One Round DKG (#589)

* Upstream GBP, divisor, circuit abstraction, and EC gadgets from FCMP++

* 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.

* Add the openings of the PCs to the eVRF as necessary

* Add implementation of secq256k1

* Make DKG Encryption a bit more flexible

No longer requires the use of an EncryptionKeyMessage, and allows pre-defined
keys for encryption.

* Make NUM_BITS an argument for the field macro

* Have the eVRF take a Zeroizing private key

* Initial eVRF-based DKG

* Add embedwards25519 curve

* 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.

* Add documentation to the eVRF-based DKG

* Add paragraph claiming robustness

* Update to the new eVRF proof

* Finish routing the eVRF functionality

Still needs errors and serialization, along with a few other TODOs.

* Add initial eVRF DKG test

* 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.

* Start using a proper error for the eVRF DKG

* 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.

* Ban zero ECDH keys, document non-zero requirements

* Implement eVRF traits, all the way up to the DKG, for secp256k1/ed25519

* Add Ristretto eVRF trait impls

* Support participating multiple times in the eVRF DKG

* Only participate once per key, not once per key share

* Rewrite processor key-gen around the eVRF DKG

Still a WIP.

* 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.

* Deduplicate and better document in processor key_gen

* Update serai-processor tests to the new key gen

* Correct amount of yx coefficients, get processor key gen test to pass

* Add embedded elliptic curve keys to Substrate

* Update processor key gen tests to the eVRF DKG

* 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.

* Update the coordinator binary for the new DKG

This does not yet update any tests.

* Add sensible Debug to key_gen::[Processor, Coordinator]Message

* 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.

* 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.

* Get coordinator tests to pass

* Update spec to the new DKG

* Get clippy to pass across the repo

* cargo machete

* Add an extra sleep to ensure expected ordering of `Participation`s

* Update orchestration

* Remove bad panic in coordinator

It expected ConfirmationShare to be n-of-n, not t-of-n.

* Improve documentation on  functions

* Update TX size limit

We now no longer have to support the ridiculous case of having 49 DKG
participations within a 101-of-150 DKG. It does remain quite high due to
needing to _sign_ so many times. It'd may be optimal for parties with multiple
key shares to independently send their preprocesses/shares (despite the
overhead that'll cause with signatures and the transaction structure).

* Correct error in the Processor spec document

* Update a few comments in the validator-sets pallet

* Send/Recv Participation one at a time

Sending all, then attempting to receive all in an expected order, wasn't working
even with notable delays between sending messages. This points to the mempool
not working as expected...

* Correct ThresholdKeys serialization in modular-frost test

* Updating existing TX size limit test for the new DKG parameters

* Increase time allowed for the DKG on the GH CI

* Correct construction of signature_participants in serai-client tests

Fault identified by akil.

* Further contextualize DkgConfirmer by ValidatorSet

Caught by a safety check we wouldn't reuse preprocesses across messages. That
raises the question of we were prior reusing preprocesses (reusing keys)?
Except that'd have caused a variety of signing failures (suggesting we had some
staggered timing avoiding it in practice but yes, this was possible in theory).

* Add necessary calls to set_embedded_elliptic_curve_key in coordinator set rotation tests

* Correct shimmed setting of a secq256k1 key

* cargo fmt

* Don't use `[0; 32]` for the embedded keys in the coordinator rotation test

The key_gen function expects the random values already decided.

* Big-endian secq256k1 scalars

Also restores the prior, safer, Encryption::register function.

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" }

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.

crypto/evrf/circuit-abstraction/README.md

@@ -0,0 +1,3 @@
+# Generalized Bulletproofs Circuit Abstraction
+
+A circuit abstraction around `generalized-bulletproofs`.

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));
+  }
+}

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))
+  }
+}