Rewrite the cross-group DLEq API to not allow proving for biased scalars

crypto/dleq/Cargo.toml

@@ -10,6 +10,8 @@ edition = "2021"
 thiserror = "1"
 rand_core = "0.6"
 
+digest = "0.10"
+
 subtle = "2.4"
 
 transcript = { package = "flexible-transcript", path = "../transcript", version = "0.1" }
@@ -21,6 +23,9 @@ multiexp = { path = "../multiexp" }
 
 [dev-dependencies]
 hex-literal = "0.3"
+
+blake2 = "0.10"
+
 k256 = { version = "0.11", features = ["arithmetic", "bits"] }
 dalek-ff-group = { path = "../dalek-ff-group" }
 

crypto/dleq/src/cross_group/mod.rs

@@ -1,6 +1,8 @@
 use thiserror::Error;
 use rand_core::{RngCore, CryptoRng};
 
+use digest::Digest;
+
 use subtle::{Choice, ConditionallySelectable};
 
 use transcript::Transcript;
@@ -182,21 +184,12 @@ impl<G0: PrimeGroup, G1: PrimeGroup> DLEqProof<G0, G1>
     transcript.append_message(b"commitment_1", commitments.1.to_bytes().as_ref());
   }
 
-  /// Prove the cross-Group Discrete Log Equality for the points derived from the provided Scalar.
-  /// Since DLEq is proven for the same Scalar in both fields, and the provided Scalar may not be
-  /// valid in the other Scalar field, the Scalar is normalized as needed and the normalized forms
-  /// are returned. These are the actually equal discrete logarithms. The passed in Scalar is
-  /// solely to enable various forms of Scalar generation, such as deterministic schemes
-  pub fn prove<R: RngCore + CryptoRng, T: Clone + Transcript>(
+  fn prove_internal<R: RngCore + CryptoRng, T: Clone + Transcript>(
     rng: &mut R,
     transcript: &mut T,
     generators: (Generators<G0>, Generators<G1>),
-    f: G0::Scalar
+    f: (G0::Scalar, G1::Scalar)
   ) -> (Self, (G0::Scalar, G1::Scalar)) {
-    // At least one bit will be dropped from either field element, making it irrelevant which one
-    // we get a random element in
-    let f = scalar_normalize::<_, G1::Scalar>(f);
-
     Self::initialize_transcript(
       transcript,
       generators,
@@ -270,6 +263,39 @@ impl<G0: PrimeGroup, G1: PrimeGroup> DLEqProof<G0, G1>
     (proof, f)
   }
 
+  /// Prove the cross-Group Discrete Log Equality for the points derived from the scalar created as
+  /// the output of the passed in Digest. Given the non-standard requirements to achieve
+  /// uniformity, needing to be < 2^x instead of less than a prime moduli, this is the simplest way
+  /// to safely and securely generate a Scalar, without risk of failure, nor bias
+  /// It also ensures a lack of determinable relation between keys, guaranteeing security in the
+  /// currently expected use case for this, atomic swaps, where each swap leaks the key. Knowing
+  /// the relationship between keys would allow breaking all swaps after just one
+  pub fn prove<R: RngCore + CryptoRng, T: Clone + Transcript, D: Digest>(
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    digest: D
+  ) -> (Self, (G0::Scalar, G1::Scalar)) {
+    Self::prove_internal(
+      rng,
+      transcript,
+      generators,
+      Self::mutual_scalar_from_bytes(digest.finalize().as_ref())
+    )
+  }
+
+  /// Prove the cross-Group Discrete Log Equality for the points derived from the scalar passed in,
+  /// failing if it's not mutually valid. This allows for rejection sampling externally derived
+  /// scalars until they're safely usable, as needed
+  pub fn prove_without_bias<R: RngCore + CryptoRng, T: Clone + Transcript>(
+    rng: &mut R,
+    transcript: &mut T,
+    generators: (Generators<G0>, Generators<G1>),
+    f0: G0::Scalar
+  ) -> Option<(Self, (G0::Scalar, G1::Scalar))> {
+    scalar_convert(f0).map(|f1| Self::prove_internal(rng, transcript, generators, (f0, f1)))
+  }
+
   /// Verify a cross-Group Discrete Log Equality statement, returning the points proven for
   pub fn verify<T: Clone + Transcript>(
     &self,

crypto/dleq/src/tests/cross_group/mod.rs

@@ -2,23 +2,26 @@ mod scalar;
 mod schnorr;
 
 use hex_literal::hex;
-use rand_core::OsRng;
+use rand_core::{RngCore, OsRng};
 
-use ff::Field;
+use ff::{Field, PrimeField};
 use group::{Group, GroupEncoding};
 
 use k256::{Scalar, ProjectivePoint};
-use dalek_ff_group::{EdwardsPoint, CompressedEdwardsY};
+use dalek_ff_group::{self as dfg, EdwardsPoint, CompressedEdwardsY};
+
+use blake2::{Digest, Blake2b512};
 
 use transcript::RecommendedTranscript;
 
 use crate::{Generators, cross_group::DLEqProof};
 
-#[test]
-fn test_dleq() {
-  let transcript = || RecommendedTranscript::new(b"Cross-Group DLEq Proof Test");
+fn transcript() -> RecommendedTranscript {
+  RecommendedTranscript::new(b"Cross-Group DLEq Proof Test")
+}
 
-  let generators = (
+fn generators() -> (Generators<ProjectivePoint>, Generators<EdwardsPoint>) {
+  (
     Generators::new(
       ProjectivePoint::GENERATOR,
       ProjectivePoint::from_bytes(
@@ -32,23 +35,72 @@ fn test_dleq() {
         hex!("8b655970153799af2aeadc9ff1add0ea6c7251d54154cfa92c173a0dd39c1f94")
       ).decompress().unwrap()
     )
+  )
+}
+
+#[test]
+fn test_rejection_sampling() {
+  let mut pow_2 = Scalar::one();
+  for _ in 0 .. dfg::Scalar::CAPACITY {
+    pow_2 = pow_2.double();
+  }
+
+  assert!(
+    DLEqProof::prove_without_bias(
+      &mut OsRng,
+      &mut RecommendedTranscript::new(b""),
+      generators(),
+      pow_2
+    ).is_none()
   );
+}
 
-  let key = Scalar::random(&mut OsRng);
-  let (proof, keys) = DLEqProof::prove(&mut OsRng, &mut transcript(), generators, key);
+#[test]
+fn test_dleq() {
+  let generators = generators();
 
-  let public_keys = proof.verify(&mut transcript(), generators).unwrap();
-  assert_eq!(generators.0.primary * keys.0, public_keys.0);
-  assert_eq!(generators.1.primary * keys.1, public_keys.1);
+  for i in 0 .. 2 {
+    let (proof, keys) = if i == 0 {
+      let mut seed = [0; 32];
+      OsRng.fill_bytes(&mut seed);
 
-  #[cfg(feature = "serialize")]
-  {
-    let mut buf = vec![];
-    proof.serialize(&mut buf).unwrap();
-    let deserialized = DLEqProof::<ProjectivePoint, EdwardsPoint>::deserialize(
-      &mut std::io::Cursor::new(&buf)
-    ).unwrap();
-    assert_eq!(proof, deserialized);
-    deserialized.verify(&mut transcript(), generators).unwrap();
+      DLEqProof::prove(
+        &mut OsRng,
+        &mut transcript(),
+        generators,
+        Blake2b512::new().chain_update(seed)
+      )
+    } else {
+      let mut key;
+      let mut res;
+      while {
+        key = Scalar::random(&mut OsRng);
+        res = DLEqProof::prove_without_bias(
+          &mut OsRng,
+          &mut transcript(),
+          generators,
+          key
+        );
+        res.is_none()
+      } {}
+      let res = res.unwrap();
+      assert_eq!(key, res.1.0);
+      res
+    };
+
+    let public_keys = proof.verify(&mut transcript(), generators).unwrap();
+    assert_eq!(generators.0.primary * keys.0, public_keys.0);
+    assert_eq!(generators.1.primary * keys.1, public_keys.1);
+
+    #[cfg(feature = "serialize")]
+    {
+      let mut buf = vec![];
+      proof.serialize(&mut buf).unwrap();
+      let deserialized = DLEqProof::<ProjectivePoint, EdwardsPoint>::deserialize(
+        &mut std::io::Cursor::new(&buf)
+      ).unwrap();
+      assert_eq!(proof, deserialized);
+      deserialized.verify(&mut transcript(), generators).unwrap();
+    }
   }
 }