Merge pull request #1 from arnaucube/main

add in-circuit EdDSA verification gadget

.gitignore

@@ -1,2 +1,3 @@
 /target
-*.py
+*.py
+Cargo.lock

Cargo.toml

@@ -5,8 +5,7 @@ rust-version = "1.75.0"
 version = "0.1.0"
 
 [dependencies]
-
-ark-crypto-primitives = {version = "^0.4.0", default-features = false, features = ["sponge", "crh"]}
+ark-crypto-primitives = {version = "^0.4.0", default-features = false, features = ["sponge", "crh", "r1cs"]}
 ark-ec = "^0.4.0"
 ark-ed-on-bn254 = {version = "0.4.0"}
 ark-ff = "^0.4.0"
@@ -16,6 +15,11 @@ digest = "0.10"
 rand = "0.8"
 rand_core = {version = "0.6", default-features = false}
 
+# r1cs deps related under feature="r1cs"
+ark-relations = { version = "^0.4.0", default-features = false, optional = true }
+ark-r1cs-std = { version = "0.4.0", default-features = false, features = ["parallel"], optional = true }
+
+
 [dev-dependencies]
 ark-algebra-test-templates = "0.4.2"
 ark-ed-on-bls12-381 = {version = "0.4.0"}
@@ -26,3 +30,4 @@ sha2 = "0.10"
 
 [features]
 default = []
+r1cs = ["ark-r1cs-std", "ark-relations"]

README.md

@@ -3,3 +3,8 @@
 Do not use in production.
 
 EDDSA signature scheme implementation with Poseidon hasher and ark-works backend. Additionally circom compatible `ed_on_bn254_twist` twist is available.
+
+The `r1cs` feature enables the in-circuit EdDSA verification.
+
+## test
+To test including the constraints use the `r1cs` feature flag: `cargo test --features=r1cs`

rust-toolchain

@@ -1 +1 @@
-1.75.0
+1.82.0

src/constraints.rs

@@ -0,0 +1,90 @@
+/// This file implements the EdDSA verification in-circuit.
+use ark_crypto_primitives::sponge::{
+    constraints::CryptographicSpongeVar,
+    poseidon::{constraints::PoseidonSpongeVar, PoseidonConfig},
+};
+use ark_ec::CurveGroup;
+use ark_ff::Field;
+use ark_r1cs_std::{
+    boolean::Boolean, fields::fp::FpVar, fields::nonnative::NonNativeFieldVar, groups::CurveVar,
+    ToBitsGadget, ToConstraintFieldGadget,
+};
+use ark_relations::r1cs::ConstraintSystemRef;
+
+/// CF stands for ConstraintField
+pub type CF<C> = <<C as CurveGroup>::BaseField as Field>::BasePrimeField;
+
+/// gadget to compute the EdDSA verification in-circuit
+pub fn verify<C, GC>(
+    cs: ConstraintSystemRef<CF<C>>,
+    poseidon_config: PoseidonConfig<CF<C>>,
+    pk: GC,
+    sig: (GC, NonNativeFieldVar<C::ScalarField, CF<C>>),
+    msg: FpVar<CF<C>>,
+) -> ark_relations::r1cs::Result<Boolean<CF<C>>>
+where
+    C: CurveGroup,
+    GC: CurveVar<C, CF<C>> + ToConstraintFieldGadget<CF<C>>,
+{
+    let (r, s): (GC, NonNativeFieldVar<C::ScalarField, CF<C>>) = sig;
+
+    let r_xy = r.to_constraint_field()?;
+    let pk_xy = pk.to_constraint_field()?;
+
+    let mut poseidon = PoseidonSpongeVar::new(cs.clone(), &poseidon_config);
+    poseidon.absorb(&r_xy)?;
+    poseidon.absorb(&pk_xy)?;
+    poseidon.absorb(&msg)?;
+    let k = poseidon.squeeze_field_elements(1)?;
+    let k = k
+        .first()
+        .ok_or(ark_relations::r1cs::SynthesisError::Unsatisfiable)?;
+
+    let kx_b = pk.scalar_mul_le(k.to_bits_le()?.iter())?;
+
+    let g = GC::new_constant(cs.clone(), C::generator())?;
+    let s_b = g.scalar_mul_le(s.to_bits_le()?.iter())?;
+    let r_rec: GC = s_b - kx_b;
+    Ok(r_rec.is_eq(&r)?)
+}
+
+#[cfg(test)]
+mod tests {
+    use ark_ff::PrimeField;
+    use ark_r1cs_std::{alloc::AllocVar, eq::EqGadget, fields::nonnative::NonNativeFieldVar};
+    use ark_relations::r1cs::ConstraintSystem;
+    use rand_core::OsRng;
+
+    use super::*;
+    use crate::ed_on_bn254_twist::{
+        constraints::EdwardsVar as GVar, BaseField as Fq, EdwardsConfig, EdwardsProjective as G,
+        ScalarField as Fr,
+    };
+    use crate::{poseidon_config, SigningKey};
+
+    #[test]
+    fn gadget_verify() {
+        let poseidon_config = poseidon_config::<Fq>(4, 8, 60);
+        let sk = SigningKey::<EdwardsConfig>::generate::<blake2::Blake2b512>(&mut OsRng).unwrap();
+        let msg_raw = b"xxx yyy <<< zzz >>> bunny";
+        let msg = Fq::from_le_bytes_mod_order(msg_raw);
+        let sig = sk
+            .sign::<blake2::Blake2b512>(&poseidon_config, &msg)
+            .unwrap();
+        let pk = sk.public_key();
+        pk.verify(&poseidon_config, &msg, &sig).unwrap();
+
+        let cs = ConstraintSystem::<Fq>::new_ref();
+        let pk_var: GVar = GVar::new_witness(cs.clone(), || Ok(*pk.as_ref())).unwrap();
+        let r_var: GVar = GVar::new_witness(cs.clone(), || Ok(*sig.r())).unwrap();
+        let s_var = NonNativeFieldVar::<Fr, Fq>::new_witness(cs.clone(), || Ok(sig.s())).unwrap();
+        let msg_var = FpVar::<Fq>::new_witness(cs.clone(), || Ok(msg)).unwrap();
+
+        let res = verify::<G, GVar>(cs.clone(), poseidon_config, pk_var, (r_var, s_var), msg_var)
+            .unwrap();
+        res.enforce_equal(&Boolean::<Fq>::TRUE).unwrap();
+
+        dbg!(cs.num_constraints());
+        assert!(cs.is_satisfied().unwrap());
+    }
+}

src/ed_on_bn254_twist.rs

@@ -103,3 +103,18 @@ fn test_twist() {
     let v2 = untwist(u1);
     assert_eq!(v1, v2);
 }
+
+// constraints related logic
+#[cfg(feature = "r1cs")]
+pub mod constraints {
+    use ark_r1cs_std::fields::fp::FpVar;
+    use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;
+
+    use crate::ed_on_bn254_twist::{BaseField as Fq, EdwardsConfig};
+
+    /// A variable that is the R1CS equivalent of `crate::Fq`.
+    pub type FqVar = FpVar<Fq>;
+
+    /// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
+    pub type EdwardsVar = AffineVar<EdwardsConfig, FqVar>;
+}

src/eddsa.rs

@@ -7,7 +7,7 @@ use ark_ec::{
     twisted_edwards::{Affine, TECurveConfig},
     AffineRepr,
 };
-use ark_ff::PrimeField;
+use ark_ff::{BigInteger, PrimeField};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use digest::Digest;
 use digest::OutputSizeUser;
@@ -48,8 +48,8 @@ impl SecretKey {
 pub struct PublicKey<TE: TECurveConfig>(Affine<TE>);
 
 impl<TE: TECurveConfig> PublicKey<TE> {
-    pub fn xy(&self) -> (&TE::BaseField, &TE::BaseField) {
-        self.as_ref().xy().unwrap()
+    pub fn xy(&self) -> Result<(&TE::BaseField, &TE::BaseField), Error> {
+        self.as_ref().xy().ok_or(Error::Coordinates)
     }
 
     pub fn to_bytes(&self) -> Vec<u8> {
@@ -121,37 +121,41 @@ where
         &self.public_key
     }
 
-    pub fn sign<D: Digest, E: Absorb>(
+    pub fn sign<D: Digest>(
         &self,
         poseidon: &PoseidonConfig<TE::BaseField>,
-        message: &[E],
-    ) -> Signature<TE> {
+        message: &TE::BaseField,
+    ) -> Result<Signature<TE>, Error> {
         let (x, prefix) = self.secret_key.expand::<TE::ScalarField, D>();
 
         let mut h = D::new();
         h.update(prefix);
-        message
-            .iter()
-            .for_each(|m| h.update(m.to_sponge_bytes_as_vec()));
+        let msg_bytes = message.into_bigint().to_bytes_le();
+        let mut msg32: [u8; 32] = [0; 32];
+        msg32[..msg_bytes.len()].copy_from_slice(&msg_bytes[..]);
+        h.update(msg32);
+
         let r: TE::ScalarField = crate::from_digest(h);
         let sig_r: Affine<TE> = (Affine::<TE>::generator() * r).into();
 
         let mut poseidon = PoseidonSponge::new(poseidon);
 
-        let (sig_r_x, sig_r_y) = sig_r.xy().unwrap();
+        let (sig_r_x, sig_r_y) = sig_r.xy().ok_or(Error::Coordinates)?;
         poseidon.absorb(sig_r_x);
         poseidon.absorb(sig_r_y);
-        let (pk_x, pk_y) = self.public_key.0.xy().unwrap();
+        let (pk_x, pk_y) = self.public_key.0.xy().ok_or(Error::Coordinates)?;
         poseidon.absorb(pk_x);
         poseidon.absorb(pk_y);
-        message.iter().for_each(|m| poseidon.absorb(m));
+        poseidon.absorb(message);
 
-        let k = poseidon.squeeze_field_elements::<TE::ScalarField>(1);
-        let k = k.first().unwrap();
+        // use poseidon over Fq, so that it can be done too in-circuit
+        let k = poseidon.squeeze_field_elements::<TE::BaseField>(1);
+        let k = k.first().ok_or(Error::BadDigestOutput)?;
+        let k = TE::ScalarField::from_le_bytes_mod_order(&k.into_bigint().to_bytes_le());
 
         let sig_s = (x * k) + r;
 
-        Signature::new(sig_r, sig_s)
+        Ok(Signature::new(sig_r, sig_s))
     }
 }
 
@@ -169,26 +173,27 @@ impl PublicKey
 where
     TE::BaseField: PrimeField + Absorb,
 {
-    pub fn verify<E: Absorb>(
+    pub fn verify(
         &self,
         poseidon: &PoseidonConfig<TE::BaseField>,
-        message: &[E],
+        message: &TE::BaseField,
         signature: &Signature<TE>,
     ) -> Result<(), Error> {
         let mut poseidon = PoseidonSponge::new(poseidon);
 
-        let (sig_r_x, sig_r_y) = signature.r().xy().unwrap();
+        let (sig_r_x, sig_r_y) = signature.r().xy().ok_or(Error::Coordinates)?;
         poseidon.absorb(sig_r_x);
         poseidon.absorb(sig_r_y);
-        let (pk_x, pk_y) = self.0.xy().unwrap();
+        let (pk_x, pk_y) = self.0.xy().ok_or(Error::Coordinates)?;
         poseidon.absorb(pk_x);
         poseidon.absorb(pk_y);
-        message.iter().for_each(|m| poseidon.absorb(m));
+        poseidon.absorb(message);
 
-        let k = poseidon.squeeze_field_elements::<TE::ScalarField>(1);
-        let k = k.first().unwrap();
+        // use poseidon over Fq, so that it can be done too in-circuit
+        let k = poseidon.squeeze_field_elements::<TE::BaseField>(1);
+        let k = k.first().ok_or(Error::BadDigestOutput)?;
 
-        let kx_b = self.0 * k;
+        let kx_b = self.0.mul_bigint(k.into_bigint());
         let s_b = Affine::<TE>::generator() * signature.s();
         let r_rec: Affine<TE> = (s_b - kx_b).into();
 

src/lib.rs

@@ -1,9 +1,15 @@
+use ark_ff::PrimeField;
+use digest::Digest;
+impl ark_std::error::Error for Error {}
+use ark_crypto_primitives::sponge::poseidon::{find_poseidon_ark_and_mds, PoseidonConfig};
+
 pub mod ed_on_bn254_twist;
 pub mod eddsa;
 pub mod signature;
 
-use ark_ff::PrimeField;
-use digest::Digest;
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+
 pub use eddsa::*;
 
 pub(crate) fn from_digest<F: PrimeField, D: Digest>(digest: D) -> F {
@@ -13,6 +19,7 @@ pub(crate) fn from_digest(digest: D) -> F {
 
 #[derive(Clone, Copy, Debug, Eq, PartialEq)]
 pub enum Error {
+    Coordinates,
     Verify,
     BadDigestOutput,
 }
@@ -20,54 +27,52 @@ pub enum Error {
 impl core::fmt::Display for Error {
     fn fmt(&self, f: &mut core::fmt::Formatter) -> core::fmt::Result {
         match *self {
+            Error::Coordinates => write!(f, "Could not obtain the coordinates of a point"),
             Error::Verify => write!(f, "Signature verification failed"),
             Error::BadDigestOutput => write!(f, "Bad digest output size"),
         }
     }
 }
 
-impl ark_std::error::Error for Error {}
+/// Generates poseidon constants and returns the config
+pub fn poseidon_config<F: PrimeField>(
+    rate: usize,
+    full_rounds: usize,
+    partial_rounds: usize,
+) -> PoseidonConfig<F> {
+    let prime_bits = F::MODULUS_BIT_SIZE as u64;
+    let (ark, mds) = find_poseidon_ark_and_mds(
+        prime_bits,
+        rate,
+        full_rounds as u64,
+        partial_rounds as u64,
+        0,
+    );
+    PoseidonConfig::new(full_rounds, partial_rounds, 5, mds, ark, rate, 1)
+}
 
 #[cfg(test)]
 mod test {
-
-    use crate::SigningKey;
-    use ark_crypto_primitives::sponge::poseidon::{find_poseidon_ark_and_mds, PoseidonConfig};
     use ark_crypto_primitives::sponge::Absorb;
     use ark_ec::twisted_edwards::TECurveConfig;
     use ark_ff::PrimeField;
     use digest::Digest;
     use rand_core::OsRng;
 
-    /// Generates poseidon constants and returns the config
-    pub fn poseidon_config<F: PrimeField>(
-        rate: usize,
-        full_rounds: usize,
-        partial_rounds: usize,
-    ) -> PoseidonConfig<F> {
-        let prime_bits = F::MODULUS_BIT_SIZE as u64;
-        let (ark, mds) = find_poseidon_ark_and_mds(
-            prime_bits,
-            rate,
-            full_rounds as u64,
-            partial_rounds as u64,
-            0,
-        );
-        PoseidonConfig::new(full_rounds, partial_rounds, 5, mds, ark, rate, 1)
-    }
+    use super::poseidon_config;
+    use crate::SigningKey;
 
     fn run_test<TE: TECurveConfig + Clone, D: Digest>()
     where
         TE::BaseField: Absorb + PrimeField,
     {
-        let poseidon = poseidon_config(4, 8, 55);
+        let poseidon = poseidon_config::<TE::BaseField>(4, 8, 55);
         let signing_key = SigningKey::<TE>::generate::<D>(&mut OsRng).unwrap();
-        let message = b"xxx yyy <<< zzz >>> bunny";
-        let signature = signing_key.sign::<D, _>(&poseidon, &message[..]);
+        let message_raw = b"xxx yyy <<< zzz >>> bunny";
+        let message = TE::BaseField::from_le_bytes_mod_order(message_raw);
+        let signature = signing_key.sign::<D>(&poseidon, &message).unwrap();
         let public_key = signing_key.public_key();
-        public_key
-            .verify::<_>(&poseidon, &message[..], &signature)
-            .unwrap();
+        public_key.verify(&poseidon, &message, &signature).unwrap();
     }
 
     #[test]