permutation argument is complete
This commit is contained in:
Alex Vlasov
parent
0a2ed705dc
commit
04454890b9
@ -112,6 +112,24 @@ impl<E: Engine> GrandProductArgument<E> {
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).into_affine()
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}
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// Make a commitment to a polynomial in a form A*B^{x+1} = [a_1...a_{n}, 0, b_1...b_{n}]
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pub fn commit_for_individual_products(a: &[E::Fr], b: &[E::Fr], srs: &SRS<E>) -> (E::G1Affine, E::G1Affine) {
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assert_eq!(a.len(), b.len());
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let n = a.len();
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let a = multiexp(
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srs.g_positive_x_alpha[0..n].iter(),
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a.iter()).into_affine();
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let b = multiexp(
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srs.g_positive_x_alpha[0..n].iter(),
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b.iter()).into_affine();
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(a, b)
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}
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pub fn open_commitments_for_grand_product(&self, y: E::Fr, z: E::Fr, srs: &SRS<E>) -> Vec<(E::Fr, E::G1Affine)> {
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let n = self.n;
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@ -288,7 +306,6 @@ impl<E: Engine> GrandProductArgument<E> {
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c
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}
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// Argument is based on an approach of main SONIC construction, but with a custom S(X,Y) polynomial of a simple form
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pub fn make_argument(self, a_zy: & Vec<E::Fr>, challenges: & Vec<E::Fr>, y: E::Fr, z: E::Fr, srs: &SRS<E>) -> GrandProductProof<E> {
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assert_eq!(a_zy.len(), self.a_polynomials.len());
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@ -8,6 +8,8 @@ use std::marker::PhantomData;
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use crate::sonic::srs::SRS;
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use crate::sonic::util::*;
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use super::wellformed_argument::{WellformednessArgument, WellformednessProof};
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use super::grand_product_argument::{GrandProductArgument, GrandProductProof};
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#[derive(Clone)]
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pub struct SpecializedSRS<E: Engine> {
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@ -22,6 +24,7 @@ pub struct SpecializedSRS<E: Engine> {
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pub struct PermutationArgument<E: Engine> {
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non_permuted_coefficients: Vec<Vec<E::Fr>>,
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permuted_coefficients: Vec<Vec<E::Fr>>,
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permuted_at_y_coefficients: Vec<Vec<E::Fr>>,
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permutations: Vec<Vec<usize>>,
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n: usize
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}
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@ -33,12 +36,20 @@ pub struct PermutationProof<E: Engine> {
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f_opening: E::G1Affine,
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}
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#[derive(Clone)]
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pub struct Proof<E: Engine> {
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j: usize,
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s_opening: E::G1Affine,
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s_zy: E::Fr
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}
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fn permute<F: Field>(coeffs: &[F], permutation: & [usize]) -> Vec<F>{
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assert_eq!(coeffs.len(), permutation.len());
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let mut result: Vec<F> = vec![F::zero(); coeffs.len()];
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for (i, j) in permutation.iter().enumerate() {
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result[*j] = coeffs[i];
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result[*j - 1] = coeffs[i];
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}
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result
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}
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@ -58,6 +69,7 @@ impl<E: Engine> PermutationArgument<E> {
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PermutationArgument {
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non_permuted_coefficients: coefficients,
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permuted_coefficients: vec![vec![]],
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permuted_at_y_coefficients: vec![vec![]],
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permutations: permutations,
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n: n
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}
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@ -128,6 +140,7 @@ impl<E: Engine> PermutationArgument<E> {
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let n = self.non_permuted_coefficients[0].len();
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let mut permuted_coefficients = vec![];
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let mut permuted_at_y_coefficients = vec![];
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for (c, p) in self.non_permuted_coefficients.iter().zip(self.permutations.iter()) {
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let mut non_permuted = c.clone();
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@ -144,14 +157,22 @@ impl<E: Engine> PermutationArgument<E> {
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result.push((s, s_prime));
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permuted_coefficients.push(permuted);
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permuted_at_y_coefficients.push(permuted_at_y);
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}
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self.permuted_coefficients = permuted_coefficients;
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self.permuted_at_y_coefficients = permuted_at_y_coefficients;
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result
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}
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pub fn open_commitments_to_s(&self, challenges: &Vec<E::Fr>, y: E::Fr, z_prime: E::Fr, srs: &SRS<E>) -> PermutationProof<E> {
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pub fn open_commitments_to_s_prime(
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&self,
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challenges: &Vec<E::Fr>,
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y: E::Fr,
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z_prime: E::Fr,
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srs: &SRS<E>
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) -> PermutationProof<E> {
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let n = self.non_permuted_coefficients[0].len();
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let mut yz = y;
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@ -168,7 +189,7 @@ impl<E: Engine> PermutationArgument<E> {
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} else {
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let mut poly = p.clone();
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mul_polynomial_by_scalar(&mut poly[..], *r);
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polynomial = Some(poly);
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}
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}
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@ -178,7 +199,7 @@ impl<E: Engine> PermutationArgument<E> {
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let mut v_neg = v;
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v_neg.negate();
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let e = polynomial_commitment_opening(
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let f = polynomial_commitment_opening(
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0,
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n,
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Some(v_neg).iter().chain_ext(polynomial.iter()),
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@ -188,7 +209,7 @@ impl<E: Engine> PermutationArgument<E> {
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mut_distribute_consequitive_powers(&mut polynomial[..], y, y);
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let f = polynomial_commitment_opening(
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let e = polynomial_commitment_opening(
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0,
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n,
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Some(v_neg).iter().chain_ext(polynomial.iter()),
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@ -203,268 +224,164 @@ impl<E: Engine> PermutationArgument<E> {
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}
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}
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// // Make a commitment for the begining of the protocol, returns commitment and `v` scalar
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// pub fn commit_to_individual_c_polynomials(&self, srs: &SRS<E>) -> Vec<(E::G1Affine, E::Fr)> {
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// let mut results = vec![];
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// let n = self.c_polynomials[0].len();
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// for (p, v) in self.c_polynomials.iter().zip(self.v_elements.iter()) {
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// let c = multiexp(
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// srs.g_positive_x_alpha[0..n].iter(),
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// p.iter()
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// ).into_affine();
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// results.push((c, *v));
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// }
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// results
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// }
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// // Argument is based on an approach of main SONIC construction, but with a custom S(X,Y) polynomial of a simple form
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// pub fn commit_to_t_polynomial(&mut self, challenges: & Vec<E::Fr>, y: E::Fr, srs: &SRS<E>) -> E::G1Affine {
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// assert_eq!(challenges.len(), self.a_polynomials.len());
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// let n = self.n;
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// let mut t_polynomial: Option<Vec<E::Fr>> = None;
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// for (((a, c), v), challenge) in self.a_polynomials.iter()
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// .zip(self.c_polynomials.iter())
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// .zip(self.v_elements.iter())
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// .zip(challenges.iter())
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// {
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// let mut a_xy = a.clone();
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// let mut c_xy = c.clone();
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// let v = *v;
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// assert_eq!(a_xy.len(), 2*n + 1);
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// assert_eq!(c_xy.len(), 2*n + 1);
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// // make a T polynomial
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// let r: Vec<E::Fr> = {
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// // p_a(X,Y)*Y
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// let mut tmp = y;
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// tmp.square();
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// mut_distribute_consequitive_powers(&mut a_xy[..], tmp, y);
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// // add extra terms
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// //v*(XY)^{n+1}*Y + X^{n+2} + X^{n+1}Y − X^{2n+2}*Y
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// // n+1 term v*(XY)^{n+1}*Y + X^{n+1}Y
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// let tmp = y.pow(&[(n+2) as u64]);
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// let mut x_n_plus_one_term = v;
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// x_n_plus_one_term.mul_assign(&tmp);
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// x_n_plus_one_term.add_assign(&y);
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// a_xy[n].add_assign(&x_n_plus_one_term);
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// // n+2 term
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// a_xy[n+1].add_assign(&E::Fr::one());
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// // 2n+2 term
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// let mut tmp = y;
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// tmp.negate();
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// a_xy.push(tmp);
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// assert_eq!(a_xy.len(), 2*n + 2);
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// let mut r = vec![E::Fr::zero(); 2*n + 3];
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// r.extend(a_xy);
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// r
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// };
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// let r_prime: Vec<E::Fr> = {
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// let mut c_prime: Vec<E::Fr> = c_xy.iter().rev().map(|el| *el).collect();
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// c_prime.push(E::Fr::one());
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// c_prime.push(E::Fr::zero());
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// assert_eq!(c_prime.len(), 2*n + 3);
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// c_prime
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// };
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// // multiply polynomials with powers [-2n-2, -1] and [1, 2n+2],
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// // expect result to be [-2n+1, 2n+1]
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// let mut t: Vec<E::Fr> = multiply_polynomials::<E>(r, r_prime);
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// assert_eq!(t.len(), 6*n + 7);
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// // drain first powers due to the padding and last element due to requirement of being zero
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// for (i, el) in t[0..(2*n+3)].iter().enumerate() {
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// assert_eq!(*el, E::Fr::zero(), "{}", format!("Element {} is non-zero", i));
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// }
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// t.drain(0..(2*n+3));
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// let last = t.pop();
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// assert_eq!(last.unwrap(), E::Fr::zero(), "last element should be zero");
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// assert_eq!(t.len(), 4*n + 3);
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// let mut val = {
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// let mut tmp = y;
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// tmp.square();
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// evaluate_at_consequitive_powers(&c_xy, tmp, y)
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// };
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// val.add_assign(&E::Fr::one());
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// // subtract at constant term
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// assert_eq!(t[2*n+1], val);
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// t[2*n+1].sub_assign(&val);
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// if t_polynomial.is_some() {
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// if let Some(t_poly) = t_polynomial.as_mut() {
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// mul_add_polynomials(&mut t_poly[..], &t, *challenge);
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// }
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// } else {
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// mul_polynomial_by_scalar(&mut t, *challenge);
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// t_polynomial = Some(t);
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// }
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// }
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// let t_polynomial = t_polynomial.unwrap();
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// let c = multiexp(srs.g_negative_x_alpha[0..(2*n+1)].iter().rev()
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// .chain_ext(srs.g_positive_x_alpha[0..(2*n+1)].iter()),
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// t_polynomial[0..(2*n+1)].iter()
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// .chain_ext(t_polynomial[(2*n+2)..].iter())).into_affine();
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// self.t_polynomial = Some(t_polynomial);
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// c
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// }
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// // Argument is based on an approach of main SONIC construction, but with a custom S(X,Y) polynomial of a simple form
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// pub fn make_argument(self, a_zy: & Vec<E::Fr>, challenges: & Vec<E::Fr>, y: E::Fr, z: E::Fr, srs: &SRS<E>) -> GrandProductProof<E> {
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// assert_eq!(a_zy.len(), self.a_polynomials.len());
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// assert_eq!(challenges.len(), self.a_polynomials.len());
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// let n = self.n;
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// let c_polynomials = self.c_polynomials;
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// let mut e_polynomial: Option<Vec<E::Fr>> = None;
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// let mut f_polynomial: Option<Vec<E::Fr>> = None;
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// let mut yz = y;
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// yz.mul_assign(&z);
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// let z_inv = z.inverse().unwrap();
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// for (((a, c), challenge), v) in a_zy.iter()
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// .zip(c_polynomials.into_iter())
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// .zip(challenges.iter())
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// .zip(self.v_elements.iter())
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// {
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// // cj = ((aj + vj(yz)n+1)y + zn+2 + zn+1y − z2n+2y)z−1
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// let mut c_zy = yz.pow([(n + 1) as u64]);
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// c_zy.mul_assign(v);
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// c_zy.add_assign(a);
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// c_zy.mul_assign(&y);
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// let mut z_n_plus_1 = z.pow([(n + 1) as u64]);
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// let mut z_n_plus_2 = z_n_plus_1;
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// z_n_plus_2.mul_assign(&z);
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// let mut z_2n_plus_2 = z_n_plus_1;
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// z_2n_plus_2.square();
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// z_2n_plus_2.mul_assign(&y);
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// z_n_plus_1.mul_assign(&y);
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// c_zy.add_assign(&z_n_plus_1);
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// c_zy.add_assign(&z_n_plus_2);
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// c_zy.sub_assign(&z_2n_plus_2);
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// c_zy.mul_assign(&z_inv);
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// let mut rc = c_zy;
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// rc.mul_assign(challenge);
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// let mut ry = y;
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// ry.mul_assign(challenge);
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// if e_polynomial.is_some() && f_polynomial.is_some() {
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// if let Some(e_poly) = e_polynomial.as_mut() {
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// if let Some(f_poly) = f_polynomial.as_mut() {
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// mul_add_polynomials(&mut e_poly[..], &c, rc);
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// mul_add_polynomials(&mut f_poly[..], &c, ry);
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// }
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// }
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// } else {
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// let mut e = c.clone();
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// let mut f = c;
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// mul_polynomial_by_scalar(&mut e, rc);
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// mul_polynomial_by_scalar(&mut f, ry);
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// e_polynomial = Some(e);
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// f_polynomial = Some(f);
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// }
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// }
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// let e_polynomial = e_polynomial.unwrap();
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// let f_polynomial = f_polynomial.unwrap();
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// // evaluate e at z^-1
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// let mut e_val = evaluate_at_consequitive_powers(&e_polynomial, z_inv, z_inv);
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// e_val.negate();
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// // evaluate f at y
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// let mut f_val = evaluate_at_consequitive_powers(&f_polynomial, y, y);
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// f_val.negate();
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// let e_opening = polynomial_commitment_opening(
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// 0,
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// 2*n + 1,
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// Some(e_val).iter().chain_ext(e_polynomial.iter()),
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// z_inv,
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// srs);
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// let f_opening = polynomial_commitment_opening(
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// 0,
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// 2*n + 1,
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// Some(f_val).iter().chain_ext(f_polynomial.iter()),
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// y,
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// srs);
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// e_val.negate();
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// f_val.negate();
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// let mut t_poly = self.t_polynomial.unwrap();
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// assert_eq!(t_poly.len(), 4*n + 3);
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// // largest negative power of t is -2n-1
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// let t_zy = {
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// let tmp = z_inv.pow([(2*n+1) as u64]);
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// evaluate_at_consequitive_powers(&t_poly, tmp, z)
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// };
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// t_poly[2*n + 1].sub_assign(&t_zy);
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// let t_opening = polynomial_commitment_opening(
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// 2*n + 1,
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// 2*n + 1,
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// t_poly.iter(),
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// z,
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// srs);
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// GrandProductProof {
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// t_opening: t_opening,
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// e_zinv: e_val,
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// e_opening: e_opening,
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// f_y: f_val,
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// f_opening: f_opening,
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// }
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// }
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pub fn verify_s_prime_commitment(n: usize,
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// Argument a permutation argument. Current implementation consumes, cause extra arguments are required
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pub fn make_argument(self,
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beta: E::Fr,
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gamma: E::Fr,
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grand_product_challenges: & Vec<E::Fr>,
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wellformed_challenges: & Vec<E::Fr>,
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y: E::Fr,
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z: E::Fr,
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specialized_srs: &SpecializedSRS<E>,
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srs: &SRS<E>
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) -> Proof<E> {
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// Sj(P4j)β(P1j)γ is equal to the product of the coefficients of Sj′(P3j)β(P1j)γ
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// also open s = \sum self.permuted_coefficients(X, y) at z
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let n = self.n;
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let j = self.non_permuted_coefficients.len();
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assert_eq!(j, grand_product_challenges.len());
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assert_eq!(2*j, wellformed_challenges.len());
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let mut s_polynomial: Option<Vec<E::Fr>> = None;
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for c in self.permuted_at_y_coefficients.iter()
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{
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if s_polynomial.is_some() {
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if let Some(poly) = s_polynomial.as_mut() {
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add_polynomials(&mut poly[..], & c[..]);
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}
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} else {
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s_polynomial = Some(c.clone());
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}
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}
|
||||
let mut s_polynomial = s_polynomial.unwrap();
|
||||
// evaluate at z
|
||||
let s_zy = evaluate_at_consequitive_powers(& s_polynomial[..], z, z);
|
||||
|
||||
let mut s_zy_neg = s_zy;
|
||||
s_zy_neg.negate();
|
||||
|
||||
let s_zy_opening = polynomial_commitment_opening(
|
||||
0,
|
||||
n,
|
||||
Some(s_zy_neg).iter().chain_ext(s_polynomial.iter()),
|
||||
z,
|
||||
&srs
|
||||
);
|
||||
|
||||
// Sj(P4j)^β (P1j)^γ is equal to the product of the coefficients of Sj′(P3j)^β (P1j)^γ
|
||||
|
||||
let p_1_values = vec![E::Fr::one(); n];
|
||||
let p_3_values: Vec<E::Fr> = (1..=n).map(|el| {
|
||||
let mut repr = <<E as ScalarEngine>::Fr as PrimeField>::Repr::default();
|
||||
repr.as_mut()[0] = el as u64;
|
||||
let fe = E::Fr::from_repr(repr).unwrap();
|
||||
|
||||
fe
|
||||
}).collect();
|
||||
|
||||
let mut grand_products = vec![];
|
||||
|
||||
for (i, ((non_permuted, permuted), permutation)) in self.non_permuted_coefficients.into_iter()
|
||||
.zip(self.permuted_coefficients.into_iter())
|
||||
.zip(self.permutations.into_iter()).enumerate()
|
||||
|
||||
{
|
||||
// \prod si+βσi+γ = \prod s'i + β*i + γ
|
||||
let mut s_j_combination = non_permuted;
|
||||
{
|
||||
let p_4_values: Vec<E::Fr> = permutation.into_iter().map(|el| {
|
||||
let mut repr = <<E as ScalarEngine>::Fr as PrimeField>::Repr::default();
|
||||
repr.as_mut()[0] = el as u64;
|
||||
let fe = E::Fr::from_repr(repr).unwrap();
|
||||
|
||||
fe
|
||||
}).collect();
|
||||
mul_add_polynomials(&mut s_j_combination[..], & p_4_values[..], beta);
|
||||
mul_add_polynomials(&mut s_j_combination[..], & p_1_values[..], gamma);
|
||||
}
|
||||
|
||||
let mut s_prime_j_combination = permuted;
|
||||
{
|
||||
mul_add_polynomials(&mut s_prime_j_combination[..], & p_3_values[..], beta);
|
||||
mul_add_polynomials(&mut s_prime_j_combination[..], & p_1_values[..], gamma);
|
||||
}
|
||||
|
||||
grand_products.push((s_j_combination, s_prime_j_combination));
|
||||
}
|
||||
|
||||
let mut a_commitments = vec![];
|
||||
let mut b_commitments = vec![];
|
||||
|
||||
for (a, b) in grand_products.iter() {
|
||||
let (c_a, c_b) = GrandProductArgument::commit_for_individual_products(& a[..], & b[..], &srs);
|
||||
a_commitments.push(c_a);
|
||||
b_commitments.push(c_b);
|
||||
}
|
||||
|
||||
{
|
||||
let mut all_polys = vec![];
|
||||
for p in grand_products.iter() {
|
||||
let (a, b) = p;
|
||||
all_polys.push(a.clone());
|
||||
all_polys.push(b.clone());
|
||||
}
|
||||
|
||||
let wellformed_argument = WellformednessArgument::new(all_polys);
|
||||
let commitments = wellformed_argument.commit(&srs);
|
||||
let proof = wellformed_argument.make_argument(wellformed_challenges.clone(), &srs);
|
||||
let valid = WellformednessArgument::verify(n, &wellformed_challenges, &commitments, &proof, &srs);
|
||||
|
||||
assert!(valid, "wellformedness argument must be valid");
|
||||
}
|
||||
|
||||
let mut grand_product_argument = GrandProductArgument::new(grand_products);
|
||||
let c_commitments = grand_product_argument.commit_to_individual_c_polynomials(&srs);
|
||||
let t_commitment = grand_product_argument.commit_to_t_polynomial(&grand_product_challenges, y, &srs);
|
||||
let grand_product_openings = grand_product_argument.open_commitments_for_grand_product(y, z, &srs);
|
||||
let a_zy: Vec<E::Fr> = grand_product_openings.iter().map(|el| el.0.clone()).collect();
|
||||
let proof = grand_product_argument.make_argument(&a_zy, &grand_product_challenges, y, z, &srs);
|
||||
|
||||
{
|
||||
use rand::{XorShiftRng, SeedableRng, Rand, Rng};
|
||||
let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
let randomness = (0..j).map(|_| E::Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
let valid = GrandProductArgument::verify_ab_commitment(n,
|
||||
&randomness,
|
||||
&a_commitments,
|
||||
& b_commitments,
|
||||
&grand_product_openings,
|
||||
y,
|
||||
z,
|
||||
&srs);
|
||||
assert!(valid, "ab part of grand product argument must be valid");
|
||||
|
||||
let randomness = (0..3).map(|_| E::Fr::rand(rng)).collect::<Vec<_>>();
|
||||
let valid = GrandProductArgument::verify(n,
|
||||
&randomness,
|
||||
&a_zy,
|
||||
&grand_product_challenges,
|
||||
t_commitment,
|
||||
&c_commitments,
|
||||
&proof,
|
||||
y,
|
||||
z,
|
||||
&srs);
|
||||
|
||||
assert!(valid, "grand product argument must be valid");
|
||||
}
|
||||
|
||||
Proof {
|
||||
j: j,
|
||||
s_opening: s_zy_opening,
|
||||
s_zy: s_zy
|
||||
}
|
||||
}
|
||||
|
||||
pub fn verify_s_prime_commitment(
|
||||
n: usize,
|
||||
randomness: & Vec<E::Fr>,
|
||||
challenges: & Vec<E::Fr>,
|
||||
commitments: &Vec<E::G1Affine>,
|
||||
@ -477,6 +394,82 @@ impl<E: Engine> PermutationArgument<E> {
|
||||
assert_eq!(randomness.len(), 2);
|
||||
assert_eq!(challenges.len(), commitments.len());
|
||||
|
||||
// let g = srs.g_positive_x[0];
|
||||
|
||||
// let h_alpha_x_precomp = srs.h_positive_x_alpha[1].prepare();
|
||||
|
||||
// let h_alpha_precomp = srs.h_positive_x_alpha[0].prepare();
|
||||
|
||||
// let mut h_prep = srs.h_positive_x[0];
|
||||
// h_prep.negate();
|
||||
// let h_prep = h_prep.prepare();
|
||||
|
||||
// let value = proof.v_zy;
|
||||
// let g_v = g.mul(value.into_repr());
|
||||
|
||||
// {
|
||||
|
||||
// let mut minus_z_prime = z_prime;
|
||||
// minus_z_prime.negate();
|
||||
|
||||
// let e_z = proof.e_opening.mul(minus_z_prime.into_repr());
|
||||
|
||||
// let mut h_alpha_term = e_z;
|
||||
|
||||
// h_alpha_term.add_assign(&g_v);
|
||||
|
||||
// let h_alpha_x_term = proof.e_opening;
|
||||
|
||||
// let s_r = multiexp(
|
||||
// commitments.iter(),
|
||||
// challenges.iter()
|
||||
// ).into_affine();
|
||||
|
||||
// let h_term = s_r;
|
||||
|
||||
// let valid = E::final_exponentiation(&E::miller_loop(&[
|
||||
// (&h_alpha_x_term.prepare(), &h_alpha_x_precomp),
|
||||
// (&h_alpha_term.into_affine().prepare(), &h_alpha_precomp),
|
||||
// (&h_term.prepare(), &h_prep),
|
||||
// ])).unwrap() == E::Fqk::one();
|
||||
|
||||
// if !valid {
|
||||
// return false;
|
||||
// }
|
||||
// }
|
||||
// {
|
||||
// let mut minus_yz = z_prime;
|
||||
// minus_yz.mul_assign(&y);
|
||||
// minus_yz.negate();
|
||||
|
||||
// let f_yz = proof.f_opening.mul(minus_yz.into_repr());
|
||||
|
||||
// let p2_r = multiexp(
|
||||
// specialized_srs.p_2.iter(),
|
||||
// challenges.iter()
|
||||
// ).into_affine();
|
||||
|
||||
// let mut h_alpha_term = f_yz;
|
||||
|
||||
// h_alpha_term.add_assign(&g_v);
|
||||
|
||||
// let h_alpha_x_term = proof.f_opening;
|
||||
|
||||
// let h_term = p2_r;
|
||||
|
||||
// let valid = E::final_exponentiation(&E::miller_loop(&[
|
||||
// (&h_alpha_x_term.prepare(), &h_alpha_x_precomp),
|
||||
// (&h_alpha_term.into_affine().prepare(), &h_alpha_precomp),
|
||||
// (&h_term.prepare(), &h_prep),
|
||||
// ])).unwrap() == E::Fqk::one();
|
||||
|
||||
// if !valid {
|
||||
// return false;
|
||||
// }
|
||||
// }
|
||||
|
||||
// true
|
||||
|
||||
// e(E,hαx)e(E−z′,hα) = e(Mj=1Sj′rj,h)e(g−v,hα)
|
||||
// e(F,hαx)e(F−yz′,hα) = e(Mj=1P2jrj,h)e(g−v,hα)
|
||||
|
||||
@ -545,217 +538,129 @@ impl<E: Engine> PermutationArgument<E> {
|
||||
])).unwrap() == E::Fqk::one()
|
||||
}
|
||||
|
||||
// pub fn verify(
|
||||
// n: usize,
|
||||
// randomness: & Vec<E::Fr>,
|
||||
// a_zy: & Vec<E::Fr>,
|
||||
// challenges: &Vec<E::Fr>,
|
||||
// t_commitment: E::G1Affine,
|
||||
// commitments: &Vec<(E::G1Affine, E::Fr)>,
|
||||
// proof: &GrandProductProof<E>,
|
||||
// y: E::Fr,
|
||||
// z: E::Fr,
|
||||
// srs: &SRS<E>
|
||||
// ) -> bool {
|
||||
// assert_eq!(randomness.len(), 3);
|
||||
// assert_eq!(a_zy.len(), challenges.len());
|
||||
// assert_eq!(commitments.len(), challenges.len());
|
||||
pub fn verify(
|
||||
s_commitments: &Vec<E::G1Affine>,
|
||||
proof: &Proof<E>,
|
||||
z: E::Fr,
|
||||
srs: &SRS<E>
|
||||
) -> bool {
|
||||
|
||||
// let d = srs.d;
|
||||
let g = srs.g_positive_x[0];
|
||||
|
||||
// let g = srs.g_positive_x[0];
|
||||
let h_alpha_x_precomp = srs.h_positive_x_alpha[1].prepare();
|
||||
|
||||
// let h_alpha_x_precomp = srs.h_positive_x_alpha[1].prepare();
|
||||
let h_alpha_precomp = srs.h_positive_x_alpha[0].prepare();
|
||||
|
||||
// let h_alpha_precomp = srs.h_positive_x_alpha[0].prepare();
|
||||
let mut h_prep = srs.h_positive_x[0];
|
||||
h_prep.negate();
|
||||
let h_prep = h_prep.prepare();
|
||||
|
||||
// let mut h_prep = srs.h_positive_x[0];
|
||||
// h_prep.negate();
|
||||
// let h_prep = h_prep.prepare();
|
||||
let mut minus_z = z;
|
||||
minus_z.negate();
|
||||
|
||||
// // first re-calculate cj and t(z,y)
|
||||
let opening_z = proof.s_opening.mul(minus_z.into_repr());
|
||||
|
||||
// let mut yz = y;
|
||||
// yz.mul_assign(&z);
|
||||
let mut h_alpha_term = opening_z;
|
||||
let g_s = g.mul(proof.s_zy.into_repr());
|
||||
|
||||
// let z_inv = z.inverse().unwrap();
|
||||
h_alpha_term.add_assign(&g_s);
|
||||
|
||||
// let mut t_zy = E::Fr::zero();
|
||||
// t_zy.add_assign(&proof.e_zinv);
|
||||
// t_zy.sub_assign(&proof.f_y);
|
||||
let h_alpha_x_term = proof.s_opening;
|
||||
|
||||
// let mut commitments_points = vec![];
|
||||
// let mut rc_vec = vec![];
|
||||
// let mut ry_vec = vec![];
|
||||
let mut s = E::G1::zero();
|
||||
for p in s_commitments {
|
||||
s.add_assign_mixed(&p);
|
||||
}
|
||||
|
||||
// for ((r, commitment), a) in challenges.iter()
|
||||
// .zip(commitments.iter())
|
||||
// .zip(a_zy.iter()) {
|
||||
// let (c, v) = commitment;
|
||||
// commitments_points.push(c.clone());
|
||||
let h_term = s.into_affine();
|
||||
|
||||
// // cj = ((aj + vj(yz)n+1)y + zn+2 + zn+1y − z2n+2y)z−1
|
||||
// let mut c_zy = yz.pow([(n + 1) as u64]);
|
||||
// c_zy.mul_assign(v);
|
||||
// c_zy.add_assign(a);
|
||||
// c_zy.mul_assign(&y);
|
||||
|
||||
// let mut z_n_plus_1 = z.pow([(n + 1) as u64]);
|
||||
|
||||
// let mut z_n_plus_2 = z_n_plus_1;
|
||||
// z_n_plus_2.mul_assign(&z);
|
||||
|
||||
// let mut z_2n_plus_2 = z_n_plus_1;
|
||||
// z_2n_plus_2.square();
|
||||
// z_2n_plus_2.mul_assign(&y);
|
||||
|
||||
// z_n_plus_1.mul_assign(&y);
|
||||
|
||||
// c_zy.add_assign(&z_n_plus_1);
|
||||
// c_zy.add_assign(&z_n_plus_2);
|
||||
// c_zy.sub_assign(&z_2n_plus_2);
|
||||
|
||||
// c_zy.mul_assign(&z_inv);
|
||||
|
||||
// let mut rc = c_zy;
|
||||
// rc.mul_assign(&r);
|
||||
// rc_vec.push(rc);
|
||||
|
||||
// let mut ry = y;
|
||||
// ry.mul_assign(&r);
|
||||
// ry_vec.push(ry);
|
||||
|
||||
// let mut val = rc;
|
||||
// val.sub_assign(r);
|
||||
// t_zy.add_assign(&val);
|
||||
// }
|
||||
|
||||
// let c_rc = multiexp(
|
||||
// commitments_points.iter(),
|
||||
// rc_vec.iter(),
|
||||
// ).into_affine();
|
||||
|
||||
// let c_ry = multiexp(
|
||||
// commitments_points.iter(),
|
||||
// ry_vec.iter(),
|
||||
// ).into_affine();
|
||||
|
||||
// let mut minus_y = y;
|
||||
// minus_y.negate();
|
||||
|
||||
// let mut f_y = proof.f_opening.mul(minus_y.into_repr());
|
||||
// let g_f = g.mul(proof.f_y.into_repr());
|
||||
// f_y.add_assign(&g_f);
|
||||
|
||||
// let mut minus_z = z;
|
||||
// minus_z.negate();
|
||||
|
||||
// let mut t_z = proof.t_opening.mul(minus_z.into_repr());
|
||||
// let g_tzy = g.mul(t_zy.into_repr());
|
||||
// t_z.add_assign(&g_tzy);
|
||||
|
||||
// let mut minus_z_inv = z_inv;
|
||||
// minus_z_inv.negate();
|
||||
|
||||
// let mut e_z_inv = proof.e_opening.mul(minus_z_inv.into_repr());
|
||||
// let g_e = g.mul(proof.e_zinv.into_repr());
|
||||
// e_z_inv.add_assign(&g_e);
|
||||
|
||||
// let h_alpha_term = multiexp(
|
||||
// vec![e_z_inv.into_affine(), f_y.into_affine(), t_z.into_affine()].iter(),
|
||||
// randomness.iter(),
|
||||
// ).into_affine();
|
||||
|
||||
// let h_alpha_x_term = multiexp(
|
||||
// Some(proof.e_opening).iter()
|
||||
// .chain_ext(Some(proof.f_opening).iter())
|
||||
// .chain_ext(Some(proof.t_opening).iter()),
|
||||
// randomness.iter(),
|
||||
// ).into_affine();
|
||||
|
||||
|
||||
// let h_term = multiexp(
|
||||
// Some(c_rc).iter()
|
||||
// .chain_ext(Some(c_ry).iter())
|
||||
// .chain_ext(Some(t_commitment).iter()),
|
||||
// randomness.iter(),
|
||||
// ).into_affine();
|
||||
|
||||
// E::final_exponentiation(&E::miller_loop(&[
|
||||
// (&h_alpha_x_term.prepare(), &h_alpha_x_precomp),
|
||||
// (&h_alpha_term.prepare(), &h_alpha_precomp),
|
||||
// (&h_term.prepare(), &h_prep),
|
||||
// ])).unwrap() == E::Fqk::one()
|
||||
|
||||
// }
|
||||
E::final_exponentiation(&E::miller_loop(&[
|
||||
(&h_alpha_x_term.prepare(), &h_alpha_x_precomp),
|
||||
(&h_alpha_term.into_affine().prepare(), &h_alpha_precomp),
|
||||
(&h_term.prepare(), &h_prep),
|
||||
])).unwrap() == E::Fqk::one()
|
||||
}
|
||||
}
|
||||
|
||||
// #[test]
|
||||
// fn test_grand_product_argument() {
|
||||
// use pairing::bls12_381::{Fr, G1Affine, G1, Bls12};
|
||||
// use rand::{XorShiftRng, SeedableRng, Rand, Rng};
|
||||
// use crate::sonic::srs::SRS;
|
||||
#[test]
|
||||
fn test_permutation_argument() {
|
||||
use pairing::bls12_381::{Fr, G1Affine, G1, Bls12};
|
||||
use rand::{XorShiftRng, SeedableRng, Rand, Rng};
|
||||
use crate::sonic::srs::SRS;
|
||||
|
||||
// let srs_x = Fr::from_str("23923").unwrap();
|
||||
// let srs_alpha = Fr::from_str("23728792").unwrap();
|
||||
// let srs = SRS::<Bls12>::dummy(830564, srs_x, srs_alpha);
|
||||
let srs_x = Fr::from_str("23923").unwrap();
|
||||
let srs_alpha = Fr::from_str("23728792").unwrap();
|
||||
let srs = SRS::<Bls12>::dummy(830564, srs_x, srs_alpha);
|
||||
|
||||
// let n: usize = 1 << 8;
|
||||
// let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
// let coeffs = (0..n).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
// let mut permutation = coeffs.clone();
|
||||
// rng.shuffle(&mut permutation);
|
||||
let n: usize = 1 << 1;
|
||||
let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
// let coeffs = (0..n).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
// let mut permutation = (0..n).collect::<Vec<_>>();
|
||||
// rng.shuffle(&mut permutation);
|
||||
|
||||
// let a_commitment = multiexp(srs.g_positive_x_alpha[0..n].iter(), coeffs.iter()).into_affine();
|
||||
// let b_commitment = multiexp(srs.g_positive_x_alpha[0..n].iter(), permutation.iter()).into_affine();
|
||||
let coeffs = vec![Fr::from_str("3").unwrap(), Fr::from_str("4").unwrap()];
|
||||
let permutation = vec![2, 1];
|
||||
|
||||
// let mut argument = GrandProductArgument::new(vec![(coeffs, permutation)]);
|
||||
let coeffs = vec![coeffs];
|
||||
let permutations = vec![permutation];
|
||||
|
||||
// let commitments_and_v_values = argument.commit_to_individual_c_polynomials(&srs);
|
||||
let specialized_srs = PermutationArgument::make_specialized_srs(&coeffs, &permutations, &srs);
|
||||
|
||||
// assert_eq!(commitments_and_v_values.len(), 1);
|
||||
let mut argument = PermutationArgument::new(coeffs, permutations);
|
||||
|
||||
// let y : Fr = rng.gen();
|
||||
let y : Fr = rng.gen();
|
||||
let y : Fr = Fr::one();
|
||||
let y : Fr = Fr::from_str("2").unwrap();
|
||||
|
||||
// let challenges = (0..1).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
// let challenges = (0..1).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
// let t_commitment = argument.commit_to_t_polynomial(&challenges, y, &srs);
|
||||
let challenges = vec![Fr::one()];
|
||||
|
||||
// let z : Fr = rng.gen();
|
||||
let commitments = argument.commit(y, &srs);
|
||||
let mut s_commitments = vec![];
|
||||
let mut s_prime_commitments = vec![];
|
||||
for (s, s_prime) in commitments.into_iter() {
|
||||
s_commitments.push(s);
|
||||
s_prime_commitments.push(s_prime);
|
||||
}
|
||||
|
||||
// let grand_product_openings = argument.open_commitments_for_grand_product(y, z, &srs);
|
||||
let z_prime : Fr = rng.gen();
|
||||
let z_prime : Fr = Fr::one();
|
||||
|
||||
// let randomness = (0..1).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
let opening = argument.open_commitments_to_s_prime(&challenges, y, z_prime, &srs);
|
||||
|
||||
// let valid = GrandProductArgument::verify_ab_commitment(n,
|
||||
// &randomness,
|
||||
// &vec![a_commitment],
|
||||
// &vec![b_commitment],
|
||||
// &grand_product_openings,
|
||||
// y,
|
||||
// z,
|
||||
// &srs);
|
||||
let randomness = (0..2).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
// assert!(valid, "grand product commitments should be valid");
|
||||
let valid = PermutationArgument::verify_s_prime_commitment(n,
|
||||
&randomness,
|
||||
&challenges,
|
||||
&s_prime_commitments,
|
||||
&opening,
|
||||
y,
|
||||
z_prime,
|
||||
&specialized_srs,
|
||||
&srs);
|
||||
|
||||
// let a_zy: Vec<Fr> = grand_product_openings.iter().map(|el| el.0.clone()).collect();
|
||||
assert!(valid, "s' commitment must be valid");
|
||||
|
||||
// let proof = argument.make_argument(&a_zy, &challenges, y, z, &srs);
|
||||
let beta : Fr = rng.gen();
|
||||
let gamma : Fr = rng.gen();
|
||||
|
||||
// let randomness = (0..3).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
let grand_product_challenges = (0..1).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
let wellformed_challenges = (0..2).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
// let valid = GrandProductArgument::verify(
|
||||
// n,
|
||||
// &randomness,
|
||||
// &a_zy,
|
||||
// &challenges,
|
||||
// t_commitment,
|
||||
// &commitments_and_v_values,
|
||||
// &proof,
|
||||
// y,
|
||||
// z,
|
||||
// &srs);
|
||||
let z : Fr = rng.gen();
|
||||
|
||||
// assert!(valid, "t commitment should be valid");
|
||||
// }
|
||||
let proof = argument.make_argument(
|
||||
beta,
|
||||
gamma,
|
||||
& grand_product_challenges,
|
||||
& wellformed_challenges,
|
||||
y, z,
|
||||
&specialized_srs, &srs);
|
||||
|
||||
let valid = PermutationArgument::verify(&s_commitments, &proof, z, &srs);
|
||||
|
||||
assert!(valid, "permutation argument must be valid");
|
||||
}
|
||||
|
||||
|
||||
@ -52,6 +52,7 @@ impl<E: Engine> WellformednessArgument<E> {
|
||||
}
|
||||
|
||||
pub fn make_argument(self, challenges: Vec<E::Fr>, srs: &SRS<E>) -> WellformednessProof<E> {
|
||||
assert_eq!(challenges.len(), self.polynomials.len());
|
||||
let mut polynomials = self.polynomials;
|
||||
let mut challenges = challenges;
|
||||
|
||||
@ -165,7 +166,7 @@ fn test_argument_soundness() {
|
||||
let srs_alpha = Fr::from_str("23728792").unwrap();
|
||||
let srs = SRS::<Bls12>::dummy(830564, srs_x, srs_alpha);
|
||||
|
||||
let n: usize = 1 << 16;
|
||||
let n: usize = 1 << 8;
|
||||
let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
let coeffs = (0..n).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user