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use ark_ec::AffineRepr;
use ark_ff::fields::PrimeField;
use ark_std::{
rand::{Rng, RngCore},
UniformRand,
};
use ark_std::{One, Zero};
use std::marker::PhantomData;
use crate::pedersen::{Commitment, Params as PedersenParams, Pedersen, Proof as PedersenProof};
use crate::transcript::Transcript;
use crate::utils::*;
pub struct R1CS<F: PrimeField> {
pub A: Vec<Vec<F>>,
pub B: Vec<Vec<F>>,
pub C: Vec<Vec<F>>,
}
// Phi: φ in the paper (later 𝖴), a folded instance
pub struct Phi<C: AffineRepr> {
cmE: Commitment<C>,
u: C::ScalarField,
cmW: Commitment<C>,
x: Vec<C::ScalarField>,
}
// FWit: Folded Witness
pub struct FWit<C: AffineRepr> {
E: Vec<C::ScalarField>,
rE: C::ScalarField,
W: Vec<C::ScalarField>,
rW: C::ScalarField,
}
impl<C: AffineRepr> FWit<C> {
pub fn new(z: Vec<C::ScalarField>, e_len: usize) -> Self {
FWit::<C> {
E: vec![C::ScalarField::zero(); e_len],
rE: C::ScalarField::one(),
W: z,
rW: C::ScalarField::one(),
}
}
pub fn commit(&self, params: &PedersenParams<C>) -> Phi<C> {
let cmE = Pedersen::commit(¶ms, &self.E, &self.rE);
let cmW = Pedersen::commit(¶ms, &self.W, &self.rW);
Phi {
cmE,
u: C::ScalarField::one(),
cmW,
x: self.W.clone(),
}
}
}
pub struct NIFS<C: AffineRepr> {
_phantom: PhantomData<C>,
}
impl<C: AffineRepr> NIFS<C> {
// comp_T: compute cross-terms T
pub fn comp_T(
r1cs: &R1CS<C::ScalarField>,
u1: C::ScalarField,
u2: C::ScalarField,
z1: &Vec<C::ScalarField>,
z2: &Vec<C::ScalarField>,
) -> Vec<C::ScalarField> {
let (A, B, C) = (r1cs.A.clone(), r1cs.B.clone(), r1cs.C.clone());
// this is parallelizable (for the future)
let Az1 = matrix_vector_product(&A, &z1);
let Bz1 = matrix_vector_product(&B, &z1);
let Cz1 = matrix_vector_product(&C, &z1);
let Az2 = matrix_vector_product(&A, &z2);
let Bz2 = matrix_vector_product(&B, &z2);
let Cz2 = matrix_vector_product(&C, &z2);
let Az1_Bz2 = hadamard_product(Az1, Bz2);
let Az2_Bz1 = hadamard_product(Az2, Bz1);
let u1Cz2 = vector_elem_product(&Cz2, &u1);
let u2Cz1 = vector_elem_product(&Cz1, &u2);
// let T = vec_sub(vec_sub(vec_add(Az1_Bz2, Az2_Bz1), u1Cz2), u2Cz1);
let T = ((Ve(Az1_Bz2) + Ve(Az2_Bz1)) - Ve(u1Cz2)) - Ve(u2Cz1);
T.0
}
pub fn fold_witness(
r: C::ScalarField,
fw1: &FWit<C>,
fw2: &FWit<C>,
T: &Vec<C::ScalarField>,
rT: C::ScalarField,
) -> FWit<C> {
let r2 = r * r;
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;
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));
}
}
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