push(binding_factor::<C>(transcript.clone(), i));
  }

-  // Multiply our private key by our binding factor
-  let mut secret_share = private_key.clone();
-  *secret_share *= binding[pos];
+  // Our secret share is our private key
+  let secret_share = private_key.clone();

  // Calculate verification shares
  let mut verification_shares = HashMap::new();
-  // When this library offers a ThresholdView for a specific signing set, it applies the lagrange
-  // factor
-  // Since this is a n-of-n scheme, there's only one possible signing set, and one possible
-  // lagrange factor
-  // In the name of simplicity, we define the group key as the sum of all bound keys
-  // Accordingly, the secret share must be multiplied by the inverse of the lagrange factor, along
-  // with all verification shares
-  // This is less performant than simply defining the group key as the sum of all post-lagrange
-  // bound keys, yet the simplicity is preferred
-  let included = (1 ..= keys_len)
-    // This error also shouldn't be possible, for the same reasons as documented above
-    .map(|l| Participant::new(l).ok_or(DkgError::InvalidSigningSet))
-    .collect::<Result<Vec<_>, _>>()?;
  let mut group_key = C::G::identity();
-  for (l, p) in included.iter().enumerate() {
-    let bound = keys[l] * binding[l];
-    group_key += bound;
+  for l in 1 ..= keys_len {
+    let key = keys[usize::from(l) - 1];
+    group_key += key * binding[usize::from(l - 1)];

-    let lagrange_inv = lagrange::<C::F>(*p, &included).invert().unwrap();
-    if params.i() == *p {
-      *secret_share *= lagrange_inv;
-    }
-    verification_shares.insert(*p, bound * lagrange_inv);
+    // These errors also shouldn't be possible, for the same reasons as documented above
+    verification_shares.insert(Participant::new(l).ok_or(DkgError::InvalidSigningSet)?, key);
  }
  debug_assert_eq!(C::generator() * secret_share.deref(), verification_shares[&params.i()]);
  debug_assert_eq!(musig_key::<C>(context, keys).unwrap(), group_key);

-  Ok(ThresholdCore { params, secret_share, group_key, verification_shares })
+  Ok(ThresholdCore::new(
+    params,
+    Interpolation::Constant(binding),
+    secret_share,
+    verification_shares,
+  ))
 }
--- a/crypto/dkg/src/pedpop.rs
+++ b/crypto/dkg/src/pedpop.rs
@@ -22,9 +22,9 @@ use multiexp::{multiexp_vartime, BatchVerifier};
 use schnorr::SchnorrSignature;

 use crate::{
-  Participant, DkgError, ThresholdParams, ThresholdCore, validate_map,
+  Participant, DkgError, ThresholdParams, Interpolation, ThresholdCore, validate_map,
  encryption::{
-    ReadWrite, EncryptionKeyMessage, EncryptedMessage, Encryption, EncryptionKeyProof,
+    ReadWrite, EncryptionKeyMessage, EncryptedMessage, Encryption, Decryption, EncryptionKeyProof,
    DecryptionError,
  },
 };
@@ -32,10 +32,10 @@ use crate::{
 type FrostError<C> = DkgError<EncryptionKeyProof<C>>;

 #[allow(non_snake_case)]
-fn challenge<C: Ciphersuite>(context: &str, l: Participant, R: &[u8], Am: &[u8]) -> C::F {
+fn challenge<C: Ciphersuite>(context: [u8; 32], l: Participant, R: &[u8], Am: &[u8]) -> C::F {
  let mut transcript = RecommendedTranscript::new(b"DKG FROST v0.2");
  transcript.domain_separate(b"schnorr_proof_of_knowledge");
-  transcript.append_message(b"context", context.as_bytes());
+  transcript.append_message(b"context", context);
  transcript.append_message(b"participant", l.to_bytes());
  transcript.append_message(b"nonce", R);
  transcript.append_message(b"commitments", Am);
@@ -86,15 +86,15 @@ impl<C: Ciphersuite> ReadWrite for Commitments<C> {
 #[derive(Debug, Zeroize)]
 pub struct KeyGenMachine<C: Ciphersuite> {
  params: ThresholdParams,
-  context: String,
+  context: [u8; 32],
  _curve: PhantomData<C>,
 }

 impl<C: Ciphersuite> KeyGenMachine<C> {
  /// Create a new machine to generate a key.
  ///
-  /// The context string should be unique among multisigs.
-  pub fn new(params: ThresholdParams, context: String) -> KeyGenMachine<C> {
+  /// The context should be unique among multisigs.
+  pub fn new(params: ThresholdParams, context: [u8; 32]) -> KeyGenMachine<C> {
    KeyGenMachine { params, context, _curve: PhantomData }
  }

@@ -129,11 +129,12 @@ impl<C: Ciphersuite> KeyGenMachine<C> {
      // There's no reason to spend the time and effort to make this deterministic besides a
      // general obsession with canonicity and determinism though
      r,
-      challenge::<C>(&self.context, self.params.i(), nonce.to_bytes().as_ref(), &cached_msg),
+      challenge::<C>(self.context, self.params.i(), nonce.to_bytes().as_ref(), &cached_msg),
    );

    // Additionally create an encryption mechanism to protect the secret shares
-    let encryption = Encryption::new(self.context.clone(), Some(self.params.i), rng);
+    let encryption =
+      Encryption::new(self.context, self.params.i, Zeroizing::new(C::random_nonzero_F(rng)));

    // Step 4: Broadcast
    let msg =
@@ -177,7 +178,7 @@ fn polynomial<F: PrimeField + Zeroize>(
 // The encryption system also explicitly uses Zeroizing<M> so it can ensure anything being
 // encrypted is within Zeroizing. Accordingly, internally having Zeroizing would be redundant.
 #[derive(Clone, PartialEq, Eq)]
-pub struct SecretShare<F: PrimeField>(F::Repr);
+pub struct SecretShare<F: PrimeField>(pub(crate) F::Repr);
 impl<F: PrimeField> AsRef<[u8]> for SecretShare<F> {
  fn as_ref(&self) -> &[u8] {
    self.0.as_ref()
@@ -225,7 +226,7 @@ impl<F: PrimeField> ReadWrite for SecretShare<F> {
 #[derive(Zeroize)]
 pub struct SecretShareMachine<C: Ciphersuite> {
  params: ThresholdParams,
-  context: String,
+  context: [u8; 32],
  coefficients: Vec<Zeroizing<C::F>>,
  our_commitments: Vec<C::G>,
  encryption: Encryption<C>,
@@ -261,7 +262,8 @@ impl<C: Ciphersuite> SecretShareMachine<C> {
    let mut commitments = HashMap::new();
    for l in (1 ..= self.params.n()).map(Participant) {
      let Some(msg) = commitment_msgs.remove(&l) else { continue };
-      let mut msg = self.encryption.register(l, msg);
+      self.encryption.register(l, msg.enc_key);
+      let mut msg = msg.msg;

      if msg.commitments.len() != self.params.t().into() {
        Err(FrostError::InvalidCommitments(l))?;
@@ -274,7 +276,7 @@ impl<C: Ciphersuite> SecretShareMachine<C> {
        &mut batch,
        l,
        msg.commitments[0],
-        challenge::<C>(&self.context, l, msg.sig.R.to_bytes().as_ref(), &msg.cached_msg),
+        challenge::<C>(self.context, l, msg.sig.R.to_bytes().as_ref(), &msg.cached_msg),
      );

      commitments.insert(l, msg.commitments.drain(..).collect::<Vec<_>>());
@@ -472,9 +474,10 @@ impl<C: Ciphersuite> KeyMachine<C> {
    let KeyMachine { commitments, encryption, params, secret } = self;
    Ok(BlameMachine {
      commitments,
-      encryption,
+      encryption: encryption.into_decryption(),
      result: Some(ThresholdCore {
        params,
+        interpolation: Interpolation::Lagrange,
        secret_share: secret,
        group_key: stripes[0],
        verification_shares,
@@ -486,7 +489,7 @@ impl<C: Ciphersuite> KeyMachine<C> {
 /// A machine capable of handling blame proofs.
 pub struct BlameMachine<C: Ciphersuite> {
  commitments: HashMap<Participant, Vec<C::G>>,
-  encryption: Encryption<C>,
+  encryption: Decryption<C>,
  result: Option<ThresholdCore<C>>,
 }

@@ -505,7 +508,6 @@ impl<C: Ciphersuite> Zeroize for BlameMachine<C> {
    for commitments in self.commitments.values_mut() {
      commitments.zeroize();
    }
-    self.encryption.zeroize();
    self.result.zeroize();
  }
 }
@@ -598,18 +600,18 @@ impl<C: Ciphersuite> AdditionalBlameMachine<C> {
  /// authenticated as having come from the supposed party and verified as valid. Usage of invalid
  /// commitments is considered undefined behavior, and may cause everything from inaccurate blame
  /// to panics.
-  pub fn new<R: RngCore + CryptoRng>(
-    rng: &mut R,
-    context: String,
+  pub fn new(
+    context: [u8; 32],
    n: u16,
    mut commitment_msgs: HashMap<Participant, EncryptionKeyMessage<C, Commitments<C>>>,
  ) -> Result<Self, FrostError<C>> {
    let mut commitments = HashMap::new();
-    let mut encryption = Encryption::new(context, None, rng);
+    let mut encryption = Decryption::new(context);
    for i in 1 ..= n {
      let i = Participant::new(i).unwrap();
      let Some(msg) = commitment_msgs.remove(&i) else { Err(DkgError::MissingParticipant(i))? };
-      commitments.insert(i, encryption.register(i, msg).commitments);
+      encryption.register(i, msg.enc_key);
+      commitments.insert(i, msg.msg.commitments);
    }
    Ok(AdditionalBlameMachine(BlameMachine { commitments, encryption, result: None }))
  }
--- a/crypto/dkg/src/promote.rs
+++ b/crypto/dkg/src/promote.rs
@@ -113,6 +113,7 @@ impl<C1: Ciphersuite, C2: Ciphersuite<F = C1::F, G = C1::G>> GeneratorPromotion<
    Ok(ThresholdKeys {
      core: Arc::new(ThresholdCore::new(
        params,
+        self.base.core.interpolation.clone(),
        self.base.secret_share().clone(),
        verification_shares,
      )),
--- a/crypto/dkg/src/tests/evrf/mod.rs
+++ b/crypto/dkg/src/tests/evrf/mod.rs
@@ -0,0 +1,79 @@
+use std::collections::HashMap;
+
+use zeroize::Zeroizing;
+use rand_core::OsRng;
+use rand::seq::SliceRandom;
+
+use ciphersuite::{group::ff::Field, Ciphersuite};
+
+use crate::{
+  Participant,
+  evrf::*,
+  tests::{THRESHOLD, PARTICIPANTS, recover_key},
+};
+
+mod proof;
+use proof::{Pallas, Vesta};
+
+#[test]
+fn evrf_dkg() {
+  let generators = EvrfGenerators::<Pallas>::new(THRESHOLD, PARTICIPANTS);
+  let context = [0; 32];
+
+  let mut priv_keys = vec![];
+  let mut pub_keys = vec![];
+  for i in 0 .. PARTICIPANTS {
+    let priv_key = <Vesta as Ciphersuite>::F::random(&mut OsRng);
+    pub_keys.push(<Vesta as Ciphersuite>::generator() * priv_key);
+    priv_keys.push((Participant::new(1 + i).unwrap(), Zeroizing::new(priv_key)));
+  }
+
+  let mut participations = HashMap::new();
+  // Shuffle the private keys so we iterate over a random subset of them
+  priv_keys.shuffle(&mut OsRng);
+  for (i, priv_key) in priv_keys.iter().take(usize::from(THRESHOLD)) {
+    participations.insert(
+      *i,
+      EvrfDkg::<Pallas>::participate(
+        &mut OsRng,
+        &generators,
+        context,
+        THRESHOLD,
+        &pub_keys,
+        priv_key,
+      )
+      .unwrap(),
+    );
+  }
+
+  let VerifyResult::Valid(dkg) = EvrfDkg::<Pallas>::verify(
+    &mut OsRng,
+    &generators,
+    context,
+    THRESHOLD,
+    &pub_keys,
+    &participations,
+  )
+  .unwrap() else {
+    panic!("verify didn't return VerifyResult::Valid")
+  };
+
+  let mut group_key = None;
+  let mut verification_shares = None;
+  let mut all_keys = HashMap::new();
+  for (i, priv_key) in priv_keys {
+    let keys = dkg.keys(&priv_key).into_iter().next().unwrap();
+    assert_eq!(keys.params().i(), i);
+    assert_eq!(keys.params().t(), THRESHOLD);
+    assert_eq!(keys.params().n(), PARTICIPANTS);
+    group_key = group_key.or(Some(keys.group_key()));
+    verification_shares = verification_shares.or(Some(keys.verification_shares()));
+    assert_eq!(Some(keys.group_key()), group_key);
+    assert_eq!(Some(keys.verification_shares()), verification_shares);
+
+    all_keys.insert(i, keys);
+  }
+
+  // TODO: Test for all possible combinations of keys
+  assert_eq!(Pallas::generator() * recover_key(&all_keys), group_key.unwrap());
+}
--- a/crypto/dkg/src/tests/evrf/proof.rs
+++ b/crypto/dkg/src/tests/evrf/proof.rs
@@ -0,0 +1,118 @@
+use std::time::Instant;
+
+use rand_core::OsRng;
+
+use zeroize::{Zeroize, Zeroizing};
+use generic_array::typenum::{Sum, Diff, Quot, U, U1, U2};
+use blake2::{Digest, Blake2b512};
+
+use ciphersuite::{
+  group::{
+    ff::{FromUniformBytes, Field, PrimeField},
+    Group,
+  },
+  Ciphersuite, Secp256k1, Ed25519, Ristretto,
+};
+use pasta_curves::{Ep, Eq, Fp, Fq};
+
+use generalized_bulletproofs::tests::generators;
+use generalized_bulletproofs_ec_gadgets::DiscreteLogParameters;
+
+use crate::evrf::proof::*;
+
+#[derive(Clone, Copy, PartialEq, Eq, Debug, Zeroize)]
+pub(crate) struct Pallas;
+impl Ciphersuite for Pallas {
+  type F = Fq;
+  type G = Ep;
+  type H = Blake2b512;
+  const ID: &'static [u8] = b"Pallas";
+  fn generator() -> Ep {
+    Ep::generator()
+  }
+  fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F {
+    // This naive concat may be insecure in a real world deployment
+    // This is solely test code so it's fine
+    Self::F::from_uniform_bytes(&Self::H::digest([dst, msg].concat()).into())
+  }
+}
+
+#[derive(Clone, Copy, PartialEq, Eq, Debug, Zeroize)]
+pub(crate) struct Vesta;
+impl Ciphersuite for Vesta {
+  type F = Fp;
+  type G = Eq;
+  type H = Blake2b512;
+  const ID: &'static [u8] = b"Vesta";
+  fn generator() -> Eq {
+    Eq::generator()
+  }
+  fn hash_to_F(dst: &[u8], msg: &[u8]) -> Self::F {
+    // This naive concat may be insecure in a real world deployment
+    // This is solely test code so it's fine
+    Self::F::from_uniform_bytes(&Self::H::digest([dst, msg].concat()).into())
+  }
+}
+
+pub struct VestaParams;
+impl DiscreteLogParameters for VestaParams {
+  type ScalarBits = U<{ <<Vesta as Ciphersuite>::F as PrimeField>::NUM_BITS as usize }>;
+  type XCoefficients = Quot<Sum<Self::ScalarBits, U1>, U2>;
+  type XCoefficientsMinusOne = Diff<Self::XCoefficients, U1>;
+  type YxCoefficients = Diff<Quot<Sum<Sum<Self::ScalarBits, U1>, U1>, U2>, U2>;
+}
+
+impl EvrfCurve for Pallas {
+  type EmbeddedCurve = Vesta;
+  type EmbeddedCurveParameters = VestaParams;
+}
+
+fn evrf_proof_test<C: EvrfCurve>() {
+  let generators = generators(1024);
+  let vesta_private_key = Zeroizing::new(<C::EmbeddedCurve as Ciphersuite>::F::random(&mut OsRng));
+  let ecdh_public_keys = [
+    <C::EmbeddedCurve as Ciphersuite>::G::random(&mut OsRng),
+    <C::EmbeddedCurve as Ciphersuite>::G::random(&mut OsRng),
+  ];
+  let time = Instant::now();
+  let res =
+    Evrf::<C>::prove(&mut OsRng, &generators, [0; 32], 1, &ecdh_public_keys, &vesta_private_key)
+      .unwrap();
+  println!("Proving time: {:?}", time.elapsed());
+
+  let time = Instant::now();
+  let mut verifier = generators.batch_verifier();
+  Evrf::<C>::verify(
+    &mut OsRng,
+    &generators,
+    &mut verifier,
+    [0; 32],
+    1,
+    &ecdh_public_keys,
+    C::EmbeddedCurve::generator() * *vesta_private_key,
+    &res.proof,
+  )
+  .unwrap();
+  assert!(generators.verify(verifier));
+  println!("Verifying time: {:?}", time.elapsed());
+}
+
+#[test]
+fn pallas_evrf_proof_test() {
+  evrf_proof_test::<Pallas>();
+}
+
+#[test]
+fn secp256k1_evrf_proof_test() {
+  evrf_proof_test::<Secp256k1>();
+}
+
+#[test]
+fn ed25519_evrf_proof_test() {
+  evrf_proof_test::<Ed25519>();
+}
+
+#[test]
+fn ristretto_evrf_proof_test() {
+  evrf_proof_test::<Ristretto>();
+}
--- a/crypto/dkg/src/tests/mod.rs
+++ b/crypto/dkg/src/tests/mod.rs
@@ -6,7 +6,7 @@ use rand_core::{RngCore, CryptoRng};

 use ciphersuite::{group::ff::Field, Ciphersuite};

-use crate::{Participant, ThresholdCore, ThresholdKeys, lagrange, musig::musig as musig_fn};
+use crate::{Participant, ThresholdCore, ThresholdKeys, musig::musig as musig_fn};

 mod musig;
 pub use musig::test_musig;
@@ -19,6 +19,9 @@ use pedpop::pedpop_gen;
 mod promote;
 use promote::test_generator_promotion;

+#[cfg(all(test, feature = "evrf"))]
+mod evrf;
+
 /// Constant amount of participants to use when testing.
 pub const PARTICIPANTS: u16 = 5;
 /// Constant threshold of participants to use when testing.
@@ -43,7 +46,8 @@ pub fn recover_key<C: Ciphersuite>(keys: &HashMap<Participant, ThresholdKeys<C>>
  let included = keys.keys().copied().collect::<Vec<_>>();

  let group_private = keys.iter().fold(C::F::ZERO, |accum, (i, keys)| {
-    accum + (lagrange::<C::F>(*i, &included) * keys.secret_share().deref())
+    accum +
+      (first.core.interpolation.interpolation_factor(*i, &included) * keys.secret_share().deref())
  });
  assert_eq!(C::generator() * group_private, first.group_key(), "failed to recover keys");
  group_private
--- a/crypto/dkg/src/tests/pedpop.rs
+++ b/crypto/dkg/src/tests/pedpop.rs
@@ -14,7 +14,7 @@ use crate::{
 type PedPoPEncryptedMessage<C> = EncryptedMessage<C, SecretShare<<C as Ciphersuite>::F>>;
 type PedPoPSecretShares<C> = HashMap<Participant, PedPoPEncryptedMessage<C>>;

-const CONTEXT: &str = "DKG Test Key Generation";
+const CONTEXT: [u8; 32] = *b"DKG Test Key Generation         ";

 // Commit, then return commitment messages, enc keys, and shares
 #[allow(clippy::type_complexity)]
@@ -31,7 +31,7 @@ fn commit_enc_keys_and_shares<R: RngCore + CryptoRng, C: Ciphersuite>(
  let mut enc_keys = HashMap::new();
  for i in (1 ..= PARTICIPANTS).map(Participant) {
    let params = ThresholdParams::new(THRESHOLD, PARTICIPANTS, i).unwrap();
-    let machine = KeyGenMachine::<C>::new(params, CONTEXT.to_string());
+    let machine = KeyGenMachine::<C>::new(params, CONTEXT);
    let (machine, these_commitments) = machine.generate_coefficients(rng);
    machines.insert(i, machine);

@@ -147,14 +147,12 @@ mod literal {

      // Verify machines constructed with AdditionalBlameMachine::new work
      assert_eq!(
-        AdditionalBlameMachine::new(
-          &mut OsRng,
-          CONTEXT.to_string(),
-          PARTICIPANTS,
-          commitment_msgs.clone()
-        )
-        .unwrap()
-        .blame(ONE, TWO, msg.clone(), blame.clone()),
+        AdditionalBlameMachine::new(CONTEXT, PARTICIPANTS, commitment_msgs.clone()).unwrap().blame(
+          ONE,
+          TWO,
+          msg.clone(),
+          blame.clone()
+        ),
        ONE,
      );
    }
--- a/crypto/evrf/circuit-abstraction/Cargo.toml
+++ b/crypto/evrf/circuit-abstraction/Cargo.toml
@@ -0,0 +1,20 @@
+[package]
+name = "generalized-bulletproofs-circuit-abstraction"
+version = "0.1.0"
+description = "An abstraction for arithmetic circuits over Generalized Bulletproofs"
+license = "MIT"
+repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/circuit-abstraction"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["bulletproofs", "circuit"]
+edition = "2021"
+
+[package.metadata.docs.rs]
+all-features = true
+rustdoc-args = ["--cfg", "docsrs"]
+
+[dependencies]
+zeroize = { version = "^1.5", default-features = false, features = ["zeroize_derive"] }
+
+ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
+
+generalized-bulletproofs = { path = "../generalized-bulletproofs" }
--- a/crypto/evrf/circuit-abstraction/LICENSE
+++ b/crypto/evrf/circuit-abstraction/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Luke Parker
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
--- a/crypto/evrf/circuit-abstraction/README.md
+++ b/crypto/evrf/circuit-abstraction/README.md
@@ -0,0 +1,3 @@
+# Generalized Bulletproofs Circuit Abstraction
+
+A circuit abstraction around `generalized-bulletproofs`.
--- a/crypto/evrf/circuit-abstraction/src/gadgets.rs
+++ b/crypto/evrf/circuit-abstraction/src/gadgets.rs
@@ -0,0 +1,39 @@
+use ciphersuite::{group::ff::Field, Ciphersuite};
+
+use crate::*;
+
+impl<C: Ciphersuite> Circuit<C> {
+  /// Constrain two linear combinations to be equal.
+  pub fn equality(&mut self, a: LinComb<C::F>, b: &LinComb<C::F>) {
+    self.constrain_equal_to_zero(a - b);
+  }
+
+  /// Calculate (and constrain) the inverse of a value.
+  ///
+  /// A linear combination may optionally be passed as a constraint for the value being inverted.
+  /// A reference to the inverted value and its inverse is returned.
+  ///
+  /// May panic if any linear combinations reference non-existent terms, the witness isn't provided
+  /// when proving/is provided when verifying, or if the witness is 0 (and accordingly doesn't have
+  /// an inverse).
+  pub fn inverse(
+    &mut self,
+    lincomb: Option<LinComb<C::F>>,
+    witness: Option<C::F>,
+  ) -> (Variable, Variable) {
+    let (l, r, o) = self.mul(lincomb, None, witness.map(|f| (f, f.invert().unwrap())));
+    // The output of a value multiplied by its inverse is 1
+    // Constrain `1 o - 1 = 0`
+    self.constrain_equal_to_zero(LinComb::from(o).constant(-C::F::ONE));
+    (l, r)
+  }
+
+  /// Constrain two linear combinations as inequal.
+  ///
+  /// May panic if any linear combinations reference non-existent terms.
+  pub fn inequality(&mut self, a: LinComb<C::F>, b: &LinComb<C::F>, witness: Option<(C::F, C::F)>) {
+    let l_constraint = a - b;
+    // The existence of a multiplicative inverse means a-b != 0, which means a != b
+    self.inverse(Some(l_constraint), witness.map(|(a, b)| a - b));
+  }
+}
--- a/crypto/evrf/circuit-abstraction/src/lib.rs
+++ b/crypto/evrf/circuit-abstraction/src/lib.rs
@@ -0,0 +1,192 @@
+#![cfg_attr(docsrs, feature(doc_auto_cfg))]
+#![doc = include_str!("../README.md")]
+#![deny(missing_docs)]
+#![allow(non_snake_case)]
+
+use zeroize::{Zeroize, ZeroizeOnDrop};
+
+use ciphersuite::{
+  group::ff::{Field, PrimeField},
+  Ciphersuite,
+};
+
+use generalized_bulletproofs::{
+  ScalarVector, PedersenCommitment, PedersenVectorCommitment, ProofGenerators,
+  transcript::{Transcript as ProverTranscript, VerifierTranscript, Commitments},
+  arithmetic_circuit_proof::{AcError, ArithmeticCircuitStatement, ArithmeticCircuitWitness},
+};
+pub use generalized_bulletproofs::arithmetic_circuit_proof::{Variable, LinComb};
+
+mod gadgets;
+
+/// A trait for the transcript, whether proving for verifying, as necessary for sampling
+/// challenges.
+pub trait Transcript {
+  /// Sample a challenge from the transacript.
+  ///
+  /// It is the caller's responsibility to have properly transcripted all variables prior to
+  /// sampling this challenge.
+  fn challenge<F: PrimeField>(&mut self) -> F;
+}
+impl Transcript for ProverTranscript {
+  fn challenge<F: PrimeField>(&mut self) -> F {
+    self.challenge()
+  }
+}
+impl Transcript for VerifierTranscript<'_> {
+  fn challenge<F: PrimeField>(&mut self) -> F {
+    self.challenge()
+  }
+}
+
+/// The witness for the satisfaction of this circuit.
+#[derive(Clone, PartialEq, Eq, Debug, Zeroize, ZeroizeOnDrop)]
+struct ProverData<C: Ciphersuite> {
+  aL: Vec<C::F>,
+  aR: Vec<C::F>,
+  C: Vec<PedersenVectorCommitment<C>>,
+  V: Vec<PedersenCommitment<C>>,
+}
+
+/// A struct representing a circuit.
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct Circuit<C: Ciphersuite> {
+  muls: usize,
+  // A series of linear combinations which must evaluate to 0.
+  constraints: Vec<LinComb<C::F>>,
+  prover: Option<ProverData<C>>,
+}
+
+impl<C: Ciphersuite> Circuit<C> {
+  /// Returns the amount of multiplications used by this circuit.
+  pub fn muls(&self) -> usize {
+    self.muls
+  }
+
+  /// Create an instance to prove satisfaction of a circuit with.
+  // TODO: Take the transcript here
+  #[allow(clippy::type_complexity)]
+  pub fn prove(
+    vector_commitments: Vec<PedersenVectorCommitment<C>>,
+    commitments: Vec<PedersenCommitment<C>>,
+  ) -> Self {
+    Self {
+      muls: 0,
+      constraints: vec![],
+      prover: Some(ProverData { aL: vec![], aR: vec![], C: vector_commitments, V: commitments }),
+    }
+  }
+
+  /// Create an instance to verify a proof with.
+  // TODO: Take the transcript here
+  pub fn verify() -> Self {
+    Self { muls: 0, constraints: vec![], prover: None }
+  }
+
+  /// Evaluate a linear combination.
+  ///
+  /// Yields WL aL + WR aR + WO aO + WCG CG + WCH CH + WV V + c.
+  ///
+  /// May panic if the linear combination references non-existent terms.
+  ///
+  /// Returns None if not a prover.
+  pub fn eval(&self, lincomb: &LinComb<C::F>) -> Option<C::F> {
+    self.prover.as_ref().map(|prover| {
+      let mut res = lincomb.c();
+      for (index, weight) in lincomb.WL() {
+        res += prover.aL[*index] * weight;
+      }
+      for (index, weight) in lincomb.WR() {
+        res += prover.aR[*index] * weight;
+      }
+      for (index, weight) in lincomb.WO() {
+        res += prover.aL[*index] * prover.aR[*index] * weight;
+      }
+      for (WCG, C) in lincomb.WCG().iter().zip(&prover.C) {
+        for (j, weight) in WCG {
+          res += C.g_values[*j] * weight;
+        }
+      }
+      for (WCH, C) in lincomb.WCH().iter().zip(&prover.C) {
+        for (j, weight) in WCH {
+          res += C.h_values[*j] * weight;
+        }
+      }
+      for (index, weight) in lincomb.WV() {
+        res += prover.V[*index].value * weight;
+      }
+      res
+    })
+  }
+
+  /// Multiply two values, optionally constrained, returning the constrainable left/right/out
+  /// terms.
+  ///
+  /// May panic if any linear combinations reference non-existent terms or if the witness isn't
+  /// provided when proving/is provided when verifying.
+  pub fn mul(
+    &mut self,
+    a: Option<LinComb<C::F>>,
+    b: Option<LinComb<C::F>>,
+    witness: Option<(C::F, C::F)>,
+  ) -> (Variable, Variable, Variable) {
+    let l = Variable::aL(self.muls);
+    let r = Variable::aR(self.muls);
+    let o = Variable::aO(self.muls);
+    self.muls += 1;
+
+    debug_assert_eq!(self.prover.is_some(), witness.is_some());
+    if let Some(witness) = witness {
+      let prover = self.prover.as_mut().unwrap();
+      prover.aL.push(witness.0);
+      prover.aR.push(witness.1);
+    }
+
+    if let Some(a) = a {
+      self.constrain_equal_to_zero(a.term(-C::F::ONE, l));
+    }
+    if let Some(b) = b {
+      self.constrain_equal_to_zero(b.term(-C::F::ONE, r));
+    }
+
+    (l, r, o)
+  }
+
+  /// Constrain a linear combination to be equal to 0.
+  ///
+  /// May panic if the linear combination references non-existent terms.
+  pub fn constrain_equal_to_zero(&mut self, lincomb: LinComb<C::F>) {
+    self.constraints.push(lincomb);
+  }
+
+  /// Obtain the statement for this circuit.
+  ///
+  /// If configured as the prover, the witness to use is also returned.
+  #[allow(clippy::type_complexity)]
+  pub fn statement(
+    self,
+    generators: ProofGenerators<'_, C>,
+    commitments: Commitments<C>,
+  ) -> Result<(ArithmeticCircuitStatement<'_, C>, Option<ArithmeticCircuitWitness<C>>), AcError> {
+    let statement = ArithmeticCircuitStatement::new(generators, self.constraints, commitments)?;
+
+    let witness = self
+      .prover
+      .map(|mut prover| {
+        // We can't deconstruct the witness as it implements Drop (per ZeroizeOnDrop)
+        // Accordingly, we take the values within it and move forward with those
+        let mut aL = vec![];
+        std::mem::swap(&mut prover.aL, &mut aL);
+        let mut aR = vec![];
+        std::mem::swap(&mut prover.aR, &mut aR);
+        let mut C = vec![];
+        std::mem::swap(&mut prover.C, &mut C);
+        let mut V = vec![];
+        std::mem::swap(&mut prover.V, &mut V);
+        ArithmeticCircuitWitness::new(ScalarVector::from(aL), ScalarVector::from(aR), C, V)
+      })
+      .transpose()?;
+
+    Ok((statement, witness))
+  }
+}
--- a/crypto/evrf/divisors/Cargo.toml
+++ b/crypto/evrf/divisors/Cargo.toml
@@ -0,0 +1,34 @@
+[package]
+name = "ec-divisors"
+version = "0.1.0"
+description = "A library for calculating elliptic curve divisors"
+license = "MIT"
+repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/divisors"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["ciphersuite", "ff", "group"]
+edition = "2021"
+
+[package.metadata.docs.rs]
+all-features = true
+rustdoc-args = ["--cfg", "docsrs"]
+
+[dependencies]
+rand_core = { version = "0.6", default-features = false }
+zeroize = { version = "^1.5", default-features = false, features = ["zeroize_derive"] }
+
+group = "0.13"
+
+hex = { version = "0.4", optional = true }
+dalek-ff-group = { path = "../../dalek-ff-group", features = ["std"], optional = true }
+pasta_curves = { version = "0.5", default-features = false, features = ["bits", "alloc"], optional = true }
+
+[dev-dependencies]
+rand_core = { version = "0.6", features = ["getrandom"] }
+
+hex = "0.4"
+dalek-ff-group = { path = "../../dalek-ff-group", features = ["std"] }
+pasta_curves = { version = "0.5", default-features = false, features = ["bits", "alloc"] }
+
+[features]
+ed25519 = ["hex", "dalek-ff-group"]
+pasta = ["pasta_curves"]
--- a/crypto/evrf/divisors/LICENSE
+++ b/crypto/evrf/divisors/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2023-2024 Luke Parker
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
--- a/crypto/evrf/divisors/README.md
+++ b/crypto/evrf/divisors/README.md
@@ -0,0 +1,4 @@
+# Elliptic Curve Divisors
+
+An implementation of a representation for and construction of elliptic curve
+divisors, intended for Eagen's [EC IP work](https://eprint.iacr.org/2022/596).
--- a/crypto/evrf/divisors/src/lib.rs
+++ b/crypto/evrf/divisors/src/lib.rs
@@ -0,0 +1,287 @@
+#![cfg_attr(docsrs, feature(doc_auto_cfg))]
+#![doc = include_str!("../README.md")]
+#![deny(missing_docs)]
+#![allow(non_snake_case)]
+
+use group::{
+  ff::{Field, PrimeField},
+  Group,
+};
+
+mod poly;
+pub use poly::*;
+
+#[cfg(test)]
+mod tests;
+
+/// A curve usable with this library.
+pub trait DivisorCurve: Group {
+  /// An element of the field this curve is defined over.
+  type FieldElement: PrimeField;
+
+  /// The A in the curve equation y^2 = x^3 + A x + B.
+  fn a() -> Self::FieldElement;
+  /// The B in the curve equation y^2 = x^3 + A x + B.
+  fn b() -> Self::FieldElement;
+
+  /// y^2 - x^3 - A x - B
+  ///
+  /// Section 2 of the security proofs define this modulus.
+  ///
+  /// This MUST NOT be overriden.
+  // TODO: Move to an extension trait
+  fn divisor_modulus() -> Poly<Self::FieldElement> {
+    Poly {
+      // 0 y**1, 1 y*2
+      y_coefficients: vec![Self::FieldElement::ZERO, Self::FieldElement::ONE],
+      yx_coefficients: vec![],
+      x_coefficients: vec![
+        // - A x
+        -Self::a(),
+        // 0 x^2
+        Self::FieldElement::ZERO,
+        // - x^3
+        -Self::FieldElement::ONE,
+      ],
+      // - B
+      zero_coefficient: -Self::b(),
+    }
+  }
+
+  /// Convert a point to its x and y coordinates.
+  ///
+  /// Returns None if passed the point at infinity.
+  fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)>;
+}
+
+/// Calculate the slope and intercept between two points.
+///
+/// This function panics when `a @ infinity`, `b @ infinity`, `a == b`, or when `a == -b`.
+pub(crate) fn slope_intercept<C: DivisorCurve>(a: C, b: C) -> (C::FieldElement, C::FieldElement) {
+  let (ax, ay) = C::to_xy(a).unwrap();
+  debug_assert_eq!(C::divisor_modulus().eval(ax, ay), C::FieldElement::ZERO);
+  let (bx, by) = C::to_xy(b).unwrap();
+  debug_assert_eq!(C::divisor_modulus().eval(bx, by), C::FieldElement::ZERO);
+  let slope = (by - ay) *
+    Option::<C::FieldElement>::from((bx - ax).invert())
+      .expect("trying to get slope/intercept of points sharing an x coordinate");
+  let intercept = by - (slope * bx);
+  debug_assert!(bool::from((ay - (slope * ax) - intercept).is_zero()));
+  debug_assert!(bool::from((by - (slope * bx) - intercept).is_zero()));
+  (slope, intercept)
+}
+
+// The line interpolating two points.
+fn line<C: DivisorCurve>(a: C, mut b: C) -> Poly<C::FieldElement> {
+  // If they're both the point at infinity, we simply set the line to one
+  if bool::from(a.is_identity() & b.is_identity()) {
+    return Poly {
+      y_coefficients: vec![],
+      yx_coefficients: vec![],
+      x_coefficients: vec![],
+      zero_coefficient: C::FieldElement::ONE,
+    };
+  }
+
+  // If either point is the point at infinity, or these are additive inverses, the line is
+  // `1 * x - x`. The first `x` is a term in the polynomial, the `x` is the `x` coordinate of these
+  // points (of which there is one, as the second point is either at infinity or has a matching `x`
+  // coordinate).
+  if bool::from(a.is_identity() | b.is_identity()) || (a == -b) {
+    let (x, _) = C::to_xy(if !bool::from(a.is_identity()) { a } else { b }).unwrap();
+    return Poly {
+      y_coefficients: vec![],
+      yx_coefficients: vec![],
+      x_coefficients: vec![C::FieldElement::ONE],
+      zero_coefficient: -x,
+    };
+  }
+
+  // If the points are equal, we use the line interpolating the sum of these points with the point
+  // at infinity
+  if a == b {
+    b = -a.double();
+  }
+
+  let (slope, intercept) = slope_intercept::<C>(a, b);
+
+  // Section 4 of the proofs explicitly state the line `L = y - lambda * x - mu`
+  // y - (slope * x) - intercept
+  Poly {
+    y_coefficients: vec![C::FieldElement::ONE],
+    yx_coefficients: vec![],
+    x_coefficients: vec![-slope],
+    zero_coefficient: -intercept,
+  }
+}
+
+/// Create a divisor interpolating the following points.
+///
+/// Returns None if:
+///   - No points were passed in
+///   - The points don't sum to the point at infinity
+///   - A passed in point was the point at infinity
+#[allow(clippy::new_ret_no_self)]
+pub fn new_divisor<C: DivisorCurve>(points: &[C]) -> Option<Poly<C::FieldElement>> {
+  // A single point is either the point at infinity, or this doesn't sum to the point at infinity
+  // Both cause us to return None
+  if points.len() < 2 {
+    None?;
+  }
+  if points.iter().sum::<C>() != C::identity() {
+    None?;
+  }
+
+  // Create the initial set of divisors
+  let mut divs = vec![];
+  let mut iter = points.iter().copied();
+  while let Some(a) = iter.next() {
+    if a == C::identity() {
+      None?;
+    }
+
+    let b = iter.next();
+    if b == Some(C::identity()) {
+      None?;
+    }
+
+    // Draw the line between those points
+    divs.push((a + b.unwrap_or(C::identity()), line::<C>(a, b.unwrap_or(-a))));
+  }
+
+  let modulus = C::divisor_modulus();
+
+  // Pair them off until only one remains
+  while divs.len() > 1 {
+    let mut next_divs = vec![];
+    // If there's an odd amount of divisors, carry the odd one out to the next iteration
+    if (divs.len() % 2) == 1 {
+      next_divs.push(divs.pop().unwrap());
+    }
+
+    while let Some((a, a_div)) = divs.pop() {
+      let (b, b_div) = divs.pop().unwrap();
+
+      // Merge the two divisors
+      let numerator = a_div.mul_mod(b_div, &modulus).mul_mod(line::<C>(a, b), &modulus);
+      let denominator = line::<C>(a, -a).mul_mod(line::<C>(b, -b), &modulus);
+      let (q, r) = numerator.div_rem(&denominator);
+      assert_eq!(r, Poly::zero());
+
+      next_divs.push((a + b, q));
+    }
+
+    divs = next_divs;
+  }
+
+  // Return the unified divisor
+  Some(divs.remove(0).1)
+}
+
+#[cfg(any(test, feature = "pasta"))]
+mod pasta {
+  use group::{ff::Field, Curve};
+  use pasta_curves::{
+    arithmetic::{Coordinates, CurveAffine},
+    Ep, Fp, Eq, Fq,
+  };
+  use crate::DivisorCurve;
+
+  impl DivisorCurve for Ep {
+    type FieldElement = Fp;
+
+    fn a() -> Self::FieldElement {
+      Self::FieldElement::ZERO
+    }
+    fn b() -> Self::FieldElement {
+      Self::FieldElement::from(5u64)
+    }
+
+    fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
+      Option::<Coordinates<_>>::from(point.to_affine().coordinates())
+        .map(|coords| (*coords.x(), *coords.y()))
+    }
+  }
+
+  impl DivisorCurve for Eq {
+    type FieldElement = Fq;
+
+    fn a() -> Self::FieldElement {
+      Self::FieldElement::ZERO
+    }
+    fn b() -> Self::FieldElement {
+      Self::FieldElement::from(5u64)
+    }
+
+    fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
+      Option::<Coordinates<_>>::from(point.to_affine().coordinates())
+        .map(|coords| (*coords.x(), *coords.y()))
+    }
+  }
+}
+
+#[cfg(any(test, feature = "ed25519"))]
+mod ed25519 {
+  use group::{
+    ff::{Field, PrimeField},
+    Group, GroupEncoding,
+  };
+  use dalek_ff_group::{FieldElement, EdwardsPoint};
+
+  impl crate::DivisorCurve for EdwardsPoint {
+    type FieldElement = FieldElement;
+
+    // Wei25519 a/b
+    // https://www.ietf.org/archive/id/draft-ietf-lwig-curve-representations-02.pdf E.3
+    fn a() -> Self::FieldElement {
+      let mut be_bytes =
+        hex::decode("2aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa984914a144").unwrap();
+      be_bytes.reverse();
+      let le_bytes = be_bytes;
+      Self::FieldElement::from_repr(le_bytes.try_into().unwrap()).unwrap()
+    }
+    fn b() -> Self::FieldElement {
+      let mut be_bytes =
+        hex::decode("7b425ed097b425ed097b425ed097b425ed097b425ed097b4260b5e9c7710c864").unwrap();
+      be_bytes.reverse();
+      let le_bytes = be_bytes;
+
+      Self::FieldElement::from_repr(le_bytes.try_into().unwrap()).unwrap()
+    }
+
+    // https://www.ietf.org/archive/id/draft-ietf-lwig-curve-representations-02.pdf E.2
+    fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
+      if bool::from(point.is_identity()) {
+        None?;
+      }
+
+      // Extract the y coordinate from the compressed point
+      let mut edwards_y = point.to_bytes();
+      let x_is_odd = edwards_y[31] >> 7;
+      edwards_y[31] &= (1 << 7) - 1;
+      let edwards_y = Self::FieldElement::from_repr(edwards_y).unwrap();
+
+      // Recover the x coordinate
+      let edwards_y_sq = edwards_y * edwards_y;
+      let D = -Self::FieldElement::from(121665u64) *
+        Self::FieldElement::from(121666u64).invert().unwrap();
+      let mut edwards_x = ((edwards_y_sq - Self::FieldElement::ONE) *
+        ((D * edwards_y_sq) + Self::FieldElement::ONE).invert().unwrap())
+      .sqrt()
+      .unwrap();
+      if u8::from(bool::from(edwards_x.is_odd())) != x_is_odd {
+        edwards_x = -edwards_x;
+      }
+
+      // Calculate the x and y coordinates for Wei25519
+      let edwards_y_plus_one = Self::FieldElement::ONE + edwards_y;
+      let one_minus_edwards_y = Self::FieldElement::ONE - edwards_y;
+      let wei_x = (edwards_y_plus_one * one_minus_edwards_y.invert().unwrap()) +
+        (Self::FieldElement::from(486662u64) * Self::FieldElement::from(3u64).invert().unwrap());
+      let c =
+        (-(Self::FieldElement::from(486662u64) + Self::FieldElement::from(2u64))).sqrt().unwrap();
+      let wei_y = c * edwards_y_plus_one * (one_minus_edwards_y * edwards_x).invert().unwrap();
+      Some((wei_x, wei_y))
+    }
+  }
+}
--- a/crypto/evrf/divisors/src/poly.rs
+++ b/crypto/evrf/divisors/src/poly.rs
@@ -0,0 +1,430 @@
+use core::ops::{Add, Neg, Sub, Mul, Rem};
+
+use zeroize::Zeroize;
+
+use group::ff::PrimeField;
+
+/// A structure representing a Polynomial with x**i, y**i, and y**i * x**j terms.
+#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+pub struct Poly<F: PrimeField + From<u64>> {
+  /// c[i] * y ** (i + 1)
+  pub y_coefficients: Vec<F>,
+  /// c[i][j] * y ** (i + 1) x ** (j + 1)
+  pub yx_coefficients: Vec<Vec<F>>,
+  /// c[i] * x ** (i + 1)
+  pub x_coefficients: Vec<F>,
+  /// Coefficient for x ** 0, y ** 0, and x ** 0 y ** 0 (the coefficient for 1)
+  pub zero_coefficient: F,
+}
+
+impl<F: PrimeField + From<u64>> Poly<F> {
+  /// A polynomial for zero.
+  pub fn zero() -> Self {
+    Poly {
+      y_coefficients: vec![],
+      yx_coefficients: vec![],
+      x_coefficients: vec![],
+      zero_coefficient: F::ZERO,
+    }
+  }
+
+  /// The amount of terms in the polynomial.
+  #[allow(clippy::len_without_is_empty)]
+  #[must_use]
+  pub fn len(&self) -> usize {
+    self.y_coefficients.len() +
+      self.yx_coefficients.iter().map(Vec::len).sum::<usize>() +
+      self.x_coefficients.len() +
+      usize::from(u8::from(self.zero_coefficient != F::ZERO))
+  }
+
+  // Remove high-order zero terms, allowing the length of the vectors to equal the amount of terms.
+  pub(crate) fn tidy(&mut self) {
+    let tidy = |vec: &mut Vec<F>| {
+      while vec.last() == Some(&F::ZERO) {
+        vec.pop();
+      }
+    };
+
+    tidy(&mut self.y_coefficients);
+    for vec in self.yx_coefficients.iter_mut() {
+      tidy(vec);
+    }
+    while self.yx_coefficients.last() == Some(&vec![]) {
+      self.yx_coefficients.pop();
+    }
+    tidy(&mut self.x_coefficients);
+  }
+}
+
+impl<F: PrimeField + From<u64>> Add<&Self> for Poly<F> {
+  type Output = Self;
+
+  fn add(mut self, other: &Self) -> Self {
+    // Expand to be the neeeded size
+    while self.y_coefficients.len() < other.y_coefficients.len() {
+      self.y_coefficients.push(F::ZERO);
+    }
+    while self.yx_coefficients.len() < other.yx_coefficients.len() {
+      self.yx_coefficients.push(vec![]);
+    }
+    for i in 0 .. other.yx_coefficients.len() {
+      while self.yx_coefficients[i].len() < other.yx_coefficients[i].len() {
+        self.yx_coefficients[i].push(F::ZERO);
+      }
+    }
+    while self.x_coefficients.len() < other.x_coefficients.len() {
+      self.x_coefficients.push(F::ZERO);
+    }
+
+    // Perform the addition
+    for (i, coeff) in other.y_coefficients.iter().enumerate() {
+      self.y_coefficients[i] += coeff;
+    }
+    for (i, coeffs) in other.yx_coefficients.iter().enumerate() {
+      for (j, coeff) in coeffs.iter().enumerate() {
+        self.yx_coefficients[i][j] += coeff;
+      }
+    }
+    for (i, coeff) in other.x_coefficients.iter().enumerate() {
+      self.x_coefficients[i] += coeff;
+    }
+    self.zero_coefficient += other.zero_coefficient;
+
+    self.tidy();
+    self
+  }
+}
+
+impl<F: PrimeField + From<u64>> Neg for Poly<F> {
+  type Output = Self;
+
+  fn neg(mut self) -> Self {
+    for y_coeff in self.y_coefficients.iter_mut() {
+      *y_coeff = -*y_coeff;
+    }
+    for yx_coeffs in self.yx_coefficients.iter_mut() {
+      for yx_coeff in yx_coeffs.iter_mut() {
+        *yx_coeff = -*yx_coeff;
+      }
+    }
+    for x_coeff in self.x_coefficients.iter_mut() {
+      *x_coeff = -*x_coeff;
+    }
+    self.zero_coefficient = -self.zero_coefficient;
+
+    self
+  }
+}
+
+impl<F: PrimeField + From<u64>> Sub for Poly<F> {
+  type Output = Self;
+
+  fn sub(self, other: Self) -> Self {
+    self + &-other
+  }
+}
+
+impl<F: PrimeField + From<u64>> Mul<F> for Poly<F> {
+  type Output = Self;
+
+  fn mul(mut self, scalar: F) -> Self {
+    if scalar == F::ZERO {
+      return Poly::zero();
+    }
+
+    for y_coeff in self.y_coefficients.iter_mut() {
+      *y_coeff *= scalar;
+    }
+    for coeffs in self.yx_coefficients.iter_mut() {
+      for coeff in coeffs.iter_mut() {
+        *coeff *= scalar;
+      }
+    }
+    for x_coeff in self.x_coefficients.iter_mut() {
+      *x_coeff *= scalar;
+    }
+    self.zero_coefficient *= scalar;
+    self
+  }
+}
+
+impl<F: PrimeField + From<u64>> Poly<F> {
+  #[must_use]
+  fn shift_by_x(mut self, power_of_x: usize) -> Self {
+    if power_of_x == 0 {
+      return self;
+    }
+
+    // Shift up every x coefficient
+    for _ in 0 .. power_of_x {
+      self.x_coefficients.insert(0, F::ZERO);
+      for yx_coeffs in &mut self.yx_coefficients {
+        yx_coeffs.insert(0, F::ZERO);
+      }
+    }
+
+    // Move the zero coefficient
+    self.x_coefficients[power_of_x - 1] = self.zero_coefficient;
+    self.zero_coefficient = F::ZERO;
+
+    // Move the y coefficients
+    // Start by creating yx coefficients with the necessary powers of x
+    let mut yx_coefficients_to_push = vec![];
+    while yx_coefficients_to_push.len() < power_of_x {
+      yx_coefficients_to_push.push(F::ZERO);
+    }
+    // Now, ensure the yx coefficients has the slots for the y coefficients we're moving
+    while self.yx_coefficients.len() < self.y_coefficients.len() {
+      self.yx_coefficients.push(yx_coefficients_to_push.clone());
+    }
+    // Perform the move
+    for (i, y_coeff) in self.y_coefficients.drain(..).enumerate() {
+      self.yx_coefficients[i][power_of_x - 1] = y_coeff;
+    }
+
+    self
+  }
+
+  #[must_use]
+  fn shift_by_y(mut self, power_of_y: usize) -> Self {
+    if power_of_y == 0 {
+      return self;
+    }
+
+    // Shift up every y coefficient
+    for _ in 0 .. power_of_y {
+      self.y_coefficients.insert(0, F::ZERO);
+      self.yx_coefficients.insert(0, vec![]);
+    }
+
+    // Move the zero coefficient
+    self.y_coefficients[power_of_y - 1] = self.zero_coefficient;
+    self.zero_coefficient = F::ZERO;
+
+    // Move the x coefficients
+    self.yx_coefficients[power_of_y - 1] = self.x_coefficients;
+    self.x_coefficients = vec![];
+
+    self
+  }
+}
+
+impl<F: PrimeField + From<u64>> Mul for Poly<F> {
+  type Output = Self;
+
+  fn mul(self, other: Self) -> Self {
+    let mut res = self.clone() * other.zero_coefficient;
+
+    for (i, y_coeff) in other.y_coefficients.iter().enumerate() {
+      let scaled = self.clone() * *y_coeff;
+      res = res + &scaled.shift_by_y(i + 1);
+    }
+
+    for (y_i, yx_coeffs) in other.yx_coefficients.iter().enumerate() {
+      for (x_i, yx_coeff) in yx_coeffs.iter().enumerate() {
+        let scaled = self.clone() * *yx_coeff;
+        res = res + &scaled.shift_by_y(y_i + 1).shift_by_x(x_i + 1);
+      }
+    }
+
+    for (i, x_coeff) in other.x_coefficients.iter().enumerate() {
+      let scaled = self.clone() * *x_coeff;
+      res = res + &scaled.shift_by_x(i + 1);
+    }
+
+    res.tidy();
+    res
+  }
+}
+
+impl<F: PrimeField + From<u64>> Poly<F> {
+  /// Perform multiplication mod `modulus`.
+  #[must_use]
+  pub fn mul_mod(self, other: Self, modulus: &Self) -> Self {
+    ((self % modulus) * (other % modulus)) % modulus
+  }
+
+  /// Perform division, returning the result and remainder.
+  ///
+  /// Panics upon division by zero, with undefined behavior if a non-tidy divisor is used.
+  #[must_use]
+  pub fn div_rem(self, divisor: &Self) -> (Self, Self) {
+    // The leading y coefficient and associated x coefficient.
+    let leading_y = |poly: &Self| -> (_, _) {
+      if poly.y_coefficients.len() > poly.yx_coefficients.len() {
+        (poly.y_coefficients.len(), 0)
+      } else if !poly.yx_coefficients.is_empty() {
+        (poly.yx_coefficients.len(), poly.yx_coefficients.last().unwrap().len())
+      } else {
+        (0, poly.x_coefficients.len())
+      }
+    };
+
+    let (div_y, div_x) = leading_y(divisor);
+    // If this divisor is actually a scalar, don't perform long division
+    if (div_y == 0) && (div_x == 0) {
+      return (self * divisor.zero_coefficient.invert().unwrap(), Poly::zero());
+    }
+
+    // Remove leading terms until the value is less than the divisor
+    let mut quotient: Poly<F> = Poly::zero();
+    let mut remainder = self.clone();
+    loop {
+      // If there's nothing left to divide, return
+      if remainder == Poly::zero() {
+        break;
+      }
+
+      let (rem_y, rem_x) = leading_y(&remainder);
+      if (rem_y < div_y) || (rem_x < div_x) {
+        break;
+      }
+
+      let get = |poly: &Poly<F>, y_pow: usize, x_pow: usize| -> F {
+        if (y_pow == 0) && (x_pow == 0) {
+          poly.zero_coefficient
+        } else if x_pow == 0 {
+          poly.y_coefficients[y_pow - 1]
+        } else if y_pow == 0 {
+          poly.x_coefficients[x_pow - 1]
+        } else {
+          poly.yx_coefficients[y_pow - 1][x_pow - 1]
+        }
+      };
+      let coeff_numerator = get(&remainder, rem_y, rem_x);
+      let coeff_denominator = get(divisor, div_y, div_x);
+
+      // We want coeff_denominator scaled by x to equal coeff_numerator
+      // x * d = n
+      // n / d = x
+      let mut quotient_term = Poly::zero();
+      // Because this is the coefficient for the leading term of a tidied polynomial, it must be
+      // non-zero
+      quotient_term.zero_coefficient = coeff_numerator * coeff_denominator.invert().unwrap();
+
+      // Add the necessary yx powers
+      let delta_y = rem_y - div_y;
+      let delta_x = rem_x - div_x;
+      let quotient_term = quotient_term.shift_by_y(delta_y).shift_by_x(delta_x);
+
+      let to_remove = quotient_term.clone() * divisor.clone();
+      debug_assert_eq!(get(&to_remove, rem_y, rem_x), coeff_numerator);
+
+      remainder = remainder - to_remove;
+      quotient = quotient + &quotient_term;
+    }
+    debug_assert_eq!((quotient.clone() * divisor.clone()) + &remainder, self);
+
+    (quotient, remainder)
+  }
+}
+
+impl<F: PrimeField + From<u64>> Rem<&Self> for Poly<F> {
+  type Output = Self;
+
+  fn rem(self, modulus: &Self) -> Self {
+    self.div_rem(modulus).1
+  }
+}
+
+impl<F: PrimeField + From<u64>> Poly<F> {
+  /// Evaluate this polynomial with the specified x/y values.
+  ///
+  /// Panics on polynomials with terms whose powers exceed 2**64.
+  #[must_use]
+  pub fn eval(&self, x: F, y: F) -> F {
+    let mut res = self.zero_coefficient;
+    for (pow, coeff) in
+      self.y_coefficients.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
+    {
+      res += y.pow([pow]) * coeff;
+    }
+    for (y_pow, coeffs) in
+      self.yx_coefficients.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
+    {
+      let y_pow = y.pow([y_pow]);
+      for (x_pow, coeff) in
+        coeffs.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
+      {
+        res += y_pow * x.pow([x_pow]) * coeff;
+      }
+    }
+    for (pow, coeff) in
+      self.x_coefficients.iter().enumerate().map(|(i, v)| (u64::try_from(i + 1).unwrap(), v))
+    {
+      res += x.pow([pow]) * coeff;
+    }
+    res
+  }
+
+  /// Differentiate a polynomial, reduced by a modulus with a leading y term y**2 x**0, by x and y.
+  ///
+  /// This function panics if a y**2 term is present within the polynomial.
+  #[must_use]
+  pub fn differentiate(&self) -> (Poly<F>, Poly<F>) {
+    assert!(self.y_coefficients.len() <= 1);
+    assert!(self.yx_coefficients.len() <= 1);
+
+    // Differentation by x practically involves:
+    // - Dropping everything without an x component
+    // - Shifting everything down a power of x
+    // - Multiplying the new coefficient by the power it prior was used with
+    let diff_x = {
+      let mut diff_x = Poly {
+        y_coefficients: vec![],
+        yx_coefficients: vec![],
+        x_coefficients: vec![],
+        zero_coefficient: F::ZERO,
+      };
+      if !self.x_coefficients.is_empty() {
+        let mut x_coeffs = self.x_coefficients.clone();
+        diff_x.zero_coefficient = x_coeffs.remove(0);
+        diff_x.x_coefficients = x_coeffs;
+
+        let mut prior_x_power = F::from(2);
+        for x_coeff in &mut diff_x.x_coefficients {
+          *x_coeff *= prior_x_power;
+          prior_x_power += F::ONE;
+        }
+      }
+
+      if !self.yx_coefficients.is_empty() {
+        let mut yx_coeffs = self.yx_coefficients[0].clone();
+        diff_x.y_coefficients = vec![yx_coeffs.remove(0)];
+        diff_x.yx_coefficients = vec![yx_coeffs];
+
+        let mut prior_x_power = F::from(2);
+        for yx_coeff in &mut diff_x.yx_coefficients[0] {
+          *yx_coeff *= prior_x_power;
+          prior_x_power += F::ONE;
+        }
+      }
+
+      diff_x.tidy();
+      diff_x
+    };
+
+    // Differentation by y is trivial
+    // It's the y coefficient as the zero coefficient, and the yx coefficients as the x
+    // coefficients
+    // This is thanks to any y term over y^2 being reduced out
+    let diff_y = Poly {
+      y_coefficients: vec![],
+      yx_coefficients: vec![],
+      x_coefficients: self.yx_coefficients.first().cloned().unwrap_or(vec![]),
+      zero_coefficient: self.y_coefficients.first().cloned().unwrap_or(F::ZERO),
+    };
+
+    (diff_x, diff_y)
+  }
+
+  /// Normalize the x coefficient to 1.
+  ///
+  /// Panics if there is no x coefficient to normalize or if it cannot be normalized to 1.
+  #[must_use]
+  pub fn normalize_x_coefficient(self) -> Self {
+    let scalar = self.x_coefficients[0].invert().unwrap();
+    self * scalar
+  }
+}
--- a/crypto/evrf/divisors/src/tests/mod.rs
+++ b/crypto/evrf/divisors/src/tests/mod.rs
@@ -0,0 +1,235 @@
+use rand_core::OsRng;
+
+use group::{ff::Field, Group};
+use dalek_ff_group::EdwardsPoint;
+use pasta_curves::{Ep, Eq};
+
+use crate::{DivisorCurve, Poly, new_divisor};
+
+// Equation 4 in the security proofs
+fn check_divisor<C: DivisorCurve>(points: Vec<C>) {
+  // Create the divisor
+  let divisor = new_divisor::<C>(&points).unwrap();
+  let eval = |c| {
+    let (x, y) = C::to_xy(c).unwrap();
+    divisor.eval(x, y)
+  };
+
+  // Decide challgenges
+  let c0 = C::random(&mut OsRng);
+  let c1 = C::random(&mut OsRng);
+  let c2 = -(c0 + c1);
+  let (slope, intercept) = crate::slope_intercept::<C>(c0, c1);
+
+  let mut rhs = <C as DivisorCurve>::FieldElement::ONE;
+  for point in points {
+    let (x, y) = C::to_xy(point).unwrap();
+    rhs *= intercept - (y - (slope * x));
+  }
+  assert_eq!(eval(c0) * eval(c1) * eval(c2), rhs);
+}
+
+fn test_divisor<C: DivisorCurve>() {
+  for i in 1 ..= 255 {
+    println!("Test iteration {i}");
+
+    // Select points
+    let mut points = vec![];
+    for _ in 0 .. i {
+      points.push(C::random(&mut OsRng));
+    }
+    points.push(-points.iter().sum::<C>());
+    println!("Points {}", points.len());
+
+    // Perform the original check
+    check_divisor(points.clone());
+
+    // Create the divisor
+    let divisor = new_divisor::<C>(&points).unwrap();
+
+    // For a divisor interpolating 256 points, as one does when interpreting a 255-bit discrete log
+    // with the result of its scalar multiplication against a fixed generator, the lengths of the
+    // yx/x coefficients shouldn't supersede the following bounds
+    assert!((divisor.yx_coefficients.first().unwrap_or(&vec![]).len()) <= 126);
+    assert!((divisor.x_coefficients.len() - 1) <= 127);
+    assert!(
+      (1 + divisor.yx_coefficients.first().unwrap_or(&vec![]).len() +
+        (divisor.x_coefficients.len() - 1) +
+        1) <=
+        255
+    );
+
+    // Decide challgenges
+    let c0 = C::random(&mut OsRng);
+    let c1 = C::random(&mut OsRng);
+    let c2 = -(c0 + c1);
+    let (slope, intercept) = crate::slope_intercept::<C>(c0, c1);
+
+    // Perform the Logarithmic derivative check
+    {
+      let dx_over_dz = {
+        let dx = Poly {
+          y_coefficients: vec![],
+          yx_coefficients: vec![],
+          x_coefficients: vec![C::FieldElement::ZERO, C::FieldElement::from(3)],
+          zero_coefficient: C::a(),
+        };
+
+        let dy = Poly {
+          y_coefficients: vec![C::FieldElement::from(2)],
+          yx_coefficients: vec![],
+          x_coefficients: vec![],
+          zero_coefficient: C::FieldElement::ZERO,
+        };
+
+        let dz = (dy.clone() * -slope) + &dx;
+
+        // We want dx/dz, and dz/dx is equal to dy/dx - slope
+        // Sagemath claims this, dy / dz, is the proper inverse
+        (dy, dz)
+      };
+
+      {
+        let sanity_eval = |c| {
+          let (x, y) = C::to_xy(c).unwrap();
+          dx_over_dz.0.eval(x, y) * dx_over_dz.1.eval(x, y).invert().unwrap()
+        };
+        let sanity = sanity_eval(c0) + sanity_eval(c1) + sanity_eval(c2);
+        // This verifies the dx/dz polynomial is correct
+        assert_eq!(sanity, C::FieldElement::ZERO);
+      }
+
+      // Logarithmic derivative check
+      let test = |divisor: Poly<_>| {
+        let (dx, dy) = divisor.differentiate();
+
+        let lhs = |c| {
+          let (x, y) = C::to_xy(c).unwrap();
+
+          let n_0 = (C::FieldElement::from(3) * (x * x)) + C::a();
+          let d_0 = (C::FieldElement::from(2) * y).invert().unwrap();
+          let p_0_n_0 = n_0 * d_0;
+
+          let n_1 = dy.eval(x, y);
+          let first = p_0_n_0 * n_1;
+
+          let second = dx.eval(x, y);
+
+          let d_1 = divisor.eval(x, y);
+
+          let fraction_1_n = first + second;
+          let fraction_1_d = d_1;
+
+          let fraction_2_n = dx_over_dz.0.eval(x, y);
+          let fraction_2_d = dx_over_dz.1.eval(x, y);
+
+          fraction_1_n * fraction_2_n * (fraction_1_d * fraction_2_d).invert().unwrap()
+        };
+        let lhs = lhs(c0) + lhs(c1) + lhs(c2);
+
+        let mut rhs = C::FieldElement::ZERO;
+        for point in &points {
+          let (x, y) = <C as DivisorCurve>::to_xy(*point).unwrap();
+          rhs += (intercept - (y - (slope * x))).invert().unwrap();
+        }
+
+        assert_eq!(lhs, rhs);
+      };
+      // Test the divisor and the divisor with a normalized x coefficient
+      test(divisor.clone());
+      test(divisor.normalize_x_coefficient());
+    }
+  }
+}
+
+fn test_same_point<C: DivisorCurve>() {
+  let mut points = vec![C::random(&mut OsRng)];
+  points.push(points[0]);
+  points.push(-points.iter().sum::<C>());
+  check_divisor(points);
+}
+
+fn test_subset_sum_to_infinity<C: DivisorCurve>() {
+  // Internally, a binary tree algorithm is used
+  // This executes the first pass to end up with [0, 0] for further reductions
+  {
+    let mut points = vec![C::random(&mut OsRng)];
+    points.push(-points[0]);
+
+    let next = C::random(&mut OsRng);
+    points.push(next);
+    points.push(-next);
+    check_divisor(points);
+  }
+
+  // This executes the first pass to end up with [0, X, -X, 0]
+  {
+    let mut points = vec![C::random(&mut OsRng)];
+    points.push(-points[0]);
+
+    let x_1 = C::random(&mut OsRng);
+    let x_2 = C::random(&mut OsRng);
+    points.push(x_1);
+    points.push(x_2);
+
+    points.push(-x_1);
+    points.push(-x_2);
+
+    let next = C::random(&mut OsRng);
+    points.push(next);
+    points.push(-next);
+    check_divisor(points);
+  }
+}
+
+#[test]
+fn test_divisor_pallas() {
+  test_divisor::<Ep>();
+  test_same_point::<Ep>();
+  test_subset_sum_to_infinity::<Ep>();
+}
+
+#[test]
+fn test_divisor_vesta() {
+  test_divisor::<Eq>();
+  test_same_point::<Eq>();
+  test_subset_sum_to_infinity::<Eq>();
+}
+
+#[test]
+fn test_divisor_ed25519() {
+  // Since we're implementing Wei25519 ourselves, check the isomorphism works as expected
+  {
+    let incomplete_add = |p1, p2| {
+      let (x1, y1) = EdwardsPoint::to_xy(p1).unwrap();
+      let (x2, y2) = EdwardsPoint::to_xy(p2).unwrap();
+
+      // mmadd-1998-cmo
+      let u = y2 - y1;
+      let uu = u * u;
+      let v = x2 - x1;
+      let vv = v * v;
+      let vvv = v * vv;
+      let R = vv * x1;
+      let A = uu - vvv - R.double();
+      let x3 = v * A;
+      let y3 = (u * (R - A)) - (vvv * y1);
+      let z3 = vvv;
+
+      // Normalize from XYZ to XY
+      let x3 = x3 * z3.invert().unwrap();
+      let y3 = y3 * z3.invert().unwrap();
+
+      // Edwards addition -> Wei25519 coordinates should be equivalent to Wei25519 addition
+      assert_eq!(EdwardsPoint::to_xy(p1 + p2).unwrap(), (x3, y3));
+    };
+
+    for _ in 0 .. 256 {
+      incomplete_add(EdwardsPoint::random(&mut OsRng), EdwardsPoint::random(&mut OsRng));
+    }
+  }
+
+  test_divisor::<EdwardsPoint>();
+  test_same_point::<EdwardsPoint>();
+  test_subset_sum_to_infinity::<EdwardsPoint>();
+}
--- a/crypto/evrf/divisors/src/tests/poly.rs
+++ b/crypto/evrf/divisors/src/tests/poly.rs
@@ -0,0 +1,129 @@
+use group::ff::Field;
+use pasta_curves::Ep;
+
+use crate::{DivisorCurve, Poly};
+
+type F = <Ep as DivisorCurve>::FieldElement;
+
+#[test]
+fn test_poly() {
+  let zero = F::ZERO;
+  let one = F::ONE;
+
+  {
+    let mut poly = Poly::zero();
+    poly.y_coefficients = vec![zero, one];
+
+    let mut modulus = Poly::zero();
+    modulus.y_coefficients = vec![one];
+    assert_eq!(poly % &modulus, Poly::zero());
+  }
+
+  {
+    let mut poly = Poly::zero();
+    poly.y_coefficients = vec![zero, one];
+
+    let mut squared = Poly::zero();
+    squared.y_coefficients = vec![zero, zero, zero, one];
+    assert_eq!(poly.clone() * poly.clone(), squared);
+  }
+
+  {
+    let mut a = Poly::zero();
+    a.zero_coefficient = F::from(2u64);
+
+    let mut b = Poly::zero();
+    b.zero_coefficient = F::from(3u64);
+
+    let mut res = Poly::zero();
+    res.zero_coefficient = F::from(6u64);
+    assert_eq!(a.clone() * b.clone(), res);
+
+    b.y_coefficients = vec![F::from(4u64)];
+    res.y_coefficients = vec![F::from(8u64)];
+    assert_eq!(a.clone() * b.clone(), res);
+    assert_eq!(b.clone() * a.clone(), res);
+
+    a.x_coefficients = vec![F::from(5u64)];
+    res.x_coefficients = vec![F::from(15u64)];
+    res.yx_coefficients = vec![vec![F::from(20u64)]];
+    assert_eq!(a.clone() * b.clone(), res);
+    assert_eq!(b * a.clone(), res);
+
+    // res is now 20xy + 8*y + 15*x + 6
+    // res ** 2 =
+    //   400*x^2*y^2 + 320*x*y^2 + 64*y^2 + 600*x^2*y + 480*x*y + 96*y + 225*x^2 + 180*x + 36
+
+    let mut squared = Poly::zero();
+    squared.y_coefficients = vec![F::from(96u64), F::from(64u64)];
+    squared.yx_coefficients =
+      vec![vec![F::from(480u64), F::from(600u64)], vec![F::from(320u64), F::from(400u64)]];
+    squared.x_coefficients = vec![F::from(180u64), F::from(225u64)];
+    squared.zero_coefficient = F::from(36u64);
+    assert_eq!(res.clone() * res, squared);
+  }
+}
+
+#[test]
+fn test_differentation() {
+  let random = || F::random(&mut OsRng);
+
+  let input = Poly {
+    y_coefficients: vec![random()],
+    yx_coefficients: vec![vec![random()]],
+    x_coefficients: vec![random(), random(), random()],
+    zero_coefficient: random(),
+  };
+  let (diff_x, diff_y) = input.differentiate();
+  assert_eq!(
+    diff_x,
+    Poly {
+      y_coefficients: vec![input.yx_coefficients[0][0]],
+      yx_coefficients: vec![],
+      x_coefficients: vec![
+        F::from(2) * input.x_coefficients[1],
+        F::from(3) * input.x_coefficients[2]
+      ],
+      zero_coefficient: input.x_coefficients[0],
+    }
+  );
+  assert_eq!(
+    diff_y,
+    Poly {
+      y_coefficients: vec![],
+      yx_coefficients: vec![],
+      x_coefficients: vec![input.yx_coefficients[0][0]],
+      zero_coefficient: input.y_coefficients[0],
+    }
+  );
+
+  let input = Poly {
+    y_coefficients: vec![random()],
+    yx_coefficients: vec![vec![random(), random()]],
+    x_coefficients: vec![random(), random(), random(), random()],
+    zero_coefficient: random(),
+  };
+  let (diff_x, diff_y) = input.differentiate();
+  assert_eq!(
+    diff_x,
+    Poly {
+      y_coefficients: vec![input.yx_coefficients[0][0]],
+      yx_coefficients: vec![vec![F::from(2) * input.yx_coefficients[0][1]]],
+      x_coefficients: vec![
+        F::from(2) * input.x_coefficients[1],
+        F::from(3) * input.x_coefficients[2],
+        F::from(4) * input.x_coefficients[3],
+      ],
+      zero_coefficient: input.x_coefficients[0],
+    }
+  );
+  assert_eq!(
+    diff_y,
+    Poly {
+      y_coefficients: vec![],
+      yx_coefficients: vec![],
+      x_coefficients: vec![input.yx_coefficients[0][0], input.yx_coefficients[0][1]],
+      zero_coefficient: input.y_coefficients[0],
+    }
+  );
+}
--- a/crypto/evrf/ec-gadgets/Cargo.toml
+++ b/crypto/evrf/ec-gadgets/Cargo.toml
@@ -0,0 +1,20 @@
+[package]
+name = "generalized-bulletproofs-ec-gadgets"
+version = "0.1.0"
+description = "Gadgets for working with an embedded Elliptic Curve in a Generalized Bulletproofs circuit"
+license = "MIT"
+repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/ec-gadgets"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["bulletproofs", "circuit", "divisors"]
+edition = "2021"
+
+[package.metadata.docs.rs]
+all-features = true
+rustdoc-args = ["--cfg", "docsrs"]
+
+[dependencies]
+generic-array = { version = "1", default-features = false, features = ["alloc"] }
+
+ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
+
+generalized-bulletproofs-circuit-abstraction = { path = "../circuit-abstraction" }
--- a/crypto/evrf/ec-gadgets/LICENSE
+++ b/crypto/evrf/ec-gadgets/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2024 Luke Parker
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
--- a/crypto/evrf/ec-gadgets/README.md
+++ b/crypto/evrf/ec-gadgets/README.md
@@ -0,0 +1,3 @@
+# Generalized Bulletproofs Circuit Abstraction
+
+A circuit abstraction around `generalized-bulletproofs`.
--- a/crypto/evrf/ec-gadgets/src/dlog.rs
+++ b/crypto/evrf/ec-gadgets/src/dlog.rs
@@ -0,0 +1,529 @@
+use core::fmt;
+
+use ciphersuite::{
+  group::ff::{Field, PrimeField, BatchInverter},
+  Ciphersuite,
+};
+
+use generalized_bulletproofs_circuit_abstraction::*;
+
+use crate::*;
+
+/// Parameters for a discrete logarithm proof.
+///
+/// This isn't required to be implemented by the Field/Group/Ciphersuite, solely a struct, to
+/// enable parameterization of discrete log proofs to the bitlength of the discrete logarithm.
+/// While that may be F::NUM_BITS, a discrete log proof a for a full scalar, it could also be 64,
+/// a discrete log proof for a u64 (such as if opening a Pedersen commitment in-circuit).
+pub trait DiscreteLogParameters {
+  /// The amount of bits used to represent a scalar.
+  type ScalarBits: ArrayLength;
+
+  /// The amount of x**i coefficients in a divisor.
+  ///
+  /// This is the amount of points in a divisor (the amount of bits in a scalar, plus one) divided
+  /// by two.
+  type XCoefficients: ArrayLength;
+
+  /// The amount of x**i coefficients in a divisor, minus one.
+  type XCoefficientsMinusOne: ArrayLength;
+
+  /// The amount of y x**i coefficients in a divisor.
+  ///
+  /// This is the amount of points in a divisor (the amount of bits in a scalar, plus one) plus
+  /// one, divided by two, minus two.
+  type YxCoefficients: ArrayLength;
+}
+
+/// A tabled generator for proving/verifying discrete logarithm claims.
+#[derive(Clone)]
+pub struct GeneratorTable<F: PrimeField, Parameters: DiscreteLogParameters>(
+  GenericArray<(F, F), Parameters::ScalarBits>,
+);
+
+impl<F: PrimeField, Parameters: DiscreteLogParameters> fmt::Debug
+  for GeneratorTable<F, Parameters>
+{
+  fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
+    fmt
+      .debug_struct("GeneratorTable")
+      .field("x", &self.0[0].0)
+      .field("y", &self.0[0].1)
+      .finish_non_exhaustive()
+  }
+}
+
+impl<F: PrimeField, Parameters: DiscreteLogParameters> GeneratorTable<F, Parameters> {
+  /// Create a new table for this generator.
+  ///
+  /// The generator is assumed to be well-formed and on-curve. This function may panic if it's not.
+  pub fn new(curve: &CurveSpec<F>, generator_x: F, generator_y: F) -> Self {
+    // mdbl-2007-bl
+    fn dbl<F: PrimeField>(a: F, x1: F, y1: F) -> (F, F) {
+      let xx = x1 * x1;
+      let w = a + (xx + xx.double());
+      let y1y1 = y1 * y1;
+      let r = y1y1 + y1y1;
+      let sss = (y1 * r).double().double();
+      let rr = r * r;
+
+      let b = x1 + r;
+      let b = (b * b) - xx - rr;
+
+      let h = (w * w) - b.double();
+      let x3 = h.double() * y1;
+      let y3 = (w * (b - h)) - rr.double();
+      let z3 = sss;
+
+      // Normalize from XYZ to XY
+      let z3_inv = z3.invert().unwrap();
+      let x3 = x3 * z3_inv;
+      let y3 = y3 * z3_inv;
+
+      (x3, y3)
+    }
+
+    let mut res = Self(GenericArray::default());
+    res.0[0] = (generator_x, generator_y);
+    for i in 1 .. Parameters::ScalarBits::USIZE {
+      let last = res.0[i - 1];
+      res.0[i] = dbl(curve.a, last.0, last.1);
+    }
+
+    res
+  }
+}
+
+/// A representation of the divisor.
+///
+/// The coefficient for x**1 is explicitly excluded as it's expected to be normalized to 1.
+#[derive(Clone)]
+pub struct Divisor<Parameters: DiscreteLogParameters> {
+  /// The coefficient for the `y` term of the divisor.
+  ///
+  /// There is never more than one `y**i x**0` coefficient as the leading term of the modulus is
+  /// `y**2`. It's assumed the coefficient is non-zero (and present) as it will be for any divisor
+  /// exceeding trivial complexity.
+  pub y: Variable,
+  /// The coefficients for the `y**1 x**i` terms of the polynomial.
+  // This subtraction enforces the divisor to have at least 4 points which is acceptable.
+  // TODO: Double check these constants
+  pub yx: GenericArray<Variable, Parameters::YxCoefficients>,
+  /// The coefficients for the `x**i` terms of the polynomial, skipping x**1.
+  ///
+  /// x**1 is skipped as it's expected to be normalized to 1, and therefore constant, in order to
+  /// ensure the divisor is non-zero (as necessary for the proof to be complete).
+  // Subtract 1 from the length due to skipping the coefficient for x**1
+  pub x_from_power_of_2: GenericArray<Variable, Parameters::XCoefficientsMinusOne>,
+  /// The constant term in the polynomial (alternatively, the coefficient for y**0 x**0).
+  pub zero: Variable,
+}
+
+/// A point, its discrete logarithm, and the divisor to prove it.
+#[derive(Clone)]
+pub struct PointWithDlog<Parameters: DiscreteLogParameters> {
+  /// The point which is supposedly the result of scaling the generator by the discrete logarithm.
+  pub point: (Variable, Variable),
+  /// The discrete logarithm, represented as coefficients of a polynomial of 2**i.
+  pub dlog: GenericArray<Variable, Parameters::ScalarBits>,
+  /// The divisor interpolating the relevant doublings of generator with the inverse of the point.
+  pub divisor: Divisor<Parameters>,
+}
+
+/// A struct containing a point used for the evaluation of a divisor.
+///
+/// Preprocesses and caches as much of the calculation as possible to minimize work upon reuse of
+/// challenge points.
+struct ChallengePoint<F: PrimeField, Parameters: DiscreteLogParameters> {
+  y: F,
+  yx: GenericArray<F, Parameters::YxCoefficients>,
+  x: GenericArray<F, Parameters::XCoefficients>,
+  p_0_n_0: F,
+  x_p_0_n_0: GenericArray<F, Parameters::YxCoefficients>,
+  p_1_n: F,
+  p_1_d: F,
+}
+
+impl<F: PrimeField, Parameters: DiscreteLogParameters> ChallengePoint<F, Parameters> {
+  fn new(
+    curve: &CurveSpec<F>,
+    // The slope between all of the challenge points
+    slope: F,
+    // The x and y coordinates
+    x: F,
+    y: F,
+    // The inversion of twice the y coordinate
+    // We accept this as an argument so that the caller can calculcate these with a batch inversion
+    inv_two_y: F,
+  ) -> Self {
+    // Powers of x, skipping x**0
+    let divisor_x_len = Parameters::XCoefficients::USIZE;
+    let mut x_pows = GenericArray::default();
+    x_pows[0] = x;
+    for i in 1 .. divisor_x_len {
+      let last = x_pows[i - 1];
+      x_pows[i] = last * x;
+    }
+
+    // Powers of x multiplied by y
+    let divisor_yx_len = Parameters::YxCoefficients::USIZE;
+    let mut yx = GenericArray::default();
+    // Skips x**0
+    yx[0] = y * x;
+    for i in 1 .. divisor_yx_len {
+      let last = yx[i - 1];
+      yx[i] = last * x;
+    }
+
+    let x_sq = x.square();
+    let three_x_sq = x_sq.double() + x_sq;
+    let three_x_sq_plus_a = three_x_sq + curve.a;
+    let two_y = y.double();
+
+    // p_0_n_0 from `DivisorChallenge`
+    let p_0_n_0 = three_x_sq_plus_a * inv_two_y;
+    let mut x_p_0_n_0 = GenericArray::default();
+    // Since this iterates over x, which skips x**0, this also skips p_0_n_0 x**0
+    for (i, x) in x_pows.iter().take(divisor_yx_len).enumerate() {
+      x_p_0_n_0[i] = p_0_n_0 * x;
+    }
+
+    // p_1_n from `DivisorChallenge`
+    let p_1_n = two_y;
+    // p_1_d from `DivisorChallenge`
+    let p_1_d = (-slope * p_1_n) + three_x_sq_plus_a;
+
+    ChallengePoint { x: x_pows, y, yx, p_0_n_0, x_p_0_n_0, p_1_n, p_1_d }
+  }
+}
+
+// `DivisorChallenge` from the section `Discrete Log Proof`
+fn divisor_challenge_eval<C: Ciphersuite, Parameters: DiscreteLogParameters>(
+  circuit: &mut Circuit<C>,
+  divisor: &Divisor<Parameters>,
+  challenge: &ChallengePoint<C::F, Parameters>,
+) -> Variable {
+  // The evaluation of the divisor differentiated by y, further multiplied by p_0_n_0
+  // Differentation drops everything without a y coefficient, and drops what remains by a power
+  // of y
+  // (y**1 -> y**0, yx**i -> x**i)
+  // This aligns with p_0_n_1  from `DivisorChallenge`
+  let p_0_n_1 = {
+    let mut p_0_n_1 = LinComb::empty().term(challenge.p_0_n_0, divisor.y);
+    for (j, var) in divisor.yx.iter().enumerate() {
+      // This does not raise by `j + 1` as x_p_0_n_0 omits x**0
+      p_0_n_1 = p_0_n_1.term(challenge.x_p_0_n_0[j], *var);
+    }
+    p_0_n_1
+  };
+
+  // The evaluation of the divisor differentiated by x
+  // This aligns with p_0_n_2  from `DivisorChallenge`
+  let p_0_n_2 = {
+    // The coefficient for x**1 is 1, so 1 becomes the new zero coefficient
+    let mut p_0_n_2 = LinComb::empty().constant(C::F::ONE);
+
+    // Handle the new y coefficient
+    p_0_n_2 = p_0_n_2.term(challenge.y, divisor.yx[0]);
+
+    // Handle the new yx coefficients
+    for (j, yx) in divisor.yx.iter().enumerate().skip(1) {
+      // For the power which was shifted down, we multiply this coefficient
+      // 3 x**2 -> 2 * 3 x**1
+      let original_power_of_x = C::F::from(u64::try_from(j + 1).unwrap());
+      // `j - 1` so `j = 1` indexes yx[0] as yx[0] is the y x**1
+      // (yx omits y x**0)
+      let this_weight = original_power_of_x * challenge.yx[j - 1];
+      p_0_n_2 = p_0_n_2.term(this_weight, *yx);
+    }
+
+    // Handle the x coefficients
+    // We don't skip the first one as `x_from_power_of_2` already omits x**1
+    for (i, x) in divisor.x_from_power_of_2.iter().enumerate() {
+      // i + 2 as the paper expects i to start from 1 and be + 1, yet we start from 0
+      let original_power_of_x = C::F::from(u64::try_from(i + 2).unwrap());
+      // Still x[i] as x[0] is x**1
+      let this_weight = original_power_of_x * challenge.x[i];
+
+      p_0_n_2 = p_0_n_2.term(this_weight, *x);
+    }
+
+    p_0_n_2
+  };
+
+  // p_0_n from `DivisorChallenge`
+  let p_0_n = p_0_n_1 + &p_0_n_2;
+
+  // Evaluation of the divisor
+  // p_0_d from `DivisorChallenge`
+  let p_0_d = {
+    let mut p_0_d = LinComb::empty().term(challenge.y, divisor.y);
+
+    for (var, c_yx) in divisor.yx.iter().zip(&challenge.yx) {
+      p_0_d = p_0_d.term(*c_yx, *var);
+    }
+
+    for (i, var) in divisor.x_from_power_of_2.iter().enumerate() {
+      // This `i+1` is preserved, despite most not being as x omits x**0, as this assumes we
+      // start with `i=1`
+      p_0_d = p_0_d.term(challenge.x[i + 1], *var);
+    }
+
+    // Adding x effectively adds a `1 x` term, ensuring the divisor isn't 0
+    p_0_d.term(C::F::ONE, divisor.zero).constant(challenge.x[0])
+  };
+
+  // Calculate the joint numerator
+  // p_n from `DivisorChallenge`
+  let p_n = p_0_n * challenge.p_1_n;
+  // Calculate the joint denominator
+  // p_d from `DivisorChallenge`
+  let p_d = p_0_d * challenge.p_1_d;
+
+  // We want `n / d = o`
+  // `n / d = o` == `n = d * o`
+  // These are safe unwraps as they're solely done by the prover and should always be non-zero
+  let witness =
+    circuit.eval(&p_d).map(|p_d| (p_d, circuit.eval(&p_n).unwrap() * p_d.invert().unwrap()));
+  let (_l, o, n_claim) = circuit.mul(Some(p_d), None, witness);
+  circuit.equality(p_n, &n_claim.into());
+  o
+}
+
+/// A challenge to evaluate divisors with.
+///
+/// This challenge must be sampled after writing the commitments to the transcript. This challenge
+/// is reusable across various divisors.
+pub struct DiscreteLogChallenge<F: PrimeField, Parameters: DiscreteLogParameters> {
+  c0: ChallengePoint<F, Parameters>,
+  c1: ChallengePoint<F, Parameters>,
+  c2: ChallengePoint<F, Parameters>,
+  slope: F,
+  intercept: F,
+}
+
+/// A generator which has been challenged and is ready for use in evaluating discrete logarithm
+/// claims.
+pub struct ChallengedGenerator<F: PrimeField, Parameters: DiscreteLogParameters>(
+  GenericArray<F, Parameters::ScalarBits>,
+);
+
+/// Gadgets for proving the discrete logarithm of points on an elliptic curve defined over the
+/// scalar field of the curve of the Bulletproof.
+pub trait EcDlogGadgets<C: Ciphersuite> {
+  /// Sample a challenge for a series of discrete logarithm claims.
+  ///
+  /// This must be called after writing the commitments to the transcript.
+  ///
+  /// The generators are assumed to be non-empty. They are not transcripted. If your generators are
+  /// dynamic, they must be properly transcripted into the context.
+  ///
+  /// May panic/have undefined behavior if an assumption is broken.
+  #[allow(clippy::type_complexity)]
+  fn discrete_log_challenge<T: Transcript, Parameters: DiscreteLogParameters>(
+    &self,
+    transcript: &mut T,
+    curve: &CurveSpec<C::F>,
+    generators: &[GeneratorTable<C::F, Parameters>],
+  ) -> (DiscreteLogChallenge<C::F, Parameters>, Vec<ChallengedGenerator<C::F, Parameters>>);
+
+  /// Prove this point has the specified discrete logarithm over the specified generator.
+  ///
+  /// The discrete logarithm is not validated to be in a canonical form. The only guarantee made on
+  /// it is that it's a consistent representation of _a_ discrete logarithm (reuse won't enable
+  /// re-interpretation as a distinct discrete logarithm).
+  ///
+  /// This does ensure the point is on-curve.
+  ///
+  /// This MUST only be called with `Variable`s present within commitments.
+  ///
+  /// May panic/have undefined behavior if an assumption is broken, or if passed an invalid
+  /// witness.
+  fn discrete_log<Parameters: DiscreteLogParameters>(
+    &mut self,
+    curve: &CurveSpec<C::F>,
+    point: PointWithDlog<Parameters>,
+    challenge: &DiscreteLogChallenge<C::F, Parameters>,
+    challenged_generator: &ChallengedGenerator<C::F, Parameters>,
+  ) -> OnCurve;
+}
+
+impl<C: Ciphersuite> EcDlogGadgets<C> for Circuit<C> {
+  // This is part of `DiscreteLog` from `Discrete Log Proof`, specifically, the challenges and
+  // the calculations dependent solely on them
+  fn discrete_log_challenge<T: Transcript, Parameters: DiscreteLogParameters>(
+    &self,
+    transcript: &mut T,
+    curve: &CurveSpec<C::F>,
+    generators: &[GeneratorTable<C::F, Parameters>],
+  ) -> (DiscreteLogChallenge<C::F, Parameters>, Vec<ChallengedGenerator<C::F, Parameters>>) {
+    // Get the challenge points
+    // TODO: Implement a proper hash to curve
+    let (c0_x, c0_y) = loop {
+      let c0_x: C::F = transcript.challenge();
+      let Some(c0_y) =
+        Option::<C::F>::from(((c0_x.square() * c0_x) + (curve.a * c0_x) + curve.b).sqrt())
+      else {
+        continue;
+      };
+      // Takes the even y coordinate as to not be dependent on whatever root the above sqrt
+      // happens to returns
+      // TODO: Randomly select which to take
+      break (c0_x, if bool::from(c0_y.is_odd()) { -c0_y } else { c0_y });
+    };
+    let (c1_x, c1_y) = loop {
+      let c1_x: C::F = transcript.challenge();
+      let Some(c1_y) =
+        Option::<C::F>::from(((c1_x.square() * c1_x) + (curve.a * c1_x) + curve.b).sqrt())
+      else {
+        continue;
+      };
+      break (c1_x, if bool::from(c1_y.is_odd()) { -c1_y } else { c1_y });
+    };
+
+    // mmadd-1998-cmo
+    fn incomplete_add<F: PrimeField>(x1: F, y1: F, x2: F, y2: F) -> Option<(F, F)> {
+      if x1 == x2 {
+        None?
+      }
+
+      let u = y2 - y1;
+      let uu = u * u;
+      let v = x2 - x1;
+      let vv = v * v;
+      let vvv = v * vv;
+      let r = vv * x1;
+      let a = uu - vvv - r.double();
+      let x3 = v * a;
+      let y3 = (u * (r - a)) - (vvv * y1);
+      let z3 = vvv;
+
+      // Normalize from XYZ to XY
+      let z3_inv = Option::<F>::from(z3.invert())?;
+      let x3 = x3 * z3_inv;
+      let y3 = y3 * z3_inv;
+
+      Some((x3, y3))
+    }
+
+    let (c2_x, c2_y) = incomplete_add::<C::F>(c0_x, c0_y, c1_x, c1_y)
+      .expect("randomly selected points shared an x coordinate");
+    // We want C0, C1, C2 = -(C0 + C1)
+    let c2_y = -c2_y;
+
+    // Calculate the slope and intercept
+    // Safe invert as these x coordinates must be distinct due to passing the above incomplete_add
+    let slope = (c1_y - c0_y) * (c1_x - c0_x).invert().unwrap();
+    let intercept = c0_y - (slope * c0_x);
+
+    // Calculate the inversions for 2 c_y (for each c) and all of the challenged generators
+    let mut inversions = vec![C::F::ZERO; 3 + (generators.len() * Parameters::ScalarBits::USIZE)];
+
+    // Needed for the left-hand side eval
+    {
+      inversions[0] = c0_y.double();
+      inversions[1] = c1_y.double();
+      inversions[2] = c2_y.double();
+    }
+
+    // Perform the inversions for the generators
+    for (i, generator) in generators.iter().enumerate() {
+      // Needed for the right-hand side eval
+      for (j, generator) in generator.0.iter().enumerate() {
+        // `DiscreteLog` has weights of `(mu - (G_i.y + (slope * G_i.x)))**-1` in its last line
+        inversions[3 + (i * Parameters::ScalarBits::USIZE) + j] =
+          intercept - (generator.1 - (slope * generator.0));
+      }
+    }
+    for challenge_inversion in &inversions {
+      // This should be unreachable barring negligible probability
+      if challenge_inversion.is_zero().into() {
+        panic!("trying to invert 0");
+      }
+    }
+    let mut scratch = vec![C::F::ZERO; inversions.len()];
+    let _ = BatchInverter::invert_with_external_scratch(&mut inversions, &mut scratch);
+
+    let mut inversions = inversions.into_iter();
+    let inv_c0_two_y = inversions.next().unwrap();
+    let inv_c1_two_y = inversions.next().unwrap();
+    let inv_c2_two_y = inversions.next().unwrap();
+
+    let c0 = ChallengePoint::new(curve, slope, c0_x, c0_y, inv_c0_two_y);
+    let c1 = ChallengePoint::new(curve, slope, c1_x, c1_y, inv_c1_two_y);
+    let c2 = ChallengePoint::new(curve, slope, c2_x, c2_y, inv_c2_two_y);
+
+    // Fill in the inverted values
+    let mut challenged_generators = Vec::with_capacity(generators.len());
+    for _ in 0 .. generators.len() {
+      let mut challenged_generator = GenericArray::default();
+      for i in 0 .. Parameters::ScalarBits::USIZE {
+        challenged_generator[i] = inversions.next().unwrap();
+      }
+      challenged_generators.push(ChallengedGenerator(challenged_generator));
+    }
+
+    (DiscreteLogChallenge { c0, c1, c2, slope, intercept }, challenged_generators)
+  }
+
+  // `DiscreteLog` from `Discrete Log Proof`
+  fn discrete_log<Parameters: DiscreteLogParameters>(
+    &mut self,
+    curve: &CurveSpec<C::F>,
+    point: PointWithDlog<Parameters>,
+    challenge: &DiscreteLogChallenge<C::F, Parameters>,
+    challenged_generator: &ChallengedGenerator<C::F, Parameters>,
+  ) -> OnCurve {
+    let PointWithDlog { divisor, dlog, point } = point;
+
+    // Ensure this is being safely called
+    let arg_iter = [point.0, point.1, divisor.y, divisor.zero];
+    let arg_iter = arg_iter.iter().chain(divisor.yx.iter());
+    let arg_iter = arg_iter.chain(divisor.x_from_power_of_2.iter());
+    let arg_iter = arg_iter.chain(dlog.iter());
+    for variable in arg_iter {
+      debug_assert!(
+        matches!(variable, Variable::CG { .. } | Variable::CH { .. } | Variable::V(_)),
+        "discrete log proofs requires all arguments belong to commitments",
+      );
+    }
+
+    // Check the point is on curve
+    let point = self.on_curve(curve, point);
+
+    // The challenge has already been sampled so those lines aren't necessary
+
+    // lhs from the paper, evaluating the divisor
+    let lhs_eval = LinComb::from(divisor_challenge_eval(self, &divisor, &challenge.c0)) +
+      &LinComb::from(divisor_challenge_eval(self, &divisor, &challenge.c1)) +
+      &LinComb::from(divisor_challenge_eval(self, &divisor, &challenge.c2));
+
+    // Interpolate the doublings of the generator
+    let mut rhs_eval = LinComb::empty();
+    // We call this `bit` yet it's not constrained to being a bit
+    // It's presumed to be yet may be malleated
+    for (bit, weight) in dlog.into_iter().zip(&challenged_generator.0) {
+      rhs_eval = rhs_eval.term(*weight, bit);
+    }
+
+    // Interpolate the output point
+    // intercept - (y - (slope * x))
+    // intercept - y + (slope * x)
+    // -y + (slope * x) + intercept
+    // EXCEPT the output point we're proving the discrete log for isn't the one interpolated
+    // Its negative is, so -y becomes y
+    // y + (slope * x) + intercept
+    let output_interpolation = LinComb::empty()
+      .constant(challenge.intercept)
+      .term(C::F::ONE, point.y)
+      .term(challenge.slope, point.x);
+    let output_interpolation_eval = self.eval(&output_interpolation);
+    let (_output_interpolation, inverse) =
+      self.inverse(Some(output_interpolation), output_interpolation_eval);
+    rhs_eval = rhs_eval.term(C::F::ONE, inverse);
+
+    self.equality(lhs_eval, &rhs_eval);
+
+    point
+  }
+}
--- a/crypto/evrf/ec-gadgets/src/lib.rs
+++ b/crypto/evrf/ec-gadgets/src/lib.rs
@@ -0,0 +1,130 @@
+#![cfg_attr(docsrs, feature(doc_auto_cfg))]
+#![doc = include_str!("../README.md")]
+#![deny(missing_docs)]
+#![allow(non_snake_case)]
+
+use generic_array::{typenum::Unsigned, ArrayLength, GenericArray};
+
+use ciphersuite::{group::ff::Field, Ciphersuite};
+
+use generalized_bulletproofs_circuit_abstraction::*;
+
+mod dlog;
+pub use dlog::*;
+
+/// The specification of a short Weierstrass curve over the field `F`.
+///
+/// The short Weierstrass curve is defined via the formula `y**2 = x**3 + a*x + b`.
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub struct CurveSpec<F> {
+  /// The `a` constant in the curve formula.
+  pub a: F,
+  /// The `b` constant in the curve formula.
+  pub b: F,
+}
+
+/// A struct for a point on a towered curve which has been confirmed to be on-curve.
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub struct OnCurve {
+  pub(crate) x: Variable,
+  pub(crate) y: Variable,
+}
+
+impl OnCurve {
+  /// The variable for the x-coordinate.
+  pub fn x(&self) -> Variable {
+    self.x
+  }
+  /// The variable for the y-coordinate.
+  pub fn y(&self) -> Variable {
+    self.y
+  }
+}
+
+/// Gadgets for working with points on an elliptic curve defined over the scalar field of the curve
+/// of the Bulletproof.
+pub trait EcGadgets<C: Ciphersuite> {
+  /// Constrain an x and y coordinate as being on the specified curve.
+  ///
+  /// The specified curve is defined over the scalar field of the curve this proof is performed
+  /// over, offering efficient arithmetic.
+  ///
+  /// May panic if the prover and the point is not actually on-curve.
+  fn on_curve(&mut self, curve: &CurveSpec<C::F>, point: (Variable, Variable)) -> OnCurve;
+
+  /// Perform incomplete addition for a fixed point and an on-curve point.
+  ///
+  /// `a` is the x and y coordinates of the fixed point, assumed to be on-curve.
+  ///
+  /// `b` is a point prior checked to be on-curve.
+  ///
+  /// `c` is a point prior checked to be on-curve, constrained to be the sum of `a` and `b`.
+  ///
+  /// `a` and `b` are checked to have distinct x coordinates.
+  ///
+  /// This function may panic if `a` is malformed or if the prover and `c` is not actually the sum
+  /// of `a` and `b`.
+  fn incomplete_add_fixed(&mut self, a: (C::F, C::F), b: OnCurve, c: OnCurve) -> OnCurve;
+}
+
+impl<C: Ciphersuite> EcGadgets<C> for Circuit<C> {
+  fn on_curve(&mut self, curve: &CurveSpec<C::F>, (x, y): (Variable, Variable)) -> OnCurve {
+    let x_eval = self.eval(&LinComb::from(x));
+    let (_x, _x_2, x2) =
+      self.mul(Some(LinComb::from(x)), Some(LinComb::from(x)), x_eval.map(|x| (x, x)));
+    let (_x, _x_2, x3) =
+      self.mul(Some(LinComb::from(x2)), Some(LinComb::from(x)), x_eval.map(|x| (x * x, x)));
+    let expected_y2 = LinComb::from(x3).term(curve.a, x).constant(curve.b);
+
+    let y_eval = self.eval(&LinComb::from(y));
+    let (_y, _y_2, y2) =
+      self.mul(Some(LinComb::from(y)), Some(LinComb::from(y)), y_eval.map(|y| (y, y)));
+
+    self.equality(y2.into(), &expected_y2);
+
+    OnCurve { x, y }
+  }
+
+  fn incomplete_add_fixed(&mut self, a: (C::F, C::F), b: OnCurve, c: OnCurve) -> OnCurve {
+    // Check b.x != a.0
+    {
+      let bx_lincomb = LinComb::from(b.x);
+      let bx_eval = self.eval(&bx_lincomb);
+      self.inequality(bx_lincomb, &LinComb::empty().constant(a.0), bx_eval.map(|bx| (bx, a.0)));
+    }
+
+    let (x0, y0) = (a.0, a.1);
+    let (x1, y1) = (b.x, b.y);
+    let (x2, y2) = (c.x, c.y);
+
+    let slope_eval = self.eval(&LinComb::from(x1)).map(|x1| {
+      let y1 = self.eval(&LinComb::from(b.y)).unwrap();
+
+      (y1 - y0) * (x1 - x0).invert().unwrap()
+    });
+
+    // slope * (x1 - x0) = y1 - y0
+    let x1_minus_x0 = LinComb::from(x1).constant(-x0);
+    let x1_minus_x0_eval = self.eval(&x1_minus_x0);
+    let (slope, _r, o) =
+      self.mul(None, Some(x1_minus_x0), slope_eval.map(|slope| (slope, x1_minus_x0_eval.unwrap())));
+    self.equality(LinComb::from(o), &LinComb::from(y1).constant(-y0));
+
+    // slope * (x2 - x0) = -y2 - y0
+    let x2_minus_x0 = LinComb::from(x2).constant(-x0);
+    let x2_minus_x0_eval = self.eval(&x2_minus_x0);
+    let (_slope, _x2_minus_x0, o) = self.mul(
+      Some(slope.into()),
+      Some(x2_minus_x0),
+      slope_eval.map(|slope| (slope, x2_minus_x0_eval.unwrap())),
+    );
+    self.equality(o.into(), &LinComb::empty().term(-C::F::ONE, y2).constant(-y0));
+
+    // slope * slope = x0 + x1 + x2
+    let (_slope, _slope_2, o) =
+      self.mul(Some(slope.into()), Some(slope.into()), slope_eval.map(|slope| (slope, slope)));
+    self.equality(o.into(), &LinComb::from(x1).term(C::F::ONE, x2).constant(x0));
+
+    OnCurve { x: x2, y: y2 }
+  }
+}
--- a/crypto/evrf/embedwards25519/Cargo.toml
+++ b/crypto/evrf/embedwards25519/Cargo.toml
@@ -0,0 +1,39 @@
+[package]
+name = "embedwards25519"
+version = "0.1.0"
+description = "A curve defined over the Ed25519 scalar field"
+license = "MIT"
+repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/embedwards25519"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["curve25519", "ed25519", "ristretto255", "group"]
+edition = "2021"
+
+[package.metadata.docs.rs]
+all-features = true
+rustdoc-args = ["--cfg", "docsrs"]
+
+[dependencies]
+rustversion = "1"
+hex-literal = { version = "0.4", default-features = false }
+
+rand_core = { version = "0.6", default-features = false, features = ["std"] }
+
+zeroize = { version = "^1.5", default-features = false, features = ["std", "zeroize_derive"] }
+subtle = { version = "^2.4", default-features = false, features = ["std"] }
+
+generic-array = { version = "0.14", default-features = false }
+crypto-bigint = { version = "0.5", default-features = false, features = ["zeroize"] }
+
+dalek-ff-group = { path = "../../dalek-ff-group", version = "0.4", default-features = false }
+
+blake2 = { version = "0.10", default-features = false, features = ["std"] }
+ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
+ec-divisors = { path = "../divisors" }
+generalized-bulletproofs-ec-gadgets = { path = "../ec-gadgets" }
+
+[dev-dependencies]
+hex = "0.4"
+
+rand_core = { version = "0.6", features = ["std"] }
+
+ff-group-tests = { path = "../../ff-group-tests" }
--- a/crypto/evrf/embedwards25519/LICENSE
+++ b/crypto/evrf/embedwards25519/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2022-2024 Luke Parker
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
--- a/crypto/evrf/embedwards25519/README.md
+++ b/crypto/evrf/embedwards25519/README.md
@@ -0,0 +1,21 @@
+# embedwards25519
+
+A curve defined over the Ed25519 scalar field.
+
+This curve was found via
+[tevador's script](https://gist.github.com/tevador/4524c2092178df08996487d4e272b096)
+for finding curves (specifically, curve cycles), modified to search for curves
+whose field is the Ed25519 scalar field (not the Ed25519 field).
+
+```
+p = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
+q = 0x0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96b
+D = -420435
+y^2 = x^3 - 3*x + 4188043517836764736459661287169077812555441231147410753119540549773825148767
+```
+
+The embedding degree is `(q-1)/2`.
+
+This curve should not be used with single-coordinate ladders, and points should
+always be represented in a compressed form (preventing receiving off-curve
+points).
--- a/crypto/evrf/embedwards25519/src/backend.rs
+++ b/crypto/evrf/embedwards25519/src/backend.rs
@@ -0,0 +1,293 @@
+use zeroize::Zeroize;
+
+// Use black_box when possible
+#[rustversion::since(1.66)]
+use core::hint::black_box;
+#[rustversion::before(1.66)]
+fn black_box<T>(val: T) -> T {
+  val
+}
+
+pub(crate) fn u8_from_bool(bit_ref: &mut bool) -> u8 {
+  let bit_ref = black_box(bit_ref);
+
+  let mut bit = black_box(*bit_ref);
+  let res = black_box(bit as u8);
+  bit.zeroize();
+  debug_assert!((res | 1) == 1);
+
+  bit_ref.zeroize();
+  res
+}
+
+macro_rules! math_op {
+  (
+    $Value: ident,
+    $Other: ident,
+    $Op: ident,
+    $op_fn: ident,
+    $Assign: ident,
+    $assign_fn: ident,
+    $function: expr
+  ) => {
+    impl $Op<$Other> for $Value {
+      type Output = $Value;
+      fn $op_fn(self, other: $Other) -> Self::Output {
+        Self($function(self.0, other.0))
+      }
+    }
+    impl $Assign<$Other> for $Value {
+      fn $assign_fn(&mut self, other: $Other) {
+        self.0 = $function(self.0, other.0);
+      }
+    }
+    impl<'a> $Op<&'a $Other> for $Value {
+      type Output = $Value;
+      fn $op_fn(self, other: &'a $Other) -> Self::Output {
+        Self($function(self.0, other.0))
+      }
+    }
+    impl<'a> $Assign<&'a $Other> for $Value {
+      fn $assign_fn(&mut self, other: &'a $Other) {
+        self.0 = $function(self.0, other.0);
+      }
+    }
+  };
+}
+
+macro_rules! from_wrapper {
+  ($wrapper: ident, $inner: ident, $uint: ident) => {
+    impl From<$uint> for $wrapper {
+      fn from(a: $uint) -> $wrapper {
+        Self(Residue::new(&$inner::from(a)))
+      }
+    }
+  };
+}
+
+macro_rules! field {
+  (
+    $FieldName: ident,
+    $ResidueType: ident,
+
+    $MODULUS_STR: ident,
+    $MODULUS: ident,
+    $WIDE_MODULUS: ident,
+
+    $NUM_BITS: literal,
+    $MULTIPLICATIVE_GENERATOR: literal,
+    $S: literal,
+    $ROOT_OF_UNITY: literal,
+    $DELTA: literal,
+  ) => {
+    use core::{
+      ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
+      iter::{Sum, Product},
+    };
+
+    use subtle::{Choice, CtOption, ConstantTimeEq, ConstantTimeLess, ConditionallySelectable};
+    use rand_core::RngCore;
+
+    use crypto_bigint::{Integer, NonZero, Encoding, impl_modulus};
+
+    use ciphersuite::group::ff::{
+      Field, PrimeField, FieldBits, PrimeFieldBits, helpers::sqrt_ratio_generic,
+    };
+
+    use $crate::backend::u8_from_bool;
+
+    fn reduce(x: U512) -> U256 {
+      U256::from_le_slice(&x.rem(&NonZero::new($WIDE_MODULUS).unwrap()).to_le_bytes()[.. 32])
+    }
+
+    impl ConstantTimeEq for $FieldName {
+      fn ct_eq(&self, other: &Self) -> Choice {
+        self.0.ct_eq(&other.0)
+      }
+    }
+
+    impl ConditionallySelectable for $FieldName {
+      fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+        $FieldName(Residue::conditional_select(&a.0, &b.0, choice))
+      }
+    }
+
+    math_op!($FieldName, $FieldName, Add, add, AddAssign, add_assign, |x: $ResidueType, y| x
+      .add(&y));
+    math_op!($FieldName, $FieldName, Sub, sub, SubAssign, sub_assign, |x: $ResidueType, y| x
+      .sub(&y));
+    math_op!($FieldName, $FieldName, Mul, mul, MulAssign, mul_assign, |x: $ResidueType, y| x
+      .mul(&y));
+
+    from_wrapper!($FieldName, U256, u8);
+    from_wrapper!($FieldName, U256, u16);
+    from_wrapper!($FieldName, U256, u32);
+    from_wrapper!($FieldName, U256, u64);
+    from_wrapper!($FieldName, U256, u128);
+
+    impl Neg for $FieldName {
+      type Output = $FieldName;
+      fn neg(self) -> $FieldName {
+        Self(self.0.neg())
+      }
+    }
+
+    impl<'a> Neg for &'a $FieldName {
+      type Output = $FieldName;
+      fn neg(self) -> Self::Output {
+        (*self).neg()
+      }
+    }
+
+    impl $FieldName {
+      /// Perform an exponentation.
+      pub fn pow(&self, other: $FieldName) -> $FieldName {
+        let mut table = [Self(Residue::ONE); 16];
+        table[1] = *self;
+        for i in 2 .. 16 {
+          table[i] = table[i - 1] * self;
+        }
+
+        let mut res = Self(Residue::ONE);
+        let mut bits = 0;
+        for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
+          bits <<= 1;
+          let mut bit = u8_from_bool(bit.deref_mut());
+          bits |= bit;
+          bit.zeroize();
+
+          if ((i + 1) % 4) == 0 {
+            if i != 3 {
+              for _ in 0 .. 4 {
+                res *= res;
+              }
+            }
+
+            let mut factor = table[0];
+            for (j, candidate) in table[1 ..].iter().enumerate() {
+              let j = j + 1;
+              factor = Self::conditional_select(&factor, &candidate, usize::from(bits).ct_eq(&j));
+            }
+            res *= factor;
+            bits = 0;
+          }
+        }
+        res
+      }
+    }
+
+    impl Field for $FieldName {
+      const ZERO: Self = Self(Residue::ZERO);
+      const ONE: Self = Self(Residue::ONE);
+
+      fn random(mut rng: impl RngCore) -> Self {
+        let mut bytes = [0; 64];
+        rng.fill_bytes(&mut bytes);
+        $FieldName(Residue::new(&reduce(U512::from_le_slice(bytes.as_ref()))))
+      }
+
+      fn square(&self) -> Self {
+        Self(self.0.square())
+      }
+      fn double(&self) -> Self {
+        *self + self
+      }
+
+      fn invert(&self) -> CtOption<Self> {
+        let res = self.0.invert();
+        CtOption::new(Self(res.0), res.1.into())
+      }
+
+      fn sqrt(&self) -> CtOption<Self> {
+        // (p + 1) // 4, as valid since p % 4 == 3
+        let mod_plus_one_div_four = $MODULUS.saturating_add(&U256::ONE).wrapping_div(&(4u8.into()));
+        let res = self.pow(Self($ResidueType::new_checked(&mod_plus_one_div_four).unwrap()));
+        CtOption::new(res, res.square().ct_eq(self))
+      }
+
+      fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
+        sqrt_ratio_generic(num, div)
+      }
+    }
+
+    impl PrimeField for $FieldName {
+      type Repr = [u8; 32];
+
+      const MODULUS: &'static str = $MODULUS_STR;
+
+      const NUM_BITS: u32 = $NUM_BITS;
+      const CAPACITY: u32 = $NUM_BITS - 1;
+
+      const TWO_INV: Self = $FieldName($ResidueType::new(&U256::from_u8(2)).invert().0);
+
+      const MULTIPLICATIVE_GENERATOR: Self =
+        Self(Residue::new(&U256::from_u8($MULTIPLICATIVE_GENERATOR)));
+      const S: u32 = $S;
+
+      const ROOT_OF_UNITY: Self = $FieldName(Residue::new(&U256::from_be_hex($ROOT_OF_UNITY)));
+      const ROOT_OF_UNITY_INV: Self = Self(Self::ROOT_OF_UNITY.0.invert().0);
+
+      const DELTA: Self = $FieldName(Residue::new(&U256::from_be_hex($DELTA)));
+
+      fn from_repr(bytes: Self::Repr) -> CtOption<Self> {
+        let res = U256::from_le_slice(&bytes);
+        CtOption::new($FieldName(Residue::new(&res)), res.ct_lt(&$MODULUS))
+      }
+      fn to_repr(&self) -> Self::Repr {
+        let mut repr = [0; 32];
+        repr.copy_from_slice(&self.0.retrieve().to_le_bytes());
+        repr
+      }
+
+      fn is_odd(&self) -> Choice {
+        self.0.retrieve().is_odd()
+      }
+    }
+
+    impl PrimeFieldBits for $FieldName {
+      type ReprBits = [u8; 32];
+
+      fn to_le_bits(&self) -> FieldBits<Self::ReprBits> {
+        self.to_repr().into()
+      }
+
+      fn char_le_bits() -> FieldBits<Self::ReprBits> {
+        let mut repr = [0; 32];
+        repr.copy_from_slice(&MODULUS.to_le_bytes());
+        repr.into()
+      }
+    }
+
+    impl Sum<$FieldName> for $FieldName {
+      fn sum<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
+        let mut res = $FieldName::ZERO;
+        for item in iter {
+          res += item;
+        }
+        res
+      }
+    }
+
+    impl<'a> Sum<&'a $FieldName> for $FieldName {
+      fn sum<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
+        iter.cloned().sum()
+      }
+    }
+
+    impl Product<$FieldName> for $FieldName {
+      fn product<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
+        let mut res = $FieldName::ONE;
+        for item in iter {
+          res *= item;
+        }
+        res
+      }
+    }
+
+    impl<'a> Product<&'a $FieldName> for $FieldName {
+      fn product<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
+        iter.cloned().product()
+      }
+    }
+  };
+}
--- a/crypto/evrf/embedwards25519/src/lib.rs
+++ b/crypto/evrf/embedwards25519/src/lib.rs
@@ -0,0 +1,47 @@
+#![cfg_attr(docsrs, feature(doc_auto_cfg))]
+#![doc = include_str!("../README.md")]
+
+use generic_array::typenum::{Sum, Diff, Quot, U, U1, U2};
+use ciphersuite::group::{ff::PrimeField, Group};
+
+#[macro_use]
+mod backend;
+
+mod scalar;
+pub use scalar::Scalar;
+
+pub use dalek_ff_group::Scalar as FieldElement;
+
+mod point;
+pub use point::Point;
+
+/// Ciphersuite for Embedwards25519.
+///
+/// hash_to_F is implemented with a naive concatenation of the dst and data, allowing transposition
+/// between the two. This means `dst: b"abc", data: b"def"`, will produce the same scalar as
+/// `dst: "abcdef", data: b""`. Please use carefully, not letting dsts be substrings of each other.
+#[derive(Clone, Copy, PartialEq, Eq, Debug, zeroize::Zeroize)]
+pub struct Embedwards25519;
+impl ciphersuite::Ciphersuite for Embedwards25519 {
+  type F = Scalar;
+  type G = Point;
+  type H = blake2::Blake2b512;
+
+  const ID: &'static [u8] = b"embedwards25519";
+
+  fn generator() -> Self::G {
+    Point::generator()
+  }
+
+  fn hash_to_F(dst: &[u8], data: &[u8]) -> Self::F {
+    use blake2::Digest;
+    Scalar::wide_reduce(Self::H::digest([dst, data].concat()).as_slice().try_into().unwrap())
+  }
+}
+
+impl generalized_bulletproofs_ec_gadgets::DiscreteLogParameters for Embedwards25519 {
+  type ScalarBits = U<{ Scalar::NUM_BITS as usize }>;
+  type XCoefficients = Quot<Sum<Self::ScalarBits, U1>, U2>;
+  type XCoefficientsMinusOne = Diff<Self::XCoefficients, U1>;
+  type YxCoefficients = Diff<Quot<Sum<Sum<Self::ScalarBits, U1>, U1>, U2>, U2>;
+}
--- a/crypto/evrf/embedwards25519/src/point.rs
+++ b/crypto/evrf/embedwards25519/src/point.rs
@@ -0,0 +1,415 @@
+use core::{
+  ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
+  iter::Sum,
+};
+
+use rand_core::RngCore;
+
+use zeroize::Zeroize;
+use subtle::{Choice, CtOption, ConstantTimeEq, ConditionallySelectable};
+
+use ciphersuite::group::{
+  ff::{Field, PrimeField, PrimeFieldBits},
+  Group, GroupEncoding,
+  prime::PrimeGroup,
+};
+
+use crate::{backend::u8_from_bool, Scalar, FieldElement};
+
+#[allow(non_snake_case)]
+fn B() -> FieldElement {
+  FieldElement::from_repr(hex_literal::hex!(
+    "5f07603a853f20370b682036210d463e64903a23ea669d07ca26cfc13f594209"
+  ))
+  .unwrap()
+}
+
+fn recover_y(x: FieldElement) -> CtOption<FieldElement> {
+  // x**3 - 3 * x + B
+  ((x.square() * x) - (x.double() + x) + B()).sqrt()
+}
+
+/// Point.
+#[derive(Clone, Copy, Debug, Zeroize)]
+#[repr(C)]
+pub struct Point {
+  x: FieldElement, // / Z
+  y: FieldElement, // / Z
+  z: FieldElement,
+}
+
+impl ConstantTimeEq for Point {
+  fn ct_eq(&self, other: &Self) -> Choice {
+    let x1 = self.x * other.z;
+    let x2 = other.x * self.z;
+
+    let y1 = self.y * other.z;
+    let y2 = other.y * self.z;
+
+    (self.x.is_zero() & other.x.is_zero()) | (x1.ct_eq(&x2) & y1.ct_eq(&y2))
+  }
+}
+
+impl PartialEq for Point {
+  fn eq(&self, other: &Point) -> bool {
+    self.ct_eq(other).into()
+  }
+}
+
+impl Eq for Point {}
+
+impl ConditionallySelectable for Point {
+  fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+    Point {
+      x: FieldElement::conditional_select(&a.x, &b.x, choice),
+      y: FieldElement::conditional_select(&a.y, &b.y, choice),
+      z: FieldElement::conditional_select(&a.z, &b.z, choice),
+    }
+  }
+}
+
+impl Add for Point {
+  type Output = Point;
+  #[allow(non_snake_case)]
+  fn add(self, other: Self) -> Self {
+    // add-2015-rcb
+
+    let a = -FieldElement::from(3u64);
+    let B = B();
+    let b3 = B + B + B;
+
+    let X1 = self.x;
+    let Y1 = self.y;
+    let Z1 = self.z;
+    let X2 = other.x;
+    let Y2 = other.y;
+    let Z2 = other.z;
+
+    let t0 = X1 * X2;
+    let t1 = Y1 * Y2;
+    let t2 = Z1 * Z2;
+    let t3 = X1 + Y1;
+    let t4 = X2 + Y2;
+    let t3 = t3 * t4;
+    let t4 = t0 + t1;
+    let t3 = t3 - t4;
+    let t4 = X1 + Z1;
+    let t5 = X2 + Z2;
+    let t4 = t4 * t5;
+    let t5 = t0 + t2;
+    let t4 = t4 - t5;
+    let t5 = Y1 + Z1;
+    let X3 = Y2 + Z2;
+    let t5 = t5 * X3;
+    let X3 = t1 + t2;
+    let t5 = t5 - X3;
+    let Z3 = a * t4;
+    let X3 = b3 * t2;
+    let Z3 = X3 + Z3;
+    let X3 = t1 - Z3;
+    let Z3 = t1 + Z3;
+    let Y3 = X3 * Z3;
+    let t1 = t0 + t0;
+    let t1 = t1 + t0;
+    let t2 = a * t2;
+    let t4 = b3 * t4;
+    let t1 = t1 + t2;
+    let t2 = t0 - t2;
+    let t2 = a * t2;
+    let t4 = t4 + t2;
+    let t0 = t1 * t4;
+    let Y3 = Y3 + t0;
+    let t0 = t5 * t4;
+    let X3 = t3 * X3;
+    let X3 = X3 - t0;
+    let t0 = t3 * t1;
+    let Z3 = t5 * Z3;
+    let Z3 = Z3 + t0;
+    Point { x: X3, y: Y3, z: Z3 }
+  }
+}
+
+impl AddAssign for Point {
+  fn add_assign(&mut self, other: Point) {
+    *self = *self + other;
+  }
+}
+
+impl Add<&Point> for Point {
+  type Output = Point;
+  fn add(self, other: &Point) -> Point {
+    self + *other
+  }
+}
+
+impl AddAssign<&Point> for Point {
+  fn add_assign(&mut self, other: &Point) {
+    *self += *other;
+  }
+}
+
+impl Neg for Point {
+  type Output = Point;
+  fn neg(self) -> Self {
+    Point { x: self.x, y: -self.y, z: self.z }
+  }
+}
+
+impl Sub for Point {
+  type Output = Point;
+  #[allow(clippy::suspicious_arithmetic_impl)]
+  fn sub(self, other: Self) -> Self {
+    self + other.neg()
+  }
+}
+
+impl SubAssign for Point {
+  fn sub_assign(&mut self, other: Point) {
+    *self = *self - other;
+  }
+}
+
+impl Sub<&Point> for Point {
+  type Output = Point;
+  fn sub(self, other: &Point) -> Point {
+    self - *other
+  }
+}
+
+impl SubAssign<&Point> for Point {
+  fn sub_assign(&mut self, other: &Point) {
+    *self -= *other;
+  }
+}
+
+impl Group for Point {
+  type Scalar = Scalar;
+  fn random(mut rng: impl RngCore) -> Self {
+    loop {
+      let mut bytes = [0; 32];
+      rng.fill_bytes(bytes.as_mut());
+      let opt = Self::from_bytes(&bytes);
+      if opt.is_some().into() {
+        return opt.unwrap();
+      }
+    }
+  }
+  fn identity() -> Self {
+    Point { x: FieldElement::ZERO, y: FieldElement::ONE, z: FieldElement::ZERO }
+  }
+  fn generator() -> Self {
+    Point {
+      x: FieldElement::from_repr(hex_literal::hex!(
+        "0100000000000000000000000000000000000000000000000000000000000000"
+      ))
+      .unwrap(),
+      y: FieldElement::from_repr(hex_literal::hex!(
+        "2e4118080a484a3dfbafe2199a0e36b7193581d676c0dadfa376b0265616020c"
+      ))
+      .unwrap(),
+      z: FieldElement::ONE,
+    }
+  }
+  fn is_identity(&self) -> Choice {
+    self.z.ct_eq(&FieldElement::ZERO)
+  }
+  #[allow(non_snake_case)]
+  fn double(&self) -> Self {
+    // dbl-2007-bl-2
+    let X1 = self.x;
+    let Y1 = self.y;
+    let Z1 = self.z;
+
+    let w = (X1 - Z1) * (X1 + Z1);
+    let w = w.double() + w;
+    let s = (Y1 * Z1).double();
+    let ss = s.square();
+    let sss = s * ss;
+    let R = Y1 * s;
+    let RR = R.square();
+    let B_ = (X1 * R).double();
+    let h = w.square() - B_.double();
+    let X3 = h * s;
+    let Y3 = w * (B_ - h) - RR.double();
+    let Z3 = sss;
+
+    let res = Self { x: X3, y: Y3, z: Z3 };
+    // If self is identity, res will not be well-formed
+    // Accordingly, we return self if self was the identity
+    Self::conditional_select(&res, self, self.is_identity())
+  }
+}
+
+impl Sum<Point> for Point {
+  fn sum<I: Iterator<Item = Point>>(iter: I) -> Point {
+    let mut res = Self::identity();
+    for i in iter {
+      res += i;
+    }
+    res
+  }
+}
+
+impl<'a> Sum<&'a Point> for Point {
+  fn sum<I: Iterator<Item = &'a Point>>(iter: I) -> Point {
+    Point::sum(iter.cloned())
+  }
+}
+
+impl Mul<Scalar> for Point {
+  type Output = Point;
+  fn mul(self, mut other: Scalar) -> Point {
+    // Precompute the optimal amount that's a multiple of 2
+    let mut table = [Point::identity(); 16];
+    table[1] = self;
+    for i in 2 .. 16 {
+      table[i] = table[i - 1] + self;
+    }
+
+    let mut res = Self::identity();
+    let mut bits = 0;
+    for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
+      bits <<= 1;
+      let mut bit = u8_from_bool(bit.deref_mut());
+      bits |= bit;
+      bit.zeroize();
+
+      if ((i + 1) % 4) == 0 {
+        if i != 3 {
+          for _ in 0 .. 4 {
+            res = res.double();
+          }
+        }
+
+        let mut term = table[0];
+        for (j, candidate) in table[1 ..].iter().enumerate() {
+          let j = j + 1;
+          term = Self::conditional_select(&term, candidate, usize::from(bits).ct_eq(&j));
+        }
+        res += term;
+        bits = 0;
+      }
+    }
+    other.zeroize();
+    res
+  }
+}
+
+impl MulAssign<Scalar> for Point {
+  fn mul_assign(&mut self, other: Scalar) {
+    *self = *self * other;
+  }
+}
+
+impl Mul<&Scalar> for Point {
+  type Output = Point;
+  fn mul(self, other: &Scalar) -> Point {
+    self * *other
+  }
+}
+
+impl MulAssign<&Scalar> for Point {
+  fn mul_assign(&mut self, other: &Scalar) {
+    *self *= *other;
+  }
+}
+
+impl GroupEncoding for Point {
+  type Repr = [u8; 32];
+
+  fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
+    // Extract and clear the sign bit
+    let mut bytes = *bytes;
+    let sign = Choice::from(bytes[31] >> 7);
+    bytes[31] &= u8::MAX >> 1;
+
+    // Parse x, recover y
+    FieldElement::from_repr(bytes).and_then(|x| {
+      let is_identity = x.is_zero();
+
+      let y = recover_y(x).map(|mut y| {
+        y = <_>::conditional_select(&y, &-y, y.is_odd().ct_eq(&!sign));
+        y
+      });
+
+      // If this the identity, set y to 1
+      let y =
+        CtOption::conditional_select(&y, &CtOption::new(FieldElement::ONE, 1.into()), is_identity);
+      // Create the point if we have a y solution
+      let point = y.map(|y| Point { x, y, z: FieldElement::ONE });
+
+      let not_negative_zero = !(is_identity & sign);
+      // Only return the point if it isn't -0
+      CtOption::conditional_select(
+        &CtOption::new(Point::identity(), 0.into()),
+        &point,
+        not_negative_zero,
+      )
+    })
+  }
+
+  fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
+    Point::from_bytes(bytes)
+  }
+
+  fn to_bytes(&self) -> Self::Repr {
+    let Some(z) = Option::<FieldElement>::from(self.z.invert()) else {
+      return [0; 32];
+    };
+    let x = self.x * z;
+    let y = self.y * z;
+
+    let mut res = [0; 32];
+    res.as_mut().copy_from_slice(&x.to_repr());
+
+    // The following conditional select normalizes the sign to 0 when x is 0
+    let y_sign = u8::conditional_select(&y.is_odd().unwrap_u8(), &0, x.ct_eq(&FieldElement::ZERO));
+    res[31] |= y_sign << 7;
+    res
+  }
+}
+
+impl PrimeGroup for Point {}
+
+impl ec_divisors::DivisorCurve for Point {
+  type FieldElement = FieldElement;
+
+  fn a() -> Self::FieldElement {
+    -FieldElement::from(3u64)
+  }
+  fn b() -> Self::FieldElement {
+    B()
+  }
+
+  fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
+    let z: Self::FieldElement = Option::from(point.z.invert())?;
+    Some((point.x * z, point.y * z))
+  }
+}
+
+#[test]
+fn test_curve() {
+  ff_group_tests::group::test_prime_group_bits::<_, Point>(&mut rand_core::OsRng);
+}
+
+#[test]
+fn generator() {
+  assert_eq!(
+    Point::generator(),
+    Point::from_bytes(&hex_literal::hex!(
+      "0100000000000000000000000000000000000000000000000000000000000000"
+    ))
+    .unwrap()
+  );
+}
+
+#[test]
+fn zero_x_is_invalid() {
+  assert!(Option::<FieldElement>::from(recover_y(FieldElement::ZERO)).is_none());
+}
+
+// Checks random won't infinitely loop
+#[test]
+fn random() {
+  Point::random(&mut rand_core::OsRng);
+}
--- a/crypto/evrf/embedwards25519/src/scalar.rs
+++ b/crypto/evrf/embedwards25519/src/scalar.rs
@@ -0,0 +1,52 @@
+use zeroize::{DefaultIsZeroes, Zeroize};
+
+use crypto_bigint::{
+  U256, U512,
+  modular::constant_mod::{ResidueParams, Residue},
+};
+
+const MODULUS_STR: &str = "0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96b";
+
+impl_modulus!(EmbedwardsQ, U256, MODULUS_STR);
+type ResidueType = Residue<EmbedwardsQ, { EmbedwardsQ::LIMBS }>;
+
+/// The Scalar field of Embedwards25519.
+///
+/// This is equivalent to the field secp256k1 is defined over.
+#[derive(Clone, Copy, PartialEq, Eq, Default, Debug)]
+#[repr(C)]
+pub struct Scalar(pub(crate) ResidueType);
+
+impl DefaultIsZeroes for Scalar {}
+
+pub(crate) const MODULUS: U256 = U256::from_be_hex(MODULUS_STR);
+
+const WIDE_MODULUS: U512 = U512::from_be_hex(concat!(
+  "0000000000000000000000000000000000000000000000000000000000000000",
+  "0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96b",
+));
+
+field!(
+  Scalar,
+  ResidueType,
+  MODULUS_STR,
+  MODULUS,
+  WIDE_MODULUS,
+  252,
+  10,
+  1,
+  "0fffffffffffffffffffffffffffffffe53f4debb78ff96877063f0306eef96a",
+  "0000000000000000000000000000000000000000000000000000000000000064",
+);
+
+impl Scalar {
+  /// Perform a wide reduction, presumably to obtain a non-biased Scalar field element.
+  pub fn wide_reduce(bytes: [u8; 64]) -> Scalar {
+    Scalar(Residue::new(&reduce(U512::from_le_slice(bytes.as_ref()))))
+  }
+}
+
+#[test]
+fn test_scalar_field() {
+  ff_group_tests::prime_field::test_prime_field_bits::<_, Scalar>(&mut rand_core::OsRng);
+}
--- a/crypto/evrf/generalized-bulletproofs/Cargo.toml
+++ b/crypto/evrf/generalized-bulletproofs/Cargo.toml
@@ -0,0 +1,33 @@
+[package]
+name = "generalized-bulletproofs"
+version = "0.1.0"
+description = "Generalized Bulletproofs"
+license = "MIT"
+repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/generalized-bulletproofs"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["ciphersuite", "ff", "group"]
+edition = "2021"
+
+[package.metadata.docs.rs]
+all-features = true
+rustdoc-args = ["--cfg", "docsrs"]
+
+[dependencies]
+rand_core = { version = "0.6", default-features = false, features = ["std"] }
+
+zeroize = { version = "^1.5", default-features = false, features = ["std", "zeroize_derive"] }
+
+blake2 = { version = "0.10", default-features = false, features = ["std"] }
+
+multiexp = { path = "../../multiexp", version = "0.4", default-features = false, features = ["std", "batch"] }
+ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
+
+[dev-dependencies]
+rand_core = { version = "0.6", features = ["getrandom"] }
+
+transcript = { package = "flexible-transcript", path = "../../transcript", features = ["recommended"] }
+
+ciphersuite = { path = "../../ciphersuite", features = ["ristretto"] }
+
+[features]
+tests = []
--- a/crypto/evrf/generalized-bulletproofs/LICENSE
+++ b/crypto/evrf/generalized-bulletproofs/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2021-2024 Luke Parker
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
--- a/crypto/evrf/generalized-bulletproofs/README.md
+++ b/crypto/evrf/generalized-bulletproofs/README.md
@@ -0,0 +1,6 @@
+# Generalized Bulletproofs
+
+An implementation of
+[Generalized Bulletproofs](https://repo.getmonero.org/monero-project/ccs-proposals/uploads/a9baa50c38c6312efc0fea5c6a188bb9/gbp.pdf),
+a variant of the Bulletproofs arithmetic circuit statement to support Pedersen
+vector commitments.
--- a/crypto/evrf/generalized-bulletproofs/src/arithmetic_circuit_proof.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/arithmetic_circuit_proof.rs
@@ -0,0 +1,679 @@
+use rand_core::{RngCore, CryptoRng};
+
+use zeroize::{Zeroize, ZeroizeOnDrop};
+
+use multiexp::{multiexp, multiexp_vartime};
+use ciphersuite::{group::ff::Field, Ciphersuite};
+
+use crate::{
+  ScalarVector, PointVector, ProofGenerators, PedersenCommitment, PedersenVectorCommitment,
+  BatchVerifier,
+  transcript::*,
+  lincomb::accumulate_vector,
+  inner_product::{IpError, IpStatement, IpWitness, P},
+};
+pub use crate::lincomb::{Variable, LinComb};
+
+/// An Arithmetic Circuit Statement.
+///
+/// Bulletproofs' constraints are of the form
+///  `aL * aR = aO, WL * aL + WR * aR + WO * aO = WV * V + c`.
+///
+/// Generalized Bulletproofs modifies this to
+/// `aL * aR = aO, WL * aL + WR * aR + WO * aO + WCG * C_G + WCH * C_H = WV * V + c`.
+///
+/// We implement the latter, yet represented (for simplicity) as
+/// `aL * aR = aO, WL * aL + WR * aR + WO * aO + WCG * C_G + WCH * C_H + WV * V + c = 0`.
+#[derive(Clone, Debug)]
+pub struct ArithmeticCircuitStatement<'a, C: Ciphersuite> {
+  generators: ProofGenerators<'a, C>,
+
+  constraints: Vec<LinComb<C::F>>,
+  C: PointVector<C>,
+  V: PointVector<C>,
+}
+
+impl<'a, C: Ciphersuite> Zeroize for ArithmeticCircuitStatement<'a, C> {
+  fn zeroize(&mut self) {
+    self.constraints.zeroize();
+    self.C.zeroize();
+    self.V.zeroize();
+  }
+}
+
+/// The witness for an arithmetic circuit statement.
+#[derive(Clone, Debug, Zeroize, ZeroizeOnDrop)]
+pub struct ArithmeticCircuitWitness<C: Ciphersuite> {
+  aL: ScalarVector<C::F>,
+  aR: ScalarVector<C::F>,
+  aO: ScalarVector<C::F>,
+
+  c: Vec<PedersenVectorCommitment<C>>,
+  v: Vec<PedersenCommitment<C>>,
+}
+
+/// An error incurred during arithmetic circuit proof operations.
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub enum AcError {
+  /// The vectors of scalars which are multiplied against each other were of different lengths.
+  DifferingLrLengths,
+  /// The matrices of constraints are of different lengths.
+  InconsistentAmountOfConstraints,
+  /// A constraint referred to a non-existent term.
+  ConstrainedNonExistentTerm,
+  /// A constraint referred to a non-existent commitment.
+  ConstrainedNonExistentCommitment,
+  /// There weren't enough generators to prove for this statement.
+  NotEnoughGenerators,
+  /// The witness was inconsistent to the statement.
+  ///
+  /// Sanity checks on the witness are always performed. If the library is compiled with debug
+  /// assertions on, the satisfaction of all constraints and validity of the commitmentsd is
+  /// additionally checked.
+  InconsistentWitness,
+  /// There was an error from the inner-product proof.
+  Ip(IpError),
+  /// The proof wasn't complete and the necessary values could not be read from the transcript.
+  IncompleteProof,
+}
+
+impl<C: Ciphersuite> ArithmeticCircuitWitness<C> {
+  /// Constructs a new witness instance.
+  pub fn new(
+    aL: ScalarVector<C::F>,
+    aR: ScalarVector<C::F>,
+    c: Vec<PedersenVectorCommitment<C>>,
+    v: Vec<PedersenCommitment<C>>,
+  ) -> Result<Self, AcError> {
+    if aL.len() != aR.len() {
+      Err(AcError::DifferingLrLengths)?;
+    }
+
+    // The Pedersen Vector Commitments don't have their variables' lengths checked as they aren't
+    // paired off with each other as aL, aR are
+
+    // The PVC commit function ensures there's enough generators for their amount of terms
+    // If there aren't enough/the same generators when this is proven for, it'll trigger
+    // InconsistentWitness
+
+    let aO = aL.clone() * &aR;
+    Ok(ArithmeticCircuitWitness { aL, aR, aO, c, v })
+  }
+}
+
+struct YzChallenges<C: Ciphersuite> {
+  y_inv: ScalarVector<C::F>,
+  z: ScalarVector<C::F>,
+}
+
+impl<'a, C: Ciphersuite> ArithmeticCircuitStatement<'a, C> {
+  // The amount of multiplications performed.
+  fn n(&self) -> usize {
+    self.generators.len()
+  }
+
+  // The amount of constraints.
+  fn q(&self) -> usize {
+    self.constraints.len()
+  }
+
+  // The amount of Pedersen vector commitments.
+  fn c(&self) -> usize {
+    self.C.len()
+  }
+
+  // The amount of Pedersen commitments.
+  fn m(&self) -> usize {
+    self.V.len()
+  }
+
+  /// Create a new ArithmeticCircuitStatement for the specified relationship.
+  ///
+  /// The `LinComb`s passed as `constraints` will be bound to evaluate to 0.
+  ///
+  /// The constraints are not transcripted. They're expected to be deterministic from the context
+  /// and higher-level statement. If your constraints are variable, you MUST transcript them before
+  /// calling prove/verify.
+  ///
+  /// The commitments are expected to have been transcripted extenally to this statement's
+  /// invocation. That's practically ensured by taking a `Commitments` struct here, which is only
+  /// obtainable via a transcript.
+  pub fn new(
+    generators: ProofGenerators<'a, C>,
+    constraints: Vec<LinComb<C::F>>,
+    commitments: Commitments<C>,
+  ) -> Result<Self, AcError> {
+    let Commitments { C, V } = commitments;
+
+    for constraint in &constraints {
+      if Some(generators.len()) <= constraint.highest_a_index {
+        Err(AcError::ConstrainedNonExistentTerm)?;
+      }
+      if Some(C.len()) <= constraint.highest_c_index {
+        Err(AcError::ConstrainedNonExistentCommitment)?;
+      }
+      if Some(V.len()) <= constraint.highest_v_index {
+        Err(AcError::ConstrainedNonExistentCommitment)?;
+      }
+    }
+
+    Ok(Self { generators, constraints, C, V })
+  }
+
+  fn yz_challenges(&self, y: C::F, z_1: C::F) -> YzChallenges<C> {
+    let y_inv = y.invert().unwrap();
+    let y_inv = ScalarVector::powers(y_inv, self.n());
+
+    // Powers of z *starting with z**1*
+    // We could reuse powers and remove the first element, yet this is cheaper than the shift that
+    // would require
+    let q = self.q();
+    let mut z = ScalarVector(Vec::with_capacity(q));
+    z.0.push(z_1);
+    for _ in 1 .. q {
+      z.0.push(*z.0.last().unwrap() * z_1);
+    }
+    z.0.truncate(q);
+
+    YzChallenges { y_inv, z }
+  }
+
+  /// Prove for this statement/witness.
+  pub fn prove<R: RngCore + CryptoRng>(
+    self,
+    rng: &mut R,
+    transcript: &mut Transcript,
+    mut witness: ArithmeticCircuitWitness<C>,
+  ) -> Result<(), AcError> {
+    let n = self.n();
+    let c = self.c();
+    let m = self.m();
+
+    // Check the witness length and pad it to the necessary power of two
+    if witness.aL.len() > n {
+      Err(AcError::NotEnoughGenerators)?;
+    }
+    while witness.aL.len() < n {
+      witness.aL.0.push(C::F::ZERO);
+      witness.aR.0.push(C::F::ZERO);
+      witness.aO.0.push(C::F::ZERO);
+    }
+    for c in &mut witness.c {
+      if c.g_values.len() > n {
+        Err(AcError::NotEnoughGenerators)?;
+      }
+      if c.h_values.len() > n {
+        Err(AcError::NotEnoughGenerators)?;
+      }
+      // The Pedersen vector commitments internally have n terms
+      while c.g_values.len() < n {
+        c.g_values.0.push(C::F::ZERO);
+      }
+      while c.h_values.len() < n {
+        c.h_values.0.push(C::F::ZERO);
+      }
+    }
+
+    // Check the witness's consistency with the statement
+    if (c != witness.c.len()) || (m != witness.v.len()) {
+      Err(AcError::InconsistentWitness)?;
+    }
+
+    #[cfg(debug_assertions)]
+    {
+      for (commitment, opening) in self.V.0.iter().zip(witness.v.iter()) {
+        if *commitment != opening.commit(self.generators.g(), self.generators.h()) {
+          Err(AcError::InconsistentWitness)?;
+        }
+      }
+      for (commitment, opening) in self.C.0.iter().zip(witness.c.iter()) {
+        if Some(*commitment) !=
+          opening.commit(
+            self.generators.g_bold_slice(),
+            self.generators.h_bold_slice(),
+            self.generators.h(),
+          )
+        {
+          Err(AcError::InconsistentWitness)?;
+        }
+      }
+      for constraint in &self.constraints {
+        let eval =
+          constraint
+            .WL
+            .iter()
+            .map(|(i, weight)| *weight * witness.aL[*i])
+            .chain(constraint.WR.iter().map(|(i, weight)| *weight * witness.aR[*i]))
+            .chain(constraint.WO.iter().map(|(i, weight)| *weight * witness.aO[*i]))
+            .chain(
+              constraint.WCG.iter().zip(&witness.c).flat_map(|(weights, c)| {
+                weights.iter().map(|(j, weight)| *weight * c.g_values[*j])
+              }),
+            )
+            .chain(
+              constraint.WCH.iter().zip(&witness.c).flat_map(|(weights, c)| {
+                weights.iter().map(|(j, weight)| *weight * c.h_values[*j])
+              }),
+            )
+            .chain(constraint.WV.iter().map(|(i, weight)| *weight * witness.v[*i].value))
+            .chain(core::iter::once(constraint.c))
+            .sum::<C::F>();
+
+        if eval != C::F::ZERO {
+          Err(AcError::InconsistentWitness)?;
+        }
+      }
+    }
+
+    let alpha = C::F::random(&mut *rng);
+    let beta = C::F::random(&mut *rng);
+    let rho = C::F::random(&mut *rng);
+
+    let AI = {
+      let alg = witness.aL.0.iter().enumerate().map(|(i, aL)| (*aL, self.generators.g_bold(i)));
+      let arh = witness.aR.0.iter().enumerate().map(|(i, aR)| (*aR, self.generators.h_bold(i)));
+      let ah = core::iter::once((alpha, self.generators.h()));
+      let mut AI_terms = alg.chain(arh).chain(ah).collect::<Vec<_>>();
+      let AI = multiexp(&AI_terms);
+      AI_terms.zeroize();
+      AI
+    };
+    let AO = {
+      let aog = witness.aO.0.iter().enumerate().map(|(i, aO)| (*aO, self.generators.g_bold(i)));
+      let bh = core::iter::once((beta, self.generators.h()));
+      let mut AO_terms = aog.chain(bh).collect::<Vec<_>>();
+      let AO = multiexp(&AO_terms);
+      AO_terms.zeroize();
+      AO
+    };
+
+    let mut sL = ScalarVector(Vec::with_capacity(n));
+    let mut sR = ScalarVector(Vec::with_capacity(n));
+    for _ in 0 .. n {
+      sL.0.push(C::F::random(&mut *rng));
+      sR.0.push(C::F::random(&mut *rng));
+    }
+    let S = {
+      let slg = sL.0.iter().enumerate().map(|(i, sL)| (*sL, self.generators.g_bold(i)));
+      let srh = sR.0.iter().enumerate().map(|(i, sR)| (*sR, self.generators.h_bold(i)));
+      let rh = core::iter::once((rho, self.generators.h()));
+      let mut S_terms = slg.chain(srh).chain(rh).collect::<Vec<_>>();
+      let S = multiexp(&S_terms);
+      S_terms.zeroize();
+      S
+    };
+
+    transcript.push_point(AI);
+    transcript.push_point(AO);
+    transcript.push_point(S);
+    let y = transcript.challenge();
+    let z = transcript.challenge();
+    let YzChallenges { y_inv, z } = self.yz_challenges(y, z);
+    let y = ScalarVector::powers(y, n);
+
+    // t is a n'-term polynomial
+    // While Bulletproofs discuss it as a 6-term polynomial, Generalized Bulletproofs re-defines it
+    // as `2(n' + 1)`-term, where `n'` is `2 (c + 1)`.
+    // When `c = 0`, `n' = 2`, and t is `6` (which lines up with Bulletproofs having a 6-term
+    // polynomial).
+
+    // ni = n'
+    let ni = 2 * (c + 1);
+    // These indexes are from the Generalized Bulletproofs paper
+    #[rustfmt::skip]
+    let ilr = ni / 2; // 1 if c = 0
+    #[rustfmt::skip]
+    let io = ni; // 2 if c = 0
+    #[rustfmt::skip]
+    let is = ni + 1; // 3 if c = 0
+    #[rustfmt::skip]
+    let jlr = ni / 2; // 1 if c = 0
+    #[rustfmt::skip]
+    let jo = 0; // 0 if c = 0
+    #[rustfmt::skip]
+    let js = ni + 1; // 3 if c = 0
+
+    // If c = 0, these indexes perfectly align with the stated powers of X from the Bulletproofs
+    // paper for the following coefficients
+
+    // Declare the l and r polynomials, assigning the traditional coefficients to their positions
+    let mut l = vec![];
+    let mut r = vec![];
+    for _ in 0 .. (is + 1) {
+      l.push(ScalarVector::new(0));
+      r.push(ScalarVector::new(0));
+    }
+
+    let mut l_weights = ScalarVector::new(n);
+    let mut r_weights = ScalarVector::new(n);
+    let mut o_weights = ScalarVector::new(n);
+    for (constraint, z) in self.constraints.iter().zip(&z.0) {
+      accumulate_vector(&mut l_weights, &constraint.WL, *z);
+      accumulate_vector(&mut r_weights, &constraint.WR, *z);
+      accumulate_vector(&mut o_weights, &constraint.WO, *z);
+    }
+
+    l[ilr] = (r_weights * &y_inv) + &witness.aL;
+    l[io] = witness.aO.clone();
+    l[is] = sL;
+    r[jlr] = l_weights + &(witness.aR.clone() * &y);
+    r[jo] = o_weights - &y;
+    r[js] = sR * &y;
+
+    // Pad as expected
+    for l in &mut l {
+      debug_assert!((l.len() == 0) || (l.len() == n));
+      if l.len() == 0 {
+        *l = ScalarVector::new(n);
+      }
+    }
+    for r in &mut r {
+      debug_assert!((r.len() == 0) || (r.len() == n));
+      if r.len() == 0 {
+        *r = ScalarVector::new(n);
+      }
+    }
+
+    // We now fill in the vector commitments
+    // We use unused coefficients of l increasing from 0 (skipping ilr), and unused coefficients of
+    // r decreasing from n' (skipping jlr)
+
+    let mut cg_weights = Vec::with_capacity(witness.c.len());
+    let mut ch_weights = Vec::with_capacity(witness.c.len());
+    for i in 0 .. witness.c.len() {
+      let mut cg = ScalarVector::new(n);
+      let mut ch = ScalarVector::new(n);
+      for (constraint, z) in self.constraints.iter().zip(&z.0) {
+        if let Some(WCG) = constraint.WCG.get(i) {
+          accumulate_vector(&mut cg, WCG, *z);
+        }
+        if let Some(WCH) = constraint.WCH.get(i) {
+          accumulate_vector(&mut ch, WCH, *z);
+        }
+      }
+      cg_weights.push(cg);
+      ch_weights.push(ch);
+    }
+
+    for (i, (c, (cg_weights, ch_weights))) in
+      witness.c.iter().zip(cg_weights.into_iter().zip(ch_weights)).enumerate()
+    {
+      let i = i + 1;
+      let j = ni - i;
+
+      l[i] = c.g_values.clone();
+      l[j] = ch_weights * &y_inv;
+      r[j] = cg_weights;
+      r[i] = (c.h_values.clone() * &y) + &r[i];
+    }
+
+    // Multiply them to obtain t
+    let mut t = ScalarVector::new(1 + (2 * (l.len() - 1)));
+    for (i, l) in l.iter().enumerate() {
+      for (j, r) in r.iter().enumerate() {
+        let new_coeff = i + j;
+        t[new_coeff] += l.inner_product(r.0.iter());
+      }
+    }
+
+    // Per Bulletproofs, calculate masks tau for each t where (i > 0) && (i != 2)
+    // Per Generalized Bulletproofs, calculate masks tau for each t where i != n'
+    // With Bulletproofs, t[0] is zero, hence its omission, yet Generalized Bulletproofs uses it
+    let mut tau_before_ni = vec![];
+    for _ in 0 .. ni {
+      tau_before_ni.push(C::F::random(&mut *rng));
+    }
+    let mut tau_after_ni = vec![];
+    for _ in 0 .. t.0[(ni + 1) ..].len() {
+      tau_after_ni.push(C::F::random(&mut *rng));
+    }
+    // Calculate commitments to the coefficients of t, blinded by tau
+    debug_assert_eq!(t.0[0 .. ni].len(), tau_before_ni.len());
+    for (t, tau) in t.0[0 .. ni].iter().zip(tau_before_ni.iter()) {
+      transcript.push_point(multiexp(&[(*t, self.generators.g()), (*tau, self.generators.h())]));
+    }
+    debug_assert_eq!(t.0[(ni + 1) ..].len(), tau_after_ni.len());
+    for (t, tau) in t.0[(ni + 1) ..].iter().zip(tau_after_ni.iter()) {
+      transcript.push_point(multiexp(&[(*t, self.generators.g()), (*tau, self.generators.h())]));
+    }
+
+    let x: ScalarVector<C::F> = ScalarVector::powers(transcript.challenge(), t.len());
+
+    let poly_eval = |poly: &[ScalarVector<C::F>], x: &ScalarVector<_>| -> ScalarVector<_> {
+      let mut res = ScalarVector::<C::F>::new(poly[0].0.len());
+      for (i, coeff) in poly.iter().enumerate() {
+        res = res + &(coeff.clone() * x[i]);
+      }
+      res
+    };
+    let l = poly_eval(&l, &x);
+    let r = poly_eval(&r, &x);
+
+    let t_caret = l.inner_product(r.0.iter());
+
+    let mut V_weights = ScalarVector::new(self.V.len());
+    for (constraint, z) in self.constraints.iter().zip(&z.0) {
+      // We use `-z`, not `z`, as we write our constraint as `... + WV V = 0` not `= WV V + ..`
+      // This means we need to subtract `WV V` from both sides, which we accomplish here
+      accumulate_vector(&mut V_weights, &constraint.WV, -*z);
+    }
+
+    let tau_x = {
+      let mut tau_x_poly = vec![];
+      tau_x_poly.extend(tau_before_ni);
+      tau_x_poly.push(V_weights.inner_product(witness.v.iter().map(|v| &v.mask)));
+      tau_x_poly.extend(tau_after_ni);
+
+      let mut tau_x = C::F::ZERO;
+      for (i, coeff) in tau_x_poly.into_iter().enumerate() {
+        tau_x += coeff * x[i];
+      }
+      tau_x
+    };
+
+    // Calculate u for the powers of x variable to ilr/io/is
+    let u = {
+      // Calculate the first part of u
+      let mut u = (alpha * x[ilr]) + (beta * x[io]) + (rho * x[is]);
+
+      // Incorporate the commitment masks multiplied by the associated power of x
+      for (i, commitment) in witness.c.iter().enumerate() {
+        let i = i + 1;
+        u += x[i] * commitment.mask;
+      }
+      u
+    };
+
+    // Use the Inner-Product argument to prove for this
+    // P = t_caret * g + l * g_bold + r * (y_inv * h_bold)
+
+    let mut P_terms = Vec::with_capacity(1 + (2 * self.generators.len()));
+    debug_assert_eq!(l.len(), r.len());
+    for (i, (l, r)) in l.0.iter().zip(r.0.iter()).enumerate() {
+      P_terms.push((*l, self.generators.g_bold(i)));
+      P_terms.push((y_inv[i] * r, self.generators.h_bold(i)));
+    }
+
+    // Protocol 1, inlined, since our IpStatement is for Protocol 2
+    transcript.push_scalar(tau_x);
+    transcript.push_scalar(u);
+    transcript.push_scalar(t_caret);
+    let ip_x = transcript.challenge();
+    P_terms.push((ip_x * t_caret, self.generators.g()));
+    IpStatement::new(
+      self.generators,
+      y_inv,
+      ip_x,
+      // Safe since IpStatement isn't a ZK proof
+      P::Prover(multiexp_vartime(&P_terms)),
+    )
+    .unwrap()
+    .prove(transcript, IpWitness::new(l, r).unwrap())
+    .map_err(AcError::Ip)
+  }
+
+  /// Verify a proof for this statement.
+  pub fn verify<R: RngCore + CryptoRng>(
+    self,
+    rng: &mut R,
+    verifier: &mut BatchVerifier<C>,
+    transcript: &mut VerifierTranscript,
+  ) -> Result<(), AcError> {
+    let n = self.n();
+    let c = self.c();
+
+    let ni = 2 * (c + 1);
+
+    let ilr = ni / 2;
+    let io = ni;
+    let is = ni + 1;
+    let jlr = ni / 2;
+
+    let l_r_poly_len = 1 + ni + 1;
+    let t_poly_len = (2 * l_r_poly_len) - 1;
+
+    let AI = transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?;
+    let AO = transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?;
+    let S = transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?;
+    let y = transcript.challenge();
+    let z = transcript.challenge();
+    let YzChallenges { y_inv, z } = self.yz_challenges(y, z);
+
+    let mut l_weights = ScalarVector::new(n);
+    let mut r_weights = ScalarVector::new(n);
+    let mut o_weights = ScalarVector::new(n);
+    for (constraint, z) in self.constraints.iter().zip(&z.0) {
+      accumulate_vector(&mut l_weights, &constraint.WL, *z);
+      accumulate_vector(&mut r_weights, &constraint.WR, *z);
+      accumulate_vector(&mut o_weights, &constraint.WO, *z);
+    }
+    let r_weights = r_weights * &y_inv;
+
+    let delta = r_weights.inner_product(l_weights.0.iter());
+
+    let mut T_before_ni = Vec::with_capacity(ni);
+    let mut T_after_ni = Vec::with_capacity(t_poly_len - ni - 1);
+    for _ in 0 .. ni {
+      T_before_ni.push(transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?);
+    }
+    for _ in 0 .. (t_poly_len - ni - 1) {
+      T_after_ni.push(transcript.read_point::<C>().map_err(|_| AcError::IncompleteProof)?);
+    }
+    let x: ScalarVector<C::F> = ScalarVector::powers(transcript.challenge(), t_poly_len);
+
+    let tau_x = transcript.read_scalar::<C>().map_err(|_| AcError::IncompleteProof)?;
+    let u = transcript.read_scalar::<C>().map_err(|_| AcError::IncompleteProof)?;
+    let t_caret = transcript.read_scalar::<C>().map_err(|_| AcError::IncompleteProof)?;
+
+    // Lines 88-90, modified per Generalized Bulletproofs as needed w.r.t. t
+    {
+      let verifier_weight = C::F::random(&mut *rng);
+      // lhs of the equation, weighted to enable batch verification
+      verifier.g += t_caret * verifier_weight;
+      verifier.h += tau_x * verifier_weight;
+
+      let mut V_weights = ScalarVector::new(self.V.len());
+      for (constraint, z) in self.constraints.iter().zip(&z.0) {
+        // We use `-z`, not `z`, as we write our constraint as `... + WV V = 0` not `= WV V + ..`
+        // This means we need to subtract `WV V` from both sides, which we accomplish here
+        accumulate_vector(&mut V_weights, &constraint.WV, -*z);
+      }
+      V_weights = V_weights * x[ni];
+
+      // rhs of the equation, negated to cause a sum to zero
+      // `delta - z...`, instead of `delta + z...`, is done for the same reason as in the above WV
+      // matrix transform
+      verifier.g -= verifier_weight *
+        x[ni] *
+        (delta - z.inner_product(self.constraints.iter().map(|constraint| &constraint.c)));
+      for pair in V_weights.0.into_iter().zip(self.V.0) {
+        verifier.additional.push((-verifier_weight * pair.0, pair.1));
+      }
+      for (i, T) in T_before_ni.into_iter().enumerate() {
+        verifier.additional.push((-verifier_weight * x[i], T));
+      }
+      for (i, T) in T_after_ni.into_iter().enumerate() {
+        verifier.additional.push((-verifier_weight * x[ni + 1 + i], T));
+      }
+    }
+
+    let verifier_weight = C::F::random(&mut *rng);
+    // Multiply `x` by `verifier_weight` as this effects `verifier_weight` onto most scalars and
+    // saves a notable amount of operations
+    let x = x * verifier_weight;
+
+    // This following block effectively calculates P, within the multiexp
+    {
+      verifier.additional.push((x[ilr], AI));
+      verifier.additional.push((x[io], AO));
+      // h' ** y is equivalent to h as h' is h ** y_inv
+      let mut log2_n = 0;
+      while (1 << log2_n) != n {
+        log2_n += 1;
+      }
+      verifier.h_sum[log2_n] -= verifier_weight;
+      verifier.additional.push((x[is], S));
+
+      // Lines 85-87 calculate WL, WR, WO
+      // We preserve them in terms of g_bold and h_bold for a more efficient multiexp
+      let mut h_bold_scalars = l_weights * x[jlr];
+      for (i, wr) in (r_weights * x[jlr]).0.into_iter().enumerate() {
+        verifier.g_bold[i] += wr;
+      }
+      // WO is weighted by x**jo where jo == 0, hence why we can ignore the x term
+      h_bold_scalars = h_bold_scalars + &(o_weights * verifier_weight);
+
+      let mut cg_weights = Vec::with_capacity(self.C.len());
+      let mut ch_weights = Vec::with_capacity(self.C.len());
+      for i in 0 .. self.C.len() {
+        let mut cg = ScalarVector::new(n);
+        let mut ch = ScalarVector::new(n);
+        for (constraint, z) in self.constraints.iter().zip(&z.0) {
+          if let Some(WCG) = constraint.WCG.get(i) {
+            accumulate_vector(&mut cg, WCG, *z);
+          }
+          if let Some(WCH) = constraint.WCH.get(i) {
+            accumulate_vector(&mut ch, WCH, *z);
+          }
+        }
+        cg_weights.push(cg);
+        ch_weights.push(ch);
+      }
+
+      // Push the terms for C, which increment from 0, and the terms for WC, which decrement from
+      // n'
+      for (i, (C, (WCG, WCH))) in
+        self.C.0.into_iter().zip(cg_weights.into_iter().zip(ch_weights)).enumerate()
+      {
+        let i = i + 1;
+        let j = ni - i;
+        verifier.additional.push((x[i], C));
+        h_bold_scalars = h_bold_scalars + &(WCG * x[j]);
+        for (i, scalar) in (WCH * &y_inv * x[j]).0.into_iter().enumerate() {
+          verifier.g_bold[i] += scalar;
+        }
+      }
+
+      // All terms for h_bold here have actually been for h_bold', h_bold * y_inv
+      h_bold_scalars = h_bold_scalars * &y_inv;
+      for (i, scalar) in h_bold_scalars.0.into_iter().enumerate() {
+        verifier.h_bold[i] += scalar;
+      }
+
+      // Remove u * h from P
+      verifier.h -= verifier_weight * u;
+    }
+
+    // Prove for lines 88, 92 with an Inner-Product statement
+    // This inlines Protocol 1, as our IpStatement implements Protocol 2
+    let ip_x = transcript.challenge();
+    // P is amended with this additional term
+    verifier.g += verifier_weight * ip_x * t_caret;
+    IpStatement::new(self.generators, y_inv, ip_x, P::Verifier { verifier_weight })
+      .unwrap()
+      .verify(verifier, transcript)
+      .map_err(AcError::Ip)?;
+
+    Ok(())
+  }
+}
--- a/crypto/evrf/generalized-bulletproofs/src/inner_product.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/inner_product.rs
@@ -0,0 +1,360 @@
+use multiexp::multiexp_vartime;
+use ciphersuite::{group::ff::Field, Ciphersuite};
+
+#[rustfmt::skip]
+use crate::{ScalarVector, PointVector, ProofGenerators, BatchVerifier, transcript::*, padded_pow_of_2};
+
+/// An error from proving/verifying Inner-Product statements.
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub enum IpError {
+  /// An incorrect amount of generators was provided.
+  IncorrectAmountOfGenerators,
+  /// The witness was inconsistent to the statement.
+  ///
+  /// Sanity checks on the witness are always performed. If the library is compiled with debug
+  /// assertions on, whether or not this witness actually opens `P` is checked.
+  InconsistentWitness,
+  /// The proof wasn't complete and the necessary values could not be read from the transcript.
+  IncompleteProof,
+}
+
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub(crate) enum P<C: Ciphersuite> {
+  Verifier { verifier_weight: C::F },
+  Prover(C::G),
+}
+
+/// The Bulletproofs Inner-Product statement.
+///
+/// This is for usage with Protocol 2 from the Bulletproofs paper.
+#[derive(Clone, Debug)]
+pub(crate) struct IpStatement<'a, C: Ciphersuite> {
+  generators: ProofGenerators<'a, C>,
+  // Weights for h_bold
+  h_bold_weights: ScalarVector<C::F>,
+  // u as the discrete logarithm of G
+  u: C::F,
+  // P
+  P: P<C>,
+}
+
+/// The witness for the Bulletproofs Inner-Product statement.
+#[derive(Clone, Debug)]
+pub(crate) struct IpWitness<C: Ciphersuite> {
+  // a
+  a: ScalarVector<C::F>,
+  // b
+  b: ScalarVector<C::F>,
+}
+
+impl<C: Ciphersuite> IpWitness<C> {
+  /// Construct a new witness for an Inner-Product statement.
+  ///
+  /// If the witness is less than a power of two, it is padded to the nearest power of two.
+  ///
+  /// This functions return None if the lengths of a, b are mismatched or either are empty.
+  pub(crate) fn new(mut a: ScalarVector<C::F>, mut b: ScalarVector<C::F>) -> Option<Self> {
+    if a.0.is_empty() || (a.len() != b.len()) {
+      None?;
+    }
+
+    // Pad to the nearest power of 2
+    let missing = padded_pow_of_2(a.len()) - a.len();
+    a.0.reserve(missing);
+    b.0.reserve(missing);
+    for _ in 0 .. missing {
+      a.0.push(C::F::ZERO);
+      b.0.push(C::F::ZERO);
+    }
+
+    Some(Self { a, b })
+  }
+}
+
+impl<'a, C: Ciphersuite> IpStatement<'a, C> {
+  /// Create a new Inner-Product statement.
+  ///
+  /// This does not perform any transcripting of any variables within this statement. They must be
+  /// deterministic to the existing transcript.
+  pub(crate) fn new(
+    generators: ProofGenerators<'a, C>,
+    h_bold_weights: ScalarVector<C::F>,
+    u: C::F,
+    P: P<C>,
+  ) -> Result<Self, IpError> {
+    if generators.h_bold_slice().len() != h_bold_weights.len() {
+      Err(IpError::IncorrectAmountOfGenerators)?
+    }
+    Ok(Self { generators, h_bold_weights, u, P })
+  }
+
+  /// Prove for this Inner-Product statement.
+  ///
+  /// Returns an error if this statement couldn't be proven for (such as if the witness isn't
+  /// consistent).
+  pub(crate) fn prove(
+    self,
+    transcript: &mut Transcript,
+    witness: IpWitness<C>,
+  ) -> Result<(), IpError> {
+    let (mut g_bold, mut h_bold, u, mut P, mut a, mut b) = {
+      let IpStatement { generators, h_bold_weights, u, P } = self;
+      let u = generators.g() * u;
+
+      // Ensure we have the exact amount of generators
+      if generators.g_bold_slice().len() != witness.a.len() {
+        Err(IpError::IncorrectAmountOfGenerators)?;
+      }
+      // Acquire a local copy of the generators
+      let g_bold = PointVector::<C>(generators.g_bold_slice().to_vec());
+      let h_bold = PointVector::<C>(generators.h_bold_slice().to_vec()).mul_vec(&h_bold_weights);
+
+      let IpWitness { a, b } = witness;
+
+      let P = match P {
+        P::Prover(point) => point,
+        P::Verifier { .. } => {
+          panic!("prove called with a P specification which was for the verifier")
+        }
+      };
+
+      // Ensure this witness actually opens this statement
+      #[cfg(debug_assertions)]
+      {
+        let ag = a.0.iter().cloned().zip(g_bold.0.iter().cloned());
+        let bh = b.0.iter().cloned().zip(h_bold.0.iter().cloned());
+        let cu = core::iter::once((a.inner_product(b.0.iter()), u));
+        if P != multiexp_vartime(&ag.chain(bh).chain(cu).collect::<Vec<_>>()) {
+          Err(IpError::InconsistentWitness)?;
+        }
+      }
+
+      (g_bold, h_bold, u, P, a, b)
+    };
+
+    // `else: (n > 1)` case, lines 18-35 of the Bulletproofs paper
+    // This interprets `g_bold.len()` as `n`
+    while g_bold.len() > 1 {
+      // Split a, b, g_bold, h_bold as needed for lines 20-24
+      let (a1, a2) = a.clone().split();
+      let (b1, b2) = b.clone().split();
+
+      let (g_bold1, g_bold2) = g_bold.split();
+      let (h_bold1, h_bold2) = h_bold.split();
+
+      let n_hat = g_bold1.len();
+
+      // Sanity
+      debug_assert_eq!(a1.len(), n_hat);
+      debug_assert_eq!(a2.len(), n_hat);
+      debug_assert_eq!(b1.len(), n_hat);
+      debug_assert_eq!(b2.len(), n_hat);
+      debug_assert_eq!(g_bold1.len(), n_hat);
+      debug_assert_eq!(g_bold2.len(), n_hat);
+      debug_assert_eq!(h_bold1.len(), n_hat);
+      debug_assert_eq!(h_bold2.len(), n_hat);
+
+      // cl, cr, lines 21-22
+      let cl = a1.inner_product(b2.0.iter());
+      let cr = a2.inner_product(b1.0.iter());
+
+      let L = {
+        let mut L_terms = Vec::with_capacity(1 + (2 * g_bold1.len()));
+        for (a, g) in a1.0.iter().zip(g_bold2.0.iter()) {
+          L_terms.push((*a, *g));
+        }
+        for (b, h) in b2.0.iter().zip(h_bold1.0.iter()) {
+          L_terms.push((*b, *h));
+        }
+        L_terms.push((cl, u));
+        // Uses vartime since this isn't a ZK proof
+        multiexp_vartime(&L_terms)
+      };
+
+      let R = {
+        let mut R_terms = Vec::with_capacity(1 + (2 * g_bold1.len()));
+        for (a, g) in a2.0.iter().zip(g_bold1.0.iter()) {
+          R_terms.push((*a, *g));
+        }
+        for (b, h) in b1.0.iter().zip(h_bold2.0.iter()) {
+          R_terms.push((*b, *h));
+        }
+        R_terms.push((cr, u));
+        multiexp_vartime(&R_terms)
+      };
+
+      // Now that we've calculate L, R, transcript them to receive x (26-27)
+      transcript.push_point(L);
+      transcript.push_point(R);
+      let x: C::F = transcript.challenge();
+      let x_inv = x.invert().unwrap();
+
+      // The prover and verifier now calculate the following (28-31)
+      g_bold = PointVector(Vec::with_capacity(g_bold1.len()));
+      for (a, b) in g_bold1.0.into_iter().zip(g_bold2.0.into_iter()) {
+        g_bold.0.push(multiexp_vartime(&[(x_inv, a), (x, b)]));
+      }
+      h_bold = PointVector(Vec::with_capacity(h_bold1.len()));
+      for (a, b) in h_bold1.0.into_iter().zip(h_bold2.0.into_iter()) {
+        h_bold.0.push(multiexp_vartime(&[(x, a), (x_inv, b)]));
+      }
+      P = (L * (x * x)) + P + (R * (x_inv * x_inv));
+
+      // 32-34
+      a = (a1 * x) + &(a2 * x_inv);
+      b = (b1 * x_inv) + &(b2 * x);
+    }
+
+    // `if n = 1` case from line 14-17
+
+    // Sanity
+    debug_assert_eq!(g_bold.len(), 1);
+    debug_assert_eq!(h_bold.len(), 1);
+    debug_assert_eq!(a.len(), 1);
+    debug_assert_eq!(b.len(), 1);
+
+    // We simply send a/b
+    transcript.push_scalar(a[0]);
+    transcript.push_scalar(b[0]);
+    Ok(())
+  }
+
+  /*
+  This has room for optimization worth investigating further. It currently takes
+  an iterative approach. It can be optimized further via divide and conquer.
+
+  Assume there are 4 challenges.
+
+  Iterative approach (current):
+    1. Do the optimal multiplications across challenge column 0 and 1.
+    2. Do the optimal multiplications across that result and column 2.
+    3. Do the optimal multiplications across that result and column 3.
+
+  Divide and conquer (worth investigating further):
+    1. Do the optimal multiplications across challenge column 0 and 1.
+    2. Do the optimal multiplications across challenge column 2 and 3.
+    3. Multiply both results together.
+
+  When there are 4 challenges (n=16), the iterative approach does 28 multiplications
+  versus divide and conquer's 24.
+  */
+  fn challenge_products(challenges: &[(C::F, C::F)]) -> Vec<C::F> {
+    let mut products = vec![C::F::ONE; 1 << challenges.len()];
+
+    if !challenges.is_empty() {
+      products[0] = challenges[0].1;
+      products[1] = challenges[0].0;
+
+      for (j, challenge) in challenges.iter().enumerate().skip(1) {
+        let mut slots = (1 << (j + 1)) - 1;
+        while slots > 0 {
+          products[slots] = products[slots / 2] * challenge.0;
+          products[slots - 1] = products[slots / 2] * challenge.1;
+
+          slots = slots.saturating_sub(2);
+        }
+      }
+
+      // Sanity check since if the above failed to populate, it'd be critical
+      for product in &products {
+        debug_assert!(!bool::from(product.is_zero()));
+      }
+    }
+
+    products
+  }
+
+  /// Queue an Inner-Product proof for batch verification.
+  ///
+  /// This will return Err if there is an error. This will return Ok if the proof was successfully
+  /// queued for batch verification. The caller is required to verify the batch in order to ensure
+  /// the proof is actually correct.
+  pub(crate) fn verify(
+    self,
+    verifier: &mut BatchVerifier<C>,
+    transcript: &mut VerifierTranscript,
+  ) -> Result<(), IpError> {
+    let IpStatement { generators, h_bold_weights, u, P } = self;
+
+    // Calculate the discrete log w.r.t. 2 for the amount of generators present
+    let mut lr_len = 0;
+    while (1 << lr_len) < generators.g_bold_slice().len() {
+      lr_len += 1;
+    }
+
+    let weight = match P {
+      P::Prover(_) => panic!("prove called with a P specification which was for the prover"),
+      P::Verifier { verifier_weight } => verifier_weight,
+    };
+
+    // Again, we start with the `else: (n > 1)` case
+
+    // We need x, x_inv per lines 25-27 for lines 28-31
+    let mut L = Vec::with_capacity(lr_len);
+    let mut R = Vec::with_capacity(lr_len);
+    let mut xs: Vec<C::F> = Vec::with_capacity(lr_len);
+    for _ in 0 .. lr_len {
+      L.push(transcript.read_point::<C>().map_err(|_| IpError::IncompleteProof)?);
+      R.push(transcript.read_point::<C>().map_err(|_| IpError::IncompleteProof)?);
+      xs.push(transcript.challenge());
+    }
+
+    // We calculate their inverse in batch
+    let mut x_invs = xs.clone();
+    {
+      let mut scratch = vec![C::F::ZERO; x_invs.len()];
+      ciphersuite::group::ff::BatchInverter::invert_with_external_scratch(
+        &mut x_invs,
+        &mut scratch,
+      );
+    }
+
+    // Now, with x and x_inv, we need to calculate g_bold', h_bold', P'
+    //
+    // For the sake of performance, we solely want to calculate all of these in terms of scalings
+    // for g_bold, h_bold, P, and don't want to actually perform intermediary scalings of the
+    // points
+    //
+    // L and R are easy, as it's simply x**2, x**-2
+    //
+    // For the series of g_bold, h_bold, we use the `challenge_products` function
+    // For how that works, please see its own documentation
+    let product_cache = {
+      let mut challenges = Vec::with_capacity(lr_len);
+
+      let x_iter = xs.into_iter().zip(x_invs);
+      let lr_iter = L.into_iter().zip(R);
+      for ((x, x_inv), (L, R)) in x_iter.zip(lr_iter) {
+        challenges.push((x, x_inv));
+        verifier.additional.push((weight * x.square(), L));
+        verifier.additional.push((weight * x_inv.square(), R));
+      }
+
+      Self::challenge_products(&challenges)
+    };
+
+    // And now for the `if n = 1` case
+    let a = transcript.read_scalar::<C>().map_err(|_| IpError::IncompleteProof)?;
+    let b = transcript.read_scalar::<C>().map_err(|_| IpError::IncompleteProof)?;
+    let c = a * b;
+
+    // The multiexp of these terms equate to the final permutation of P
+    // We now add terms for a * g_bold' + b * h_bold' b + c * u, with the scalars negative such
+    // that the terms sum to 0 for an honest prover
+
+    // The g_bold * a term case from line 16
+    #[allow(clippy::needless_range_loop)]
+    for i in 0 .. generators.g_bold_slice().len() {
+      verifier.g_bold[i] -= weight * product_cache[i] * a;
+    }
+    // The h_bold * b term case from line 16
+    for i in 0 .. generators.h_bold_slice().len() {
+      verifier.h_bold[i] -=
+        weight * product_cache[product_cache.len() - 1 - i] * b * h_bold_weights[i];
+    }
+    // The c * u term case from line 16
+    verifier.g -= weight * c * u;
+
+    Ok(())
+  }
+}
--- a/crypto/evrf/generalized-bulletproofs/src/lib.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/lib.rs
@@ -0,0 +1,328 @@
+#![cfg_attr(docsrs, feature(doc_auto_cfg))]
+#![doc = include_str!("../README.md")]
+#![deny(missing_docs)]
+#![allow(non_snake_case)]
+
+use core::fmt;
+use std::collections::HashSet;
+
+use zeroize::Zeroize;
+
+use multiexp::{multiexp, multiexp_vartime};
+use ciphersuite::{
+  group::{ff::Field, Group, GroupEncoding},
+  Ciphersuite,
+};
+
+mod scalar_vector;
+pub use scalar_vector::ScalarVector;
+mod point_vector;
+pub use point_vector::PointVector;
+
+/// The transcript formats.
+pub mod transcript;
+
+pub(crate) mod inner_product;
+
+pub(crate) mod lincomb;
+
+/// The arithmetic circuit proof.
+pub mod arithmetic_circuit_proof;
+
+/// Functionlity useful when testing.
+#[cfg(any(test, feature = "tests"))]
+pub mod tests;
+
+/// Calculate the nearest power of two greater than or equivalent to the argument.
+pub(crate) fn padded_pow_of_2(i: usize) -> usize {
+  let mut next_pow_of_2 = 1;
+  while next_pow_of_2 < i {
+    next_pow_of_2 <<= 1;
+  }
+  next_pow_of_2
+}
+
+/// An error from working with generators.
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+pub enum GeneratorsError {
+  /// The provided list of generators for `g` (bold) was empty.
+  GBoldEmpty,
+  /// The provided list of generators for `h` (bold) did not match `g` (bold) in length.
+  DifferingGhBoldLengths,
+  /// The amount of provided generators were not a power of two.
+  NotPowerOfTwo,
+  /// A generator was used multiple times.
+  DuplicatedGenerator,
+}
+
+/// A full set of generators.
+#[derive(Clone)]
+pub struct Generators<C: Ciphersuite> {
+  g: C::G,
+  h: C::G,
+
+  g_bold: Vec<C::G>,
+  h_bold: Vec<C::G>,
+  h_sum: Vec<C::G>,
+}
+
+/// A batch verifier of proofs.
+#[must_use]
+#[derive(Clone)]
+pub struct BatchVerifier<C: Ciphersuite> {
+  g: C::F,
+  h: C::F,
+
+  g_bold: Vec<C::F>,
+  h_bold: Vec<C::F>,
+  h_sum: Vec<C::F>,
+
+  additional: Vec<(C::F, C::G)>,
+}
+
+impl<C: Ciphersuite> fmt::Debug for Generators<C> {
+  fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
+    let g = self.g.to_bytes();
+    let g: &[u8] = g.as_ref();
+
+    let h = self.h.to_bytes();
+    let h: &[u8] = h.as_ref();
+
+    fmt.debug_struct("Generators").field("g", &g).field("h", &h).finish_non_exhaustive()
+  }
+}
+
+/// The generators for a specific proof.
+///
+/// This potentially have been reduced in size from the original set of generators, as beneficial
+/// to performance.
+#[derive(Copy, Clone)]
+pub struct ProofGenerators<'a, C: Ciphersuite> {
+  g: &'a C::G,
+  h: &'a C::G,
+
+  g_bold: &'a [C::G],
+  h_bold: &'a [C::G],
+}
+
+impl<C: Ciphersuite> fmt::Debug for ProofGenerators<'_, C> {
+  fn fmt(&self, fmt: &mut fmt::Formatter<'_>) -> fmt::Result {
+    let g = self.g.to_bytes();
+    let g: &[u8] = g.as_ref();
+
+    let h = self.h.to_bytes();
+    let h: &[u8] = h.as_ref();
+
+    fmt.debug_struct("ProofGenerators").field("g", &g).field("h", &h).finish_non_exhaustive()
+  }
+}
+
+impl<C: Ciphersuite> Generators<C> {
+  /// Construct an instance of Generators for usage with Bulletproofs.
+  pub fn new(
+    g: C::G,
+    h: C::G,
+    g_bold: Vec<C::G>,
+    h_bold: Vec<C::G>,
+  ) -> Result<Self, GeneratorsError> {
+    if g_bold.is_empty() {
+      Err(GeneratorsError::GBoldEmpty)?;
+    }
+    if g_bold.len() != h_bold.len() {
+      Err(GeneratorsError::DifferingGhBoldLengths)?;
+    }
+    if padded_pow_of_2(g_bold.len()) != g_bold.len() {
+      Err(GeneratorsError::NotPowerOfTwo)?;
+    }
+
+    let mut set = HashSet::new();
+    let mut add_generator = |generator: &C::G| {
+      assert!(!bool::from(generator.is_identity()));
+      let bytes = generator.to_bytes();
+      !set.insert(bytes.as_ref().to_vec())
+    };
+
+    assert!(!add_generator(&g), "g was prior present in empty set");
+    if add_generator(&h) {
+      Err(GeneratorsError::DuplicatedGenerator)?;
+    }
+    for g in &g_bold {
+      if add_generator(g) {
+        Err(GeneratorsError::DuplicatedGenerator)?;
+      }
+    }
+    for h in &h_bold {
+      if add_generator(h) {
+        Err(GeneratorsError::DuplicatedGenerator)?;
+      }
+    }
+
+    let mut running_h_sum = C::G::identity();
+    let mut h_sum = vec![];
+    let mut next_pow_of_2 = 1;
+    for (i, h) in h_bold.iter().enumerate() {
+      running_h_sum += h;
+      if (i + 1) == next_pow_of_2 {
+        h_sum.push(running_h_sum);
+        next_pow_of_2 *= 2;
+      }
+    }
+
+    Ok(Generators { g, h, g_bold, h_bold, h_sum })
+  }
+
+  /// Create a BatchVerifier for proofs which use these generators.
+  pub fn batch_verifier(&self) -> BatchVerifier<C> {
+    BatchVerifier {
+      g: C::F::ZERO,
+      h: C::F::ZERO,
+
+      g_bold: vec![C::F::ZERO; self.g_bold.len()],
+      h_bold: vec![C::F::ZERO; self.h_bold.len()],
+      h_sum: vec![C::F::ZERO; self.h_sum.len()],
+
+      additional: Vec::with_capacity(128),
+    }
+  }
+
+  /// Verify all proofs queued for batch verification in this BatchVerifier.
+  #[must_use]
+  pub fn verify(&self, verifier: BatchVerifier<C>) -> bool {
+    multiexp_vartime(
+      &[(verifier.g, self.g), (verifier.h, self.h)]
+        .into_iter()
+        .chain(verifier.g_bold.into_iter().zip(self.g_bold.iter().cloned()))
+        .chain(verifier.h_bold.into_iter().zip(self.h_bold.iter().cloned()))
+        .chain(verifier.h_sum.into_iter().zip(self.h_sum.iter().cloned()))
+        .chain(verifier.additional)
+        .collect::<Vec<_>>(),
+    )
+    .is_identity()
+    .into()
+  }
+
+  /// The `g` generator.
+  pub fn g(&self) -> C::G {
+    self.g
+  }
+
+  /// The `h` generator.
+  pub fn h(&self) -> C::G {
+    self.h
+  }
+
+  /// A slice to view the `g` (bold) generators.
+  pub fn g_bold_slice(&self) -> &[C::G] {
+    &self.g_bold
+  }
+
+  /// A slice to view the `h` (bold) generators.
+  pub fn h_bold_slice(&self) -> &[C::G] {
+    &self.h_bold
+  }
+
+  /// Reduce a set of generators to the quantity necessary to support a certain amount of
+  /// in-circuit multiplications/terms in a Pedersen vector commitment.
+  ///
+  /// Returns None if reducing to 0 or if the generators reduced are insufficient to provide this
+  /// many generators.
+  pub fn reduce(&self, generators: usize) -> Option<ProofGenerators<'_, C>> {
+    if generators == 0 {
+      None?;
+    }
+
+    // Round to the nearest power of 2
+    let generators = padded_pow_of_2(generators);
+    if generators > self.g_bold.len() {
+      None?;
+    }
+
+    Some(ProofGenerators {
+      g: &self.g,
+      h: &self.h,
+
+      g_bold: &self.g_bold[.. generators],
+      h_bold: &self.h_bold[.. generators],
+    })
+  }
+}
+
+impl<'a, C: Ciphersuite> ProofGenerators<'a, C> {
+  pub(crate) fn len(&self) -> usize {
+    self.g_bold.len()
+  }
+
+  pub(crate) fn g(&self) -> C::G {
+    *self.g
+  }
+
+  pub(crate) fn h(&self) -> C::G {
+    *self.h
+  }
+
+  pub(crate) fn g_bold(&self, i: usize) -> C::G {
+    self.g_bold[i]
+  }
+
+  pub(crate) fn h_bold(&self, i: usize) -> C::G {
+    self.h_bold[i]
+  }
+
+  pub(crate) fn g_bold_slice(&self) -> &[C::G] {
+    self.g_bold
+  }
+
+  pub(crate) fn h_bold_slice(&self) -> &[C::G] {
+    self.h_bold
+  }
+}
+
+/// The opening of a Pedersen commitment.
+#[derive(Clone, Copy, PartialEq, Eq, Debug, Zeroize)]
+pub struct PedersenCommitment<C: Ciphersuite> {
+  /// The value committed to.
+  pub value: C::F,
+  /// The mask blinding the value committed to.
+  pub mask: C::F,
+}
+
+impl<C: Ciphersuite> PedersenCommitment<C> {
+  /// Commit to this value, yielding the Pedersen commitment.
+  pub fn commit(&self, g: C::G, h: C::G) -> C::G {
+    multiexp(&[(self.value, g), (self.mask, h)])
+  }
+}
+
+/// The opening of a Pedersen vector commitment.
+#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+pub struct PedersenVectorCommitment<C: Ciphersuite> {
+  /// The values committed to across the `g` (bold) generators.
+  pub g_values: ScalarVector<C::F>,
+  /// The values committed to across the `h` (bold) generators.
+  pub h_values: ScalarVector<C::F>,
+  /// The mask blinding the values committed to.
+  pub mask: C::F,
+}
+
+impl<C: Ciphersuite> PedersenVectorCommitment<C> {
+  /// Commit to the vectors of values.
+  ///
+  /// This function returns None if the amount of generators is less than the amount of values
+  /// within the relevant vector.
+  pub fn commit(&self, g_bold: &[C::G], h_bold: &[C::G], h: C::G) -> Option<C::G> {
+    if (g_bold.len() < self.g_values.len()) || (h_bold.len() < self.h_values.len()) {
+      None?;
+    };
+
+    let mut terms = vec![(self.mask, h)];
+    for pair in self.g_values.0.iter().cloned().zip(g_bold.iter().cloned()) {
+      terms.push(pair);
+    }
+    for pair in self.h_values.0.iter().cloned().zip(h_bold.iter().cloned()) {
+      terms.push(pair);
+    }
+    let res = multiexp(&terms);
+    terms.zeroize();
+    Some(res)
+  }
+}
--- a/crypto/evrf/generalized-bulletproofs/src/lincomb.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/lincomb.rs
@@ -0,0 +1,265 @@
+use core::ops::{Add, Sub, Mul};
+
+use zeroize::Zeroize;
+
+use ciphersuite::group::ff::PrimeField;
+
+use crate::ScalarVector;
+
+/// A reference to a variable usable within linear combinations.
+#[derive(Clone, Copy, PartialEq, Eq, Debug)]
+#[allow(non_camel_case_types)]
+pub enum Variable {
+  /// A variable within the left vector of vectors multiplied against each other.
+  aL(usize),
+  /// A variable within the right vector of vectors multiplied against each other.
+  aR(usize),
+  /// A variable within the output vector of the left vector multiplied by the right vector.
+  aO(usize),
+  /// A variable within a Pedersen vector commitment, committed to with a generator from `g` (bold).
+  CG {
+    /// The commitment being indexed.
+    commitment: usize,
+    /// The index of the variable.
+    index: usize,
+  },
+  /// A variable within a Pedersen vector commitment, committed to with a generator from `h` (bold).
+  CH {
+    /// The commitment being indexed.
+    commitment: usize,
+    /// The index of the variable.
+    index: usize,
+  },
+  /// A variable within a Pedersen commitment.
+  V(usize),
+}
+
+// Does a NOP as there shouldn't be anything critical here
+impl Zeroize for Variable {
+  fn zeroize(&mut self) {}
+}
+
+/// A linear combination.
+///
+/// Specifically, `WL aL + WR aR + WO aO + WCG C_G + WCH C_H + WV V + c`.
+#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+#[must_use]
+pub struct LinComb<F: PrimeField> {
+  pub(crate) highest_a_index: Option<usize>,
+  pub(crate) highest_c_index: Option<usize>,
+  pub(crate) highest_v_index: Option<usize>,
+
+  // Sparse representation of WL/WR/WO
+  pub(crate) WL: Vec<(usize, F)>,
+  pub(crate) WR: Vec<(usize, F)>,
+  pub(crate) WO: Vec<(usize, F)>,
+  // Sparse representation once within a commitment
+  pub(crate) WCG: Vec<Vec<(usize, F)>>,
+  pub(crate) WCH: Vec<Vec<(usize, F)>>,
+  // Sparse representation of WV
+  pub(crate) WV: Vec<(usize, F)>,
+  pub(crate) c: F,
+}
+
+impl<F: PrimeField> From<Variable> for LinComb<F> {
+  fn from(constrainable: Variable) -> LinComb<F> {
+    LinComb::empty().term(F::ONE, constrainable)
+  }
+}
+
+impl<F: PrimeField> Add<&LinComb<F>> for LinComb<F> {
+  type Output = Self;
+
+  fn add(mut self, constraint: &Self) -> Self {
+    self.highest_a_index = self.highest_a_index.max(constraint.highest_a_index);
+    self.highest_c_index = self.highest_c_index.max(constraint.highest_c_index);
+    self.highest_v_index = self.highest_v_index.max(constraint.highest_v_index);
+
+    self.WL.extend(&constraint.WL);
+    self.WR.extend(&constraint.WR);
+    self.WO.extend(&constraint.WO);
+    while self.WCG.len() < constraint.WCG.len() {
+      self.WCG.push(vec![]);
+    }
+    while self.WCH.len() < constraint.WCH.len() {
+      self.WCH.push(vec![]);
+    }
+    for (sWC, cWC) in self.WCG.iter_mut().zip(&constraint.WCG) {
+      sWC.extend(cWC);
+    }
+    for (sWC, cWC) in self.WCH.iter_mut().zip(&constraint.WCH) {
+      sWC.extend(cWC);
+    }
+    self.WV.extend(&constraint.WV);
+    self.c += constraint.c;
+    self
+  }
+}
+
+impl<F: PrimeField> Sub<&LinComb<F>> for LinComb<F> {
+  type Output = Self;
+
+  fn sub(mut self, constraint: &Self) -> Self {
+    self.highest_a_index = self.highest_a_index.max(constraint.highest_a_index);
+    self.highest_c_index = self.highest_c_index.max(constraint.highest_c_index);
+    self.highest_v_index = self.highest_v_index.max(constraint.highest_v_index);
+
+    self.WL.extend(constraint.WL.iter().map(|(i, weight)| (*i, -*weight)));
+    self.WR.extend(constraint.WR.iter().map(|(i, weight)| (*i, -*weight)));
+    self.WO.extend(constraint.WO.iter().map(|(i, weight)| (*i, -*weight)));
+    while self.WCG.len() < constraint.WCG.len() {
+      self.WCG.push(vec![]);
+    }
+    while self.WCH.len() < constraint.WCH.len() {
+      self.WCH.push(vec![]);
+    }
+    for (sWC, cWC) in self.WCG.iter_mut().zip(&constraint.WCG) {
+      sWC.extend(cWC.iter().map(|(i, weight)| (*i, -*weight)));
+    }
+    for (sWC, cWC) in self.WCH.iter_mut().zip(&constraint.WCH) {
+      sWC.extend(cWC.iter().map(|(i, weight)| (*i, -*weight)));
+    }
+    self.WV.extend(constraint.WV.iter().map(|(i, weight)| (*i, -*weight)));
+    self.c -= constraint.c;
+    self
+  }
+}
+
+impl<F: PrimeField> Mul<F> for LinComb<F> {
+  type Output = Self;
+
+  fn mul(mut self, scalar: F) -> Self {
+    for (_, weight) in self.WL.iter_mut() {
+      *weight *= scalar;
+    }
+    for (_, weight) in self.WR.iter_mut() {
+      *weight *= scalar;
+    }
+    for (_, weight) in self.WO.iter_mut() {
+      *weight *= scalar;
+    }
+    for WC in self.WCG.iter_mut() {
+      for (_, weight) in WC {
+        *weight *= scalar;
+      }
+    }
+    for WC in self.WCH.iter_mut() {
+      for (_, weight) in WC {
+        *weight *= scalar;
+      }
+    }
+    for (_, weight) in self.WV.iter_mut() {
+      *weight *= scalar;
+    }
+    self.c *= scalar;
+    self
+  }
+}
+
+impl<F: PrimeField> LinComb<F> {
+  /// Create an empty linear combination.
+  pub fn empty() -> Self {
+    Self {
+      highest_a_index: None,
+      highest_c_index: None,
+      highest_v_index: None,
+      WL: vec![],
+      WR: vec![],
+      WO: vec![],
+      WCG: vec![],
+      WCH: vec![],
+      WV: vec![],
+      c: F::ZERO,
+    }
+  }
+
+  /// Add a new instance of a term to this linear combination.
+  pub fn term(mut self, scalar: F, constrainable: Variable) -> Self {
+    match constrainable {
+      Variable::aL(i) => {
+        self.highest_a_index = self.highest_a_index.max(Some(i));
+        self.WL.push((i, scalar))
+      }
+      Variable::aR(i) => {
+        self.highest_a_index = self.highest_a_index.max(Some(i));
+        self.WR.push((i, scalar))
+      }
+      Variable::aO(i) => {
+        self.highest_a_index = self.highest_a_index.max(Some(i));
+        self.WO.push((i, scalar))
+      }
+      Variable::CG { commitment: i, index: j } => {
+        self.highest_c_index = self.highest_c_index.max(Some(i));
+        self.highest_a_index = self.highest_a_index.max(Some(j));
+        while self.WCG.len() <= i {
+          self.WCG.push(vec![]);
+        }
+        self.WCG[i].push((j, scalar))
+      }
+      Variable::CH { commitment: i, index: j } => {
+        self.highest_c_index = self.highest_c_index.max(Some(i));
+        self.highest_a_index = self.highest_a_index.max(Some(j));
+        while self.WCH.len() <= i {
+          self.WCH.push(vec![]);
+        }
+        self.WCH[i].push((j, scalar))
+      }
+      Variable::V(i) => {
+        self.highest_v_index = self.highest_v_index.max(Some(i));
+        self.WV.push((i, scalar));
+      }
+    };
+    self
+  }
+
+  /// Add to the constant c.
+  pub fn constant(mut self, scalar: F) -> Self {
+    self.c += scalar;
+    self
+  }
+
+  /// View the current weights for aL.
+  pub fn WL(&self) -> &[(usize, F)] {
+    &self.WL
+  }
+
+  /// View the current weights for aR.
+  pub fn WR(&self) -> &[(usize, F)] {
+    &self.WR
+  }
+
+  /// View the current weights for aO.
+  pub fn WO(&self) -> &[(usize, F)] {
+    &self.WO
+  }
+
+  /// View the current weights for CG.
+  pub fn WCG(&self) -> &[Vec<(usize, F)>] {
+    &self.WCG
+  }
+
+  /// View the current weights for CH.
+  pub fn WCH(&self) -> &[Vec<(usize, F)>] {
+    &self.WCH
+  }
+
+  /// View the current weights for V.
+  pub fn WV(&self) -> &[(usize, F)] {
+    &self.WV
+  }
+
+  /// View the current constant.
+  pub fn c(&self) -> F {
+    self.c
+  }
+}
+
+pub(crate) fn accumulate_vector<F: PrimeField>(
+  accumulator: &mut ScalarVector<F>,
+  values: &[(usize, F)],
+  weight: F,
+) {
+  for (i, coeff) in values {
+    accumulator[*i] += *coeff * weight;
+  }
+}
--- a/crypto/evrf/generalized-bulletproofs/src/point_vector.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/point_vector.rs
@@ -0,0 +1,121 @@
+use core::ops::{Index, IndexMut};
+
+use zeroize::Zeroize;
+
+use ciphersuite::Ciphersuite;
+
+#[cfg(test)]
+use multiexp::multiexp;
+
+use crate::ScalarVector;
+
+/// A point vector struct with the functionality necessary for Bulletproofs.
+///
+/// The math operations for this panic upon any invalid operation, such as if vectors of different
+/// lengths are added. The full extent of invalidity is not fully defined. Only field access is
+/// guaranteed to have a safe, public API.
+#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+pub struct PointVector<C: Ciphersuite>(pub(crate) Vec<C::G>);
+
+impl<C: Ciphersuite> Index<usize> for PointVector<C> {
+  type Output = C::G;
+  fn index(&self, index: usize) -> &C::G {
+    &self.0[index]
+  }
+}
+
+impl<C: Ciphersuite> IndexMut<usize> for PointVector<C> {
+  fn index_mut(&mut self, index: usize) -> &mut C::G {
+    &mut self.0[index]
+  }
+}
+
+impl<C: Ciphersuite> PointVector<C> {
+  /*
+  pub(crate) fn add(&self, point: impl AsRef<C::G>) -> Self {
+    let mut res = self.clone();
+    for val in res.0.iter_mut() {
+      *val += point.as_ref();
+    }
+    res
+  }
+  pub(crate) fn sub(&self, point: impl AsRef<C::G>) -> Self {
+    let mut res = self.clone();
+    for val in res.0.iter_mut() {
+      *val -= point.as_ref();
+    }
+    res
+  }
+
+  pub(crate) fn mul(&self, scalar: impl core::borrow::Borrow<C::F>) -> Self {
+    let mut res = self.clone();
+    for val in res.0.iter_mut() {
+      *val *= scalar.borrow();
+    }
+    res
+  }
+
+  pub(crate) fn add_vec(&self, vector: &Self) -> Self {
+    debug_assert_eq!(self.len(), vector.len());
+    let mut res = self.clone();
+    for (i, val) in res.0.iter_mut().enumerate() {
+      *val += vector.0[i];
+    }
+    res
+  }
+
+  pub(crate) fn sub_vec(&self, vector: &Self) -> Self {
+    debug_assert_eq!(self.len(), vector.len());
+    let mut res = self.clone();
+    for (i, val) in res.0.iter_mut().enumerate() {
+      *val -= vector.0[i];
+    }
+    res
+  }
+  */
+
+  pub(crate) fn mul_vec(&self, vector: &ScalarVector<C::F>) -> Self {
+    debug_assert_eq!(self.len(), vector.len());
+    let mut res = self.clone();
+    for (i, val) in res.0.iter_mut().enumerate() {
+      *val *= vector.0[i];
+    }
+    res
+  }
+
+  #[cfg(test)]
+  pub(crate) fn multiexp(&self, vector: &crate::ScalarVector<C::F>) -> C::G {
+    debug_assert_eq!(self.len(), vector.len());
+    let mut res = Vec::with_capacity(self.len());
+    for (point, scalar) in self.0.iter().copied().zip(vector.0.iter().copied()) {
+      res.push((scalar, point));
+    }
+    multiexp(&res)
+  }
+
+  /*
+  pub(crate) fn multiexp_vartime(&self, vector: &ScalarVector<C::F>) -> C::G {
+    debug_assert_eq!(self.len(), vector.len());
+    let mut res = Vec::with_capacity(self.len());
+    for (point, scalar) in self.0.iter().copied().zip(vector.0.iter().copied()) {
+      res.push((scalar, point));
+    }
+    multiexp_vartime(&res)
+  }
+
+  pub(crate) fn sum(&self) -> C::G {
+    self.0.iter().sum()
+  }
+  */
+
+  pub(crate) fn len(&self) -> usize {
+    self.0.len()
+  }
+
+  pub(crate) fn split(mut self) -> (Self, Self) {
+    assert!(self.len() > 1);
+    let r = self.0.split_off(self.0.len() / 2);
+    debug_assert_eq!(self.len(), r.len());
+    (self, PointVector(r))
+  }
+}
--- a/crypto/evrf/generalized-bulletproofs/src/scalar_vector.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/scalar_vector.rs
@@ -0,0 +1,146 @@
+use core::ops::{Index, IndexMut, Add, Sub, Mul};
+
+use zeroize::Zeroize;
+
+use ciphersuite::group::ff::PrimeField;
+
+/// A scalar vector struct with the functionality necessary for Bulletproofs.
+///
+/// The math operations for this panic upon any invalid operation, such as if vectors of different
+/// lengths are added. The full extent of invalidity is not fully defined. Only `new`, `len`,
+/// and field access is guaranteed to have a safe, public API.
+#[derive(Clone, PartialEq, Eq, Debug)]
+pub struct ScalarVector<F: PrimeField>(pub(crate) Vec<F>);
+
+impl<F: PrimeField + Zeroize> Zeroize for ScalarVector<F> {
+  fn zeroize(&mut self) {
+    self.0.zeroize()
+  }
+}
+
+impl<F: PrimeField> Index<usize> for ScalarVector<F> {
+  type Output = F;
+  fn index(&self, index: usize) -> &F {
+    &self.0[index]
+  }
+}
+impl<F: PrimeField> IndexMut<usize> for ScalarVector<F> {
+  fn index_mut(&mut self, index: usize) -> &mut F {
+    &mut self.0[index]
+  }
+}
+
+impl<F: PrimeField> Add<F> for ScalarVector<F> {
+  type Output = ScalarVector<F>;
+  fn add(mut self, scalar: F) -> Self {
+    for s in &mut self.0 {
+      *s += scalar;
+    }
+    self
+  }
+}
+impl<F: PrimeField> Sub<F> for ScalarVector<F> {
+  type Output = ScalarVector<F>;
+  fn sub(mut self, scalar: F) -> Self {
+    for s in &mut self.0 {
+      *s -= scalar;
+    }
+    self
+  }
+}
+impl<F: PrimeField> Mul<F> for ScalarVector<F> {
+  type Output = ScalarVector<F>;
+  fn mul(mut self, scalar: F) -> Self {
+    for s in &mut self.0 {
+      *s *= scalar;
+    }
+    self
+  }
+}
+
+impl<F: PrimeField> Add<&ScalarVector<F>> for ScalarVector<F> {
+  type Output = ScalarVector<F>;
+  fn add(mut self, other: &ScalarVector<F>) -> Self {
+    assert_eq!(self.len(), other.len());
+    for (s, o) in self.0.iter_mut().zip(other.0.iter()) {
+      *s += o;
+    }
+    self
+  }
+}
+impl<F: PrimeField> Sub<&ScalarVector<F>> for ScalarVector<F> {
+  type Output = ScalarVector<F>;
+  fn sub(mut self, other: &ScalarVector<F>) -> Self {
+    assert_eq!(self.len(), other.len());
+    for (s, o) in self.0.iter_mut().zip(other.0.iter()) {
+      *s -= o;
+    }
+    self
+  }
+}
+impl<F: PrimeField> Mul<&ScalarVector<F>> for ScalarVector<F> {
+  type Output = ScalarVector<F>;
+  fn mul(mut self, other: &ScalarVector<F>) -> Self {
+    assert_eq!(self.len(), other.len());
+    for (s, o) in self.0.iter_mut().zip(other.0.iter()) {
+      *s *= o;
+    }
+    self
+  }
+}
+
+impl<F: PrimeField> ScalarVector<F> {
+  /// Create a new scalar vector, initialized with `len` zero scalars.
+  pub fn new(len: usize) -> Self {
+    ScalarVector(vec![F::ZERO; len])
+  }
+
+  pub(crate) fn powers(x: F, len: usize) -> Self {
+    assert!(len != 0);
+
+    let mut res = Vec::with_capacity(len);
+    res.push(F::ONE);
+    res.push(x);
+    for i in 2 .. len {
+      res.push(res[i - 1] * x);
+    }
+    res.truncate(len);
+    ScalarVector(res)
+  }
+
+  /// The length of this scalar vector.
+  #[allow(clippy::len_without_is_empty)]
+  pub fn len(&self) -> usize {
+    self.0.len()
+  }
+
+  /*
+  pub(crate) fn sum(mut self) -> F {
+    self.0.drain(..).sum()
+  }
+  */
+
+  pub(crate) fn inner_product<'a, V: Iterator<Item = &'a F>>(&self, vector: V) -> F {
+    let mut count = 0;
+    let mut res = F::ZERO;
+    for (a, b) in self.0.iter().zip(vector) {
+      res += *a * b;
+      count += 1;
+    }
+    debug_assert_eq!(self.len(), count);
+    res
+  }
+
+  pub(crate) fn split(mut self) -> (Self, Self) {
+    assert!(self.len() > 1);
+    let r = self.0.split_off(self.0.len() / 2);
+    debug_assert_eq!(self.len(), r.len());
+    (self, ScalarVector(r))
+  }
+}
+
+impl<F: PrimeField> From<Vec<F>> for ScalarVector<F> {
+  fn from(vec: Vec<F>) -> Self {
+    Self(vec)
+  }
+}
--- a/crypto/evrf/generalized-bulletproofs/src/tests/arithmetic_circuit_proof.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/tests/arithmetic_circuit_proof.rs
@@ -0,0 +1,250 @@
+use rand_core::{RngCore, OsRng};
+
+use ciphersuite::{group::ff::Field, Ciphersuite, Ristretto};
+
+use crate::{
+  ScalarVector, PedersenCommitment, PedersenVectorCommitment,
+  transcript::*,
+  arithmetic_circuit_proof::{
+    Variable, LinComb, ArithmeticCircuitStatement, ArithmeticCircuitWitness,
+  },
+  tests::generators,
+};
+
+#[test]
+fn test_zero_arithmetic_circuit() {
+  let generators = generators(1);
+
+  let value = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+  let gamma = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+  let commitment = (generators.g() * value) + (generators.h() * gamma);
+  let V = vec![commitment];
+
+  let aL = ScalarVector::<<Ristretto as Ciphersuite>::F>(vec![<Ristretto as Ciphersuite>::F::ZERO]);
+  let aR = aL.clone();
+
+  let mut transcript = Transcript::new([0; 32]);
+  let commitments = transcript.write_commitments(vec![], V);
+  let statement = ArithmeticCircuitStatement::<Ristretto>::new(
+    generators.reduce(1).unwrap(),
+    vec![],
+    commitments.clone(),
+  )
+  .unwrap();
+  let witness = ArithmeticCircuitWitness::<Ristretto>::new(
+    aL,
+    aR,
+    vec![],
+    vec![PedersenCommitment { value, mask: gamma }],
+  )
+  .unwrap();
+
+  let proof = {
+    statement.clone().prove(&mut OsRng, &mut transcript, witness).unwrap();
+    transcript.complete()
+  };
+  let mut verifier = generators.batch_verifier();
+
+  let mut transcript = VerifierTranscript::new([0; 32], &proof);
+  let verifier_commmitments = transcript.read_commitments(0, 1);
+  assert_eq!(commitments, verifier_commmitments.unwrap());
+  statement.verify(&mut OsRng, &mut verifier, &mut transcript).unwrap();
+  assert!(generators.verify(verifier));
+}
+
+#[test]
+fn test_vector_commitment_arithmetic_circuit() {
+  let generators = generators(2);
+  let reduced = generators.reduce(2).unwrap();
+
+  let v1 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+  let v2 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+  let v3 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+  let v4 = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+  let gamma = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+  let commitment = (reduced.g_bold(0) * v1) +
+    (reduced.g_bold(1) * v2) +
+    (reduced.h_bold(0) * v3) +
+    (reduced.h_bold(1) * v4) +
+    (generators.h() * gamma);
+  let V = vec![];
+  let C = vec![commitment];
+
+  let zero_vec =
+    || ScalarVector::<<Ristretto as Ciphersuite>::F>(vec![<Ristretto as Ciphersuite>::F::ZERO]);
+
+  let aL = zero_vec();
+  let aR = zero_vec();
+
+  let mut transcript = Transcript::new([0; 32]);
+  let commitments = transcript.write_commitments(C, V);
+  let statement = ArithmeticCircuitStatement::<Ristretto>::new(
+    reduced,
+    vec![LinComb::empty()
+      .term(<Ristretto as Ciphersuite>::F::ONE, Variable::CG { commitment: 0, index: 0 })
+      .term(<Ristretto as Ciphersuite>::F::from(2u64), Variable::CG { commitment: 0, index: 1 })
+      .term(<Ristretto as Ciphersuite>::F::from(3u64), Variable::CH { commitment: 0, index: 0 })
+      .term(<Ristretto as Ciphersuite>::F::from(4u64), Variable::CH { commitment: 0, index: 1 })
+      .constant(-(v1 + (v2 + v2) + (v3 + v3 + v3) + (v4 + v4 + v4 + v4)))],
+    commitments.clone(),
+  )
+  .unwrap();
+  let witness = ArithmeticCircuitWitness::<Ristretto>::new(
+    aL,
+    aR,
+    vec![PedersenVectorCommitment {
+      g_values: ScalarVector(vec![v1, v2]),
+      h_values: ScalarVector(vec![v3, v4]),
+      mask: gamma,
+    }],
+    vec![],
+  )
+  .unwrap();
+
+  let proof = {
+    statement.clone().prove(&mut OsRng, &mut transcript, witness).unwrap();
+    transcript.complete()
+  };
+  let mut verifier = generators.batch_verifier();
+
+  let mut transcript = VerifierTranscript::new([0; 32], &proof);
+  let verifier_commmitments = transcript.read_commitments(1, 0);
+  assert_eq!(commitments, verifier_commmitments.unwrap());
+  statement.verify(&mut OsRng, &mut verifier, &mut transcript).unwrap();
+  assert!(generators.verify(verifier));
+}
+
+#[test]
+fn fuzz_test_arithmetic_circuit() {
+  let generators = generators(32);
+
+  for i in 0 .. 100 {
+    dbg!(i);
+
+    // Create aL, aR, aO
+    let mut aL = ScalarVector(vec![]);
+    let mut aR = ScalarVector(vec![]);
+    while aL.len() < ((OsRng.next_u64() % 8) + 1).try_into().unwrap() {
+      aL.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
+    }
+    while aR.len() < aL.len() {
+      aR.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
+    }
+    let aO = aL.clone() * &aR;
+
+    // Create C
+    let mut C = vec![];
+    while C.len() < (OsRng.next_u64() % 16).try_into().unwrap() {
+      let mut g_values = ScalarVector(vec![]);
+      while g_values.0.len() < ((OsRng.next_u64() % 8) + 1).try_into().unwrap() {
+        g_values.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
+      }
+      let mut h_values = ScalarVector(vec![]);
+      while h_values.0.len() < ((OsRng.next_u64() % 8) + 1).try_into().unwrap() {
+        h_values.0.push(<Ristretto as Ciphersuite>::F::random(&mut OsRng));
+      }
+      C.push(PedersenVectorCommitment {
+        g_values,
+        h_values,
+        mask: <Ristretto as Ciphersuite>::F::random(&mut OsRng),
+      });
+    }
+
+    // Create V
+    let mut V = vec![];
+    while V.len() < (OsRng.next_u64() % 4).try_into().unwrap() {
+      V.push(PedersenCommitment {
+        value: <Ristretto as Ciphersuite>::F::random(&mut OsRng),
+        mask: <Ristretto as Ciphersuite>::F::random(&mut OsRng),
+      });
+    }
+
+    // Generate random constraints
+    let mut constraints = vec![];
+    for _ in 0 .. (OsRng.next_u64() % 8).try_into().unwrap() {
+      let mut eval = <Ristretto as Ciphersuite>::F::ZERO;
+      let mut constraint = LinComb::empty();
+
+      for _ in 0 .. (OsRng.next_u64() % 4) {
+        let index = usize::try_from(OsRng.next_u64()).unwrap() % aL.len();
+        let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+        constraint = constraint.term(weight, Variable::aL(index));
+        eval += weight * aL[index];
+      }
+
+      for _ in 0 .. (OsRng.next_u64() % 4) {
+        let index = usize::try_from(OsRng.next_u64()).unwrap() % aR.len();
+        let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+        constraint = constraint.term(weight, Variable::aR(index));
+        eval += weight * aR[index];
+      }
+
+      for _ in 0 .. (OsRng.next_u64() % 4) {
+        let index = usize::try_from(OsRng.next_u64()).unwrap() % aO.len();
+        let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+        constraint = constraint.term(weight, Variable::aO(index));
+        eval += weight * aO[index];
+      }
+
+      for (commitment, C) in C.iter().enumerate() {
+        for _ in 0 .. (OsRng.next_u64() % 4) {
+          let index = usize::try_from(OsRng.next_u64()).unwrap() % C.g_values.len();
+          let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+          constraint = constraint.term(weight, Variable::CG { commitment, index });
+          eval += weight * C.g_values[index];
+        }
+
+        for _ in 0 .. (OsRng.next_u64() % 4) {
+          let index = usize::try_from(OsRng.next_u64()).unwrap() % C.h_values.len();
+          let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+          constraint = constraint.term(weight, Variable::CH { commitment, index });
+          eval += weight * C.h_values[index];
+        }
+      }
+
+      if !V.is_empty() {
+        for _ in 0 .. (OsRng.next_u64() % 4) {
+          let index = usize::try_from(OsRng.next_u64()).unwrap() % V.len();
+          let weight = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+          constraint = constraint.term(weight, Variable::V(index));
+          eval += weight * V[index].value;
+        }
+      }
+
+      constraint = constraint.constant(-eval);
+
+      constraints.push(constraint);
+    }
+
+    let mut transcript = Transcript::new([0; 32]);
+    let commitments = transcript.write_commitments(
+      C.iter()
+        .map(|C| {
+          C.commit(generators.g_bold_slice(), generators.h_bold_slice(), generators.h()).unwrap()
+        })
+        .collect(),
+      V.iter().map(|V| V.commit(generators.g(), generators.h())).collect(),
+    );
+
+    let statement = ArithmeticCircuitStatement::<Ristretto>::new(
+      generators.reduce(16).unwrap(),
+      constraints,
+      commitments.clone(),
+    )
+    .unwrap();
+
+    let witness = ArithmeticCircuitWitness::<Ristretto>::new(aL, aR, C.clone(), V.clone()).unwrap();
+
+    let proof = {
+      statement.clone().prove(&mut OsRng, &mut transcript, witness).unwrap();
+      transcript.complete()
+    };
+    let mut verifier = generators.batch_verifier();
+
+    let mut transcript = VerifierTranscript::new([0; 32], &proof);
+    let verifier_commmitments = transcript.read_commitments(C.len(), V.len());
+    assert_eq!(commitments, verifier_commmitments.unwrap());
+    statement.verify(&mut OsRng, &mut verifier, &mut transcript).unwrap();
+    assert!(generators.verify(verifier));
+  }
+}
--- a/crypto/evrf/generalized-bulletproofs/src/tests/inner_product.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/tests/inner_product.rs
@@ -0,0 +1,113 @@
+// The inner product relation is P = sum(g_bold * a, h_bold * b, g * (a * b))
+
+use rand_core::OsRng;
+
+use ciphersuite::{
+  group::{ff::Field, Group},
+  Ciphersuite, Ristretto,
+};
+
+use crate::{
+  ScalarVector, PointVector,
+  transcript::*,
+  inner_product::{P, IpStatement, IpWitness},
+  tests::generators,
+};
+
+#[test]
+fn test_zero_inner_product() {
+  let P = <Ristretto as Ciphersuite>::G::identity();
+
+  let generators = generators::<Ristretto>(1);
+  let reduced = generators.reduce(1).unwrap();
+  let witness = IpWitness::<Ristretto>::new(
+    ScalarVector::<<Ristretto as Ciphersuite>::F>::new(1),
+    ScalarVector::<<Ristretto as Ciphersuite>::F>::new(1),
+  )
+  .unwrap();
+
+  let proof = {
+    let mut transcript = Transcript::new([0; 32]);
+    IpStatement::<Ristretto>::new(
+      reduced,
+      ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; 1]),
+      <Ristretto as Ciphersuite>::F::ONE,
+      P::Prover(P),
+    )
+    .unwrap()
+    .clone()
+    .prove(&mut transcript, witness)
+    .unwrap();
+    transcript.complete()
+  };
+
+  let mut verifier = generators.batch_verifier();
+  IpStatement::<Ristretto>::new(
+    reduced,
+    ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; 1]),
+    <Ristretto as Ciphersuite>::F::ONE,
+    P::Verifier { verifier_weight: <Ristretto as Ciphersuite>::F::ONE },
+  )
+  .unwrap()
+  .verify(&mut verifier, &mut VerifierTranscript::new([0; 32], &proof))
+  .unwrap();
+  assert!(generators.verify(verifier));
+}
+
+#[test]
+fn test_inner_product() {
+  // P = sum(g_bold * a, h_bold * b)
+  let generators = generators::<Ristretto>(32);
+  let mut verifier = generators.batch_verifier();
+  for i in [1, 2, 4, 8, 16, 32] {
+    let generators = generators.reduce(i).unwrap();
+    let g = generators.g();
+    assert_eq!(generators.len(), i);
+    let mut g_bold = vec![];
+    let mut h_bold = vec![];
+    for i in 0 .. i {
+      g_bold.push(generators.g_bold(i));
+      h_bold.push(generators.h_bold(i));
+    }
+    let g_bold = PointVector::<Ristretto>(g_bold);
+    let h_bold = PointVector::<Ristretto>(h_bold);
+
+    let mut a = ScalarVector::<<Ristretto as Ciphersuite>::F>::new(i);
+    let mut b = ScalarVector::<<Ristretto as Ciphersuite>::F>::new(i);
+
+    for i in 0 .. i {
+      a[i] = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+      b[i] = <Ristretto as Ciphersuite>::F::random(&mut OsRng);
+    }
+
+    let P = g_bold.multiexp(&a) + h_bold.multiexp(&b) + (g * a.inner_product(b.0.iter()));
+
+    let witness = IpWitness::<Ristretto>::new(a, b).unwrap();
+
+    let proof = {
+      let mut transcript = Transcript::new([0; 32]);
+      IpStatement::<Ristretto>::new(
+        generators,
+        ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; i]),
+        <Ristretto as Ciphersuite>::F::ONE,
+        P::Prover(P),
+      )
+      .unwrap()
+      .prove(&mut transcript, witness)
+      .unwrap();
+      transcript.complete()
+    };
+
+    verifier.additional.push((<Ristretto as Ciphersuite>::F::ONE, P));
+    IpStatement::<Ristretto>::new(
+      generators,
+      ScalarVector(vec![<Ristretto as Ciphersuite>::F::ONE; i]),
+      <Ristretto as Ciphersuite>::F::ONE,
+      P::Verifier { verifier_weight: <Ristretto as Ciphersuite>::F::ONE },
+    )
+    .unwrap()
+    .verify(&mut verifier, &mut VerifierTranscript::new([0; 32], &proof))
+    .unwrap();
+  }
+  assert!(generators.verify(verifier));
+}
--- a/crypto/evrf/generalized-bulletproofs/src/tests/mod.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/tests/mod.rs
@@ -0,0 +1,27 @@
+use rand_core::OsRng;
+
+use ciphersuite::{group::Group, Ciphersuite};
+
+use crate::{Generators, padded_pow_of_2};
+
+#[cfg(test)]
+mod inner_product;
+
+#[cfg(test)]
+mod arithmetic_circuit_proof;
+
+/// Generate a set of generators for testing purposes.
+///
+/// This should not be considered secure.
+pub fn generators<C: Ciphersuite>(n: usize) -> Generators<C> {
+  assert_eq!(padded_pow_of_2(n), n, "amount of generators wasn't a power of 2");
+
+  let gens = || {
+    let mut res = Vec::with_capacity(n);
+    for _ in 0 .. n {
+      res.push(C::G::random(&mut OsRng));
+    }
+    res
+  };
+  Generators::new(C::G::random(&mut OsRng), C::G::random(&mut OsRng), gens(), gens()).unwrap()
+}
--- a/crypto/evrf/generalized-bulletproofs/src/transcript.rs
+++ b/crypto/evrf/generalized-bulletproofs/src/transcript.rs
@@ -0,0 +1,188 @@
+use std::io;
+
+use blake2::{Digest, Blake2b512};
+
+use ciphersuite::{
+  group::{ff::PrimeField, GroupEncoding},
+  Ciphersuite,
+};
+
+use crate::PointVector;
+
+const SCALAR: u8 = 0;
+const POINT: u8 = 1;
+const CHALLENGE: u8 = 2;
+
+fn challenge<F: PrimeField>(digest: &mut Blake2b512) -> F {
+  // Panic if this is such a wide field, we won't successfully perform a reduction into an unbiased
+  // scalar
+  debug_assert!((F::NUM_BITS + 128) < 512);
+
+  digest.update([CHALLENGE]);
+  let chl = digest.clone().finalize();
+
+  let mut res = F::ZERO;
+  for (i, mut byte) in chl.iter().cloned().enumerate() {
+    for j in 0 .. 8 {
+      let lsb = byte & 1;
+      let mut bit = F::from(u64::from(lsb));
+      for _ in 0 .. ((i * 8) + j) {
+        bit = bit.double();
+      }
+      res += bit;
+
+      byte >>= 1;
+    }
+  }
+
+  // Negligible probability
+  if bool::from(res.is_zero()) {
+    panic!("zero challenge");
+  }
+
+  res
+}
+
+/// Commitments written to/read from a transcript.
+// We use a dedicated type for this to coerce the caller into transcripting the commitments as
+// expected.
+#[cfg_attr(test, derive(Clone, PartialEq, Debug))]
+pub struct Commitments<C: Ciphersuite> {
+  pub(crate) C: PointVector<C>,
+  pub(crate) V: PointVector<C>,
+}
+
+impl<C: Ciphersuite> Commitments<C> {
+  /// The vector commitments.
+  pub fn C(&self) -> &[C::G] {
+    &self.C.0
+  }
+  /// The non-vector commitments.
+  pub fn V(&self) -> &[C::G] {
+    &self.V.0
+  }
+}
+
+/// A transcript for proving proofs.
+pub struct Transcript {
+  digest: Blake2b512,
+  transcript: Vec<u8>,
+}
+
+/*
+  We define our proofs as Vec<u8> and derive our transcripts from the values we deserialize from
+  them. This format assumes the order of the values read, their size, and their quantity are
+  constant to the context.
+*/
+impl Transcript {
+  /// Create a new transcript off some context.
+  pub fn new(context: [u8; 32]) -> Self {
+    let mut digest = Blake2b512::new();
+    digest.update(context);
+    Self { digest, transcript: Vec::with_capacity(1024) }
+  }
+
+  /// Push a scalar onto the transcript.
+  pub fn push_scalar(&mut self, scalar: impl PrimeField) {
+    self.digest.update([SCALAR]);
+    let bytes = scalar.to_repr();
+    self.digest.update(bytes);
+    self.transcript.extend(bytes.as_ref());
+  }
+
+  /// Push a point onto the transcript.
+  pub fn push_point(&mut self, point: impl GroupEncoding) {
+    self.digest.update([POINT]);
+    let bytes = point.to_bytes();
+    self.digest.update(bytes);
+    self.transcript.extend(bytes.as_ref());
+  }
+
+  /// Write the Pedersen (vector) commitments to this transcript.
+  pub fn write_commitments<C: Ciphersuite>(
+    &mut self,
+    C: Vec<C::G>,
+    V: Vec<C::G>,
+  ) -> Commitments<C> {
+    for C in &C {
+      self.push_point(*C);
+    }
+    for V in &V {
+      self.push_point(*V);
+    }
+    Commitments { C: PointVector(C), V: PointVector(V) }
+  }
+
+  /// Sample a challenge.
+  pub fn challenge<F: PrimeField>(&mut self) -> F {
+    challenge(&mut self.digest)
+  }
+
+  /// Complete a transcript, yielding the fully serialized proof.
+  pub fn complete(self) -> Vec<u8> {
+    self.transcript
+  }
+}
+
+/// A transcript for verifying proofs.
+pub struct VerifierTranscript<'a> {
+  digest: Blake2b512,
+  transcript: &'a [u8],
+}
+
+impl<'a> VerifierTranscript<'a> {
+  /// Create a new transcript to verify a proof with.
+  pub fn new(context: [u8; 32], proof: &'a [u8]) -> Self {
+    let mut digest = Blake2b512::new();
+    digest.update(context);
+    Self { digest, transcript: proof }
+  }
+
+  /// Read a scalar from the transcript.
+  pub fn read_scalar<C: Ciphersuite>(&mut self) -> io::Result<C::F> {
+    let scalar = C::read_F(&mut self.transcript)?;
+    self.digest.update([SCALAR]);
+    let bytes = scalar.to_repr();
+    self.digest.update(bytes);
+    Ok(scalar)
+  }
+
+  /// Read a point from the transcript.
+  pub fn read_point<C: Ciphersuite>(&mut self) -> io::Result<C::G> {
+    let point = C::read_G(&mut self.transcript)?;
+    self.digest.update([POINT]);
+    let bytes = point.to_bytes();
+    self.digest.update(bytes);
+    Ok(point)
+  }
+
+  /// Read the Pedersen (Vector) Commitments from the transcript.
+  ///
+  /// The lengths of the vectors are not transcripted.
+  #[allow(clippy::type_complexity)]
+  pub fn read_commitments<C: Ciphersuite>(
+    &mut self,
+    C: usize,
+    V: usize,
+  ) -> io::Result<Commitments<C>> {
+    let mut C_vec = Vec::with_capacity(C);
+    for _ in 0 .. C {
+      C_vec.push(self.read_point::<C>()?);
+    }
+    let mut V_vec = Vec::with_capacity(V);
+    for _ in 0 .. V {
+      V_vec.push(self.read_point::<C>()?);
+    }
+    Ok(Commitments { C: PointVector(C_vec), V: PointVector(V_vec) })
+  }
+
+  /// Sample a challenge.
+  pub fn challenge<F: PrimeField>(&mut self) -> F {
+    challenge(&mut self.digest)
+  }
+
+  /// Complete the transcript, returning the advanced slice.
+  pub fn complete(self) -> &'a [u8] {
+    self.transcript
+  }
+}
--- a/crypto/evrf/secq256k1/Cargo.toml
+++ b/crypto/evrf/secq256k1/Cargo.toml
@@ -0,0 +1,39 @@
+[package]
+name = "secq256k1"
+version = "0.1.0"
+description = "An implementation of the curve secp256k1 cycles with"
+license = "MIT"
+repository = "https://github.com/serai-dex/serai/tree/develop/crypto/evrf/secq256k1"
+authors = ["Luke Parker <lukeparker5132@gmail.com>"]
+keywords = ["secp256k1", "secq256k1", "group"]
+edition = "2021"
+
+[package.metadata.docs.rs]
+all-features = true
+rustdoc-args = ["--cfg", "docsrs"]
+
+[dependencies]
+rustversion = "1"
+hex-literal = { version = "0.4", default-features = false }
+
+rand_core = { version = "0.6", default-features = false, features = ["std"] }
+
+zeroize = { version = "^1.5", default-features = false, features = ["std", "zeroize_derive"] }
+subtle = { version = "^2.4", default-features = false, features = ["std"] }
+
+generic-array = { version = "0.14", default-features = false }
+crypto-bigint = { version = "0.5", default-features = false, features = ["zeroize"] }
+
+k256 = { version = "0.13", default-features = false, features = ["arithmetic"] }
+
+blake2 = { version = "0.10", default-features = false, features = ["std"] }
+ciphersuite = { path = "../../ciphersuite", version = "0.4", default-features = false, features = ["std"] }
+ec-divisors = { path = "../divisors" }
+generalized-bulletproofs-ec-gadgets = { path = "../ec-gadgets" }
+
+[dev-dependencies]
+hex = "0.4"
+
+rand_core = { version = "0.6", features = ["std"] }
+
+ff-group-tests = { path = "../../ff-group-tests" }
--- a/crypto/evrf/secq256k1/LICENSE
+++ b/crypto/evrf/secq256k1/LICENSE
@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2022-2024 Luke Parker
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
--- a/crypto/evrf/secq256k1/README.md
+++ b/crypto/evrf/secq256k1/README.md
@@ -0,0 +1,6 @@
+# secq256k1
+
+An implementation of the curve secp256k1 cycles with.
+
+Scalars are encoded as little-endian and field elements are encoded as
+big-endian.
--- a/crypto/evrf/secq256k1/src/backend.rs
+++ b/crypto/evrf/secq256k1/src/backend.rs
@@ -0,0 +1,293 @@
+use zeroize::Zeroize;
+
+// Use black_box when possible
+#[rustversion::since(1.66)]
+use core::hint::black_box;
+#[rustversion::before(1.66)]
+fn black_box<T>(val: T) -> T {
+  val
+}
+
+pub(crate) fn u8_from_bool(bit_ref: &mut bool) -> u8 {
+  let bit_ref = black_box(bit_ref);
+
+  let mut bit = black_box(*bit_ref);
+  let res = black_box(bit as u8);
+  bit.zeroize();
+  debug_assert!((res | 1) == 1);
+
+  bit_ref.zeroize();
+  res
+}
+
+macro_rules! math_op {
+  (
+    $Value: ident,
+    $Other: ident,
+    $Op: ident,
+    $op_fn: ident,
+    $Assign: ident,
+    $assign_fn: ident,
+    $function: expr
+  ) => {
+    impl $Op<$Other> for $Value {
+      type Output = $Value;
+      fn $op_fn(self, other: $Other) -> Self::Output {
+        Self($function(self.0, other.0))
+      }
+    }
+    impl $Assign<$Other> for $Value {
+      fn $assign_fn(&mut self, other: $Other) {
+        self.0 = $function(self.0, other.0);
+      }
+    }
+    impl<'a> $Op<&'a $Other> for $Value {
+      type Output = $Value;
+      fn $op_fn(self, other: &'a $Other) -> Self::Output {
+        Self($function(self.0, other.0))
+      }
+    }
+    impl<'a> $Assign<&'a $Other> for $Value {
+      fn $assign_fn(&mut self, other: &'a $Other) {
+        self.0 = $function(self.0, other.0);
+      }
+    }
+  };
+}
+
+macro_rules! from_wrapper {
+  ($wrapper: ident, $inner: ident, $uint: ident) => {
+    impl From<$uint> for $wrapper {
+      fn from(a: $uint) -> $wrapper {
+        Self(Residue::new(&$inner::from(a)))
+      }
+    }
+  };
+}
+
+macro_rules! field {
+  (
+    $FieldName: ident,
+    $ResidueType: ident,
+
+    $MODULUS_STR: ident,
+    $MODULUS: ident,
+    $WIDE_MODULUS: ident,
+
+    $NUM_BITS: literal,
+    $MULTIPLICATIVE_GENERATOR: literal,
+    $S: literal,
+    $ROOT_OF_UNITY: literal,
+    $DELTA: literal,
+  ) => {
+    use core::{
+      ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
+      iter::{Sum, Product},
+    };
+
+    use subtle::{Choice, CtOption, ConstantTimeEq, ConstantTimeLess, ConditionallySelectable};
+    use rand_core::RngCore;
+
+    use crypto_bigint::{Integer, NonZero, Encoding, impl_modulus};
+
+    use ciphersuite::group::ff::{
+      Field, PrimeField, FieldBits, PrimeFieldBits, helpers::sqrt_ratio_generic,
+    };
+
+    use $crate::backend::u8_from_bool;
+
+    fn reduce(x: U512) -> U256 {
+      U256::from_le_slice(&x.rem(&NonZero::new($WIDE_MODULUS).unwrap()).to_le_bytes()[.. 32])
+    }
+
+    impl ConstantTimeEq for $FieldName {
+      fn ct_eq(&self, other: &Self) -> Choice {
+        self.0.ct_eq(&other.0)
+      }
+    }
+
+    impl ConditionallySelectable for $FieldName {
+      fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+        $FieldName(Residue::conditional_select(&a.0, &b.0, choice))
+      }
+    }
+
+    math_op!($FieldName, $FieldName, Add, add, AddAssign, add_assign, |x: $ResidueType, y| x
+      .add(&y));
+    math_op!($FieldName, $FieldName, Sub, sub, SubAssign, sub_assign, |x: $ResidueType, y| x
+      .sub(&y));
+    math_op!($FieldName, $FieldName, Mul, mul, MulAssign, mul_assign, |x: $ResidueType, y| x
+      .mul(&y));
+
+    from_wrapper!($FieldName, U256, u8);
+    from_wrapper!($FieldName, U256, u16);
+    from_wrapper!($FieldName, U256, u32);
+    from_wrapper!($FieldName, U256, u64);
+    from_wrapper!($FieldName, U256, u128);
+
+    impl Neg for $FieldName {
+      type Output = $FieldName;
+      fn neg(self) -> $FieldName {
+        Self(self.0.neg())
+      }
+    }
+
+    impl<'a> Neg for &'a $FieldName {
+      type Output = $FieldName;
+      fn neg(self) -> Self::Output {
+        (*self).neg()
+      }
+    }
+
+    impl $FieldName {
+      /// Perform an exponentation.
+      pub fn pow(&self, other: $FieldName) -> $FieldName {
+        let mut table = [Self(Residue::ONE); 16];
+        table[1] = *self;
+        for i in 2 .. 16 {
+          table[i] = table[i - 1] * self;
+        }
+
+        let mut res = Self(Residue::ONE);
+        let mut bits = 0;
+        for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
+          bits <<= 1;
+          let mut bit = u8_from_bool(bit.deref_mut());
+          bits |= bit;
+          bit.zeroize();
+
+          if ((i + 1) % 4) == 0 {
+            if i != 3 {
+              for _ in 0 .. 4 {
+                res *= res;
+              }
+            }
+
+            let mut factor = table[0];
+            for (j, candidate) in table[1 ..].iter().enumerate() {
+              let j = j + 1;
+              factor = Self::conditional_select(&factor, &candidate, usize::from(bits).ct_eq(&j));
+            }
+            res *= factor;
+            bits = 0;
+          }
+        }
+        res
+      }
+    }
+
+    impl Field for $FieldName {
+      const ZERO: Self = Self(Residue::ZERO);
+      const ONE: Self = Self(Residue::ONE);
+
+      fn random(mut rng: impl RngCore) -> Self {
+        let mut bytes = [0; 64];
+        rng.fill_bytes(&mut bytes);
+        $FieldName(Residue::new(&reduce(U512::from_le_slice(bytes.as_ref()))))
+      }
+
+      fn square(&self) -> Self {
+        Self(self.0.square())
+      }
+      fn double(&self) -> Self {
+        *self + self
+      }
+
+      fn invert(&self) -> CtOption<Self> {
+        let res = self.0.invert();
+        CtOption::new(Self(res.0), res.1.into())
+      }
+
+      fn sqrt(&self) -> CtOption<Self> {
+        // (p + 1) // 4, as valid since p % 4 == 3
+        let mod_plus_one_div_four = $MODULUS.saturating_add(&U256::ONE).wrapping_div(&(4u8.into()));
+        let res = self.pow(Self($ResidueType::new_checked(&mod_plus_one_div_four).unwrap()));
+        CtOption::new(res, res.square().ct_eq(self))
+      }
+
+      fn sqrt_ratio(num: &Self, div: &Self) -> (Choice, Self) {
+        sqrt_ratio_generic(num, div)
+      }
+    }
+
+    impl PrimeField for $FieldName {
+      type Repr = [u8; 32];
+
+      const MODULUS: &'static str = $MODULUS_STR;
+
+      const NUM_BITS: u32 = $NUM_BITS;
+      const CAPACITY: u32 = $NUM_BITS - 1;
+
+      const TWO_INV: Self = $FieldName($ResidueType::new(&U256::from_u8(2)).invert().0);
+
+      const MULTIPLICATIVE_GENERATOR: Self =
+        Self(Residue::new(&U256::from_u8($MULTIPLICATIVE_GENERATOR)));
+      const S: u32 = $S;
+
+      const ROOT_OF_UNITY: Self = $FieldName(Residue::new(&U256::from_be_hex($ROOT_OF_UNITY)));
+      const ROOT_OF_UNITY_INV: Self = Self(Self::ROOT_OF_UNITY.0.invert().0);
+
+      const DELTA: Self = $FieldName(Residue::new(&U256::from_be_hex($DELTA)));
+
+      fn from_repr(bytes: Self::Repr) -> CtOption<Self> {
+        let res = U256::from_le_slice(&bytes);
+        CtOption::new($FieldName(Residue::new(&res)), res.ct_lt(&$MODULUS))
+      }
+      fn to_repr(&self) -> Self::Repr {
+        let mut repr = [0; 32];
+        repr.copy_from_slice(&self.0.retrieve().to_le_bytes());
+        repr
+      }
+
+      fn is_odd(&self) -> Choice {
+        self.0.retrieve().is_odd()
+      }
+    }
+
+    impl PrimeFieldBits for $FieldName {
+      type ReprBits = [u8; 32];
+
+      fn to_le_bits(&self) -> FieldBits<Self::ReprBits> {
+        self.to_repr().into()
+      }
+
+      fn char_le_bits() -> FieldBits<Self::ReprBits> {
+        let mut repr = [0; 32];
+        repr.copy_from_slice(&MODULUS.to_le_bytes());
+        repr.into()
+      }
+    }
+
+    impl Sum<$FieldName> for $FieldName {
+      fn sum<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
+        let mut res = $FieldName::ZERO;
+        for item in iter {
+          res += item;
+        }
+        res
+      }
+    }
+
+    impl<'a> Sum<&'a $FieldName> for $FieldName {
+      fn sum<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
+        iter.cloned().sum()
+      }
+    }
+
+    impl Product<$FieldName> for $FieldName {
+      fn product<I: Iterator<Item = $FieldName>>(iter: I) -> $FieldName {
+        let mut res = $FieldName::ONE;
+        for item in iter {
+          res *= item;
+        }
+        res
+      }
+    }
+
+    impl<'a> Product<&'a $FieldName> for $FieldName {
+      fn product<I: Iterator<Item = &'a $FieldName>>(iter: I) -> $FieldName {
+        iter.cloned().product()
+      }
+    }
+  };
+}
--- a/crypto/evrf/secq256k1/src/lib.rs
+++ b/crypto/evrf/secq256k1/src/lib.rs
@@ -0,0 +1,47 @@
+#![cfg_attr(docsrs, feature(doc_auto_cfg))]
+#![doc = include_str!("../README.md")]
+
+use generic_array::typenum::{Sum, Diff, Quot, U, U1, U2};
+use ciphersuite::group::{ff::PrimeField, Group};
+
+#[macro_use]
+mod backend;
+
+mod scalar;
+pub use scalar::Scalar;
+
+pub use k256::Scalar as FieldElement;
+
+mod point;
+pub use point::Point;
+
+/// Ciphersuite for Secq256k1.
+///
+/// hash_to_F is implemented with a naive concatenation of the dst and data, allowing transposition
+/// between the two. This means `dst: b"abc", data: b"def"`, will produce the same scalar as
+/// `dst: "abcdef", data: b""`. Please use carefully, not letting dsts be substrings of each other.
+#[derive(Clone, Copy, PartialEq, Eq, Debug, zeroize::Zeroize)]
+pub struct Secq256k1;
+impl ciphersuite::Ciphersuite for Secq256k1 {
+  type F = Scalar;
+  type G = Point;
+  type H = blake2::Blake2b512;
+
+  const ID: &'static [u8] = b"secq256k1";
+
+  fn generator() -> Self::G {
+    Point::generator()
+  }
+
+  fn hash_to_F(dst: &[u8], data: &[u8]) -> Self::F {
+    use blake2::Digest;
+    Scalar::wide_reduce(Self::H::digest([dst, data].concat()).as_slice().try_into().unwrap())
+  }
+}
+
+impl generalized_bulletproofs_ec_gadgets::DiscreteLogParameters for Secq256k1 {
+  type ScalarBits = U<{ Scalar::NUM_BITS as usize }>;
+  type XCoefficients = Quot<Sum<Self::ScalarBits, U1>, U2>;
+  type XCoefficientsMinusOne = Diff<Self::XCoefficients, U1>;
+  type YxCoefficients = Diff<Quot<Sum<Sum<Self::ScalarBits, U1>, U1>, U2>, U2>;
+}
--- a/crypto/evrf/secq256k1/src/point.rs
+++ b/crypto/evrf/secq256k1/src/point.rs
@@ -0,0 +1,414 @@
+use core::{
+  ops::{DerefMut, Add, AddAssign, Neg, Sub, SubAssign, Mul, MulAssign},
+  iter::Sum,
+};
+
+use rand_core::RngCore;
+
+use zeroize::Zeroize;
+use subtle::{Choice, CtOption, ConstantTimeEq, ConditionallySelectable, ConditionallyNegatable};
+
+use generic_array::{typenum::U33, GenericArray};
+
+use ciphersuite::group::{
+  ff::{Field, PrimeField, PrimeFieldBits},
+  Group, GroupEncoding,
+  prime::PrimeGroup,
+};
+
+use crate::{backend::u8_from_bool, Scalar, FieldElement};
+
+fn recover_y(x: FieldElement) -> CtOption<FieldElement> {
+  // x**3 + B since a = 0
+  ((x.square() * x) + FieldElement::from(7u64)).sqrt()
+}
+
+/// Point.
+#[derive(Clone, Copy, Debug, Zeroize)]
+#[repr(C)]
+pub struct Point {
+  x: FieldElement, // / Z
+  y: FieldElement, // / Z
+  z: FieldElement,
+}
+
+impl ConstantTimeEq for Point {
+  fn ct_eq(&self, other: &Self) -> Choice {
+    let x1 = self.x * other.z;
+    let x2 = other.x * self.z;
+
+    let y1 = self.y * other.z;
+    let y2 = other.y * self.z;
+
+    (self.x.is_zero() & other.x.is_zero()) | (x1.ct_eq(&x2) & y1.ct_eq(&y2))
+  }
+}
+
+impl PartialEq for Point {
+  fn eq(&self, other: &Point) -> bool {
+    self.ct_eq(other).into()
+  }
+}
+
+impl Eq for Point {}
+
+impl ConditionallySelectable for Point {
+  fn conditional_select(a: &Self, b: &Self, choice: Choice) -> Self {
+    Point {
+      x: FieldElement::conditional_select(&a.x, &b.x, choice),
+      y: FieldElement::conditional_select(&a.y, &b.y, choice),
+      z: FieldElement::conditional_select(&a.z, &b.z, choice),
+    }
+  }
+}
+
+impl Add for Point {
+  type Output = Point;
+  #[allow(non_snake_case)]
+  fn add(self, other: Self) -> Self {
+    // add-2015-rcb
+
+    let a = FieldElement::ZERO;
+    let B = FieldElement::from(7u64);
+    let b3 = B + B + B;
+
+    let X1 = self.x;
+    let Y1 = self.y;
+    let Z1 = self.z;
+    let X2 = other.x;
+    let Y2 = other.y;
+    let Z2 = other.z;
+
+    let t0 = X1 * X2;
+    let t1 = Y1 * Y2;
+    let t2 = Z1 * Z2;
+    let t3 = X1 + Y1;
+    let t4 = X2 + Y2;
+    let t3 = t3 * t4;
+    let t4 = t0 + t1;
+    let t3 = t3 - t4;
+    let t4 = X1 + Z1;
+    let t5 = X2 + Z2;
+    let t4 = t4 * t5;
+    let t5 = t0 + t2;
+    let t4 = t4 - t5;
+    let t5 = Y1 + Z1;
+    let X3 = Y2 + Z2;
+    let t5 = t5 * X3;
+    let X3 = t1 + t2;
+    let t5 = t5 - X3;
+    let Z3 = a * t4;
+    let X3 = b3 * t2;
+    let Z3 = X3 + Z3;
+    let X3 = t1 - Z3;
+    let Z3 = t1 + Z3;
+    let Y3 = X3 * Z3;
+    let t1 = t0 + t0;
+    let t1 = t1 + t0;
+    let t2 = a * t2;
+    let t4 = b3 * t4;
+    let t1 = t1 + t2;
+    let t2 = t0 - t2;
+    let t2 = a * t2;
+    let t4 = t4 + t2;
+    let t0 = t1 * t4;
+    let Y3 = Y3 + t0;
+    let t0 = t5 * t4;
+    let X3 = t3 * X3;
+    let X3 = X3 - t0;
+    let t0 = t3 * t1;
+    let Z3 = t5 * Z3;
+    let Z3 = Z3 + t0;
+    Point { x: X3, y: Y3, z: Z3 }
+  }
+}
+
+impl AddAssign for Point {
+  fn add_assign(&mut self, other: Point) {
+    *self = *self + other;
+  }
+}
+
+impl Add<&Point> for Point {
+  type Output = Point;
+  fn add(self, other: &Point) -> Point {
+    self + *other
+  }
+}
+
+impl AddAssign<&Point> for Point {
+  fn add_assign(&mut self, other: &Point) {
+    *self += *other;
+  }
+}
+
+impl Neg for Point {
+  type Output = Point;
+  fn neg(self) -> Self {
+    Point { x: self.x, y: -self.y, z: self.z }
+  }
+}
+
+impl Sub for Point {
+  type Output = Point;
+  #[allow(clippy::suspicious_arithmetic_impl)]
+  fn sub(self, other: Self) -> Self {
+    self + other.neg()
+  }
+}
+
+impl SubAssign for Point {
+  fn sub_assign(&mut self, other: Point) {
+    *self = *self - other;
+  }
+}
+
+impl Sub<&Point> for Point {
+  type Output = Point;
+  fn sub(self, other: &Point) -> Point {
+    self - *other
+  }
+}
+
+impl SubAssign<&Point> for Point {
+  fn sub_assign(&mut self, other: &Point) {
+    *self -= *other;
+  }
+}
+
+impl Group for Point {
+  type Scalar = Scalar;
+  fn random(mut rng: impl RngCore) -> Self {
+    loop {
+      let mut bytes = GenericArray::default();
+      rng.fill_bytes(bytes.as_mut());
+      let opt = Self::from_bytes(&bytes);
+      if opt.is_some().into() {
+        return opt.unwrap();
+      }
+    }
+  }
+  fn identity() -> Self {
+    Point { x: FieldElement::ZERO, y: FieldElement::ONE, z: FieldElement::ZERO }
+  }
+  fn generator() -> Self {
+    Point {
+      x: FieldElement::from_repr(
+        hex_literal::hex!("0000000000000000000000000000000000000000000000000000000000000001")
+          .into(),
+      )
+      .unwrap(),
+      y: FieldElement::from_repr(
+        hex_literal::hex!("0C7C97045A2074634909ABDF82C9BD0248916189041F2AF0C1B800D1FFC278C0")
+          .into(),
+      )
+      .unwrap(),
+      z: FieldElement::ONE,
+    }
+  }
+  fn is_identity(&self) -> Choice {
+    self.z.ct_eq(&FieldElement::ZERO)
+  }
+  #[allow(non_snake_case)]
+  fn double(&self) -> Self {
+    // dbl-2007-bl
+
+    let a = FieldElement::ZERO;
+
+    let X1 = self.x;
+    let Y1 = self.y;
+    let Z1 = self.z;
+
+    let XX = X1 * X1;
+    let ZZ = Z1 * Z1;
+    let w = (a * ZZ) + XX.double() + XX;
+    let s = (Y1 * Z1).double();
+    let ss = s * s;
+    let sss = s * ss;
+    let R = Y1 * s;
+    let RR = R * R;
+    let B = X1 + R;
+    let B = (B * B) - XX - RR;
+    let h = (w * w) - B.double();
+    let X3 = h * s;
+    let Y3 = w * (B - h) - RR.double();
+    let Z3 = sss;
+
+    let res = Self { x: X3, y: Y3, z: Z3 };
+    // If self is identity, res will not be well-formed
+    // Accordingly, we return self if self was the identity
+    Self::conditional_select(&res, self, self.is_identity())
+  }
+}
+
+impl Sum<Point> for Point {
+  fn sum<I: Iterator<Item = Point>>(iter: I) -> Point {
+    let mut res = Self::identity();
+    for i in iter {
+      res += i;
+    }
+    res
+  }
+}
+
+impl<'a> Sum<&'a Point> for Point {
+  fn sum<I: Iterator<Item = &'a Point>>(iter: I) -> Point {
+    Point::sum(iter.cloned())
+  }
+}
+
+impl Mul<Scalar> for Point {
+  type Output = Point;
+  fn mul(self, mut other: Scalar) -> Point {
+    // Precompute the optimal amount that's a multiple of 2
+    let mut table = [Point::identity(); 16];
+    table[1] = self;
+    for i in 2 .. 16 {
+      table[i] = table[i - 1] + self;
+    }
+
+    let mut res = Self::identity();
+    let mut bits = 0;
+    for (i, mut bit) in other.to_le_bits().iter_mut().rev().enumerate() {
+      bits <<= 1;
+      let mut bit = u8_from_bool(bit.deref_mut());
+      bits |= bit;
+      bit.zeroize();
+
+      if ((i + 1) % 4) == 0 {
+        if i != 3 {
+          for _ in 0 .. 4 {
+            res = res.double();
+          }
+        }
+
+        let mut term = table[0];
+        for (j, candidate) in table[1 ..].iter().enumerate() {
+          let j = j + 1;
+          term = Self::conditional_select(&term, candidate, usize::from(bits).ct_eq(&j));
+        }
+        res += term;
+        bits = 0;
+      }
+    }
+    other.zeroize();
+    res
+  }
+}
+
+impl MulAssign<Scalar> for Point {
+  fn mul_assign(&mut self, other: Scalar) {
+    *self = *self * other;
+  }
+}
+
+impl Mul<&Scalar> for Point {
+  type Output = Point;
+  fn mul(self, other: &Scalar) -> Point {
+    self * *other
+  }
+}
+
+impl MulAssign<&Scalar> for Point {
+  fn mul_assign(&mut self, other: &Scalar) {
+    *self *= *other;
+  }
+}
+
+impl GroupEncoding for Point {
+  type Repr = GenericArray<u8, U33>;
+
+  fn from_bytes(bytes: &Self::Repr) -> CtOption<Self> {
+    // Extract and clear the sign bit
+    let sign = Choice::from(bytes[0] & 1);
+
+    // Parse x, recover y
+    FieldElement::from_repr(*GenericArray::from_slice(&bytes[1 ..])).and_then(|x| {
+      let is_identity = x.is_zero();
+
+      let y = recover_y(x).map(|mut y| {
+        y.conditional_negate(y.is_odd().ct_eq(&!sign));
+        y
+      });
+
+      // If this the identity, set y to 1
+      let y =
+        CtOption::conditional_select(&y, &CtOption::new(FieldElement::ONE, 1.into()), is_identity);
+      // Create the point if we have a y solution
+      let point = y.map(|y| Point { x, y, z: FieldElement::ONE });
+
+      let not_negative_zero = !(is_identity & sign);
+      // Only return the point if it isn't -0 and the sign byte wasn't malleated
+      CtOption::conditional_select(
+        &CtOption::new(Point::identity(), 0.into()),
+        &point,
+        not_negative_zero & ((bytes[0] & 1).ct_eq(&bytes[0])),
+      )
+    })
+  }
+
+  fn from_bytes_unchecked(bytes: &Self::Repr) -> CtOption<Self> {
+    Point::from_bytes(bytes)
+  }
+
+  fn to_bytes(&self) -> Self::Repr {
+    let Some(z) = Option::<FieldElement>::from(self.z.invert()) else {
+      return *GenericArray::from_slice(&[0; 33]);
+    };
+    let x = self.x * z;
+    let y = self.y * z;
+
+    let mut res = *GenericArray::from_slice(&[0; 33]);
+    res[1 ..].as_mut().copy_from_slice(&x.to_repr());
+
+    // The following conditional select normalizes the sign to 0 when x is 0
+    let y_sign = u8::conditional_select(&y.is_odd().unwrap_u8(), &0, x.ct_eq(&FieldElement::ZERO));
+    res[0] |= y_sign;
+    res
+  }
+}
+
+impl PrimeGroup for Point {}
+
+impl ec_divisors::DivisorCurve for Point {
+  type FieldElement = FieldElement;
+
+  fn a() -> Self::FieldElement {
+    FieldElement::from(0u64)
+  }
+  fn b() -> Self::FieldElement {
+    FieldElement::from(7u64)
+  }
+
+  fn to_xy(point: Self) -> Option<(Self::FieldElement, Self::FieldElement)> {
+    let z: Self::FieldElement = Option::from(point.z.invert())?;
+    Some((point.x * z, point.y * z))
+  }
+}
+
+#[test]
+fn test_curve() {
+  ff_group_tests::group::test_prime_group_bits::<_, Point>(&mut rand_core::OsRng);
+}
+
+#[test]
+fn generator() {
+  assert_eq!(
+    Point::generator(),
+    Point::from_bytes(GenericArray::from_slice(&hex_literal::hex!(
+      "000000000000000000000000000000000000000000000000000000000000000001"
+    )))
+    .unwrap()
+  );
+}
+
+#[test]
+fn zero_x_is_invalid() {
+  assert!(Option::<FieldElement>::from(recover_y(FieldElement::ZERO)).is_none());
+}
+
+// Checks random won't infinitely loop
+#[test]
+fn random() {
+  Point::random(&mut rand_core::OsRng);
+}
--- a/crypto/evrf/secq256k1/src/scalar.rs
+++ b/crypto/evrf/secq256k1/src/scalar.rs
@@ -0,0 +1,52 @@
+use zeroize::{DefaultIsZeroes, Zeroize};
+
+use crypto_bigint::{
+  U256, U512,
+  modular::constant_mod::{ResidueParams, Residue},
+};
+
+const MODULUS_STR: &str = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F";
+
+impl_modulus!(SecQ, U256, MODULUS_STR);
+type ResidueType = Residue<SecQ, { SecQ::LIMBS }>;
+
+/// The Scalar field of secq256k1.
+///
+/// This is equivalent to the field secp256k1 is defined over.
+#[derive(Clone, Copy, PartialEq, Eq, Default, Debug)]
+#[repr(C)]
+pub struct Scalar(pub(crate) ResidueType);
+
+impl DefaultIsZeroes for Scalar {}
+
+pub(crate) const MODULUS: U256 = U256::from_be_hex(MODULUS_STR);
+
+const WIDE_MODULUS: U512 = U512::from_be_hex(concat!(
+  "0000000000000000000000000000000000000000000000000000000000000000",
+  "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F",
+));
+
+field!(
+  Scalar,
+  ResidueType,
+  MODULUS_STR,
+  MODULUS,
+  WIDE_MODULUS,
+  256,
+  3,
+  1,
+  "fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2e",
+  "0000000000000000000000000000000000000000000000000000000000000009",
+);
+
+impl Scalar {
+  /// Perform a wide reduction, presumably to obtain a non-biased Scalar field element.
+  pub fn wide_reduce(bytes: [u8; 64]) -> Scalar {
+    Scalar(Residue::new(&reduce(U512::from_le_slice(bytes.as_ref()))))
+  }
+}
+
+#[test]
+fn test_scalar_field() {
+  ff_group_tests::prime_field::test_prime_field_bits::<_, Scalar>(&mut rand_core::OsRng);
+}
--- a/deny.toml
+++ b/deny.toml
@@ -99,4 +99,5 @@ allow-git = [
  "https://github.com/serai-dex/substrate-bip39",
  "https://github.com/serai-dex/substrate",
  "https://github.com/orcalabs/dockertest-rs",
+  "https://github.com/kayabaNerve/pasta_curves",
 ]
--- a/networks/monero/ringct/clsag/src/multisig.rs
+++ b/networks/monero/ringct/clsag/src/multisig.rs
@@ -20,7 +20,6 @@ use group::{
 use transcript::{Transcript, RecommendedTranscript};
 use dalek_ff_group as dfg;
 use frost::{
-  dkg::lagrange,
  curve::Ed25519,
  Participant, FrostError, ThresholdKeys, ThresholdView,
  algorithm::{WriteAddendum, Algorithm},
@@ -233,8 +232,10 @@ impl Algorithm<Ed25519> for ClsagMultisig {
      .append_message(b"key_image_share", addendum.key_image_share.compress().to_bytes());

    // Accumulate the interpolated share
-    let interpolated_key_image_share =
-      addendum.key_image_share * lagrange::<dfg::Scalar>(l, view.included());
+    let interpolated_key_image_share = addendum.key_image_share *
+      view
+        .interpolation_factor(l)
+        .ok_or(FrostError::InternalError("processing addendum of non-participant"))?;
    *self.image.as_mut().unwrap() += interpolated_key_image_share;

    self
--- a/networks/monero/wallet/src/send/multisig.rs
+++ b/networks/monero/wallet/src/send/multisig.rs
@@ -14,7 +14,6 @@ use transcript::{Transcript, RecommendedTranscript};
 use frost::{
  curve::Ed25519,
  Participant, FrostError, ThresholdKeys,
-  dkg::lagrange,
  sign::{
    Preprocess, CachedPreprocess, SignatureShare, PreprocessMachine, SignMachine, SignatureMachine,
    AlgorithmMachine, AlgorithmSignMachine, AlgorithmSignatureMachine,
@@ -34,7 +33,7 @@ use crate::send::{SendError, SignableTransaction, key_image_sort};
 pub struct TransactionMachine {
  signable: SignableTransaction,

-  i: Participant,
+  keys: ThresholdKeys<Ed25519>,

  // The key image generator, and the scalar offset from the spend key
  key_image_generators_and_offsets: Vec<(EdwardsPoint, Scalar)>,
@@ -45,7 +44,7 @@ pub struct TransactionMachine {
 pub struct TransactionSignMachine {
  signable: SignableTransaction,

-  i: Participant,
+  keys: ThresholdKeys<Ed25519>,

  key_image_generators_and_offsets: Vec<(EdwardsPoint, Scalar)>,
  clsags: Vec<(ClsagMultisigMaskSender, AlgorithmSignMachine<Ed25519, ClsagMultisig>)>,
@@ -61,7 +60,7 @@ pub struct TransactionSignatureMachine {

 impl SignableTransaction {
  /// Create a FROST signing machine out of this signable transaction.
-  pub fn multisig(self, keys: &ThresholdKeys<Ed25519>) -> Result<TransactionMachine, SendError> {
+  pub fn multisig(self, keys: ThresholdKeys<Ed25519>) -> Result<TransactionMachine, SendError> {
    let mut clsags = vec![];

    let mut key_image_generators_and_offsets = vec![];
@@ -85,12 +84,7 @@ impl SignableTransaction {
      clsags.push((clsag_mask_send, AlgorithmMachine::new(clsag, offset)));
    }

-    Ok(TransactionMachine {
-      signable: self,
-      i: keys.params().i(),
-      key_image_generators_and_offsets,
-      clsags,
-    })
+    Ok(TransactionMachine { signable: self, keys, key_image_generators_and_offsets, clsags })
  }
 }

@@ -120,7 +114,7 @@ impl PreprocessMachine for TransactionMachine {
      TransactionSignMachine {
        signable: self.signable,

-        i: self.i,
+        keys: self.keys,

        key_image_generators_and_offsets: self.key_image_generators_and_offsets,
        clsags,
@@ -173,12 +167,12 @@ impl SignMachine<Transaction> for TransactionSignMachine {
    // We do not need to be included here, yet this set of signers has yet to be validated
    // We explicitly remove ourselves to ensure we aren't included twice, if we were redundantly
    // included
-    commitments.remove(&self.i);
+    commitments.remove(&self.keys.params().i());

    // Find out who's included
    let mut included = commitments.keys().copied().collect::<Vec<_>>();
    // This push won't duplicate due to the above removal
-    included.push(self.i);
+    included.push(self.keys.params().i());
    // unstable sort may reorder elements of equal order
    // Given our lack of duplicates, we should have no elements of equal order
    included.sort_unstable();
@@ -192,12 +186,15 @@ impl SignMachine<Transaction> for TransactionSignMachine {
    }

    // Convert the serialized nonces commitments to a parallelized Vec
+    let view = self.keys.view(included.clone()).map_err(|_| {
+      FrostError::InvalidSigningSet("couldn't form an interpolated view of the key")
+    })?;
    let mut commitments = (0 .. self.clsags.len())
      .map(|c| {
        included
          .iter()
          .map(|l| {
-            let preprocess = if *l == self.i {
+            let preprocess = if *l == self.keys.params().i() {
              self.our_preprocess[c].clone()
            } else {
              commitments.get_mut(l).ok_or(FrostError::MissingParticipant(*l))?[c].clone()
@@ -206,7 +203,7 @@ impl SignMachine<Transaction> for TransactionSignMachine {
            // While here, calculate the key image as needed to call sign
            // The CLSAG algorithm will independently calculate the key image/verify these shares
            key_images[c] +=
-              preprocess.addendum.key_image_share().0 * lagrange::<dfg::Scalar>(*l, &included).0;
+              preprocess.addendum.key_image_share().0 * view.interpolation_factor(*l).unwrap().0;

            Ok((*l, preprocess))
          })
@@ -217,7 +214,7 @@ impl SignMachine<Transaction> for TransactionSignMachine {
    // The above inserted our own preprocess into these maps (which is unnecessary)
    // Remove it now
    for map in &mut commitments {
-      map.remove(&self.i);
+      map.remove(&self.keys.params().i());
    }

    // The actual TX will have sorted its inputs by key image
--- a/networks/monero/wallet/tests/runner/mod.rs
+++ b/networks/monero/wallet/tests/runner/mod.rs
@@ -281,7 +281,7 @@ macro_rules! test {
              {
                let mut machines = HashMap::new();
                for i in (1 ..= THRESHOLD).map(|i| Participant::new(i).unwrap()) {
-                  machines.insert(i, tx.clone().multisig(&keys[&i]).unwrap());
+                  machines.insert(i, tx.clone().multisig(keys[&i].clone()).unwrap());
                }

                frost::tests::sign_without_caching(&mut OsRng, machines, &[])
--- a/orchestration/Cargo.toml
+++ b/orchestration/Cargo.toml
@@ -24,6 +24,8 @@ rand_chacha = { version = "0.3", default-features = false, features = ["std"] }

 transcript = { package = "flexible-transcript", path = "../crypto/transcript", default-features = false, features = ["std", "recommended"] }
 ciphersuite = { path = "../crypto/ciphersuite", default-features = false, features = ["std", "ristretto"] }
+embedwards25519 = { path = "../crypto/evrf/embedwards25519" }
+secq256k1 = { path = "../crypto/evrf/secq256k1" }

 zalloc = { path = "../common/zalloc" }

--- a/orchestration/src/main.rs
+++ b/orchestration/src/main.rs
@@ -25,6 +25,8 @@ use ciphersuite::{
  },
  Ciphersuite, Ristretto,
 };
+use embedwards25519::Embedwards25519;
+use secq256k1::Secq256k1;

 mod mimalloc;
 use mimalloc::mimalloc;
@@ -267,6 +269,55 @@ fn infrastructure_keys(network: Network) -> InfrastructureKeys {
  ])
 }

+struct EmbeddedCurveKeys {
+  embedwards25519: (Zeroizing<Vec<u8>>, Vec<u8>),
+  secq256k1: (Zeroizing<Vec<u8>>, Vec<u8>),
+}
+
+fn embedded_curve_keys(network: Network) -> EmbeddedCurveKeys {
+  // Generate entropy for the embedded curve keys
+
+  let entropy = {
+    let path = home::home_dir()
+      .unwrap()
+      .join(".serai")
+      .join(network.label())
+      .join("embedded_curve_keys_entropy");
+    // Check if there's existing entropy
+    if let Ok(entropy) = fs::read(&path).map(Zeroizing::new) {
+      assert_eq!(entropy.len(), 32, "entropy saved to disk wasn't 32 bytes");
+      let mut res = Zeroizing::new([0; 32]);
+      res.copy_from_slice(entropy.as_ref());
+      res
+    } else {
+      // If there isn't, generate fresh entropy
+      let mut res = Zeroizing::new([0; 32]);
+      OsRng.fill_bytes(res.as_mut());
+      fs::write(&path, &res).unwrap();
+      res
+    }
+  };
+
+  let mut transcript =
+    RecommendedTranscript::new(b"Serai Orchestrator Embedded Curve Keys Transcript");
+  transcript.append_message(b"network", network.label().as_bytes());
+  transcript.append_message(b"entropy", entropy);
+  let mut rng = ChaCha20Rng::from_seed(transcript.rng_seed(b"embedded_curve_keys"));
+
+  EmbeddedCurveKeys {
+    embedwards25519: {
+      let key = Zeroizing::new(<Embedwards25519 as Ciphersuite>::F::random(&mut rng));
+      let pub_key = Embedwards25519::generator() * key.deref();
+      (Zeroizing::new(key.to_repr().as_slice().to_vec()), pub_key.to_bytes().to_vec())
+    },
+    secq256k1: {
+      let key = Zeroizing::new(<Secq256k1 as Ciphersuite>::F::random(&mut rng));
+      let pub_key = Secq256k1::generator() * key.deref();
+      (Zeroizing::new(key.to_repr().as_slice().to_vec()), pub_key.to_bytes().to_vec())
+    },
+  }
+}
+
 fn dockerfiles(network: Network) {
  let orchestration_path = orchestration_path(network);

@@ -294,18 +345,15 @@ fn dockerfiles(network: Network) {
    monero_key.1,
  );

-  let new_entropy = || {
-    let mut res = Zeroizing::new([0; 32]);
-    OsRng.fill_bytes(res.as_mut());
-    res
-  };
+  let embedded_curve_keys = embedded_curve_keys(network);
  processor(
    &orchestration_path,
    network,
    "bitcoin",
    coordinator_key.1,
    bitcoin_key.0,
-    new_entropy(),
+    embedded_curve_keys.embedwards25519.0.clone(),
+    embedded_curve_keys.secq256k1.0.clone(),
  );
  processor(
    &orchestration_path,
@@ -313,9 +361,18 @@ fn dockerfiles(network: Network) {
    "ethereum",
    coordinator_key.1,
    ethereum_key.0,
-    new_entropy(),
+    embedded_curve_keys.embedwards25519.0.clone(),
+    embedded_curve_keys.secq256k1.0.clone(),
+  );
+  processor(
+    &orchestration_path,
+    network,
+    "monero",
+    coordinator_key.1,
+    monero_key.0,
+    embedded_curve_keys.embedwards25519.0.clone(),
+    embedded_curve_keys.embedwards25519.0.clone(),
  );
-  processor(&orchestration_path, network, "monero", coordinator_key.1, monero_key.0, new_entropy());

  let serai_key = {
    let serai_key = Zeroizing::new(
@@ -346,6 +403,7 @@ fn key_gen(network: Network) {
  let _ = fs::create_dir_all(&serai_dir);
  fs::write(key_file, key.to_repr()).expect("couldn't write key");

+  // TODO: Move embedded curve key gen here, and print them
  println!(
    "Public Key: {}",
    hex::encode((<Ristretto as Ciphersuite>::generator() * key).to_bytes())
--- a/orchestration/src/processor.rs
+++ b/orchestration/src/processor.rs
@@ -12,8 +12,9 @@ pub fn processor(
  network: Network,
  coin: &'static str,
  _coordinator_key: <Ristretto as Ciphersuite>::G,
-  coin_key: Zeroizing<<Ristretto as Ciphersuite>::F>,
-  entropy: Zeroizing<[u8; 32]>,
+  processor_key: Zeroizing<<Ristretto as Ciphersuite>::F>,
+  substrate_evrf_key: Zeroizing<Vec<u8>>,
+  network_evrf_key: Zeroizing<Vec<u8>>,
 ) {
  let setup = mimalloc(Os::Debian).to_string() +
    &build_serai_service(
@@ -53,8 +54,9 @@ RUN apt install -y ca-certificates

  let mut env_vars = vec![
    ("MESSAGE_QUEUE_RPC", format!("serai-{}-message-queue", network.label())),
-    ("MESSAGE_QUEUE_KEY", hex::encode(coin_key.to_repr())),
-    ("ENTROPY", hex::encode(entropy.as_ref())),
+    ("MESSAGE_QUEUE_KEY", hex::encode(processor_key.to_repr())),
+    ("SUBSTRATE_EVRF_KEY", hex::encode(substrate_evrf_key)),
+    ("NETWORK_EVRF_KEY", hex::encode(network_evrf_key)),
    ("NETWORK", coin.to_string()),
    ("NETWORK_RPC_LOGIN", format!("{RPC_USER}:{RPC_PASS}")),
    ("NETWORK_RPC_HOSTNAME", hostname),
--- a/processor/Cargo.toml
+++ b/processor/Cargo.toml
@@ -36,7 +36,10 @@ serde_json = { version = "1", default-features = false, features = ["std"] }
 # Cryptography
 ciphersuite = { path = "../crypto/ciphersuite", default-features = false, features = ["std", "ristretto"] }

+blake2 = { version = "0.10", default-features = false, features = ["std"] }
 transcript = { package = "flexible-transcript", path = "../crypto/transcript", default-features = false, features = ["std"] }
+ec-divisors = { package = "ec-divisors", path = "../crypto/evrf/divisors", default-features = false }
+dkg = { package = "dkg", path = "../crypto/dkg", default-features = false, features = ["std", "evrf-ristretto"] }
 frost = { package = "modular-frost", path = "../crypto/frost", default-features = false, features = ["ristretto"] }
 frost-schnorrkel = { path = "../crypto/schnorrkel", default-features = false }

@@ -81,12 +84,12 @@ dockertest = "0.4"
 serai-docker-tests = { path = "../tests/docker" }

 [features]
-secp256k1 = ["k256", "frost/secp256k1"]
+secp256k1 = ["k256", "dkg/evrf-secp256k1", "frost/secp256k1"]
 bitcoin = ["dep:secp256k1", "secp256k1", "bitcoin-serai", "serai-client/bitcoin"]

 ethereum = ["secp256k1", "ethereum-serai/tests"]

-ed25519 = ["dalek-ff-group", "frost/ed25519"]
+ed25519 = ["dalek-ff-group", "dkg/evrf-ed25519", "frost/ed25519"]
 monero = ["ed25519", "monero-simple-request-rpc", "monero-wallet", "serai-client/monero"]

 binaries = ["env_logger", "serai-env", "message-queue"]
--- a/processor/messages/src/lib.rs
+++ b/processor/messages/src/lib.rs
@@ -3,7 +3,7 @@ use std::collections::HashMap;
 use scale::{Encode, Decode};
 use borsh::{BorshSerialize, BorshDeserialize};

-use dkg::{Participant, ThresholdParams};
+use dkg::Participant;

 use serai_primitives::BlockHash;
 use in_instructions_primitives::{Batch, SignedBatch};
@@ -19,41 +19,31 @@ pub struct SubstrateContext {
 pub mod key_gen {
  use super::*;

-  #[derive(
-    Clone, Copy, PartialEq, Eq, Hash, Debug, Encode, Decode, BorshSerialize, BorshDeserialize,
-  )]
-  pub struct KeyGenId {
-    pub session: Session,
-    pub attempt: u32,
-  }
-
-  #[derive(Clone, PartialEq, Eq, Debug, BorshSerialize, BorshDeserialize)]
+  #[derive(Clone, PartialEq, Eq, BorshSerialize, BorshDeserialize)]
  pub enum CoordinatorMessage {
    // Instructs the Processor to begin the key generation process.
    // TODO: Should this be moved under Substrate?
-    GenerateKey {
-      id: KeyGenId,
-      params: ThresholdParams,
-      shares: u16,
-    },
-    // Received commitments for the specified key generation protocol.
-    Commitments {
-      id: KeyGenId,
-      commitments: HashMap<Participant, Vec<u8>>,
-    },
-    // Received shares for the specified key generation protocol.
-    Shares {
-      id: KeyGenId,
-      shares: Vec<HashMap<Participant, Vec<u8>>>,
-    },
-    /// Instruction to verify a blame accusation.
-    VerifyBlame {
-      id: KeyGenId,
-      accuser: Participant,
-      accused: Participant,
-      share: Vec<u8>,
-      blame: Option<Vec<u8>>,
-    },
+    GenerateKey { session: Session, threshold: u16, evrf_public_keys: Vec<([u8; 32], Vec<u8>)> },
+    // Received participations for the specified key generation protocol.
+    Participation { session: Session, participant: Participant, participation: Vec<u8> },
+  }
+
+  impl core::fmt::Debug for CoordinatorMessage {
+    fn fmt(&self, fmt: &mut core::fmt::Formatter<'_>) -> Result<(), core::fmt::Error> {
+      match self {
+        CoordinatorMessage::GenerateKey { session, threshold, evrf_public_keys } => fmt
+          .debug_struct("CoordinatorMessage::GenerateKey")
+          .field("session", &session)
+          .field("threshold", &threshold)
+          .field("evrf_public_keys.len()", &evrf_public_keys.len())
+          .finish_non_exhaustive(),
+        CoordinatorMessage::Participation { session, participant, .. } => fmt
+          .debug_struct("CoordinatorMessage::Participation")
+          .field("session", &session)
+          .field("participant", &participant)
+          .finish_non_exhaustive(),
+      }
+    }
  }

  impl CoordinatorMessage {
@@ -62,42 +52,34 @@ pub mod key_gen {
    }
  }

-  #[derive(Clone, PartialEq, Eq, Debug, BorshSerialize, BorshDeserialize)]
+  #[derive(Clone, PartialEq, Eq, BorshSerialize, BorshDeserialize)]
  pub enum ProcessorMessage {
-    // Created commitments for the specified key generation protocol.
-    Commitments {
-      id: KeyGenId,
-      commitments: Vec<Vec<u8>>,
-    },
-    // Participant published invalid commitments.
-    InvalidCommitments {
-      id: KeyGenId,
-      faulty: Participant,
-    },
-    // Created shares for the specified key generation protocol.
-    Shares {
-      id: KeyGenId,
-      shares: Vec<HashMap<Participant, Vec<u8>>>,
-    },
-    // Participant published an invalid share.
-    #[rustfmt::skip]
-    InvalidShare {
-      id: KeyGenId,
-      accuser: Participant,
-      faulty: Participant,
-      blame: Option<Vec<u8>>,
-    },
+    // Participated in the specified key generation protocol.
+    Participation { session: Session, participation: Vec<u8> },
    // Resulting keys from the specified key generation protocol.
-    GeneratedKeyPair {
-      id: KeyGenId,
-      substrate_key: [u8; 32],
-      network_key: Vec<u8>,
-    },
+    GeneratedKeyPair { session: Session, substrate_key: [u8; 32], network_key: Vec<u8> },
    // Blame this participant.
-    Blame {
-      id: KeyGenId,
-      participant: Participant,
-    },
+    Blame { session: Session, participant: Participant },
+  }
+
+  impl core::fmt::Debug for ProcessorMessage {
+    fn fmt(&self, fmt: &mut core::fmt::Formatter<'_>) -> Result<(), core::fmt::Error> {
+      match self {
+        ProcessorMessage::Participation { session, .. } => fmt
+          .debug_struct("ProcessorMessage::Participation")
+          .field("session", &session)
+          .finish_non_exhaustive(),
+        ProcessorMessage::GeneratedKeyPair { session, .. } => fmt
+          .debug_struct("ProcessorMessage::GeneratedKeyPair")
+          .field("session", &session)
+          .finish_non_exhaustive(),
+        ProcessorMessage::Blame { session, participant } => fmt
+          .debug_struct("ProcessorMessage::Blame")
+          .field("session", &session)
+          .field("participant", &participant)
+          .finish_non_exhaustive(),
+      }
+    }
  }
 }

@@ -328,16 +310,19 @@ impl CoordinatorMessage {
  pub fn intent(&self) -> Vec<u8> {
    match self {
      CoordinatorMessage::KeyGen(msg) => {
-        // Unique since key gen ID embeds the session and attempt
        let (sub, id) = match msg {
-          key_gen::CoordinatorMessage::GenerateKey { id, .. } => (0, id),
-          key_gen::CoordinatorMessage::Commitments { id, .. } => (1, id),
-          key_gen::CoordinatorMessage::Shares { id, .. } => (2, id),
-          key_gen::CoordinatorMessage::VerifyBlame { id, .. } => (3, id),
+          // Unique since we only have one attempt per session
+          key_gen::CoordinatorMessage::GenerateKey { session, .. } => {
+            (0, borsh::to_vec(session).unwrap())
+          }
+          // Unique since one participation per participant per session
+          key_gen::CoordinatorMessage::Participation { session, participant, .. } => {
+            (1, borsh::to_vec(&(session, participant)).unwrap())
+          }
        };

        let mut res = vec![COORDINATOR_UID, TYPE_KEY_GEN_UID, sub];
-        res.extend(&id.encode());
+        res.extend(&id);
        res
      }
      CoordinatorMessage::Sign(msg) => {
@@ -400,17 +385,21 @@ impl ProcessorMessage {
    match self {
      ProcessorMessage::KeyGen(msg) => {
        let (sub, id) = match msg {
-          // Unique since KeyGenId
-          key_gen::ProcessorMessage::Commitments { id, .. } => (0, id),
-          key_gen::ProcessorMessage::InvalidCommitments { id, .. } => (1, id),
-          key_gen::ProcessorMessage::Shares { id, .. } => (2, id),
-          key_gen::ProcessorMessage::InvalidShare { id, .. } => (3, id),
-          key_gen::ProcessorMessage::GeneratedKeyPair { id, .. } => (4, id),
-          key_gen::ProcessorMessage::Blame { id, .. } => (5, id),
+          // Unique since we only have one participation per session (due to no re-attempts)
+          key_gen::ProcessorMessage::Participation { session, .. } => {
+            (0, borsh::to_vec(session).unwrap())
+          }
+          key_gen::ProcessorMessage::GeneratedKeyPair { session, .. } => {
+            (1, borsh::to_vec(session).unwrap())
+          }
+          // Unique since we only blame a participant once (as this is fatal)
+          key_gen::ProcessorMessage::Blame { session, participant } => {
+            (2, borsh::to_vec(&(session, participant)).unwrap())
+          }
        };

        let mut res = vec![PROCESSOR_UID, TYPE_KEY_GEN_UID, sub];
-        res.extend(&id.encode());
+        res.extend(&id);
        res
      }
      ProcessorMessage::Sign(msg) => {
--- a/processor/src/key_gen.rs
+++ b/processor/src/key_gen.rs
@@ -1,18 +1,20 @@
-use std::collections::HashMap;
+use std::{
+  io,
+  collections::{HashSet, HashMap},
+};

 use zeroize::Zeroizing;

-use rand_core::SeedableRng;
+use rand_core::{RngCore, SeedableRng, OsRng};
 use rand_chacha::ChaCha20Rng;

+use blake2::{Digest, Blake2s256};
 use transcript::{Transcript, RecommendedTranscript};
-use ciphersuite::group::GroupEncoding;
-use frost::{
-  curve::{Ciphersuite, Ristretto},
-  dkg::{
-    DkgError, Participant, ThresholdParams, ThresholdCore, ThresholdKeys, encryption::*, pedpop::*,
-  },
+use ciphersuite::{
+  group::{Group, GroupEncoding},
+  Ciphersuite, Ristretto,
 };
+use dkg::{Participant, ThresholdCore, ThresholdKeys, evrf::*};

 use log::info;

@@ -21,6 +23,48 @@ use messages::key_gen::*;

 use crate::{Get, DbTxn, Db, create_db, networks::Network};

+mod generators {
+  use core::any::{TypeId, Any};
+  use std::{
+    sync::{LazyLock, Mutex},
+    collections::HashMap,
+  };
+
+  use frost::dkg::evrf::*;
+
+  use serai_client::validator_sets::primitives::MAX_KEY_SHARES_PER_SET;
+
+  /// A cache of the generators used by the eVRF DKG.
+  ///
+  /// This performs a lookup of the Ciphersuite to its generators. Since the Ciphersuite is a
+  /// generic, this takes advantage of `Any`. This static is isolated in a module to ensure
+  /// correctness can be evaluated solely by reviewing these few lines of code.
+  ///
+  /// This is arguably over-engineered as of right now, as we only need generators for Ristretto
+  /// and N::Curve. By having this HashMap, we enable de-duplication of the Ristretto == N::Curve
+  /// case, and we automatically support the n-curve case (rather than hard-coding to the 2-curve
+  /// case).
+  static GENERATORS: LazyLock<Mutex<HashMap<TypeId, &'static (dyn Send + Sync + Any)>>> =
+    LazyLock::new(|| Mutex::new(HashMap::new()));
+
+  pub(crate) fn generators<C: EvrfCurve>() -> &'static EvrfGenerators<C> {
+    GENERATORS
+      .lock()
+      .unwrap()
+      .entry(TypeId::of::<C>())
+      .or_insert_with(|| {
+        // If we haven't prior needed generators for this Ciphersuite, generate new ones
+        Box::leak(Box::new(EvrfGenerators::<C>::new(
+          ((MAX_KEY_SHARES_PER_SET * 2 / 3) + 1).try_into().unwrap(),
+          MAX_KEY_SHARES_PER_SET.try_into().unwrap(),
+        )))
+      })
+      .downcast_ref()
+      .unwrap()
+  }
+}
+use generators::generators;
+
 #[derive(Debug)]
 pub struct KeyConfirmed<C: Ciphersuite> {
  pub substrate_keys: Vec<ThresholdKeys<Ristretto>>,
@@ -29,15 +73,18 @@ pub struct KeyConfirmed<C: Ciphersuite> {

 create_db!(
  KeyGenDb {
-    ParamsDb: (session: &Session, attempt: u32) -> (ThresholdParams, u16),
-    // Not scoped to the set since that'd have latter attempts overwrite former
-    // A former attempt may become the finalized attempt, even if it doesn't in a timely manner
-    // Overwriting its commitments would be accordingly poor
-    CommitmentsDb: (key: &KeyGenId) -> HashMap<Participant, Vec<u8>>,
-    GeneratedKeysDb: (session: &Session, substrate_key: &[u8; 32], network_key: &[u8]) -> Vec<u8>,
-    // These do assume a key is only used once across sets, which holds true so long as a single
-    // participant is honest in their execution of the protocol
-    KeysDb: (network_key: &[u8]) -> Vec<u8>,
+    ParamsDb: (session: &Session) -> (u16, Vec<[u8; 32]>, Vec<Vec<u8>>),
+    ParticipationDb: (session: &Session) -> (
+      HashMap<Participant, Vec<u8>>,
+      HashMap<Participant, Vec<u8>>,
+    ),
+    // GeneratedKeysDb, KeysDb use `()` for their value as we manually serialize their values
+    // TODO: Don't do that
+    GeneratedKeysDb: (session: &Session) -> (),
+    // These do assume a key is only used once across sets, which holds true if the threshold is
+    // honest
+    // TODO: Remove this assumption
+    KeysDb: (network_key: &[u8]) -> (),
    SessionDb: (network_key: &[u8]) -> Session,
    NetworkKeyDb: (session: Session) -> Vec<u8>,
  }
@@ -65,8 +112,8 @@ impl GeneratedKeysDb {

  fn save_keys<N: Network>(
    txn: &mut impl DbTxn,
-    id: &KeyGenId,
-    substrate_keys: &[ThresholdCore<Ristretto>],
+    session: &Session,
+    substrate_keys: &[ThresholdKeys<Ristretto>],
    network_keys: &[ThresholdKeys<N::Curve>],
  ) {
    let mut keys = Zeroizing::new(vec![]);
@@ -74,14 +121,7 @@ impl GeneratedKeysDb {
      keys.extend(substrate_keys.serialize().as_slice());
      keys.extend(network_keys.serialize().as_slice());
    }
-    txn.put(
-      Self::key(
-        &id.session,
-        &substrate_keys[0].group_key().to_bytes(),
-        network_keys[0].group_key().to_bytes().as_ref(),
-      ),
-      keys,
-    );
+    txn.put(Self::key(session), keys);
  }
 }

@@ -91,11 +131,8 @@ impl KeysDb {
    session: Session,
    key_pair: &KeyPair,
  ) -> (Vec<ThresholdKeys<Ristretto>>, Vec<ThresholdKeys<N::Curve>>) {
-    let (keys_vec, keys) = GeneratedKeysDb::read_keys::<N>(
-      txn,
-      &GeneratedKeysDb::key(&session, &key_pair.0 .0, key_pair.1.as_ref()),
-    )
-    .unwrap();
+    let (keys_vec, keys) =
+      GeneratedKeysDb::read_keys::<N>(txn, &GeneratedKeysDb::key(&session)).unwrap();
    assert_eq!(key_pair.0 .0, keys.0[0].group_key().to_bytes());
    assert_eq!(
      {
@@ -130,32 +167,105 @@ impl KeysDb {
  }
 }

-type SecretShareMachines<N> =
-  Vec<(SecretShareMachine<Ristretto>, SecretShareMachine<<N as Network>::Curve>)>;
-type KeyMachines<N> = Vec<(KeyMachine<Ristretto>, KeyMachine<<N as Network>::Curve>)>;
+/*
+  On the Serai blockchain, users specify their public keys on the embedded curves. Substrate does
+  not have the libraries for the embedded curves and is unable to evaluate if the keys are valid
+  or not.
+
+  We could add the libraries for the embedded curves to the blockchain, yet this would be a
+  non-trivial scope for what's effectively an embedded context. It'd also permanently bind our
+  consensus to these arbitrary curves. We would have the benefit of being able to also require PoKs
+  for the keys, ensuring no one uses someone else's key (creating oddities there). Since someone
+  who uses someone else's key can't actually participate, all it does in effect is give more key
+  shares to the holder of the private key, and make us unable to rely on eVRF keys as a secure way
+  to index validators (hence the usage of `Participant` throughout the messages here).
+
+  We could remove invalid keys from the DKG, yet this would create a view of the DKG only the
+  processor (which does have the embedded curves) has. We'd need to reconcile it with the view of
+  the DKG which does include all keys (even the invalid keys).
+
+  The easiest solution is to keep the views consistent by replacing invalid keys with valid keys
+  (which no one has the private key for). This keeps the view consistent. This does prevent those
+  who posted invalid keys from participating, and receiving their keys, which is the understood and
+  declared effect of them posting invalid keys. Since at least `t` people must honestly participate
+  for the DKG to complete, and since their honest participation means they had valid keys, we do
+  ensure at least `t` people participated and the DKG result can be reconstructed.
+
+  We do lose fault tolerance, yet only by losing those faulty. Accordingly, this is accepted.
+
+  Returns the coerced keys and faulty participants.
+*/
+fn coerce_keys<C: EvrfCurve>(
+  key_bytes: &[impl AsRef<[u8]>],
+) -> (Vec<<C::EmbeddedCurve as Ciphersuite>::G>, Vec<Participant>) {
+  fn evrf_key<C: EvrfCurve>(key: &[u8]) -> Option<<C::EmbeddedCurve as Ciphersuite>::G> {
+    let mut repr = <<C::EmbeddedCurve as Ciphersuite>::G as GroupEncoding>::Repr::default();
+    if repr.as_ref().len() != key.len() {
+      None?;
+    }
+    repr.as_mut().copy_from_slice(key);
+    let point = Option::<<C::EmbeddedCurve as Ciphersuite>::G>::from(<_>::from_bytes(&repr))?;
+    if bool::from(point.is_identity()) {
+      None?;
+    }
+    Some(point)
+  }
+
+  let mut keys = Vec::with_capacity(key_bytes.len());
+  let mut faulty = vec![];
+  for (i, key) in key_bytes.iter().enumerate() {
+    let i = Participant::new(
+      1 + u16::try_from(i).expect("performing a key gen with more than u16::MAX participants"),
+    )
+    .unwrap();
+    keys.push(match evrf_key::<C>(key.as_ref()) {
+      Some(key) => key,
+      None => {
+        // Mark this participant faulty
+        faulty.push(i);
+
+        // Generate a random key
+        let mut rng = ChaCha20Rng::from_seed(Blake2s256::digest(key).into());
+        loop {
+          let mut repr = <<C::EmbeddedCurve as Ciphersuite>::G as GroupEncoding>::Repr::default();
+          rng.fill_bytes(repr.as_mut());
+          if let Some(key) =
+            Option::<<C::EmbeddedCurve as Ciphersuite>::G>::from(<_>::from_bytes(&repr))
+          {
+            break key;
+          }
+        }
+      }
+    });
+  }
+
+  (keys, faulty)
+}

 #[derive(Debug)]
 pub struct KeyGen<N: Network, D: Db> {
  db: D,
-  entropy: Zeroizing<[u8; 32]>,
-
-  active_commit: HashMap<Session, (SecretShareMachines<N>, Vec<Vec<u8>>)>,
-  #[allow(clippy::type_complexity)]
-  active_share: HashMap<Session, (KeyMachines<N>, Vec<HashMap<Participant, Vec<u8>>>)>,
+  substrate_evrf_private_key:
+    Zeroizing<<<Ristretto as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F>,
+  network_evrf_private_key: Zeroizing<<<N::Curve as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F>,
 }

 impl<N: Network, D: Db> KeyGen<N, D> {
  #[allow(clippy::new_ret_no_self)]
-  pub fn new(db: D, entropy: Zeroizing<[u8; 32]>) -> KeyGen<N, D> {
-    KeyGen { db, entropy, active_commit: HashMap::new(), active_share: HashMap::new() }
+  pub fn new(
+    db: D,
+    substrate_evrf_private_key: Zeroizing<
+      <<Ristretto as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F,
+    >,
+    network_evrf_private_key: Zeroizing<<<N::Curve as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F>,
+  ) -> KeyGen<N, D> {
+    KeyGen { db, substrate_evrf_private_key, network_evrf_private_key }
  }

  pub fn in_set(&self, session: &Session) -> bool {
    // We determine if we're in set using if we have the parameters for a session's key generation
-    // The usage of 0 for the attempt is valid so long as we aren't malicious and accordingly
-    // aren't fatally slashed
-    // TODO: Revisit once we do DKG removals for being offline
-    ParamsDb::get(&self.db, session, 0).is_some()
+    // We only have these if we were told to generate a key for this session
+    ParamsDb::get(&self.db, session).is_some()
  }

  #[allow(clippy::type_complexity)]
@@ -179,406 +289,351 @@ impl<N: Network, D: Db> KeyGen<N, D> {
    &mut self,
    txn: &mut D::Transaction<'_>,
    msg: CoordinatorMessage,
-  ) -> ProcessorMessage {
-    const SUBSTRATE_KEY_CONTEXT: &str = "substrate";
-    const NETWORK_KEY_CONTEXT: &str = "network";
-    let context = |id: &KeyGenId, key| {
+  ) -> Vec<ProcessorMessage> {
+    const SUBSTRATE_KEY_CONTEXT: &[u8] = b"substrate";
+    const NETWORK_KEY_CONTEXT: &[u8] = b"network";
+    fn context<N: Network>(session: Session, key_context: &[u8]) -> [u8; 32] {
      // TODO2: Also embed the chain ID/genesis block
-      format!(
-        "Serai Key Gen. Session: {:?}, Network: {:?}, Attempt: {}, Key: {}",
-        id.session,
-        N::NETWORK,
-        id.attempt,
-        key,
-      )
-    };
-
-    let rng = |label, id: KeyGenId| {
-      let mut transcript = RecommendedTranscript::new(label);
-      transcript.append_message(b"entropy", &self.entropy);
-      transcript.append_message(b"context", context(&id, "rng"));
-      ChaCha20Rng::from_seed(transcript.rng_seed(b"rng"))
-    };
-    let coefficients_rng = |id| rng(b"Key Gen Coefficients", id);
-    let secret_shares_rng = |id| rng(b"Key Gen Secret Shares", id);
-    let share_rng = |id| rng(b"Key Gen Share", id);
-
-    let key_gen_machines = |id, params: ThresholdParams, shares| {
-      let mut rng = coefficients_rng(id);
-      let mut machines = vec![];
-      let mut commitments = vec![];
-      for s in 0 .. shares {
-        let params = ThresholdParams::new(
-          params.t(),
-          params.n(),
-          Participant::new(u16::from(params.i()) + s).unwrap(),
-        )
-        .unwrap();
-        let substrate = KeyGenMachine::new(params, context(&id, SUBSTRATE_KEY_CONTEXT))
-          .generate_coefficients(&mut rng);
-        let network = KeyGenMachine::new(params, context(&id, NETWORK_KEY_CONTEXT))
-          .generate_coefficients(&mut rng);
-        machines.push((substrate.0, network.0));
-        let mut serialized = vec![];
-        substrate.1.write(&mut serialized).unwrap();
-        network.1.write(&mut serialized).unwrap();
-        commitments.push(serialized);
-      }
-      (machines, commitments)
-    };
-
-    let secret_share_machines = |id,
-                                 params: ThresholdParams,
-                                 machines: SecretShareMachines<N>,
-                                 commitments: HashMap<Participant, Vec<u8>>|
-     -> Result<_, ProcessorMessage> {
-      let mut rng = secret_shares_rng(id);
-
-      #[allow(clippy::type_complexity)]
-      fn handle_machine<C: Ciphersuite>(
-        rng: &mut ChaCha20Rng,
-        id: KeyGenId,
-        machine: SecretShareMachine<C>,
-        commitments: HashMap<Participant, EncryptionKeyMessage<C, Commitments<C>>>,
-      ) -> Result<
-        (KeyMachine<C>, HashMap<Participant, EncryptedMessage<C, SecretShare<C::F>>>),
-        ProcessorMessage,
-      > {
-        match machine.generate_secret_shares(rng, commitments) {
-          Ok(res) => Ok(res),
-          Err(e) => match e {
-            DkgError::ZeroParameter(_, _) |
-            DkgError::InvalidThreshold(_, _) |
-            DkgError::InvalidParticipant(_, _) |
-            DkgError::InvalidSigningSet |
-            DkgError::InvalidShare { .. } => unreachable!("{e:?}"),
-            DkgError::InvalidParticipantQuantity(_, _) |
-            DkgError::DuplicatedParticipant(_) |
-            DkgError::MissingParticipant(_) => {
-              panic!("coordinator sent invalid DKG commitments: {e:?}")
-            }
-            DkgError::InvalidCommitments(i) => {
-              Err(ProcessorMessage::InvalidCommitments { id, faulty: i })?
-            }
-          },
-        }
-      }
-
-      let mut substrate_commitments = HashMap::new();
-      let mut network_commitments = HashMap::new();
-      for i in 1 ..= params.n() {
-        let i = Participant::new(i).unwrap();
-        let mut commitments = commitments[&i].as_slice();
-        substrate_commitments.insert(
-          i,
-          EncryptionKeyMessage::<Ristretto, Commitments<Ristretto>>::read(&mut commitments, params)
-            .map_err(|_| ProcessorMessage::InvalidCommitments { id, faulty: i })?,
-        );
-        network_commitments.insert(
-          i,
-          EncryptionKeyMessage::<N::Curve, Commitments<N::Curve>>::read(&mut commitments, params)
-            .map_err(|_| ProcessorMessage::InvalidCommitments { id, faulty: i })?,
-        );
-        if !commitments.is_empty() {
-          // Malicious Participant included extra bytes in their commitments
-          // (a potential DoS attack)
-          Err(ProcessorMessage::InvalidCommitments { id, faulty: i })?;
-        }
-      }
-
-      let mut key_machines = vec![];
-      let mut shares = vec![];
-      for (m, (substrate_machine, network_machine)) in machines.into_iter().enumerate() {
-        let actual_i = Participant::new(u16::from(params.i()) + u16::try_from(m).unwrap()).unwrap();
-
-        let mut substrate_commitments = substrate_commitments.clone();
-        substrate_commitments.remove(&actual_i);
-        let (substrate_machine, mut substrate_shares) =
-          handle_machine::<Ristretto>(&mut rng, id, substrate_machine, substrate_commitments)?;
-
-        let mut network_commitments = network_commitments.clone();
-        network_commitments.remove(&actual_i);
-        let (network_machine, network_shares) =
-          handle_machine(&mut rng, id, network_machine, network_commitments.clone())?;
-
-        key_machines.push((substrate_machine, network_machine));
-
-        let mut these_shares: HashMap<_, _> =
-          substrate_shares.drain().map(|(i, share)| (i, share.serialize())).collect();
-        for (i, share) in &mut these_shares {
-          share.extend(network_shares[i].serialize());
-        }
-        shares.push(these_shares);
-      }
-      Ok((key_machines, shares))
-    };
+      let mut transcript = RecommendedTranscript::new(b"Serai eVRF Key Gen");
+      transcript.append_message(b"network", N::ID);
+      transcript.append_message(b"session", session.0.to_le_bytes());
+      transcript.append_message(b"key", key_context);
+      (&(&transcript.challenge(b"context"))[.. 32]).try_into().unwrap()
+    }

    match msg {
-      CoordinatorMessage::GenerateKey { id, params, shares } => {
-        info!("Generating new key. ID: {id:?} Params: {params:?} Shares: {shares}");
+      CoordinatorMessage::GenerateKey { session, threshold, evrf_public_keys } => {
+        info!("Generating new key. Session: {session:?}");

-        // Remove old attempts
-        if self.active_commit.remove(&id.session).is_none() &&
-          self.active_share.remove(&id.session).is_none()
+        // Unzip the vector of eVRF keys
+        let substrate_evrf_public_keys =
+          evrf_public_keys.iter().map(|(key, _)| *key).collect::<Vec<_>>();
+        let network_evrf_public_keys =
+          evrf_public_keys.into_iter().map(|(_, key)| key).collect::<Vec<_>>();
+
+        let mut participation = Vec::with_capacity(2048);
+        let mut faulty = HashSet::new();
+
+        // Participate for both Substrate and the network
+        fn participate<C: EvrfCurve>(
+          context: [u8; 32],
+          threshold: u16,
+          evrf_public_keys: &[impl AsRef<[u8]>],
+          evrf_private_key: &Zeroizing<<C::EmbeddedCurve as Ciphersuite>::F>,
+          faulty: &mut HashSet<Participant>,
+          output: &mut impl io::Write,
+        ) {
+          let (coerced_keys, faulty_is) = coerce_keys::<C>(evrf_public_keys);
+          for faulty_i in faulty_is {
+            faulty.insert(faulty_i);
+          }
+          let participation = EvrfDkg::<C>::participate(
+            &mut OsRng,
+            generators(),
+            context,
+            threshold,
+            &coerced_keys,
+            evrf_private_key,
+          );
+          participation.unwrap().write(output).unwrap();
+        }
+        participate::<Ristretto>(
+          context::<N>(session, SUBSTRATE_KEY_CONTEXT),
+          threshold,
+          &substrate_evrf_public_keys,
+          &self.substrate_evrf_private_key,
+          &mut faulty,
+          &mut participation,
+        );
+        participate::<N::Curve>(
+          context::<N>(session, NETWORK_KEY_CONTEXT),
+          threshold,
+          &network_evrf_public_keys,
+          &self.network_evrf_private_key,
+          &mut faulty,
+          &mut participation,
+        );
+
+        // Save the params
+        ParamsDb::set(
+          txn,
+          &session,
+          &(threshold, substrate_evrf_public_keys, network_evrf_public_keys),
+        );
+
+        // Send back our Participation and all faulty parties
+        let mut faulty = faulty.into_iter().collect::<Vec<_>>();
+        faulty.sort();
+
+        let mut res = Vec::with_capacity(faulty.len() + 1);
+        for faulty in faulty {
+          res.push(ProcessorMessage::Blame { session, participant: faulty });
+        }
+        res.push(ProcessorMessage::Participation { session, participation });
+
+        res
+      }
+
+      CoordinatorMessage::Participation { session, participant, participation } => {
+        info!("received participation from {:?} for {:?}", participant, session);
+
+        let (threshold, substrate_evrf_public_keys, network_evrf_public_keys) =
+          ParamsDb::get(txn, &session).unwrap();
+
+        let n = substrate_evrf_public_keys
+          .len()
+          .try_into()
+          .expect("performing a key gen with more than u16::MAX participants");
+
+        // Read these `Participation`s
+        // If they fail basic sanity checks, fail fast
+        let (substrate_participation, network_participation) = {
+          let network_participation_start_pos = {
+            let mut participation = participation.as_slice();
+            let start_len = participation.len();
+
+            let blame = vec![ProcessorMessage::Blame { session, participant }];
+            let Ok(substrate_participation) =
+              Participation::<Ristretto>::read(&mut participation, n)
+            else {
+              return blame;
+            };
+            let len_at_network_participation_start_pos = participation.len();
+            let Ok(network_participation) = Participation::<N::Curve>::read(&mut participation, n)
+            else {
+              return blame;
+            };
+
+            // If they added random noise after their participations, they're faulty
+            // This prevents DoS by causing a slash upon such spam
+            if !participation.is_empty() {
+              return blame;
+            }
+
+            // If we've already generated these keys, we don't actually need to save these
+            // participations and continue. We solely have to verify them, as to identify malicious
+            // participants and prevent DoSs, before returning
+            if txn.get(GeneratedKeysDb::key(&session)).is_some() {
+              info!("already finished generating a key for {:?}", session);
+
+              match EvrfDkg::<Ristretto>::verify(
+                &mut OsRng,
+                generators(),
+                context::<N>(session, SUBSTRATE_KEY_CONTEXT),
+                threshold,
+                // Ignores the list of participants who were faulty, as they were prior blamed
+                &coerce_keys::<Ristretto>(&substrate_evrf_public_keys).0,
+                &HashMap::from([(participant, substrate_participation)]),
+              )
+              .unwrap()
+              {
+                VerifyResult::Valid(_) | VerifyResult::NotEnoughParticipants => {}
+                VerifyResult::Invalid(faulty) => {
+                  assert_eq!(faulty, vec![participant]);
+                  return vec![ProcessorMessage::Blame { session, participant }];
+                }
+              }
+
+              match EvrfDkg::<N::Curve>::verify(
+                &mut OsRng,
+                generators(),
+                context::<N>(session, NETWORK_KEY_CONTEXT),
+                threshold,
+                // Ignores the list of participants who were faulty, as they were prior blamed
+                &coerce_keys::<N::Curve>(&network_evrf_public_keys).0,
+                &HashMap::from([(participant, network_participation)]),
+              )
+              .unwrap()
+              {
+                VerifyResult::Valid(_) | VerifyResult::NotEnoughParticipants => return vec![],
+                VerifyResult::Invalid(faulty) => {
+                  assert_eq!(faulty, vec![participant]);
+                  return vec![ProcessorMessage::Blame { session, participant }];
+                }
+              }
+            }
+
+            // Return the position the network participation starts at
+            start_len - len_at_network_participation_start_pos
+          };
+
+          // Instead of re-serializing the `Participation`s we read, we just use the relevant
+          // sections of the existing byte buffer
+          (
+            participation[.. network_participation_start_pos].to_vec(),
+            participation[network_participation_start_pos ..].to_vec(),
+          )
+        };
+
+        // Since these are valid `Participation`s, save them
+        let (mut substrate_participations, mut network_participations) =
+          ParticipationDb::get(txn, &session)
+            .unwrap_or((HashMap::with_capacity(1), HashMap::with_capacity(1)));
+        assert!(
+          substrate_participations.insert(participant, substrate_participation).is_none() &&
+            network_participations.insert(participant, network_participation).is_none(),
+          "received participation for someone multiple times"
+        );
+        ParticipationDb::set(
+          txn,
+          &session,
+          &(substrate_participations.clone(), network_participations.clone()),
+        );
+
+        // This block is taken from the eVRF DKG itself to evaluate the amount participating
        {
-          // If we haven't handled this session before, save the params
-          ParamsDb::set(txn, &id.session, id.attempt, &(params, shares));
-        }
+          let mut participating_weight = 0;
+          // This uses the Substrate maps as the maps are kept in synchrony
+          let mut evrf_public_keys_mut = substrate_evrf_public_keys.clone();
+          for i in substrate_participations.keys() {
+            let evrf_public_key = substrate_evrf_public_keys[usize::from(u16::from(*i)) - 1];

-        let (machines, commitments) = key_gen_machines(id, params, shares);
-        self.active_commit.insert(id.session, (machines, commitments.clone()));
+            // Remove this key from the Vec to prevent double-counting
+            /*
+              Double-counting would be a risk if multiple participants shared an eVRF public key
+              and participated. This code does still allow such participants (in order to let
+              participants be weighted), and any one of them participating will count as all
+              participating. This is fine as any one such participant will be able to decrypt
+              the shares for themselves and all other participants, so this is still a key
+              generated by an amount of participants who could simply reconstruct the key.
+            */
+            let start_len = evrf_public_keys_mut.len();
+            evrf_public_keys_mut.retain(|key| *key != evrf_public_key);
+            let end_len = evrf_public_keys_mut.len();
+            let count = start_len - end_len;

-        ProcessorMessage::Commitments { id, commitments }
-      }
-
-      CoordinatorMessage::Commitments { id, mut commitments } => {
-        info!("Received commitments for {:?}", id);
-
-        if self.active_share.contains_key(&id.session) {
-          // We should've been told of a new attempt before receiving commitments again
-          // The coordinator is either missing messages or repeating itself
-          // Either way, it's faulty
-          panic!("commitments when already handled commitments");
-        }
-
-        let (params, share_quantity) = ParamsDb::get(txn, &id.session, id.attempt).unwrap();
-
-        // Unwrap the machines, rebuilding them if we didn't have them in our cache
-        // We won't if the processor rebooted
-        // This *may* be inconsistent if we receive a KeyGen for attempt x, then commitments for
-        // attempt y
-        // The coordinator is trusted to be proper in this regard
-        let (prior, our_commitments) = self
-          .active_commit
-          .remove(&id.session)
-          .unwrap_or_else(|| key_gen_machines(id, params, share_quantity));
-
-        for (i, our_commitments) in our_commitments.into_iter().enumerate() {
-          assert!(commitments
-            .insert(
-              Participant::new(u16::from(params.i()) + u16::try_from(i).unwrap()).unwrap(),
-              our_commitments,
-            )
-            .is_none());
-        }
-
-        CommitmentsDb::set(txn, &id, &commitments);
-
-        match secret_share_machines(id, params, prior, commitments) {
-          Ok((machines, shares)) => {
-            self.active_share.insert(id.session, (machines, shares.clone()));
-            ProcessorMessage::Shares { id, shares }
+            participating_weight += count;
          }
-          Err(e) => e,
-        }
-      }
-
-      CoordinatorMessage::Shares { id, shares } => {
-        info!("Received shares for {:?}", id);
-
-        let (params, share_quantity) = ParamsDb::get(txn, &id.session, id.attempt).unwrap();
-
-        // Same commentary on inconsistency as above exists
-        let (machines, our_shares) = self.active_share.remove(&id.session).unwrap_or_else(|| {
-          let prior = key_gen_machines(id, params, share_quantity).0;
-          let (machines, shares) =
-            secret_share_machines(id, params, prior, CommitmentsDb::get(txn, &id).unwrap())
-              .expect("got Shares for a key gen which faulted");
-          (machines, shares)
-        });
-
-        let mut rng = share_rng(id);
-
-        fn handle_machine<C: Ciphersuite>(
-          rng: &mut ChaCha20Rng,
-          id: KeyGenId,
-          // These are the params of our first share, not this machine's shares
-          params: ThresholdParams,
-          m: usize,
-          machine: KeyMachine<C>,
-          shares_ref: &mut HashMap<Participant, &[u8]>,
-        ) -> Result<ThresholdCore<C>, ProcessorMessage> {
-          let params = ThresholdParams::new(
-            params.t(),
-            params.n(),
-            Participant::new(u16::from(params.i()) + u16::try_from(m).unwrap()).unwrap(),
-          )
-          .unwrap();
-
-          // Parse the shares
-          let mut shares = HashMap::new();
-          for i in 1 ..= params.n() {
-            let i = Participant::new(i).unwrap();
-            let Some(share) = shares_ref.get_mut(&i) else { continue };
-            shares.insert(
-              i,
-              EncryptedMessage::<C, SecretShare<C::F>>::read(share, params).map_err(|_| {
-                ProcessorMessage::InvalidShare { id, accuser: params.i(), faulty: i, blame: None }
-              })?,
-            );
+          if participating_weight < usize::from(threshold) {
+            return vec![];
          }
-
-          Ok(
-            (match machine.calculate_share(rng, shares) {
-              Ok(res) => res,
-              Err(e) => match e {
-                DkgError::ZeroParameter(_, _) |
-                DkgError::InvalidThreshold(_, _) |
-                DkgError::InvalidParticipant(_, _) |
-                DkgError::InvalidSigningSet |
-                DkgError::InvalidCommitments(_) => unreachable!("{e:?}"),
-                DkgError::InvalidParticipantQuantity(_, _) |
-                DkgError::DuplicatedParticipant(_) |
-                DkgError::MissingParticipant(_) => {
-                  panic!("coordinator sent invalid DKG shares: {e:?}")
-                }
-                DkgError::InvalidShare { participant, blame } => {
-                  Err(ProcessorMessage::InvalidShare {
-                    id,
-                    accuser: params.i(),
-                    faulty: participant,
-                    blame: Some(blame.map(|blame| blame.serialize())).flatten(),
-                  })?
-                }
-              },
-            })
-            .complete(),
-          )
        }

-        let mut substrate_keys = vec![];
-        let mut network_keys = vec![];
-        for (m, machines) in machines.into_iter().enumerate() {
-          let mut shares_ref: HashMap<Participant, &[u8]> =
-            shares[m].iter().map(|(i, shares)| (*i, shares.as_ref())).collect();
-          for (i, our_shares) in our_shares.iter().enumerate() {
-            if m != i {
-              assert!(shares_ref
-                .insert(
-                  Participant::new(u16::from(params.i()) + u16::try_from(i).unwrap()).unwrap(),
-                  our_shares
-                    [&Participant::new(u16::from(params.i()) + u16::try_from(m).unwrap()).unwrap()]
-                    .as_ref(),
-                )
-                .is_none());
-            }
-          }
-
-          let these_substrate_keys =
-            match handle_machine(&mut rng, id, params, m, machines.0, &mut shares_ref) {
-              Ok(keys) => keys,
-              Err(msg) => return msg,
-            };
-          let these_network_keys =
-            match handle_machine(&mut rng, id, params, m, machines.1, &mut shares_ref) {
-              Ok(keys) => keys,
-              Err(msg) => return msg,
-            };
-
-          for i in 1 ..= params.n() {
-            let i = Participant::new(i).unwrap();
-            let Some(shares) = shares_ref.get(&i) else { continue };
-            if !shares.is_empty() {
-              return ProcessorMessage::InvalidShare {
-                id,
-                accuser: these_substrate_keys.params().i(),
-                faulty: i,
-                blame: None,
-              };
-            }
-          }
-
-          let mut these_network_keys = ThresholdKeys::new(these_network_keys);
-          N::tweak_keys(&mut these_network_keys);
-
-          substrate_keys.push(these_substrate_keys);
-          network_keys.push(these_network_keys);
-        }
-
-        let mut generated_substrate_key = None;
-        let mut generated_network_key = None;
-        for keys in substrate_keys.iter().zip(&network_keys) {
-          if generated_substrate_key.is_none() {
-            generated_substrate_key = Some(keys.0.group_key());
-            generated_network_key = Some(keys.1.group_key());
+        // If we now have the threshold participating, verify their `Participation`s
+        fn verify_dkg<N: Network, C: EvrfCurve>(
+          txn: &mut impl DbTxn,
+          session: Session,
+          true_if_substrate_false_if_network: bool,
+          threshold: u16,
+          evrf_public_keys: &[impl AsRef<[u8]>],
+          substrate_participations: &mut HashMap<Participant, Vec<u8>>,
+          network_participations: &mut HashMap<Participant, Vec<u8>>,
+        ) -> Result<EvrfDkg<C>, Vec<ProcessorMessage>> {
+          // Parse the `Participation`s
+          let participations = (if true_if_substrate_false_if_network {
+            &*substrate_participations
          } else {
-            assert_eq!(generated_substrate_key, Some(keys.0.group_key()));
-            assert_eq!(generated_network_key, Some(keys.1.group_key()));
+            &*network_participations
+          })
+          .iter()
+          .map(|(key, participation)| {
+            (
+              *key,
+              Participation::read(
+                &mut participation.as_slice(),
+                evrf_public_keys.len().try_into().unwrap(),
+              )
+              .expect("prior read participation was invalid"),
+            )
+          })
+          .collect();
+
+          // Actually call verify on the DKG
+          match EvrfDkg::<C>::verify(
+            &mut OsRng,
+            generators(),
+            context::<N>(
+              session,
+              if true_if_substrate_false_if_network {
+                SUBSTRATE_KEY_CONTEXT
+              } else {
+                NETWORK_KEY_CONTEXT
+              },
+            ),
+            threshold,
+            // Ignores the list of participants who were faulty, as they were prior blamed
+            &coerce_keys::<C>(evrf_public_keys).0,
+            &participations,
+          )
+          .unwrap()
+          {
+            // If the DKG was valid, return it
+            VerifyResult::Valid(dkg) => Ok(dkg),
+            // This DKG had faulty participants, so create blame messages for them
+            VerifyResult::Invalid(faulty) => {
+              let mut blames = vec![];
+              for participant in faulty {
+                // Remove from both maps for simplicity's sake
+                // There's no point in having one DKG complete yet not the other
+                assert!(substrate_participations.remove(&participant).is_some());
+                assert!(network_participations.remove(&participant).is_some());
+                blames.push(ProcessorMessage::Blame { session, participant });
+              }
+              // Since we removed `Participation`s, write the updated versions to the database
+              ParticipationDb::set(
+                txn,
+                &session,
+                &(substrate_participations.clone(), network_participations.clone()),
+              );
+              Err(blames)?
+            }
+            VerifyResult::NotEnoughParticipants => {
+              // This is the first DKG, and we checked we were at the threshold OR
+              // This is the second DKG, as the first had no invalid participants, so we're still
+              // at the threshold
+              panic!("not enough participants despite checking we were at the threshold")
+            }
          }
        }

-        GeneratedKeysDb::save_keys::<N>(txn, &id, &substrate_keys, &network_keys);
+        let substrate_dkg = match verify_dkg::<N, Ristretto>(
+          txn,
+          session,
+          true,
+          threshold,
+          &substrate_evrf_public_keys,
+          &mut substrate_participations,
+          &mut network_participations,
+        ) {
+          Ok(dkg) => dkg,
+          // If we had any blames, immediately return them as necessary for the safety of
+          // `verify_dkg` (it assumes we don't call it again upon prior errors)
+          Err(blames) => return blames,
+        };

-        ProcessorMessage::GeneratedKeyPair {
-          id,
-          substrate_key: generated_substrate_key.unwrap().to_bytes(),
+        let network_dkg = match verify_dkg::<N, N::Curve>(
+          txn,
+          session,
+          false,
+          threshold,
+          &network_evrf_public_keys,
+          &mut substrate_participations,
+          &mut network_participations,
+        ) {
+          Ok(dkg) => dkg,
+          Err(blames) => return blames,
+        };
+
+        // Get our keys from each DKG
+        // TODO: Some of these keys may be decrypted by us, yet not actually meant for us, if
+        // another validator set our eVRF public key as their eVRF public key. We either need to
+        // ensure the coordinator tracks amount of shares we're supposed to have by the eVRF public
+        // keys OR explicitly reduce to the keys we're supposed to have based on our `i` index.
+        let substrate_keys = substrate_dkg.keys(&self.substrate_evrf_private_key);
+        let mut network_keys = network_dkg.keys(&self.network_evrf_private_key);
+        // Tweak the keys for the network
+        for network_keys in &mut network_keys {
+          N::tweak_keys(network_keys);
+        }
+        GeneratedKeysDb::save_keys::<N>(txn, &session, &substrate_keys, &network_keys);
+
+        // Since no one we verified was invalid, and we had the threshold, yield the new keys
+        vec![ProcessorMessage::GeneratedKeyPair {
+          session,
+          substrate_key: substrate_keys[0].group_key().to_bytes(),
          // TODO: This can be made more efficient since tweaked keys may be a subset of keys
-          network_key: generated_network_key.unwrap().to_bytes().as_ref().to_vec(),
-        }
-      }
-
-      CoordinatorMessage::VerifyBlame { id, accuser, accused, share, blame } => {
-        let params = ParamsDb::get(txn, &id.session, id.attempt).unwrap().0;
-
-        let mut share_ref = share.as_slice();
-        let Ok(substrate_share) = EncryptedMessage::<
-          Ristretto,
-          SecretShare<<Ristretto as Ciphersuite>::F>,
-        >::read(&mut share_ref, params) else {
-          return ProcessorMessage::Blame { id, participant: accused };
-        };
-        let Ok(network_share) = EncryptedMessage::<
-          N::Curve,
-          SecretShare<<N::Curve as Ciphersuite>::F>,
-        >::read(&mut share_ref, params) else {
-          return ProcessorMessage::Blame { id, participant: accused };
-        };
-        if !share_ref.is_empty() {
-          return ProcessorMessage::Blame { id, participant: accused };
-        }
-
-        let mut substrate_commitment_msgs = HashMap::new();
-        let mut network_commitment_msgs = HashMap::new();
-        let commitments = CommitmentsDb::get(txn, &id).unwrap();
-        for (i, commitments) in commitments {
-          let mut commitments = commitments.as_slice();
-          substrate_commitment_msgs
-            .insert(i, EncryptionKeyMessage::<_, _>::read(&mut commitments, params).unwrap());
-          network_commitment_msgs
-            .insert(i, EncryptionKeyMessage::<_, _>::read(&mut commitments, params).unwrap());
-        }
-
-        // There is a mild DoS here where someone with a valid blame bloats it to the maximum size
-        // Given the ambiguity, and limited potential to DoS (this being called means *someone* is
-        // getting fatally slashed) voids the need to ensure blame is minimal
-        let substrate_blame =
-          blame.clone().and_then(|blame| EncryptionKeyProof::read(&mut blame.as_slice()).ok());
-        let network_blame =
-          blame.clone().and_then(|blame| EncryptionKeyProof::read(&mut blame.as_slice()).ok());
-
-        let substrate_blame = AdditionalBlameMachine::new(
-          &mut rand_core::OsRng,
-          context(&id, SUBSTRATE_KEY_CONTEXT),
-          params.n(),
-          substrate_commitment_msgs,
-        )
-        .unwrap()
-        .blame(accuser, accused, substrate_share, substrate_blame);
-        let network_blame = AdditionalBlameMachine::new(
-          &mut rand_core::OsRng,
-          context(&id, NETWORK_KEY_CONTEXT),
-          params.n(),
-          network_commitment_msgs,
-        )
-        .unwrap()
-        .blame(accuser, accused, network_share, network_blame);
-
-        // If the accused was blamed for either, mark them as at fault
-        if (substrate_blame == accused) || (network_blame == accused) {
-          return ProcessorMessage::Blame { id, participant: accused };
-        }
-
-        ProcessorMessage::Blame { id, participant: accuser }
+          network_key: network_keys[0].group_key().to_bytes().as_ref().to_vec(),
+        }]
      }
    }
  }
--- a/processor/src/main.rs
+++ b/processor/src/main.rs
@@ -2,8 +2,11 @@ use std::{time::Duration, collections::HashMap};

 use zeroize::{Zeroize, Zeroizing};

-use transcript::{Transcript, RecommendedTranscript};
-use ciphersuite::{group::GroupEncoding, Ciphersuite};
+use ciphersuite::{
+  group::{ff::PrimeField, GroupEncoding},
+  Ciphersuite, Ristretto,
+};
+use dkg::evrf::EvrfCurve;

 use log::{info, warn};
 use tokio::time::sleep;
@@ -128,7 +131,7 @@ struct TributaryMutable<N: Network, D: Db> {
  `Burn`s.

  Substrate also decides when to move to a new multisig, hence why this entire object is
-  Substate-mutable.
+  Substrate-mutable.

  Since MultisigManager should always be verifiable, and the Tributary is temporal, MultisigManager
  being entirely SubstrateMutable shows proper data pipe-lining.
@@ -224,7 +227,9 @@ async fn handle_coordinator_msg<D: Db, N: Network, Co: Coordinator>(

  match msg.msg.clone() {
    CoordinatorMessage::KeyGen(msg) => {
-      coordinator.send(tributary_mutable.key_gen.handle(txn, msg)).await;
+      for msg in tributary_mutable.key_gen.handle(txn, msg) {
+        coordinator.send(msg).await;
+      }
    }

    CoordinatorMessage::Sign(msg) => {
@@ -485,41 +490,31 @@ async fn boot<N: Network, D: Db, Co: Coordinator>(
  network: &N,
  coordinator: &mut Co,
 ) -> (D, TributaryMutable<N, D>, SubstrateMutable<N, D>) {
-  let mut entropy_transcript = {
-    let entropy = Zeroizing::new(env::var("ENTROPY").expect("entropy wasn't specified"));
-    if entropy.len() != 64 {
-      panic!("entropy isn't the right length");
+  fn read_key_from_env<C: Ciphersuite>(label: &'static str) -> Zeroizing<C::F> {
+    let key_hex =
+      Zeroizing::new(env::var(label).unwrap_or_else(|| panic!("{label} wasn't provided")));
+    let bytes = Zeroizing::new(
+      hex::decode(key_hex).unwrap_or_else(|_| panic!("{label} wasn't a valid hex string")),
+    );
+
+    let mut repr = <C::F as PrimeField>::Repr::default();
+    if repr.as_ref().len() != bytes.len() {
+      panic!("{label} wasn't the correct length");
    }
-    let mut bytes =
-      Zeroizing::new(hex::decode(entropy).map_err(|_| ()).expect("entropy wasn't hex-formatted"));
-    if bytes.len() != 32 {
-      bytes.zeroize();
-      panic!("entropy wasn't 32 bytes");
-    }
-    let mut entropy = Zeroizing::new([0; 32]);
-    let entropy_mut: &mut [u8] = entropy.as_mut();
-    entropy_mut.copy_from_slice(bytes.as_ref());
-
-    let mut transcript = RecommendedTranscript::new(b"Serai Processor Entropy");
-    transcript.append_message(b"entropy", entropy);
-    transcript
-  };
-
-  // TODO: Save a hash of the entropy to the DB and make sure the entropy didn't change
-
-  let mut entropy = |label| {
-    let mut challenge = entropy_transcript.challenge(label);
-    let mut res = Zeroizing::new([0; 32]);
-    let res_mut: &mut [u8] = res.as_mut();
-    res_mut.copy_from_slice(&challenge[.. 32]);
-    challenge.zeroize();
+    repr.as_mut().copy_from_slice(bytes.as_slice());
+    let res = Zeroizing::new(
+      Option::from(<C::F as PrimeField>::from_repr(repr))
+        .unwrap_or_else(|| panic!("{label} wasn't a valid scalar")),
+    );
+    repr.as_mut().zeroize();
    res
-  };
+  }

-  // We don't need to re-issue GenerateKey orders because the coordinator is expected to
-  // schedule/notify us of new attempts
-  // TODO: Is this above comment still true? Not at all due to the planned lack of DKG timeouts?
-  let key_gen = KeyGen::<N, _>::new(raw_db.clone(), entropy(b"key-gen_entropy"));
+  let key_gen = KeyGen::<N, _>::new(
+    raw_db.clone(),
+    read_key_from_env::<<Ristretto as EvrfCurve>::EmbeddedCurve>("SUBSTRATE_EVRF_KEY"),
+    read_key_from_env::<<N::Curve as EvrfCurve>::EmbeddedCurve>("NETWORK_EVRF_KEY"),
+  );

  let (multisig_manager, current_keys, actively_signing) =
    MultisigManager::new(raw_db, network).await;
--- a/processor/src/networks/mod.rs
+++ b/processor/src/networks/mod.rs
@@ -5,6 +5,7 @@ use async_trait::async_trait;
 use thiserror::Error;

 use frost::{
+  dkg::evrf::EvrfCurve,
  curve::{Ciphersuite, Curve},
  ThresholdKeys,
  sign::PreprocessMachine,
@@ -240,9 +241,11 @@ pub struct PreparedSend<N: Network> {
 }

 #[async_trait]
+#[rustfmt::skip]
 pub trait Network: 'static + Send + Sync + Clone + PartialEq + Debug {
  /// The elliptic curve used for this network.
-  type Curve: Curve;
+  type Curve: Curve
+    + EvrfCurve<EmbeddedCurve: Ciphersuite<G: ec_divisors::DivisorCurve<FieldElement = <Self::Curve as Ciphersuite>::F>>>;

  /// The type representing the transaction for this network.
  type Transaction: Transaction<Self>; // TODO: Review use of
--- a/processor/src/networks/monero.rs
+++ b/processor/src/networks/monero.rs
@@ -657,7 +657,7 @@ impl Network for Monero {
    keys: ThresholdKeys<Self::Curve>,
    transaction: SignableTransaction,
  ) -> Result<Self::TransactionMachine, NetworkError> {
-    match transaction.0.clone().multisig(&keys) {
+    match transaction.0.clone().multisig(keys) {
      Ok(machine) => Ok(machine),
      Err(e) => panic!("failed to create a multisig machine for TX: {e}"),
    }
--- a/processor/src/tests/key_gen.rs
+++ b/processor/src/tests/key_gen.rs
@@ -2,10 +2,13 @@ use std::collections::HashMap;

 use zeroize::Zeroizing;

-use rand_core::{RngCore, OsRng};
+use rand_core::OsRng;

-use ciphersuite::group::GroupEncoding;
-use frost::{Participant, ThresholdParams, tests::clone_without};
+use ciphersuite::{
+  group::{ff::Field, GroupEncoding},
+  Ciphersuite, Ristretto,
+};
+use dkg::{Participant, ThresholdParams, evrf::*};

 use serai_db::{DbTxn, Db, MemDb};

@@ -18,113 +21,102 @@ use crate::{
  key_gen::{KeyConfirmed, KeyGen},
 };

-const ID: KeyGenId = KeyGenId { session: Session(1), attempt: 3 };
+const SESSION: Session = Session(1);

 pub fn test_key_gen<N: Network>() {
-  let mut entropies = HashMap::new();
  let mut dbs = HashMap::new();
+  let mut substrate_evrf_keys = HashMap::new();
+  let mut network_evrf_keys = HashMap::new();
+  let mut evrf_public_keys = vec![];
  let mut key_gens = HashMap::new();
  for i in 1 ..= 5 {
-    let mut entropy = Zeroizing::new([0; 32]);
-    OsRng.fill_bytes(entropy.as_mut());
-    entropies.insert(i, entropy);
    let db = MemDb::new();
    dbs.insert(i, db.clone());
-    key_gens.insert(i, KeyGen::<N, MemDb>::new(db, entropies[&i].clone()));
+
+    let substrate_evrf_key = Zeroizing::new(
+      <<Ristretto as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F::random(&mut OsRng),
+    );
+    substrate_evrf_keys.insert(i, substrate_evrf_key.clone());
+    let network_evrf_key = Zeroizing::new(
+      <<N::Curve as EvrfCurve>::EmbeddedCurve as Ciphersuite>::F::random(&mut OsRng),
+    );
+    network_evrf_keys.insert(i, network_evrf_key.clone());
+
+    evrf_public_keys.push((
+      (<<Ristretto as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator() * *substrate_evrf_key)
+        .to_bytes(),
+      (<<N::Curve as EvrfCurve>::EmbeddedCurve as Ciphersuite>::generator() * *network_evrf_key)
+        .to_bytes()
+        .as_ref()
+        .to_vec(),
+    ));
+    key_gens
+      .insert(i, KeyGen::<N, MemDb>::new(db, substrate_evrf_key.clone(), network_evrf_key.clone()));
  }

-  let mut all_commitments = HashMap::new();
+  let mut participations = HashMap::new();
  for i in 1 ..= 5 {
    let key_gen = key_gens.get_mut(&i).unwrap();
    let mut txn = dbs.get_mut(&i).unwrap().txn();
-    if let ProcessorMessage::Commitments { id, mut commitments } = key_gen.handle(
+    let mut msgs = key_gen.handle(
      &mut txn,
      CoordinatorMessage::GenerateKey {
-        id: ID,
-        params: ThresholdParams::new(3, 5, Participant::new(u16::try_from(i).unwrap()).unwrap())
-          .unwrap(),
-        shares: 1,
+        session: SESSION,
+        threshold: 3,
+        evrf_public_keys: evrf_public_keys.clone(),
      },
-    ) {
-      assert_eq!(id, ID);
-      assert_eq!(commitments.len(), 1);
-      all_commitments
-        .insert(Participant::new(u16::try_from(i).unwrap()).unwrap(), commitments.swap_remove(0));
-    } else {
-      panic!("didn't get commitments back");
-    }
+    );
+    assert_eq!(msgs.len(), 1);
+    let ProcessorMessage::Participation { session, participation } = msgs.swap_remove(0) else {
+      panic!("didn't get a participation")
+    };
+    assert_eq!(session, SESSION);
+    participations.insert(i, participation);
    txn.commit();
  }

-  // 1 is rebuilt on every step
-  // 2 is rebuilt here
-  // 3 ... are rebuilt once, one at each of the following steps
-  let rebuild = |key_gens: &mut HashMap<_, _>, dbs: &HashMap<_, MemDb>, i| {
-    key_gens.remove(&i);
-    key_gens.insert(i, KeyGen::<N, _>::new(dbs[&i].clone(), entropies[&i].clone()));
-  };
-  rebuild(&mut key_gens, &dbs, 1);
-  rebuild(&mut key_gens, &dbs, 2);
-
-  let mut all_shares = HashMap::new();
-  for i in 1 ..= 5 {
-    let key_gen = key_gens.get_mut(&i).unwrap();
-    let mut txn = dbs.get_mut(&i).unwrap().txn();
-    let i = Participant::new(u16::try_from(i).unwrap()).unwrap();
-    if let ProcessorMessage::Shares { id, mut shares } = key_gen.handle(
-      &mut txn,
-      CoordinatorMessage::Commitments { id: ID, commitments: clone_without(&all_commitments, &i) },
-    ) {
-      assert_eq!(id, ID);
-      assert_eq!(shares.len(), 1);
-      all_shares.insert(i, shares.swap_remove(0));
-    } else {
-      panic!("didn't get shares back");
-    }
-    txn.commit();
-  }
-
-  // Rebuild 1 and 3
-  rebuild(&mut key_gens, &dbs, 1);
-  rebuild(&mut key_gens, &dbs, 3);
-
  let mut res = None;
  for i in 1 ..= 5 {
    let key_gen = key_gens.get_mut(&i).unwrap();
    let mut txn = dbs.get_mut(&i).unwrap().txn();
-    let i = Participant::new(u16::try_from(i).unwrap()).unwrap();
-    if let ProcessorMessage::GeneratedKeyPair { id, substrate_key, network_key } = key_gen.handle(
-      &mut txn,
-      CoordinatorMessage::Shares {
-        id: ID,
-        shares: vec![all_shares
-          .iter()
-          .filter_map(|(l, shares)| if i == *l { None } else { Some((*l, shares[&i].clone())) })
-          .collect()],
-      },
-    ) {
-      assert_eq!(id, ID);
-      if res.is_none() {
-        res = Some((substrate_key, network_key.clone()));
+    for j in 1 ..= 5 {
+      let mut msgs = key_gen.handle(
+        &mut txn,
+        CoordinatorMessage::Participation {
+          session: SESSION,
+          participant: Participant::new(u16::try_from(j).unwrap()).unwrap(),
+          participation: participations[&j].clone(),
+        },
+      );
+      if j != 3 {
+        assert!(msgs.is_empty());
+      }
+      if j == 3 {
+        assert_eq!(msgs.len(), 1);
+        let ProcessorMessage::GeneratedKeyPair { session, substrate_key, network_key } =
+          msgs.swap_remove(0)
+        else {
+          panic!("didn't get a generated key pair")
+        };
+        assert_eq!(session, SESSION);
+
+        if res.is_none() {
+          res = Some((substrate_key, network_key.clone()));
+        }
+        assert_eq!(res.as_ref().unwrap(), &(substrate_key, network_key));
      }
-      assert_eq!(res.as_ref().unwrap(), &(substrate_key, network_key));
-    } else {
-      panic!("didn't get key back");
    }
+
    txn.commit();
  }
  let res = res.unwrap();

-  // Rebuild 1 and 4
-  rebuild(&mut key_gens, &dbs, 1);
-  rebuild(&mut key_gens, &dbs, 4);
-
  for i in 1 ..= 5 {
    let key_gen = key_gens.get_mut(&i).unwrap();
    let mut txn = dbs.get_mut(&i).unwrap().txn();
    let KeyConfirmed { mut substrate_keys, mut network_keys } = key_gen.confirm(
      &mut txn,
-      ID.session,
+      SESSION,
      &KeyPair(sr25519::Public(res.0), res.1.clone().try_into().unwrap()),
    );
    txn.commit();
--- a/Exclusions.md
+++ b/Exclusions.md
@@ -1,23 +0,0 @@
-Upon an issue with the DKG, the honest validators must remove the malicious
-validators. Ideally, a threshold signature would be used, yet that would require
-a threshold key (which would require authentication by a MuSig signature). A
-MuSig signature which specifies the signing set (or rather, the excluded
-signers) achieves the most efficiency.
-
-While that resolves the on-chain behavior, the Tributary also has to perform
-exclusion. This has the following forms:
-
-1) Rejecting further transactions (required)
-2) Rejecting further participation in Tendermint
-
-With regards to rejecting further participation in Tendermint, it's *ideal* to
-remove the validator from the list of validators. Each validator removed from
-participation, yet not from the list of validators, increases the likelihood of
-the network failing to form consensus.
-
-With regards to the economic security, an honest 67% may remove a faulty
-(explicitly or simply offline) 33%, letting 67% of the remaining 67% (4/9ths)
-take control of the associated private keys. In such a case, the malicious
-parties are defined as the 4/9ths of validators with access to the private key
-and the 33% removed (who together form >67% of the originally intended
-validator set and have presumably provided enough stake to cover losses).
--- a/spec/cryptography/Distributed
+++ b/spec/cryptography/Distributed
@@ -1,35 +1,7 @@
 # Distributed Key Generation

-Serai uses a modification of Pedersen's Distributed Key Generation, which is
-actually Feldman's Verifiable Secret Sharing Scheme run by every participant, as
-described in the FROST paper. The modification included in FROST was to include
-a Schnorr Proof of Knowledge for coefficient zero, preventing rogue key attacks.
-This results in a two-round protocol.
-
-### Encryption
-
-In order to protect the secret shares during communication, the `dkg` library
-establishes a public key for encryption at the start of a given protocol.
-Every encrypted message (such as the secret shares) then includes a per-message
-encryption key. These two keys are used in an Elliptic-curve Diffie-Hellman
-handshake to derive a shared key. This shared key is then hashed to obtain a key
-and IV for use in a ChaCha20 stream cipher instance, which is xor'd against a
-message to encrypt it.
-
-### Blame
-
-Since each message has a distinct key attached, and accordingly a distinct
-shared key, it's possible to reveal the shared key for a specific message
-without revealing any other message's decryption keys. This is utilized when a
-participant misbehaves. A participant who receives an invalid encrypted message
-publishes its key, able to without concern for side effects, With the key
-published, all participants can decrypt the message in order to decide blame.
-
-While key reuse by a participant is considered as them revealing the messages
-themselves, and therefore out of scope, there is an attack where a malicious
-adversary claims another participant's encryption key. They'll fail to encrypt
-their message, and the recipient will issue a blame statement. This blame
-statement, intended to reveal the malicious adversary, also reveals the message
-by the participant whose keys were co-opted. To resolve this, a
-proof-of-possession is also included with encrypted messages, ensuring only
-those actually with per-message keys can claim to use them.
+Serai uses a modification of the one-round Distributed Key Generation described
+in the [eVRF](https://eprint.iacr.org/2024/397) paper. We only require a
+threshold to participate, sacrificing unbiased for robustness, and implement a
+verifiable encryption scheme such that anyone can can verify a ciphertext
+encrypts the expected secret share.
--- a/spec/processor/Processor.md
+++ b/spec/processor/Processor.md
@@ -9,29 +9,22 @@ This document primarily discusses its flow with regards to the coordinator.
 ### Generate Key

 On `key_gen::CoordinatorMessage::GenerateKey`, the processor begins a pair of
-instances of the distributed key generation protocol specified in the FROST
-paper.
+instances of the distributed key generation protocol.

-The first instance is for a key to use on the external network. The second
-instance is for a Ristretto public key used to publish data to the Serai
-blockchain. This pair of FROST DKG instances is considered a single instance of
-Serai's overall key generation protocol.
+The first instance is for a Ristretto public key used to publish data to the
+Serai blockchain. The second instance is for a key to use on the external
+network. This pair of DKG instances is considered a single instance of Serai's
+overall DKG protocol.

-The commitments for both protocols are sent to the coordinator in a single
-`key_gen::ProcessorMessage::Commitments`.
+The participations in both protocols are sent to the coordinator in a single
+`key_gen::ProcessorMessage::Participation`.

-### Key Gen Commitments
+### Key Gen Participations

-On `key_gen::CoordinatorMessage::Commitments`, the processor continues the
-specified key generation instance. The secret shares for each fellow
-participant are sent to the coordinator in a
-`key_gen::ProcessorMessage::Shares`.
-
-#### Key Gen Shares
-
-On `key_gen::CoordinatorMessage::Shares`, the processor completes the specified
-key generation instance. The generated key pair is sent to the coordinator in a
-`key_gen::ProcessorMessage::GeneratedKeyPair`.
+On `key_gen::CoordinatorMessage::Participation`, the processor stores the
+contained participation, verifying participations as sane. Once it receives `t`
+honest participations, the processor completes the DKG and sends the generated
+key pair to the coordinator in a `key_gen::ProcessorMessage::GeneratedKeyPair`.

 ### Confirm Key Pair

--- a/substrate/abi/Cargo.toml
+++ b/substrate/abi/Cargo.toml
@@ -16,8 +16,10 @@ rustdoc-args = ["--cfg", "docsrs"]
 workspace = true

 [dependencies]
-scale = { package = "parity-scale-codec", version = "3", default-features = false, features = ["derive"] }
-scale-info = { version = "2", default-features = false, features = ["derive"] }
+bitvec = { version = "1", default-features = false, features = ["alloc", "serde"] }
+
+scale = { package = "parity-scale-codec", version = "3", default-features = false, features = ["derive", "bit-vec"] }
+scale-info = { version = "2", default-features = false, features = ["derive", "bit-vec"] }

 borsh = { version = "1", default-features = false, features = ["derive", "de_strict_order"], optional = true }
 serde = { version = "1", default-features = false, features = ["derive", "alloc"], optional = true }
@@ -39,6 +41,8 @@ serai-signals-primitives = { path = "../signals/primitives", version = "0.1", de

 [features]
 std = [
+  "bitvec/std",
+
  "scale/std",
  "scale-info/std",

--- a/substrate/abi/src/validator_sets.rs
+++ b/substrate/abi/src/validator_sets.rs
@@ -11,10 +11,14 @@ use serai_validator_sets_primitives::*;
 pub enum Call {
  set_keys {
    network: NetworkId,
-    removed_participants: BoundedVec<SeraiAddress, ConstU32<{ MAX_KEY_SHARES_PER_SET / 3 }>>,
    key_pair: KeyPair,
+    signature_participants: bitvec::vec::BitVec<u8, bitvec::order::Lsb0>,
    signature: Signature,
  },
+  set_embedded_elliptic_curve_key {
+    embedded_elliptic_curve: EmbeddedEllipticCurve,
+    key: BoundedVec<u8, ConstU32<{ MAX_KEY_LEN }>>,
+  },
  report_slashes {
    network: NetworkId,
    slashes: BoundedVec<(SeraiAddress, u32), ConstU32<{ MAX_KEY_SHARES_PER_SET / 3 }>>,
--- a/substrate/client/Cargo.toml
+++ b/substrate/client/Cargo.toml
@@ -20,6 +20,8 @@ workspace = true
 zeroize = "^1.5"
 thiserror = { version = "1", optional = true }

+bitvec = { version = "1", default-features = false, features = ["alloc", "serde"] }
+
 hex = "0.4"
 scale = { package = "parity-scale-codec", version = "3" }
 serde = { version = "1", features = ["derive"], optional = true }
--- a/substrate/client/src/serai/validator_sets.rs
+++ b/substrate/client/src/serai/validator_sets.rs
@@ -1,13 +1,14 @@
 use scale::Encode;

 use sp_core::sr25519::{Public, Signature};
+use sp_runtime::BoundedVec;

 use serai_abi::primitives::Amount;
 pub use serai_abi::validator_sets::primitives;
-use primitives::{Session, ValidatorSet, KeyPair};
+use primitives::{MAX_KEY_LEN, Session, ValidatorSet, KeyPair};

 use crate::{
-  primitives::{NetworkId, SeraiAddress},
+  primitives::{EmbeddedEllipticCurve, NetworkId, SeraiAddress},
  Transaction, Serai, TemporalSerai, SeraiError,
 };

@@ -107,6 +108,21 @@ impl<'a> SeraiValidatorSets<'a> {
    self.0.storage(PALLET, "CurrentSession", network).await
  }

+  pub async fn embedded_elliptic_curve_key(
+    &self,
+    validator: Public,
+    embedded_elliptic_curve: EmbeddedEllipticCurve,
+  ) -> Result<Option<Vec<u8>>, SeraiError> {
+    self
+      .0
+      .storage(
+        PALLET,
+        "EmbeddedEllipticCurveKeys",
+        (sp_core::hashing::blake2_128(&validator.encode()), validator, embedded_elliptic_curve),
+      )
+      .await
+  }
+
  pub async fn participants(
    &self,
    network: NetworkId,
@@ -180,21 +196,30 @@ impl<'a> SeraiValidatorSets<'a> {

  pub fn set_keys(
    network: NetworkId,
-    removed_participants: sp_runtime::BoundedVec<
-      SeraiAddress,
-      sp_core::ConstU32<{ primitives::MAX_KEY_SHARES_PER_SET / 3 }>,
-    >,
    key_pair: KeyPair,
+    signature_participants: bitvec::vec::BitVec<u8, bitvec::order::Lsb0>,
    signature: Signature,
  ) -> Transaction {
    Serai::unsigned(serai_abi::Call::ValidatorSets(serai_abi::validator_sets::Call::set_keys {
      network,
-      removed_participants,
      key_pair,
+      signature_participants,
      signature,
    }))
  }

+  pub fn set_embedded_elliptic_curve_key(
+    embedded_elliptic_curve: EmbeddedEllipticCurve,
+    key: BoundedVec<u8, sp_core::ConstU32<{ MAX_KEY_LEN }>>,
+  ) -> serai_abi::Call {
+    serai_abi::Call::ValidatorSets(
+      serai_abi::validator_sets::Call::set_embedded_elliptic_curve_key {
+        embedded_elliptic_curve,
+        key,
+      },
+    )
+  }
+
  pub fn allocate(network: NetworkId, amount: Amount) -> serai_abi::Call {
    serai_abi::Call::ValidatorSets(serai_abi::validator_sets::Call::allocate { network, amount })
  }
--- a/substrate/client/tests/common/validator_sets.rs
+++ b/substrate/client/tests/common/validator_sets.rs
@@ -5,6 +5,8 @@ use zeroize::Zeroizing;
 use rand_core::OsRng;

 use sp_core::{
+  ConstU32,
+  bounded_vec::BoundedVec,
  sr25519::{Pair, Signature},
  Pair as PairTrait,
 };
@@ -14,8 +16,9 @@ use frost::dkg::musig::musig;
 use schnorrkel::Schnorrkel;

 use serai_client::{
+  primitives::EmbeddedEllipticCurve,
  validator_sets::{
-    primitives::{ValidatorSet, KeyPair, musig_context, set_keys_message},
+    primitives::{MAX_KEY_LEN, ValidatorSet, KeyPair, musig_context, set_keys_message},
    ValidatorSetsEvent,
  },
  Amount, Serai, SeraiValidatorSets,
@@ -58,7 +61,7 @@ pub async fn set_keys(
  let sig = frost::tests::sign_without_caching(
    &mut OsRng,
    frost::tests::algorithm_machines(&mut OsRng, &Schnorrkel::new(b"substrate"), &musig_keys),
-    &set_keys_message(&set, &[], &key_pair),
+    &set_keys_message(&set, &key_pair),
  );

  // Set the key pair
@@ -66,8 +69,8 @@ pub async fn set_keys(
    serai,
    &SeraiValidatorSets::set_keys(
      set.network,
-      vec![].try_into().unwrap(),
      key_pair.clone(),
+      vec![1; musig_keys.len()].try_into().unwrap(),
      Signature(sig.to_bytes()),
    ),
  )
@@ -82,6 +85,24 @@ pub async fn set_keys(
  block
 }

+#[allow(dead_code)]
+pub async fn set_embedded_elliptic_curve_key(
+  serai: &Serai,
+  pair: &Pair,
+  embedded_elliptic_curve: EmbeddedEllipticCurve,
+  key: BoundedVec<u8, ConstU32<{ MAX_KEY_LEN }>>,
+  nonce: u32,
+) -> [u8; 32] {
+  // get the call
+  let tx = serai.sign(
+    pair,
+    SeraiValidatorSets::set_embedded_elliptic_curve_key(embedded_elliptic_curve, key),
+    nonce,
+    0,
+  );
+  publish_tx(serai, &tx).await
+}
+
 #[allow(dead_code)]
 pub async fn allocate_stake(
  serai: &Serai,
--- a/substrate/client/tests/validator_sets.rs
+++ b/substrate/client/tests/validator_sets.rs
@@ -6,7 +6,7 @@ use sp_core::{
 };

 use serai_client::{
-  primitives::{NETWORKS, NetworkId, BlockHash, insecure_pair_from_name},
+  primitives::{NETWORKS, EmbeddedEllipticCurve, NetworkId, BlockHash, insecure_pair_from_name},
  validator_sets::{
    primitives::{Session, ValidatorSet, KeyPair},
    ValidatorSetsEvent,
@@ -21,7 +21,7 @@ use serai_client::{
 mod common;
 use common::{
  tx::publish_tx,
-  validator_sets::{allocate_stake, deallocate_stake, set_keys},
+  validator_sets::{set_embedded_elliptic_curve_key, allocate_stake, deallocate_stake, set_keys},
 };

 fn get_random_key_pair() -> KeyPair {
@@ -221,12 +221,31 @@ async fn validator_set_rotation() {

        // add 1 participant
        let last_participant = accounts[4].clone();
+
+        // If this is the first iteration, set embedded elliptic curve keys
+        if i == 0 {
+          for (i, embedded_elliptic_curve) in
+            [EmbeddedEllipticCurve::Embedwards25519, EmbeddedEllipticCurve::Secq256k1]
+              .into_iter()
+              .enumerate()
+          {
+            set_embedded_elliptic_curve_key(
+              &serai,
+              &last_participant,
+              embedded_elliptic_curve,
+              vec![0; 32].try_into().unwrap(),
+              i.try_into().unwrap(),
+            )
+            .await;
+          }
+        }
+
        let hash = allocate_stake(
          &serai,
          network,
          key_shares[&network],
          &last_participant,
-          i.try_into().unwrap(),
+          (2 + i).try_into().unwrap(),
        )
        .await;
        participants.push(last_participant.public());
--- a/substrate/node/Cargo.toml
+++ b/substrate/node/Cargo.toml
@@ -27,6 +27,10 @@ log = "0.4"

 schnorrkel = "0.11"

+ciphersuite = { path = "../../crypto/ciphersuite" }
+embedwards25519 = { path = "../../crypto/evrf/embedwards25519" }
+secq256k1 = { path = "../../crypto/evrf/secq256k1" }
+
 libp2p = "0.52"

 sp-core = { git = "https://github.com/serai-dex/substrate" }
--- a/substrate/node/src/chain_spec.rs
+++ b/substrate/node/src/chain_spec.rs
@@ -1,13 +1,17 @@
 use core::marker::PhantomData;
-use std::collections::HashSet;

-use sp_core::{Decode, Pair as PairTrait, sr25519::Public};
+use sp_core::Pair as PairTrait;

 use sc_service::ChainType;

+use ciphersuite::{group::GroupEncoding, Ciphersuite};
+use embedwards25519::Embedwards25519;
+use secq256k1::Secq256k1;
+
 use serai_runtime::{
-  primitives::*, WASM_BINARY, BABE_GENESIS_EPOCH_CONFIG, RuntimeGenesisConfig, SystemConfig,
-  CoinsConfig, DexConfig, ValidatorSetsConfig, SignalsConfig, BabeConfig, GrandpaConfig,
+  primitives::*, validator_sets::AllEmbeddedEllipticCurveKeysAtGenesis, WASM_BINARY,
+  BABE_GENESIS_EPOCH_CONFIG, RuntimeGenesisConfig, SystemConfig, CoinsConfig, DexConfig,
+  ValidatorSetsConfig, SignalsConfig, BabeConfig, GrandpaConfig,
 };

 pub type ChainSpec = sc_service::GenericChainSpec<RuntimeGenesisConfig>;
@@ -16,6 +20,11 @@ fn account_from_name(name: &'static str) -> PublicKey {
  insecure_pair_from_name(name).public()
 }

+fn insecure_arbitrary_public_key_from_name<C: Ciphersuite>(name: &'static str) -> Vec<u8> {
+  let key = insecure_arbitrary_key_from_name::<C>(name);
+  (C::generator() * key).to_bytes().as_ref().to_vec()
+}
+
 fn wasm_binary() -> Vec<u8> {
  // TODO: Accept a config of runtime path
  const WASM_PATH: &str = "/runtime/serai.wasm";
@@ -32,7 +41,21 @@ fn devnet_genesis(
  validators: &[&'static str],
  endowed_accounts: Vec<PublicKey>,
 ) -> RuntimeGenesisConfig {
-  let validators = validators.iter().map(|name| account_from_name(name)).collect::<Vec<_>>();
+  let validators = validators
+    .iter()
+    .map(|name| {
+      (
+        account_from_name(name),
+        AllEmbeddedEllipticCurveKeysAtGenesis {
+          embedwards25519: insecure_arbitrary_public_key_from_name::<Embedwards25519>(name)
+            .try_into()
+            .unwrap(),
+          secq256k1: insecure_arbitrary_public_key_from_name::<Secq256k1>(name).try_into().unwrap(),
+        },
+      )
+    })
+    .collect::<Vec<_>>();
+
  RuntimeGenesisConfig {
    system: SystemConfig { code: wasm_binary.to_vec(), _config: PhantomData },

@@ -65,17 +88,18 @@ fn devnet_genesis(
    },
    signals: SignalsConfig::default(),
    babe: BabeConfig {
-      authorities: validators.iter().map(|validator| ((*validator).into(), 1)).collect(),
+      authorities: validators.iter().map(|validator| (validator.0.into(), 1)).collect(),
      epoch_config: Some(BABE_GENESIS_EPOCH_CONFIG),
      _config: PhantomData,
    },
    grandpa: GrandpaConfig {
-      authorities: validators.into_iter().map(|validator| (validator.into(), 1)).collect(),
+      authorities: validators.into_iter().map(|validator| (validator.0.into(), 1)).collect(),
      _config: PhantomData,
    },
  }
 }

+/*
 fn testnet_genesis(wasm_binary: &[u8], validators: Vec<&'static str>) -> RuntimeGenesisConfig {
  let validators = validators
    .into_iter()
@@ -126,6 +150,7 @@ fn testnet_genesis(wasm_binary: &[u8], validators: Vec<&'static str>) -> Runtime
    },
  }
 }
+*/

 pub fn development_config() -> ChainSpec {
  let wasm_binary = wasm_binary();
@@ -204,7 +229,7 @@ pub fn local_config() -> ChainSpec {
 }

 pub fn testnet_config() -> ChainSpec {
-  let wasm_binary = wasm_binary();
+  // let wasm_binary = wasm_binary();

  ChainSpec::from_genesis(
    // Name
@@ -213,7 +238,7 @@ pub fn testnet_config() -> ChainSpec {
    "testnet-2",
    ChainType::Live,
    move || {
-      let _ = testnet_genesis(&wasm_binary, vec![]);
+      // let _ = testnet_genesis(&wasm_binary, vec![])
      todo!()
    },
    // Bootnodes
--- a/substrate/primitives/Cargo.toml
+++ b/substrate/primitives/Cargo.toml
@@ -18,6 +18,8 @@ workspace = true
 [dependencies]
 zeroize = { version = "^1.5", features = ["derive"], optional = true }

+ciphersuite = { path = "../../crypto/ciphersuite", default-features = false, optional = true }
+
 scale = { package = "parity-scale-codec", version = "3", default-features = false, features = ["derive"] }
 scale-info = { version = "2", default-features = false, features = ["derive"] }

@@ -35,7 +37,7 @@ frame-support = { git = "https://github.com/serai-dex/substrate", default-featur
 rand_core = { version = "0.6", default-features = false, features = ["getrandom"] }

 [features]
-std = ["zeroize", "scale/std", "borsh?/std", "serde?/std", "scale-info/std", "sp-core/std", "sp-runtime/std", "frame-support/std"]
+std = ["zeroize", "ciphersuite/std", "scale/std", "borsh?/std", "serde?/std", "scale-info/std", "sp-core/std", "sp-runtime/std", "frame-support/std"]
 borsh = ["dep:borsh"]
 serde = ["dep:serde"]
 default = ["std"]
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Luke Parker	8c50a31633	Improve documentation on functions	2024-08-06 00:27:54 -04:00
Luke Parker	d943e037e5	Remove bad panic in coordinator It expected ConfirmationShare to be n-of-n, not t-of-n.	2024-08-06 00:27:19 -04:00
Luke Parker	3042697243	Update orchestration	2024-08-06 00:27:07 -04:00
Luke Parker	8de696f169	Add an extra sleep to ensure expected ordering of `Participation`s	2024-08-05 23:50:23 -04:00
Luke Parker	b8912e4b7b	cargo machete	2024-08-05 23:43:38 -04:00
Luke Parker	89fc88b283	Get clippy to pass across the repo	2024-08-05 23:29:51 -04:00
Luke Parker	2ae2883106	Update spec to the new DKG	2024-08-05 06:58:44 -04:00
Luke Parker	e74c8f38d5	Get coordinator tests to pass	2024-08-05 06:50:26 -04:00
Luke Parker	9e8e134ef7	Replace Interpolation::None with Interpolation::Constant Allows the MuSig DKG to keep the secret share as the original private key, enabling deriving FROST nonces consistently regardless of the MuSig context.	2024-08-05 06:32:37 -04:00
Luke Parker	f08faeadff	Have the DKG explicitly declare how to interpolate its shares Removes the hack for MuSig where we multiply keys by the inverse of their lagrange interpolation factor.	2024-08-05 06:06:56 -04:00
Luke Parker	1b7613329c	Add sensible Debug to key_gen::[Processor, Coordinator]Message	2024-08-05 04:04:02 -04:00
Luke Parker	54eefbde0c	Update the coordinator binary for the new DKG This does not yet update any tests.	2024-08-04 04:48:12 -04:00
Luke Parker	58a435d4e9	Have set_keys take signature_participants, not removed_participants Now no one is removed from the DKG. Only `t` people publish the key however. Uses a BitVec for an efficient encoding of the participants.	2024-08-04 01:19:08 -04:00
Luke Parker	5ed355902b	Update processor key gen tests to the eVRF DKG	2024-08-03 03:17:55 -04:00
Luke Parker	fc51c9b71c	Add embedded elliptic curve keys to Substrate	2024-08-03 02:24:08 -04:00
Luke Parker	9e716c07fc	Correct amount of yx coefficients, get processor key gen test to pass	2024-08-02 05:03:14 -04:00
Luke Parker	b5bf70bdb1	Update serai-processor tests to the new key gen	2024-08-02 00:53:24 -04:00
Luke Parker	d3f0378f66	Deduplicate and better document in processor key_gen	2024-08-02 00:53:24 -04:00
Luke Parker	2f564c230e	Finish routing the new key gen in the processor Doesn't touch the tests, coordinator, nor Substrate yet. `cargo +nightly fmt && cargo +nightly-2024-07-01 clippy --all-features -p serai-processor` does pass.	2024-08-02 00:53:24 -04:00
Luke Parker	12f74e1813	Rewrite processor key-gen around the eVRF DKG Still a WIP.	2024-08-02 00:53:24 -04:00
Luke Parker	fb7e966b94	Only participate once per key, not once per key share	2024-08-02 00:53:24 -04:00
Luke Parker	65efbf46c7	Support participating multiple times in the eVRF DKG	2024-08-02 00:53:23 -04:00
Luke Parker	c5cc0dc883	Add Ristretto eVRF trait impls	2024-08-02 00:53:23 -04:00
Luke Parker	a6775d7dc5	Implement eVRF traits, all the way up to the DKG, for secp256k1/ed25519	2024-08-02 00:53:23 -04:00
Luke Parker	681010f422	Ban zero ECDH keys, document non-zero requirements	2024-08-02 00:53:23 -04:00
Luke Parker	f93bd42b99	Resolve various TODOs Supports recovering multiple key shares from the eVRF DKG. Inlines two loops to save 2**16 iterations. Adds support for creating a constant time representation of scalars < NUM_BITS.	2024-08-02 00:53:23 -04:00
Luke Parker	c960d6baaf	Start using a proper error for the eVRF DKG	2024-08-02 00:53:23 -04:00
Luke Parker	31ac0ac299	Improve eVRF DKG Updates how we calculcate verification shares, improves performance when extracting multiple sets of keys, and adds more to the test for it.	2024-08-02 00:53:23 -04:00
Luke Parker	4bd0d71406	Add initial eVRF DKG test	2024-08-02 00:53:23 -04:00
Luke Parker	ef68885600	Finish routing the eVRF functionality Still needs errors and serialization, along with a few other TODOs.	2024-08-02 00:53:23 -04:00
Luke Parker	00dc3087bd	Update to the new eVRF proof	2024-08-02 00:53:23 -04:00
Luke Parker	eca82f3f7b	Add paragraph claiming robustness	2024-08-02 00:53:23 -04:00
Luke Parker	05c26d7818	Add documentation to the eVRF-based DKG	2024-08-02 00:53:23 -04:00
Luke Parker	96175e115d	Inline the eVRF into the DKG library Due to how we're handling share encryption, we'd either need two circuits or to dedicate this circuit to the DKG. The latter makes sense at this time.	2024-08-02 00:53:23 -04:00
Luke Parker	fa31f26397	Add embedwards25519 curve	2024-08-02 00:53:23 -04:00
Luke Parker	7710da4db3	Initial eVRF-based DKG	2024-08-02 00:53:23 -04:00
Luke Parker	b7103038cb	Have the eVRF take a Zeroizing private key	2024-08-02 00:53:23 -04:00
Luke Parker	b6e688076f	Make NUM_BITS an argument for the field macro	2024-08-02 00:53:23 -04:00
Luke Parker	b8472963c9	Make DKG Encryption a bit more flexible No longer requires the use of an EncryptionKeyMessage, and allows pre-defined keys for encryption.	2024-08-02 00:53:23 -04:00
Luke Parker	772d033bb2	Add implementation of secq256k1	2024-08-02 00:53:23 -04:00
Luke Parker	49a183194d	Add the openings of the PCs to the eVRF as necessary	2024-08-02 00:53:23 -04:00
Luke Parker	db31809708	Initial eVRF implementation Not quite done yet. It needs to communicate the resulting points and proofs to extract them from the Pedersen Commitments in order to return those, and then be tested.	2024-08-02 00:53:23 -04:00
Luke Parker	dcc26ecf33	Upstream GBP, divisor, circuit abstraction, and EC gadgets from FCMP++	2024-08-02 00:53:22 -04:00