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/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
+  }
+}