folding witness & crossterms works, add Ve helpers

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, 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.
+This repo is an ongoing implementation, the code will be dirty for a while and not optimized 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

@@ -1,17 +1,24 @@
 use ark_ec::AffineRepr;
 use ark_std::ops::Add;
+use ark_std::One;
 use std::marker::PhantomData;
 
-use crate::pedersen::{Commitment, CommitmentVec};
+use crate::pedersen::{Commitment, CommitmentVec, Params as PedersenParams, Pedersen};
 use crate::r1cs::*;
 use crate::transcript::Transcript;
 use crate::utils::*;
+use ark_std::{
+    rand::{Rng, RngCore},
+    UniformRand,
+};
 
 // Phi: φ in the paper (later 𝖴), a folded instance
 pub struct Phi<C: AffineRepr> {
-    cmE: Commitment<C>, // TODO not Commitment but directly C (without rE)
+    // cmE: CommitmentVec<C>, // TODO not Commitment but directly C (without rE)
+    cmE: C,
     u: C::ScalarField,
-    cmW: Commitment<C>, // TODO not Commitment but directly C (without rW)
+    // cmW: CommitmentVec<C>, // TODO not Commitment but directly C (without rW)
+    cmW: C,
     x: Vec<C::ScalarField>,
 }
 
@@ -24,8 +31,21 @@ pub struct FWit<C: AffineRepr> {
 }
 
 impl<C: AffineRepr> FWit<C> {
-    pub fn commit(&self) -> Phi<C> {
+    pub fn commit<R: Rng>(
-        unimplemented!();
+        &self,
+        rng: &mut R,
+        params: &PedersenParams<C>,
+        x: Vec<C::ScalarField>,
+    ) -> Phi<C> {
+        // TODO instead of rand r, use self.rE and self.rW for the commit_vec
+        let cmE = Pedersen::commit_vec(rng, &params, &self.E);
+        let cmW = Pedersen::commit_vec(rng, &params, &self.W);
+        Phi {
+            cmE: cmE.cm,
+            u: C::ScalarField::one(),
+            cmW: cmW.cm,
+            x,
+        }
     }
 }
 
@@ -46,17 +66,19 @@ impl<C: AffineRepr> NIFS<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 Cz1 = matrix_vector_product(&C, &z1);
         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 Az1_Bz2 = hadamard_product(Az1, Bz2);
+        let Az2_Bz1 = hadamard_product(Az2, Bz1);
         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);
+        // let T = vec_sub(vec_sub(vec_add(Az1_Bz2, Az2_Bz1), u1Cz2), u2Cz1);
-        T
+        let T = ((Ve(Az1_Bz2) + Ve(Az2_Bz1)) - Ve(u1Cz2)) - Ve(u2Cz1);
+        T.0
     }
 
     pub fn fold_witness(
@@ -67,12 +89,15 @@ impl<C: AffineRepr> NIFS<C> {
     ) -> FWit<C> {
         let r2 = r * r;
         let E: Vec<C::ScalarField> = vec_add(
-            // TODO this syntax will be simplified with future operators impl
+            // this syntax will be simplified with future operators impl (or at least a method
+            // for r-lin)
             vec_add(fw1.E.clone(), vector_elem_product(&T, &r)),
+            // rlin(fw1.E.clone(), T, r),
             vector_elem_product(&fw2.E, &r2),
         );
-        let rE = fw1.rE + r * fw2.rE;
+        let rE = fw1.rE + r2 * fw2.rE; // TODO rT
         let W = vec_add(fw1.W.clone(), vector_elem_product(&fw2.W, &r));
+        // let W = rlin(fw1.W.clone(), fw2.W.clone(), r);
         let rW = fw1.rW + r * fw2.rW;
         FWit::<C> {
             E: E.into(),
@@ -90,21 +115,24 @@ impl<C: AffineRepr> NIFS<C> {
     ) -> Phi<C> {
         let r2 = r * r;
 
-        let cmE = phi1.cmE.cm + cmT.cm.mul(r) + phi2.cmE.cm.mul(r2);
+        let cmE = phi1.cmE + cmT.cm.mul(r) + phi2.cmE.mul(r2);
         let u = phi1.u + r * phi2.u;
-        let cmW = phi1.cmW.cm + phi2.cmW.cm.mul(r);
+        let cmW = phi1.cmW + phi2.cmW.mul(r);
         let x = vec_add(phi1.x, vector_elem_product(&phi2.x, &r));
+        // let x = rlin(phi1.x, phi2.x, r);
 
         Phi::<C> {
-            cmE: Commitment::<C> {
+            // cmE: Commitment::<C> {
-                cm: cmE.into(),
+            //     cm: cmE.into(),
-                r: phi1.cmE.r,
+            //     r: phi1.cmE.r,
-            },
+            // },
+            cmE: cmE.into(),
             u,
-            cmW: Commitment::<C> {
+            // cmW: Commitment::<C> {
-                cm: cmW.into(),
+            //     cm: cmW.into(),
-                r: phi1.cmW.r,
+            //     r: phi1.cmW.r,
-            },
+            // },
+            cmW: cmW.into(),
             x,
         }
     }
@@ -127,7 +155,8 @@ mod tests {
     fn test_simple_folding() {
         let mut rng = ark_std::test_rng();
 
-        // R1CS for: x^3 + x + 5 = y
+        // R1CS for: x^3 + x + 5 = y (example from article
+        // https://www.vitalik.ca/general/2016/12/10/qap.html )
         let A = to_F_matrix::<Fr>(vec![
             vec![0, 1, 0, 0, 0, 0],
             vec![0, 0, 0, 1, 0, 0],
@@ -147,7 +176,9 @@ mod tests {
             vec![0, 0, 1, 0, 0, 0],
         ]);
         let z1 = to_F_vec::<Fr>(vec![1, 3, 35, 9, 27, 30]);
+        let x1 = to_F_vec::<Fr>(vec![35]);
         let z2 = to_F_vec::<Fr>(vec![1, 4, 73, 16, 64, 68]);
+        let x2 = to_F_vec::<Fr>(vec![73]);
 
         let relaxed_r1cs_1 = R1CS::<Fr> {
             A: A.clone(),
@@ -155,7 +186,12 @@ mod tests {
             C: C.clone(),
         }
         .relax();
-        let relaxed_r1cs_2 = R1CS::<Fr> { A, B, C }.relax();
+        let relaxed_r1cs_2 = R1CS::<Fr> {
+            A: A.clone(),
+            B: B.clone(),
+            C: C.clone(),
+        }
+        .relax();
 
         let T = NIFS::<G1Affine>::comp_T(relaxed_r1cs_1, relaxed_r1cs_2, &z1, &z2);
         let params = Pedersen::<G1Affine>::new_params(&mut rng);
@@ -179,11 +215,23 @@ mod tests {
 
         // fold witness
         let folded_witness = NIFS::<G1Affine>::fold_witness(r, &fw1, &fw2, T);
-        let phi1 = fw1.commit(); // <- unimplemented
+
-        let phi2 = fw2.commit();
+        let pedersen_params = Pedersen::<G1Affine>::new_params(&mut rng);
+        let phi1 = fw1.commit(&mut rng, &pedersen_params, x1); // wip
+        let phi2 = fw2.commit(&mut rng, &pedersen_params, x2);
         // 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));
+        // naive check that the folded witness satisfies the relaxed r1cs
+        let Az = matrix_vector_product(&A, &folded_witness.W);
+        let Bz = matrix_vector_product(&B, &folded_witness.W);
+        let Cz = matrix_vector_product(&C, &folded_witness.W);
+        assert_eq!(
+            hadamard_product(Az, Bz),
+            vec_add(
+                vector_elem_product(&Cz, &folded_instance.u),
+                folded_witness.E
+            )
+        );
     }
 }

src/utils.rs

@@ -1,6 +1,7 @@
 use ark_ec::AffineRepr;
 use ark_ff::fields::PrimeField;
-use core::ops::Add;
+use core::ops::{Add, Sub};
+use std::fmt;
 
 pub fn vector_elem_product<F: PrimeField>(a: &Vec<F>, e: &F) -> Vec<F> {
     // maybe move this method to operator a * e
@@ -30,6 +31,11 @@ pub fn hadamard_product<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
     r
 }
 
+// rlin: random linear combination
+// pub fn rlin<F: PrimeField>(a: Vec<F>, b: Vec<F>, r: F) -> Vec<F> {
+//     vec_add(a, vector_elem_product(&b, &r)) // WIP probably group loops
+// }
+
 pub fn naive_msm<C: AffineRepr>(s: &Vec<C::ScalarField>, p: &Vec<C>) -> C {
     // check lengths
 
@@ -47,17 +53,6 @@ pub fn vec_add<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
     }
     r
 }
-// TODO instead of vec_add do:
-// impl<'a, 'b, F> Add<&'b Vec<F>> for &'a Vec<F> {
-//     type Output = Vec<F>;
-//     fn add(self, rhs: &'b Vec<F>) -> Vec<F> {
-//         let mut r: Vec<F> = vec![F::zero(); self.len()];
-//         for i in 0..self.len() {
-//             r[i] = self[i] + rhs[i];
-//         }
-//         r
-//     }
-// }
 pub fn vec_sub<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() {
@@ -66,6 +61,48 @@ pub fn vec_sub<F: PrimeField>(a: Vec<F>, b: Vec<F>) -> Vec<F> {
     r
 }
 
+// instead of vec_{add/sub} can use Ve wrapper which has '+', '-' operators
+#[derive(Debug, Clone, PartialEq)]
+pub struct Ve<F: PrimeField>(pub Vec<F>);
+
+impl<F: PrimeField> fmt::Display for Ve<F> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        for (i, e) in self.0.iter().enumerate() {
+            if i == self.0.len() - 1 {
+                write!(f, "{}", e)?;
+                break;
+            }
+            write!(f, "{}, ", e)?;
+        }
+        Ok(())
+    }
+}
+
+impl<F: PrimeField> Add<Ve<F>> for Ve<F> {
+    type Output = Ve<F>;
+    fn add(self, rhs_vec: Self) -> Ve<F> {
+        let lhs = self.0.clone();
+        let rhs = rhs_vec.0.clone();
+        let mut r: Vec<F> = vec![F::zero(); lhs.len()];
+        for i in 0..self.0.len() {
+            r[i] = lhs[i] + rhs[i];
+        }
+        Ve(r)
+    }
+}
+impl<F: PrimeField> Sub<Ve<F>> for Ve<F> {
+    type Output = Ve<F>;
+    fn sub(self, rhs_vec: Self) -> Ve<F> {
+        let lhs = self.0.clone();
+        let rhs = rhs_vec.0.clone();
+        let mut r: Vec<F> = vec![F::zero(); lhs.len()];
+        for i in 0..self.0.len() {
+            r[i] = lhs[i] - rhs[i];
+        }
+        Ve(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() {
@@ -114,6 +151,12 @@ mod tests {
             to_F_vec(vec![7, 16, 27, 40, 55, 72])
         );
     }
+    #[test]
+    fn test_vec_add() {
+        let a: Vec<Fr> = to_F_vec::<Fr>(vec![1, 2, 3, 4, 5, 6]);
+        let b: Vec<Fr> = to_F_vec(vec![7, 8, 9, 10, 11, 12]);
+        assert_eq!(vec_add(a.clone(), b.clone()), (Ve(a) + Ve(b)).0);
+    }
 
     #[test]
     fn test_ABC_hadamard() {