use ark_ec::AffineRepr;
|
|
use ark_std::{One, Zero};
|
|
use std::marker::PhantomData;
|
|
|
|
use crate::pedersen::{Commitment, 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 do not contain Commitment, only Commitment.cm (without the randomness)
|
|
u: C::ScalarField,
|
|
cmW: Commitment<C>, // TODO same as in cmE
|
|
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 commit(&self, params: &PedersenParams<C>, x: &Vec<C::ScalarField>) -> 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: x.clone(),
|
|
}
|
|
}
|
|
}
|
|
|
|
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 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, &cs1.u);
|
|
let u2Cz1 = vector_elem_product(&Cz1, &cs2.u);
|
|
|
|
// 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,
|
|
}
|
|
}
|
|
}
|
|
|
|
#[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 (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],
|
|
]);
|
|
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(),
|
|
B: B.clone(),
|
|
C: C.clone(),
|
|
}
|
|
.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 pedersen_params = Pedersen::<G1Affine>::new_params(&mut rng, 100); // 100 is wip, will get it from actual vec
|
|
let rT: Fr = Fr::rand(&mut rng);
|
|
let cmT = Pedersen::commit(&pedersen_params, &T, &rT);
|
|
|
|
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::one(),
|
|
W: z1,
|
|
rW: Fr::one(),
|
|
};
|
|
let fw2 = FWit::<G1Affine> {
|
|
E: vec![Fr::zero(); T.len()],
|
|
rE: Fr::one(),
|
|
W: z2,
|
|
rW: Fr::one(),
|
|
};
|
|
|
|
// fold witness
|
|
let fw3 = NIFS::<G1Affine>::fold_witness(r, &fw1, &fw2, T, rT);
|
|
|
|
// get committed instances
|
|
let phi1 = fw1.commit(&pedersen_params, &x1); // wip
|
|
let phi2 = fw2.commit(&pedersen_params, &x2);
|
|
|
|
// 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
|
|
// witnesses and committing into it
|
|
let x3 = vec_add(&x1, &vector_elem_product(&x2, &r));
|
|
// use folded rE, rW to commit fw3
|
|
let phi3_expected = fw3.commit(&pedersen_params, &x3);
|
|
assert_eq!(phi3_expected.cmE.0, phi3.cmE.0);
|
|
assert_eq!(phi3_expected.cmW.0, phi3.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 phi3.cmE and phi3.cmW
|
|
let phi3_cmE_proof = Pedersen::prove(
|
|
&pedersen_params,
|
|
&mut transcript_p,
|
|
&phi3.cmE,
|
|
fw3.E,
|
|
fw3.rE,
|
|
);
|
|
let v = Pedersen::verify(
|
|
&pedersen_params,
|
|
&mut transcript_v,
|
|
phi3.cmE,
|
|
phi3_cmE_proof,
|
|
);
|
|
|
|
let phi3_cmW_proof = Pedersen::prove(
|
|
&pedersen_params,
|
|
&mut transcript_p,
|
|
&phi3.cmW,
|
|
fw3.W,
|
|
fw3.rW,
|
|
);
|
|
let v = Pedersen::verify(
|
|
&pedersen_params,
|
|
&mut transcript_v,
|
|
phi3.cmW,
|
|
phi3_cmW_proof,
|
|
);
|
|
}
|
|
}
|