start preparing grand product argument
This commit is contained in:
Alex Vlasov
parent
cbf95acb11
commit
be62b361ed
@ -1,3 +1,230 @@
|
||||
/// One must prove that for commitments to two polynomials of degree n products of the coefficients
|
||||
/// in those two polynomials are equal (part of the permutation argument)
|
||||
/// in those two polynomials are equal (part of the permutation argument) with additional assumption that
|
||||
/// those coefficients are never equal to zero
|
||||
|
||||
use ff::{Field, PrimeField, PrimeFieldRepr};
|
||||
use pairing::{Engine, CurveProjective, CurveAffine};
|
||||
use std::marker::PhantomData;
|
||||
|
||||
use crate::sonic::srs::SRS;
|
||||
use crate::sonic::util::*;
|
||||
|
||||
#[derive(Clone)]
|
||||
pub struct GrandProductArgument<E: Engine> {
|
||||
c_polynomials: Vec<Vec<E::Fr>>,
|
||||
v_elements: Vec<E::Fr>
|
||||
}
|
||||
|
||||
#[derive(Clone)]
|
||||
pub struct GrandProductProof<E: Engine> {
|
||||
l: E::G1Affine,
|
||||
r: E::G1Affine
|
||||
}
|
||||
|
||||
impl<E: Engine> GrandProductArgument<E> {
|
||||
pub fn new(polynomials: Vec<(Vec<E::Fr>, Vec<E::Fr>)>) -> Self {
|
||||
assert!(polynomials.len() > 0);
|
||||
|
||||
let length = polynomials[0].0.len();
|
||||
let mut c_polynomials = vec![];
|
||||
let mut v_elements = vec![];
|
||||
|
||||
// a_{1..n} = first poly
|
||||
// a_{n+1..2n+1} = b_{1..n} = second poly
|
||||
|
||||
// c_1 = a_1
|
||||
// c_2 = a_2 * c_1 = a_2 * a_1
|
||||
// c_3 = a_3 * c_2 = a_3 * a_2 * a_1
|
||||
// ...
|
||||
// c_n = a_n * c_{n-1} = \prod a_i
|
||||
// a_{n+1} = c_{n-1}^-1
|
||||
// c_{n+1} = 1
|
||||
// c_{n+1} = a_{n+2} * c_{n+1} = a_{n+2}
|
||||
// ...
|
||||
// c_{2n+1} = \prod a_{n+1+i} = \prod b_{i}
|
||||
// v = c_{n}^-1
|
||||
|
||||
// calculate c, serially for now
|
||||
|
||||
for p in polynomials.iter() {
|
||||
assert!(p.0.len() == p.1.len());
|
||||
assert!(p.0.len() == length);
|
||||
let mut c_poly: Vec<E::Fr> = Vec::with_capacity(2*length + 1);
|
||||
let mut c_coeff = E::Fr::one();
|
||||
// add a
|
||||
for a in p.0.iter() {
|
||||
c_coeff.mul_assign(a);
|
||||
c_poly.push(c_coeff);
|
||||
}
|
||||
let v = c_coeff.inverse().unwrap();
|
||||
// add c_{n+1}
|
||||
let mut c_coeff = E::Fr::one();
|
||||
c_poly.push(c_coeff);
|
||||
// add b
|
||||
for b in p.1.iter() {
|
||||
c_coeff.mul_assign(b);
|
||||
c_poly.push(c_coeff);
|
||||
}
|
||||
|
||||
assert_eq!(c_poly.len(), 2*length + 1);
|
||||
c_polynomials.push(c_poly);
|
||||
v_elements.push(v);
|
||||
}
|
||||
|
||||
GrandProductArgument {
|
||||
c_polynomials: c_polynomials,
|
||||
v_elements: v_elements
|
||||
}
|
||||
}
|
||||
|
||||
// // Make a commitment to polynomial in a form \sum_{i=1}^{N} a_{i} X^{i} Y^{i}
|
||||
// pub fn commit(&self, srs: &SRS<E>) -> Vec<E::G1Affine> {
|
||||
|
||||
// let mut results = vec![];
|
||||
|
||||
// let n = self.polynomials[0].len();
|
||||
|
||||
// for p in self.polynomials.iter() {
|
||||
// let c = multiexp(
|
||||
// srs.g_positive_x_alpha[0..n].iter(),
|
||||
// p.iter()
|
||||
// ).into_affine();
|
||||
|
||||
// results.push(c);
|
||||
// }
|
||||
|
||||
// results
|
||||
// }
|
||||
|
||||
// pub fn make_argument(self, challenges: Vec<E::Fr>, srs: &SRS<E>) -> WellformednessProof<E> {
|
||||
// let mut polynomials = self.polynomials;
|
||||
// let mut challenges = challenges;
|
||||
|
||||
// let mut p0 = polynomials.pop().unwrap();
|
||||
// let r0 = challenges.pop().unwrap();
|
||||
// let n = p0.len();
|
||||
// mul_polynomial_by_scalar(&mut p0[..], r0);
|
||||
|
||||
// let m = polynomials.len();
|
||||
|
||||
// for _ in 0..m {
|
||||
// let p = polynomials.pop().unwrap();
|
||||
// let r = challenges.pop().unwrap();
|
||||
// mul_add_polynomials(&mut p0[..], & p[..], r);
|
||||
// }
|
||||
|
||||
// let d = srs.d;
|
||||
|
||||
// assert!(n < d);
|
||||
|
||||
// // here the multiplier is x^-d, so largest negative power is -(d - 1), smallest negative power is -(d - n)
|
||||
// let l = multiexp(
|
||||
// srs.g_negative_x[(d - n)..d].iter().rev(),
|
||||
// p0.iter()
|
||||
// ).into_affine();
|
||||
|
||||
// // here the multiplier is x^d-n, so largest positive power is d, smallest positive power is d - n + 1
|
||||
|
||||
// let r = multiexp(
|
||||
// srs.g_positive_x[(d - n + 1)..].iter().rev(),
|
||||
// p0.iter()
|
||||
// ).into_affine();
|
||||
|
||||
// WellformednessProof {
|
||||
// l: l,
|
||||
// r: r
|
||||
// }
|
||||
// }
|
||||
|
||||
// pub fn verify(n: usize, challenges: &Vec<E::Fr>, commitments: &Vec<E::G1Affine>, proof: &WellformednessProof<E>, srs: &SRS<E>) -> bool {
|
||||
// let d = srs.d;
|
||||
|
||||
// let alpha_x_d_precomp = srs.h_positive_x_alpha[d].prepare();
|
||||
// let alpha_x_n_minus_d_precomp = srs.h_negative_x_alpha[d - n].prepare();
|
||||
// let mut h_prep = srs.h_positive_x[0];
|
||||
// h_prep.negate();
|
||||
// let h_prep = h_prep.prepare();
|
||||
|
||||
// let a = multiexp(
|
||||
// commitments.iter(),
|
||||
// challenges.iter(),
|
||||
// ).into_affine();
|
||||
|
||||
// let a = a.prepare();
|
||||
|
||||
// let valid = E::final_exponentiation(&E::miller_loop(&[
|
||||
// (&a, &h_prep),
|
||||
// (&proof.l.prepare(), &alpha_x_d_precomp)
|
||||
// ])).unwrap() == E::Fqk::one();
|
||||
|
||||
// if !valid {
|
||||
// return false;
|
||||
// }
|
||||
|
||||
// let valid = E::final_exponentiation(&E::miller_loop(&[
|
||||
// (&a, &h_prep),
|
||||
// (&proof.r.prepare(), &alpha_x_n_minus_d_precomp)
|
||||
// ])).unwrap() == E::Fqk::one();
|
||||
|
||||
// if !valid {
|
||||
// return false;
|
||||
// }
|
||||
|
||||
// true
|
||||
// }
|
||||
}
|
||||
|
||||
// #[test]
|
||||
// fn test_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 n: usize = 1 << 16;
|
||||
// let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
// let coeffs = (0..n).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
// let argument = WellformednessArgument::new(vec![coeffs]);
|
||||
// let challenges = (0..1).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
// let commitments = argument.commit(&srs);
|
||||
|
||||
// let proof = argument.make_argument(challenges.clone(), &srs);
|
||||
|
||||
// let valid = WellformednessArgument::verify(n, &challenges, &commitments, &proof, &srs);
|
||||
|
||||
// assert!(valid);
|
||||
// }
|
||||
|
||||
// #[test]
|
||||
// fn test_argument_soundness() {
|
||||
// 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 n: usize = 1 << 16;
|
||||
// let rng = &mut XorShiftRng::from_seed([0x3dbe6259, 0x8d313d76, 0x3237db17, 0xe5bc0654]);
|
||||
// let coeffs = (0..n).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
// let argument = WellformednessArgument::new(vec![coeffs]);
|
||||
// let commitments = argument.commit(&srs);
|
||||
|
||||
// let coeffs = (0..n).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
// let argument = WellformednessArgument::new(vec![coeffs]);
|
||||
// let challenges = (0..1).map(|_| Fr::rand(rng)).collect::<Vec<_>>();
|
||||
|
||||
// let proof = argument.make_argument(challenges.clone(), &srs);
|
||||
|
||||
// let valid = WellformednessArgument::verify(n, &challenges, &commitments, &proof, &srs);
|
||||
|
||||
// assert!(!valid);
|
||||
// }
|
||||
|
||||
|
||||
@ -3,5 +3,8 @@
|
||||
/// s1(X, Y) = ...
|
||||
/// s1 part requires grand product and permutation arguments, that are also implemented
|
||||
|
||||
pub mod s2_proof;
|
||||
mod wellformed_argument;
|
||||
mod s2_proof;
|
||||
mod wellformed_argument;
|
||||
mod coefficient_product_argument;
|
||||
|
||||
pub use self::wellformed_argument::{WellformednessArgument, WellformednessProof};
|
||||
Loading…
Reference in New Issue
Block a user