Use a challenge from the FROST transcript as context in the DLEq proofs

Cargo.lock

@@ -4631,8 +4631,8 @@ dependencies = [
  "hkdf",
  "minimal-ed448",
  "multiexp",
+ "rand 0.8.5",
  "rand_chacha 0.3.1",
- "rand_core 0.6.4",
  "schnorr-signatures",
  "serde_json",
  "subtle",

crypto/frost/src/nonce.rs

@@ -27,8 +27,19 @@ use dleq::DLEqProof;
 
 use crate::curve::Curve;
 
-fn dleq_transcript<T: Transcript>() -> T {
+// Every participant proves for their commitments at the start of the protocol
-  T::new(b"FROST_nonce_dleq")
+// These proofs are verified sequentially, requiring independent transcripts
+// In order to make these transcripts more robust, the FROST transcript (at time of preprocess) is
+// challenged in order to create a commitment to it, carried in each independent transcript
+// (effectively forking the original transcript)
+//
+// For FROST, as defined by the IETF, this will do nothing (and this transcript will never even be
+// constructed). For higher level protocols, the transcript may have contextual info these proofs
+// will then be bound to
+fn dleq_transcript<T: Transcript>(context: &[u8]) -> T {
+  let mut transcript = T::new(b"FROST_commitments");
+  transcript.append_message(b"context", context);
+  transcript
 }
 
 // Each nonce is actually a pair of random scalars, notated as d, e under the FROST paper
@@ -67,6 +78,7 @@ impl<C: Curve> NonceCommitments<C> {
     rng: &mut R,
     secret_share: &Zeroizing<C::F>,
     generators: &[C::G],
+    context: &[u8],
   ) -> (Nonce<C>, NonceCommitments<C>) {
     let nonce = Nonce::<C>([
       C::random_nonce(secret_share, &mut *rng),
@@ -87,8 +99,7 @@ impl<C: Curve> NonceCommitments<C> {
         // Uses an independent transcript as each signer must prove this with their commitments,
         // yet they're validated while processing everyone's data sequentially, by the global order
         // This avoids needing to clone and fork the transcript around
-        // TODO: At least include a challenge from the existing transcript
+        DLEqProof::prove(&mut *rng, &mut dleq_transcript::<T>(context), generators, nonce)
-        DLEqProof::prove(&mut *rng, &mut dleq_transcript::<T>(), generators, nonce)
       };
       dleqs = Some([dleq(&nonce.0[0]), dleq(&nonce.0[1])]);
     }
@@ -99,6 +110,7 @@ impl<C: Curve> NonceCommitments<C> {
   fn read<R: Read, T: Transcript>(
     reader: &mut R,
     generators: &[C::G],
+    context: &[u8],
   ) -> io::Result<NonceCommitments<C>> {
     let commitments: Vec<GeneratorCommitments<C>> = (0 .. generators.len())
       .map(|_| GeneratorCommitments::read(reader))
@@ -110,7 +122,7 @@ impl<C: Curve> NonceCommitments<C> {
         let dleq = DLEqProof::deserialize(reader)?;
         dleq
           .verify(
-            &mut dleq_transcript::<T>(),
+            &mut dleq_transcript::<T>(context),
             generators,
             &commitments.iter().map(|commitments| commitments.0[i]).collect::<Vec<_>>(),
           )
@@ -146,12 +158,13 @@ impl<C: Curve> Commitments<C> {
     rng: &mut R,
     secret_share: &Zeroizing<C::F>,
     planned_nonces: &[Vec<C::G>],
+    context: &[u8],
   ) -> (Vec<Nonce<C>>, Commitments<C>) {
     let mut nonces = vec![];
     let mut commitments = vec![];
     for generators in planned_nonces {
       let (nonce, these_commitments) =
-        NonceCommitments::new::<_, T>(&mut *rng, secret_share, generators);
+        NonceCommitments::new::<_, T>(&mut *rng, secret_share, generators, context);
       nonces.push(nonce);
       commitments.push(these_commitments);
     }
@@ -183,10 +196,11 @@ impl<C: Curve> Commitments<C> {
   pub(crate) fn read<R: Read, T: Transcript>(
     reader: &mut R,
     nonces: &[Vec<C::G>],
+    context: &[u8],
   ) -> io::Result<Self> {
     Ok(Commitments {
       nonces: (0 .. nonces.len())
-        .map(|i| NonceCommitments::read::<_, T>(reader, &nonces[i]))
+        .map(|i| NonceCommitments::read::<_, T>(reader, &nonces[i], context))
         .collect::<Result<_, _>>()?,
     })
   }

crypto/frost/src/sign.rs

@@ -115,10 +115,13 @@ impl<C: Curve, A: Algorithm<C>> AlgorithmMachine<C, A> {
     let mut params = self.params;
 
     let mut rng = ChaCha20Rng::from_seed(seed.0);
+    // Get a challenge to the existing transcript for use when proving for the commitments
+    let commitments_challenge = params.algorithm.transcript().challenge(b"commitments");
     let (nonces, commitments) = Commitments::new::<_, A::Transcript>(
       &mut rng,
       params.keys.secret_share(),
       &params.algorithm.nonces(),
+      commitments_challenge.as_ref(),
     );
     let addendum = params.algorithm.preprocess_addendum(&mut rng, &params.keys);
 
@@ -128,22 +131,35 @@ impl<C: Curve, A: Algorithm<C>> AlgorithmMachine<C, A> {
     let mut blame_entropy = [0; 32];
     rng.fill_bytes(&mut blame_entropy);
     (
-      AlgorithmSignMachine { params, seed, nonces, preprocess: preprocess.clone(), blame_entropy },
+      AlgorithmSignMachine {
+        params,
+        seed,
+        commitments_challenge,
+        nonces,
+        preprocess: preprocess.clone(),
+        blame_entropy,
+      },
       preprocess,
     )
   }
 
   #[cfg(any(test, feature = "tests"))]
   pub(crate) fn unsafe_override_preprocess(
-    self,
+    mut self,
     nonces: Vec<Nonce<C>>,
     preprocess: Preprocess<C, A::Addendum>,
   ) -> AlgorithmSignMachine<C, A> {
     AlgorithmSignMachine {
+      commitments_challenge: self.params.algorithm.transcript().challenge(b"commitments"),
+
       params: self.params,
       seed: Zeroizing::new(CachedPreprocess([0; 32])),
+
       nonces,
       preprocess,
+      // Uses 0s since this is just used to protect against a malicious participant from
+      // deliberately increasing the amount of time needed to identify them (and is accordingly
+      // not necessary to function)
       blame_entropy: [0; 32],
     }
   }
@@ -221,6 +237,7 @@ pub struct AlgorithmSignMachine<C: Curve, A: Algorithm<C>> {
   params: Params<C, A>,
   seed: Zeroizing<CachedPreprocess>,
 
+  commitments_challenge: <A::Transcript as Transcript>::Challenge,
   pub(crate) nonces: Vec<Nonce<C>>,
   #[zeroize(skip)]
   pub(crate) preprocess: Preprocess<C, A::Addendum>,
@@ -249,7 +266,11 @@ impl<C: Curve, A: Algorithm<C>> SignMachine<A::Signature> for AlgorithmSignMachi
 
   fn read_preprocess<R: Read>(&self, reader: &mut R) -> io::Result<Self::Preprocess> {
     Ok(Preprocess {
-      commitments: Commitments::read::<_, A::Transcript>(reader, &self.params.algorithm.nonces())?,
+      commitments: Commitments::read::<_, A::Transcript>(
+        reader,
+        &self.params.algorithm.nonces(),
+        self.commitments_challenge.as_ref(),
+      )?,
       addendum: self.params.algorithm.read_addendum(reader)?,
     })
   }