use ark_ec::AffineRepr;
|
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use ark_ff::fields::PrimeField;
|
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use ark_std::{
|
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rand::{Rng, RngCore},
|
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UniformRand,
|
|
};
|
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use ark_std::{One, Zero};
|
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use std::marker::PhantomData;
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use crate::pedersen::{Commitment, Params as PedersenParams, Pedersen, Proof as PedersenProof};
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use crate::transcript::Transcript;
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use crate::utils::*;
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|
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pub struct R1CS<F: PrimeField> {
|
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pub A: Vec<Vec<F>>,
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pub B: Vec<Vec<F>>,
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pub C: Vec<Vec<F>>,
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}
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// Phi: φ in the paper (later 𝖴), a folded instance
|
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pub struct Phi<C: AffineRepr> {
|
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cmE: Commitment<C>,
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u: C::ScalarField,
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cmW: Commitment<C>,
|
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x: Vec<C::ScalarField>,
|
|
}
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|
|
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// FWit: Folded Witness
|
|
pub struct FWit<C: AffineRepr> {
|
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E: Vec<C::ScalarField>,
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rE: C::ScalarField,
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W: Vec<C::ScalarField>,
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|
rW: C::ScalarField,
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|
}
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|
|
|
impl<C: AffineRepr> FWit<C> {
|
|
pub fn new(z: Vec<C::ScalarField>, e_len: usize) -> Self {
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|
FWit::<C> {
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|
E: vec![C::ScalarField::zero(); e_len],
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|
rE: C::ScalarField::one(),
|
|
W: z,
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rW: C::ScalarField::one(),
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|
}
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|
}
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pub fn commit(&self, params: &PedersenParams<C>) -> Phi<C> {
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|
let cmE = Pedersen::commit(¶ms, &self.E, &self.rE);
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let cmW = Pedersen::commit(¶ms, &self.W, &self.rW);
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|
Phi {
|
|
cmE,
|
|
u: C::ScalarField::one(),
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|
cmW,
|
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x: self.W.clone(),
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|
}
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|
}
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|
}
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|
|
|
pub struct NIFS<C: AffineRepr> {
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|
_phantom: PhantomData<C>,
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|
}
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impl<C: AffineRepr> NIFS<C> {
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|
// comp_T: compute cross-terms T
|
|
pub fn comp_T(
|
|
r1cs: &R1CS<C::ScalarField>,
|
|
u1: C::ScalarField,
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u2: C::ScalarField,
|
|
z1: &Vec<C::ScalarField>,
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|
z2: &Vec<C::ScalarField>,
|
|
) -> Vec<C::ScalarField> {
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|
let (A, B, C) = (r1cs.A.clone(), r1cs.B.clone(), r1cs.C.clone());
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|
|
|
// this is parallelizable (for the future)
|
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let Az1 = matrix_vector_product(&A, &z1);
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let Bz1 = matrix_vector_product(&B, &z1);
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let Cz1 = matrix_vector_product(&C, &z1);
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|
let Az2 = matrix_vector_product(&A, &z2);
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let Bz2 = matrix_vector_product(&B, &z2);
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|
let Cz2 = matrix_vector_product(&C, &z2);
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|
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let Az1_Bz2 = hadamard_product(Az1, Bz2);
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let Az2_Bz1 = hadamard_product(Az2, Bz1);
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let u1Cz2 = vector_elem_product(&Cz2, &u1);
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|
let u2Cz1 = vector_elem_product(&Cz1, &u2);
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|
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// let T = vec_sub(vec_sub(vec_add(Az1_Bz2, Az2_Bz1), u1Cz2), u2Cz1);
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let T = ((Ve(Az1_Bz2) + Ve(Az2_Bz1)) - Ve(u1Cz2)) - Ve(u2Cz1);
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|
T.0
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|
}
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|
|
|
pub fn fold_witness(
|
|
r: C::ScalarField,
|
|
fw1: &FWit<C>,
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|
fw2: &FWit<C>,
|
|
T: &Vec<C::ScalarField>,
|
|
rT: C::ScalarField,
|
|
) -> FWit<C> {
|
|
let r2 = r * r;
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|
let E: Vec<C::ScalarField> = vec_add(
|
|
// this syntax will be simplified with future operators impl (or at least a method
|
|
// for r-lin)
|
|
&vec_add(&fw1.E, &vector_elem_product(&T, &r)),
|
|
&vector_elem_product(&fw2.E, &r2),
|
|
);
|
|
let rE = fw1.rE + r * rT + r2 * fw2.rE;
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|
let W = vec_add(&fw1.W, &vector_elem_product(&fw2.W, &r));
|
|
let rW = fw1.rW + r * fw2.rW;
|
|
FWit::<C> {
|
|
E: E.into(),
|
|
rE,
|
|
W: W.into(),
|
|
rW,
|
|
}
|
|
}
|
|
|
|
pub fn fold_instance(
|
|
r: C::ScalarField,
|
|
phi1: &Phi<C>,
|
|
phi2: &Phi<C>,
|
|
cmT: &Commitment<C>,
|
|
) -> Phi<C> {
|
|
let r2 = r * r;
|
|
|
|
let cmE = phi1.cmE.0 + cmT.0.mul(r) + phi2.cmE.0.mul(r2);
|
|
let u = phi1.u + r * phi2.u;
|
|
let cmW = phi1.cmW.0 + phi2.cmW.0.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(cmE.into()),
|
|
u,
|
|
cmW: Commitment(cmW.into()),
|
|
x,
|
|
}
|
|
}
|
|
|
|
// NIFS.P
|
|
pub fn P(
|
|
tr: &mut Transcript<C::ScalarField>,
|
|
pedersen_params: &PedersenParams<C>,
|
|
r: C::ScalarField,
|
|
r1cs: &R1CS<C::ScalarField>,
|
|
fw1: FWit<C>,
|
|
fw2: FWit<C>,
|
|
) -> (FWit<C>, Phi<C>, Phi<C>, Vec<C::ScalarField>, Commitment<C>) {
|
|
// compute committed instances
|
|
let phi1 = fw1.commit(&pedersen_params); // wip
|
|
let phi2 = fw2.commit(&pedersen_params);
|
|
|
|
// compute cross terms
|
|
let T = Self::comp_T(&r1cs, phi1.u, phi2.u, &fw1.W, &fw2.W);
|
|
let rT = tr.get_challenge(b"rT");
|
|
let cmT = Pedersen::commit(&pedersen_params, &T, &rT);
|
|
|
|
// fold witness
|
|
let fw3 = NIFS::<C>::fold_witness(r, &fw1, &fw2, &T, rT);
|
|
|
|
// fold committed instancs
|
|
// let phi3 = NIFS::<C>::fold_instance(r, &phi1, &phi2, &cmT);
|
|
return (fw3, phi1, phi2, T, cmT); // maybe return phi3
|
|
}
|
|
|
|
// NIFS.V
|
|
pub fn V(r: C::ScalarField, phi1: &Phi<C>, phi2: &Phi<C>, cmT: &Commitment<C>) -> Phi<C> {
|
|
NIFS::<C>::fold_instance(r, &phi1, &phi2, &cmT)
|
|
}
|
|
|
|
// verify commited folded instance (phi) relations
|
|
pub fn verify(
|
|
r: C::ScalarField,
|
|
phi1: &Phi<C>,
|
|
phi2: &Phi<C>,
|
|
phi3: &Phi<C>,
|
|
cmT: &Commitment<C>,
|
|
) -> bool {
|
|
let r2 = r * r;
|
|
if phi3.cmE.0 != (phi1.cmE.0 + cmT.0.mul(r) + phi2.cmE.0.mul(r2)).into() {
|
|
return false;
|
|
}
|
|
if phi3.u != phi1.u + r * phi2.u {
|
|
return false;
|
|
}
|
|
if phi3.cmW.0 != (phi1.cmW.0 + phi2.cmW.0.mul(r)).into() {
|
|
return false;
|
|
}
|
|
if phi3.x != vec_add(&phi1.x, &vector_elem_product(&phi2.x, &r)) {
|
|
return false;
|
|
}
|
|
true
|
|
}
|
|
|
|
pub fn open_commitments(
|
|
tr: &mut Transcript<C::ScalarField>,
|
|
pedersen_params: &PedersenParams<C>,
|
|
fw: &FWit<C>,
|
|
phi: &Phi<C>,
|
|
T: Vec<C::ScalarField>,
|
|
rT: C::ScalarField,
|
|
cmT: &Commitment<C>,
|
|
) -> (PedersenProof<C>, PedersenProof<C>, PedersenProof<C>) {
|
|
let cmE_proof = Pedersen::prove(&pedersen_params, tr, &phi.cmE, &fw.E, &fw.rE);
|
|
let cmW_proof = Pedersen::prove(&pedersen_params, tr, &phi.cmW, &fw.W, &fw.rW);
|
|
let cmT_proof = Pedersen::prove(&pedersen_params, tr, &cmT, &T, &rT);
|
|
(cmE_proof, cmW_proof, cmT_proof)
|
|
}
|
|
pub fn verify_commitments(
|
|
tr: &mut Transcript<C::ScalarField>,
|
|
pedersen_params: &PedersenParams<C>,
|
|
phi: Phi<C>,
|
|
cmT: Commitment<C>,
|
|
cmE_proof: PedersenProof<C>,
|
|
cmW_proof: PedersenProof<C>,
|
|
cmT_proof: PedersenProof<C>,
|
|
) -> bool {
|
|
if !Pedersen::verify(&pedersen_params, tr, phi.cmE, cmE_proof) {
|
|
return false;
|
|
}
|
|
if !Pedersen::verify(&pedersen_params, tr, phi.cmW, cmW_proof) {
|
|
return false;
|
|
}
|
|
if !Pedersen::verify(&pedersen_params, tr, cmT, cmT_proof) {
|
|
return false;
|
|
}
|
|
true
|
|
}
|
|
}
|
|
|
|
#[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;
|
|
|
|
fn gen_test_values<R: Rng>(
|
|
rng: &mut R,
|
|
) -> (
|
|
R1CS<Fr>,
|
|
Vec<Fr>,
|
|
Vec<Fr>,
|
|
Vec<Fr>,
|
|
Vec<Fr>,
|
|
Vec<Fr>,
|
|
Vec<Fr>,
|
|
) {
|
|
// 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],
|
|
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],
|
|
]);
|
|
// TODO in the future update this method to generate witness, and generate n witnesses
|
|
// instances, x: pub
|
|
let w1 = to_F_vec::<Fr>(vec![1, 3, 35, 9, 27, 30]);
|
|
let x1 = to_F_vec::<Fr>(vec![35]);
|
|
let w2 = to_F_vec::<Fr>(vec![1, 4, 73, 16, 64, 68]);
|
|
let x2 = to_F_vec::<Fr>(vec![73]);
|
|
let w3 = to_F_vec::<Fr>(vec![1, 5, 135, 25, 125, 130]);
|
|
let x3 = to_F_vec::<Fr>(vec![135]);
|
|
|
|
let r1cs = R1CS::<Fr> {
|
|
A: A.clone(),
|
|
B: B.clone(),
|
|
C: C.clone(),
|
|
};
|
|
(r1cs, w1, w2, w3, x1, x2, x3)
|
|
}
|
|
|
|
// fold 2 instances into one
|
|
#[test]
|
|
fn test_one_fold() {
|
|
let mut rng = ark_std::test_rng();
|
|
let pedersen_params = Pedersen::<G1Affine>::new_params(&mut rng, 100); // 100 is wip, will get it from actual vec
|
|
|
|
let (r1cs, w1, w2, _, x1, x2, _) = gen_test_values(&mut rng);
|
|
let (A, B, C) = (r1cs.A.clone(), r1cs.B.clone(), r1cs.C.clone());
|
|
|
|
let r = Fr::rand(&mut rng); // this would come from the transcript
|
|
|
|
let fw1 = FWit::<G1Affine>::new(w1.clone(), A.len());
|
|
let fw2 = FWit::<G1Affine>::new(w2.clone(), A.len());
|
|
|
|
// get committed instances
|
|
let phi1 = fw1.commit(&pedersen_params); // wip
|
|
let phi2 = fw2.commit(&pedersen_params);
|
|
|
|
let T = NIFS::<G1Affine>::comp_T(&r1cs, phi1.u, phi2.u, &w1, &w2);
|
|
let rT: Fr = Fr::rand(&mut rng);
|
|
let cmT = Pedersen::commit(&pedersen_params, &T, &rT);
|
|
|
|
// fold witness
|
|
let fw3 = NIFS::<G1Affine>::fold_witness(r, &fw1, &fw2, &T, rT);
|
|
|
|
// fold instance
|
|
let phi3 = NIFS::<G1Affine>::fold_instance(r, &phi1, &phi2, &cmT);
|
|
|
|
// naive check that the folded witness satisfies the relaxed r1cs
|
|
let Az = matrix_vector_product(&A, &fw3.W);
|
|
let Bz = matrix_vector_product(&B, &fw3.W);
|
|
let Cz = matrix_vector_product(&C, &fw3.W);
|
|
assert_eq!(
|
|
hadamard_product(Az, Bz),
|
|
vec_add(&vector_elem_product(&Cz, &phi3.u), &fw3.E)
|
|
);
|
|
|
|
// check that folded commitments from folded instance (phi) are equal to folding the
|
|
// use folded rE, rW to commit fw3
|
|
let phi3_expected = fw3.commit(&pedersen_params);
|
|
assert_eq!(phi3_expected.cmE.0, phi3.cmE.0);
|
|
assert_eq!(phi3_expected.cmW.0, phi3.cmW.0);
|
|
|
|
// NIFS.Verify:
|
|
assert!(NIFS::<G1Affine>::verify(r, &phi1, &phi2, &phi3, &cmT));
|
|
|
|
// init Prover's transcript
|
|
let mut transcript_p: Transcript<Fr> = Transcript::<Fr>::new();
|
|
// init Verifier's transcript
|
|
let mut transcript_v: Transcript<Fr> = Transcript::<Fr>::new();
|
|
|
|
// check openings of phi3.cmE, phi3.cmW and cmT
|
|
let (cmE_proof, cmW_proof, cmT_proof) = NIFS::<G1Affine>::open_commitments(
|
|
&mut transcript_p,
|
|
&pedersen_params,
|
|
&fw3,
|
|
&phi3,
|
|
T,
|
|
rT,
|
|
&cmT,
|
|
);
|
|
let v = NIFS::<G1Affine>::verify_commitments(
|
|
&mut transcript_v,
|
|
&pedersen_params,
|
|
phi3,
|
|
cmT,
|
|
cmE_proof,
|
|
cmW_proof,
|
|
cmT_proof,
|
|
);
|
|
}
|
|
|
|
// fold i_1, i_2 instances into i_12, and then i_12, i_3 into i_123
|
|
#[test]
|
|
fn test_two_fold() {
|
|
let mut rng = ark_std::test_rng();
|
|
let pedersen_params = Pedersen::<G1Affine>::new_params(&mut rng, 6);
|
|
|
|
let (r1cs, w1, w2, w3, x1, x2, x3) = gen_test_values(&mut rng);
|
|
|
|
let u1: Fr = Fr::one();
|
|
let u2: Fr = Fr::one();
|
|
|
|
let T_12 = NIFS::<G1Affine>::comp_T(&r1cs, u1, u2, &w1, &w2);
|
|
let rT_12: Fr = Fr::rand(&mut rng);
|
|
let cmT_12 = Pedersen::commit(&pedersen_params, &T_12, &rT_12);
|
|
|
|
let r = Fr::rand(&mut rng); // this would come from the transcript
|
|
|
|
let fw1 = FWit::<G1Affine>::new(w1, T_12.len());
|
|
let fw2 = FWit::<G1Affine>::new(w2, T_12.len());
|
|
|
|
// fold witness
|
|
let fw_12 = NIFS::<G1Affine>::fold_witness(r, &fw1, &fw2, &T_12, rT_12);
|
|
|
|
// get committed instances
|
|
let phi1 = fw1.commit(&pedersen_params); // wip
|
|
let phi2 = fw2.commit(&pedersen_params);
|
|
|
|
// fold instance
|
|
let phi_12 = NIFS::<G1Affine>::fold_instance(r, &phi1, &phi2, &cmT_12);
|
|
|
|
// NIFS.Verify:
|
|
assert!(NIFS::<G1Affine>::verify(r, &phi1, &phi2, &phi_12, &cmT_12));
|
|
|
|
//----
|
|
// 2nd fold
|
|
let fw3 = FWit::<G1Affine>::new(w3, r1cs.A.len());
|
|
|
|
// compute cross terms
|
|
let T_123 = NIFS::<G1Affine>::comp_T(&r1cs, phi_12.u, Fr::one(), &fw_12.W, &fw3.W);
|
|
let rT_123: Fr = Fr::rand(&mut rng);
|
|
let cmT_123 = Pedersen::commit(&pedersen_params, &T_123, &rT_123);
|
|
|
|
// V sets rand challenge r
|
|
let r = Fr::rand(&mut rng); // this would come from the transcript
|
|
|
|
// fold witness
|
|
let fw_123 = NIFS::<G1Affine>::fold_witness(r, &fw_12, &fw3, &T_123, rT_123);
|
|
|
|
// get committed instances
|
|
// phi_12 is already known for Verifier from folding phi1, phi2
|
|
// rm: let phi_12 = fw_12.commit(&pedersen_params); // wip
|
|
let phi3 = fw3.commit(&pedersen_params);
|
|
|
|
// fold instance
|
|
let phi_123 = NIFS::<G1Affine>::fold_instance(r, &phi_12, &phi3, &cmT_123);
|
|
|
|
// NIFS.Verify:
|
|
assert!(NIFS::<G1Affine>::verify(
|
|
r, &phi_12, &phi3, &phi_123, &cmT_123
|
|
));
|
|
|
|
// naive check that the folded witness satisfies the relaxed r1cs
|
|
let Az = matrix_vector_product(&r1cs.A, &fw_123.W);
|
|
let Bz = matrix_vector_product(&r1cs.B, &fw_123.W);
|
|
let Cz = matrix_vector_product(&r1cs.C, &fw_123.W);
|
|
assert_eq!(
|
|
hadamard_product(Az, Bz),
|
|
vec_add(&vector_elem_product(&Cz, &phi_123.u), &fw_123.E)
|
|
);
|
|
|
|
// check that folded commitments from folded instance (phi) are equal to folding the
|
|
// use folded rE, rW to commit fw3
|
|
let phi_123_expected = fw_123.commit(&pedersen_params);
|
|
assert_eq!(phi_123_expected.cmE.0, phi_123.cmE.0);
|
|
assert_eq!(phi_123_expected.cmW.0, phi_123.cmW.0);
|
|
|
|
// init Prover's transcript
|
|
let mut transcript_p: Transcript<Fr> = Transcript::<Fr>::new();
|
|
// init Verifier's transcript
|
|
let mut transcript_v: Transcript<Fr> = Transcript::<Fr>::new();
|
|
|
|
// check openings of phi_123.cmE, phi_123.cmW and cmT_123
|
|
let (cmE_proof, cmW_proof, cmT_proof) = NIFS::<G1Affine>::open_commitments(
|
|
&mut transcript_p,
|
|
&pedersen_params,
|
|
&fw_123,
|
|
&phi_123,
|
|
T_123,
|
|
rT_123,
|
|
&cmT_123,
|
|
);
|
|
let v = NIFS::<G1Affine>::verify_commitments(
|
|
&mut transcript_v,
|
|
&pedersen_params,
|
|
phi_123,
|
|
cmT_123,
|
|
cmE_proof,
|
|
cmW_proof,
|
|
cmT_proof,
|
|
);
|
|
assert!(v);
|
|
}
|
|
|
|
#[test]
|
|
fn test_nifs_interface() {
|
|
let mut rng = ark_std::test_rng();
|
|
let pedersen_params = Pedersen::<G1Affine>::new_params(&mut rng, 100); // 100 is wip, will get it from actual vec
|
|
|
|
let (r1cs, w1, w2, _, x1, x2, _) = gen_test_values(&mut rng);
|
|
let (A, B, C) = (r1cs.A.clone(), r1cs.B.clone(), r1cs.C.clone());
|
|
|
|
let r = Fr::rand(&mut rng); // this would come from the transcript
|
|
|
|
let fw1 = FWit::<G1Affine>::new(w1.clone(), A.len());
|
|
let fw2 = FWit::<G1Affine>::new(w2.clone(), A.len());
|
|
|
|
// init Prover's transcript
|
|
let mut transcript_p: Transcript<Fr> = Transcript::<Fr>::new();
|
|
|
|
// NIFS.P
|
|
let (fw3, phi1, phi2, T, cmT) =
|
|
NIFS::<G1Affine>::P(&mut transcript_p, &pedersen_params, r, &r1cs, fw1, fw2);
|
|
|
|
// init Verifier's transcript
|
|
let mut transcript_v: Transcript<Fr> = Transcript::<Fr>::new();
|
|
|
|
// NIFS.V
|
|
let phi3 = NIFS::<G1Affine>::V(r, &phi1, &phi2, &cmT);
|
|
|
|
assert!(NIFS::<G1Affine>::verify(r, &phi1, &phi2, &phi3, &cmT));
|
|
}
|
|
}
|