Implement CycleFold's EC RLC check circuit (#9)

src/folding/circuits/cyclefold.rs

@@ -0,0 +1,62 @@
+/// Implements the C_{EC} circuit described in CycleFold paper https://eprint.iacr.org/2023/1192.pdf
+use ark_ec::CurveGroup;
+use ark_r1cs_std::{fields::nonnative::NonNativeFieldVar, prelude::CurveVar, ToBitsGadget};
+use ark_relations::r1cs::SynthesisError;
+use core::marker::PhantomData;
+
+use super::ConstraintF;
+
+/// ECRLC implements gadget that checks the Elliptic Curve points RandomLinearCombination described
+/// in CycleFold (https://eprint.iacr.org/2023/1192.pdf).
+#[derive(Debug)]
+pub struct ECRLC<C: CurveGroup, GC: CurveVar<C, ConstraintF<C>>> {
+    _c: PhantomData<C>,
+    _gc: PhantomData<GC>,
+}
+impl<C: CurveGroup, GC: CurveVar<C, ConstraintF<C>>> ECRLC<C, GC> {
+    pub fn check(
+        r: NonNativeFieldVar<C::ScalarField, ConstraintF<C>>,
+        p1: GC,
+        p2: GC,
+        p3: GC,
+    ) -> Result<(), SynthesisError> {
+        p3.enforce_equal(&(p1 + p2.scalar_mul_le(r.to_bits_le()?.iter())?))?;
+        Ok(())
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::*;
+    use ark_bls12_377::{constraints::G1Var, Fq, Fr, G1Projective};
+    use ark_r1cs_std::alloc::AllocVar;
+    use ark_relations::r1cs::ConstraintSystem;
+    use ark_std::UniformRand;
+    use std::ops::Mul;
+
+    /// Let Curve1=bls12-377::G1 and Curve2=bw6-761::G1. Here we have our constraint system will
+    /// work over Curve2::Fr = bw6-761::Fr (=bls12-377::Fq), thus our points are P_i \in Curve1
+    /// (=bls12-377).
+    #[test]
+    fn test_ecrlc_check() {
+        let mut rng = ark_std::test_rng();
+
+        let r = Fr::rand(&mut rng);
+        let p1 = G1Projective::rand(&mut rng);
+        let p2 = G1Projective::rand(&mut rng);
+        let p3 = p1 + p2.mul(r);
+
+        let cs = ConstraintSystem::<Fq>::new_ref(); // CS over Curve2::Fr = Curve1::Fq
+
+        // prepare circuit inputs
+        let rVar = NonNativeFieldVar::<Fr, Fq>::new_witness(cs.clone(), || Ok(r)).unwrap();
+        let p1Var = G1Var::new_witness(cs.clone(), || Ok(p1)).unwrap();
+        let p2Var = G1Var::new_witness(cs.clone(), || Ok(p2)).unwrap();
+        let p3Var = G1Var::new_witness(cs.clone(), || Ok(p3)).unwrap();
+
+        // check ECRLC circuit
+        ECRLC::<G1Projective, G1Var>::check(rVar, p1Var, p2Var, p3Var).unwrap();
+        assert!(cs.is_satisfied().unwrap());
+        // dbg!(cs.num_constraints());
+    }
+}