add compute T, start test of simple folding

README.md

@@ -4,6 +4,6 @@ Implementation of [Nova](https://eprint.iacr.org/2021/370.pdf) using [arkworks-r
 
 > Warning: Implementation from scratch to learn the internals of Nova. Do not use in production.
 
-This repo is an ongoing implementation, not to be used but just to understand and experiment with the internals of the scheme and try experimental combinations.
+This repo is an ongoing implementation, the code will be dirty for a while and not optimized and not to be used but just to understand and experiment with the internals of the scheme and try experimental combinations.
 
 Thanks to [levs57](https://twitter.com/levs57) for clarifications on the Nova folding.

src/nifs.rs

@@ -2,16 +2,16 @@ use ark_ec::AffineRepr;
 use ark_std::ops::Add;
 use std::marker::PhantomData;
 
-use crate::pedersen::Commitment;
+use crate::pedersen::{Commitment, CommitmentVec};
 use crate::r1cs::*;
 use crate::transcript::Transcript;
 use crate::utils::*;
 
 // Phi: φ in the paper (later 𝖴), a folded instance
 pub struct Phi<C: AffineRepr> {
-    cmE: Commitment<C>,
+    cmE: Commitment<C>, // TODO not Commitment but directly C (without rE)
     u: C::ScalarField,
-    cmW: Commitment<C>,
+    cmW: Commitment<C>, // TODO not Commitment but directly C (without rW)
     x: Vec<C::ScalarField>,
 }
 
@@ -23,25 +23,56 @@ pub struct FWit<C: AffineRepr> {
     rW: C::ScalarField,
 }
 
+impl<C: AffineRepr> FWit<C> {
+    pub fn commit(&self) -> Phi<C> {
+        unimplemented!();
+    }
+}
+
 pub struct NIFS<C: AffineRepr> {
     _phantom: PhantomData<C>,
 }
 
 impl<C: AffineRepr> NIFS<C> {
+    pub fn comp_T(
+        cs1: RelaxedR1CS<C::ScalarField>,
+        cs2: RelaxedR1CS<C::ScalarField>,
+        z1: &Vec<C::ScalarField>,
+        z2: &Vec<C::ScalarField>,
+    ) -> Vec<C::ScalarField> {
+        // assuming cs1.R1CS == cs2.R1CS
+        let (A, B, C) = (cs1.ABC.A, cs1.ABC.B, cs1.ABC.C);
+
+        // this is parallelizable (for the future)
+        let Az1 = matrix_vector_product(&A, &z1);
+        let Bz1 = matrix_vector_product(&B, &z1);
+        let Az1_Bz1 = hadamard_product(Az1, Bz1);
+        let Az2 = matrix_vector_product(&A, &z2);
+        let Bz2 = matrix_vector_product(&B, &z2);
+        let Az2_Bz2 = hadamard_product(Az2, Bz2);
+        let Cz2 = matrix_vector_product(&C, &z2);
+        let Cz1 = matrix_vector_product(&C, &z1);
+        let u1Cz2 = vector_elem_product(&Cz2, &cs1.u);
+        let u2Cz1 = vector_elem_product(&Cz1, &cs2.u);
+        // this will get simplifyied with future operators from Add trait
+        let T = vec_sub(vec_sub(vec_add(Az1_Bz1, Az2_Bz2), u1Cz2), u2Cz1);
+        T
+    }
+
     pub fn fold_witness(
         r: C::ScalarField,
-        fw1: FWit<C>,
+        fw1: &FWit<C>,
-        fw2: FWit<C>,
+        fw2: &FWit<C>,
         T: Vec<C::ScalarField>,
     ) -> FWit<C> {
         let r2 = r * r;
         let E: Vec<C::ScalarField> = vec_add(
             // TODO this syntax will be simplified with future operators impl
-            vec_add(fw1.E, vector_elem_product(&T, &r)),
+            vec_add(fw1.E.clone(), vector_elem_product(&T, &r)),
             vector_elem_product(&fw2.E, &r2),
         );
         let rE = fw1.rE + r * fw2.rE;
-        let W = vec_add(fw1.W, vector_elem_product(&fw2.W, &r));
+        let W = vec_add(fw1.W.clone(), vector_elem_product(&fw2.W, &r));
         let rW = fw1.rW + r * fw2.rW;
         FWit::<C> {
             E: E.into(),
@@ -55,7 +86,7 @@ impl<C: AffineRepr> NIFS<C> {
         r: C::ScalarField,
         phi1: Phi<C>,
         phi2: Phi<C>,
-        cmT: Commitment<C>,
+        cmT: CommitmentVec<C>,
     ) -> Phi<C> {
         let r2 = r * r;
 
@@ -78,3 +109,81 @@ impl<C: AffineRepr> NIFS<C> {
         }
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::pedersen::Pedersen;
+    use ark_bn254::{g1::G1Affine, Fr};
+    use ark_ec::CurveGroup;
+    use ark_std::{
+        rand::{Rng, RngCore},
+        UniformRand,
+    };
+    use ark_std::{One, Zero};
+    use std::ops::Mul;
+
+    #[test]
+    fn test_simple_folding() {
+        let mut rng = ark_std::test_rng();
+
+        // R1CS for: x^3 + x + 5 = y
+        let A = to_F_matrix::<Fr>(vec![
+            vec![0, 1, 0, 0, 0, 0],
+            vec![0, 0, 0, 1, 0, 0],
+            vec![0, 1, 0, 0, 1, 0],
+            vec![5, 0, 0, 0, 0, 1],
+        ]);
+        let B = to_F_matrix::<Fr>(vec![
+            vec![0, 1, 0, 0, 0, 0],
+            vec![0, 1, 0, 0, 0, 0],
+            vec![1, 0, 0, 0, 0, 0],
+            vec![1, 0, 0, 0, 0, 0],
+        ]);
+        let C = to_F_matrix::<Fr>(vec![
+            vec![0, 0, 0, 1, 0, 0],
+            vec![0, 0, 0, 0, 1, 0],
+            vec![0, 0, 0, 0, 0, 1],
+            vec![0, 0, 1, 0, 0, 0],
+        ]);
+        let z1 = to_F_vec::<Fr>(vec![1, 3, 35, 9, 27, 30]);
+        let z2 = to_F_vec::<Fr>(vec![1, 4, 73, 16, 64, 68]);
+
+        let relaxed_r1cs_1 = R1CS::<Fr> {
+            A: A.clone(),
+            B: B.clone(),
+            C: C.clone(),
+        }
+        .relax();
+        let relaxed_r1cs_2 = R1CS::<Fr> { A, B, C }.relax();
+
+        let T = NIFS::<G1Affine>::comp_T(relaxed_r1cs_1, relaxed_r1cs_2, &z1, &z2);
+        let params = Pedersen::<G1Affine>::new_params(&mut rng);
+        let cmT = Pedersen::commit_vec(&mut rng, &params, &T);
+
+        let r = Fr::rand(&mut rng); // this would come from the transcript
+
+        // WIP TMP
+        let fw1 = FWit::<G1Affine> {
+            E: vec![Fr::zero(); T.len()],
+            rE: Fr::zero(),
+            W: z1,
+            rW: Fr::zero(),
+        };
+        let fw2 = FWit::<G1Affine> {
+            E: vec![Fr::zero(); T.len()],
+            rE: Fr::zero(),
+            W: z2,
+            rW: Fr::zero(),
+        };
+
+        // fold witness
+        let folded_witness = NIFS::<G1Affine>::fold_witness(r, &fw1, &fw2, T);
+        let phi1 = fw1.commit(); // <- unimplemented
+        let phi2 = fw2.commit();
+        // fold instance
+        let folded_instance = NIFS::<G1Affine>::fold_instance(r, phi1, phi2, cmT);
+        // naive check r1cs of the folded witness
+        // assert_eq!(hadamard_product(Az, Bz), vec_add(vector_elem_product(Cz, u), E));
+    }
+}

src/pedersen.rs

@@ -1,8 +1,12 @@
 use ark_ec::AffineRepr;
-use ark_std::{rand::RngCore, UniformRand};
+use ark_std::{
+    rand::{Rng, RngCore},
+    UniformRand,
+};
 use std::marker::PhantomData;
 
 use crate::transcript::Transcript;
+use crate::utils::naive_msm;
 
 pub struct Proof<C: AffineRepr> {
     R: C,
@@ -20,15 +24,35 @@ pub struct Pedersen<C: AffineRepr> {
 }
 
 impl<C: AffineRepr> Pedersen<C> {
-    pub fn commit<R: RngCore>(
+    pub fn new_params<R: Rng>(rng: &mut R) -> Params<C> {
+        let h_scalar = C::ScalarField::rand(rng);
+        let g: C = C::generator();
+        let params: Params<C> = Params::<C> {
+            g,
+            h: g.mul(h_scalar).into(),
+        };
+        params
+    }
+
+    pub fn commit_elem<R: RngCore>(
         rng: &mut R,
         params: &Params<C>,
         v: &C::ScalarField,
-    ) -> (C, C::ScalarField) {
+    ) -> Commitment<C> {
         let r = C::ScalarField::rand(rng);
         let cm: C = (params.g.mul(v) + params.h.mul(r)).into();
-        (cm, r)
+        Commitment::<C> { cm, r }
     }
+    pub fn commit_vec<R: RngCore>(
+        rng: &mut R,
+        params: &Params<C>,
+        v: &Vec<C::ScalarField>,
+    ) -> CommitmentVec<C> {
+        let r: Vec<C> = vec![C::rand(rng); v.len()]; // wip
+        let cm = naive_msm(v, &r);
+        CommitmentVec::<C> { cm, r }
+    }
+
     pub fn prove(
         params: &Params<C>,
         transcript: &mut Transcript<C::ScalarField>,
@@ -73,13 +97,18 @@ impl<C: AffineRepr> Pedersen<C> {
     }
 }
 
+pub struct CommitmentVec<C: AffineRepr> {
+    // WIP
+    pub cm: C,
+    pub r: Vec<C>,
+}
 pub struct Commitment<C: AffineRepr> {
     pub cm: C,
     pub r: C::ScalarField,
 }
 impl<C: AffineRepr> Commitment<C> {
     pub fn prove(
-        self,
+        &self,
         params: &Params<C>,
         transcript: &mut Transcript<C::ScalarField>,
         v: C::ScalarField,
@@ -100,12 +129,7 @@ mod tests {
         let mut rng = ark_std::test_rng();
 
         // setup params
-        let h_scalar = Fr::rand(&mut rng);
+        let params = Pedersen::<G1Affine>::new_params(&mut rng);
-        let g: G1Affine = G1Affine::generator();
-        let params: Params<G1Affine> = Params::<G1Affine> {
-            g,
-            h: g.mul(h_scalar).into_affine(),
-        };
 
         // init Prover's transcript
         let mut transcript_p: Transcript<Fr> = Transcript::<Fr>::new();
@@ -114,9 +138,11 @@ mod tests {
 
         let v = Fr::rand(&mut rng);
 
-        let (cm, r) = Pedersen::commit(&mut rng, &params, &v);
+        let cm = Pedersen::commit_elem(&mut rng, &params, &v);
-        let proof = Pedersen::prove(&params, &mut transcript_p, cm, v, r);
+        let proof = cm.prove(&params, &mut transcript_p, v);
-        let v = Pedersen::verify(&params, &mut transcript_v, cm, proof);
+        // also can use:
+        // let proof = Pedersen::prove(&params, &mut transcript_p, cm.cm, v, cm.r);
+        let v = Pedersen::verify(&params, &mut transcript_v, cm.cm, proof);
         assert!(v);
     }
 }

src/utils.rs

@@ -1,3 +1,4 @@
+use ark_ec::AffineRepr;
 use ark_ff::fields::PrimeField;
 use core::ops::Add;
 
@@ -29,6 +30,16 @@ pub fn hadamard_product<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
     r
 }
 
+pub fn naive_msm<C: AffineRepr>(s: &Vec<C::ScalarField>, p: &Vec<C>) -> C {
+    // check lengths
+
+    let mut r = p[0].mul(s[0]);
+    for i in 1..s.len() {
+        r = p[i].mul(s[i]);
+    }
+    r.into()
+}
+
 pub fn vec_add<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
     let mut r: Vec<F> = vec![F::zero(); a.len()];
     for i in 0..a.len() {
@@ -55,6 +66,24 @@ pub fn vec_sub<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
     r
 }
 
+pub fn to_F_matrix<F: PrimeField>(M: Vec<Vec<usize>>) -> Vec<Vec<F>> {
+    let mut R: Vec<Vec<F>> = vec![Vec::new(); M.len()];
+    for i in 0..M.len() {
+        R[i] = vec![F::zero(); M[i].len()];
+        for j in 0..M[i].len() {
+            R[i][j] = F::from(M[i][j] as u64);
+        }
+    }
+    R
+}
+pub fn to_F_vec<F: PrimeField>(z: Vec<usize>) -> Vec<F> {
+    let mut r: Vec<F> = vec![F::zero(); z.len()];
+    for i in 0..z.len() {
+        r[i] = F::from(z[i] as u64);
+    }
+    r
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -63,24 +92,6 @@ mod tests {
     use ark_std::{One, Zero};
     use std::ops::Mul;
 
-    fn to_F_matrix<F: PrimeField>(M: Vec<Vec<usize>>) -> Vec<Vec<F>> {
-        let mut R: Vec<Vec<F>> = vec![Vec::new(); M.len()];
-        for i in 0..M.len() {
-            R[i] = vec![F::zero(); M[i].len()];
-            for j in 0..M[i].len() {
-                R[i][j] = F::from(M[i][j] as u64);
-            }
-        }
-        R
-    }
-    fn to_F_vec<F: PrimeField>(z: Vec<usize>) -> Vec<F> {
-        let mut r: Vec<F> = vec![F::zero(); z.len()];
-        for i in 0..z.len() {
-            r[i] = F::from(z[i] as u64);
-        }
-        r
-    }
-
     #[test]
     fn test_matrix_vector_product() {
         let A = to_F_matrix::<Fr>(vec![