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// this file contains a sum-check protocol initial implementation, not used by the rest of the repo
// but implemented as an exercise and it will probably be used in the future.
use ark_ec::CurveGroup;
use ark_ff::{BigInteger, PrimeField};
use ark_poly::{
multivariate::{SparsePolynomial, SparseTerm, Term},
DenseMVPolynomial, DenseUVPolynomial, Polynomial,
};
use ark_std::log2;
use ark_std::marker::PhantomData;
use ark_crypto_primitives::sponge::{poseidon::PoseidonConfig, Absorb};
use crate::transcript::Transcript;
pub struct SumCheck<
F: PrimeField + Absorb,
C: CurveGroup,
UV: Polynomial<F> + DenseUVPolynomial<F>,
MV: Polynomial<F> + DenseMVPolynomial<F>,
> {
_f: PhantomData<F>,
_c: PhantomData<C>,
_uv: PhantomData<UV>,
_mv: PhantomData<MV>,
}
impl<
F: PrimeField + Absorb,
C: CurveGroup,
UV: Polynomial<F> + DenseUVPolynomial<F>,
MV: Polynomial<F> + DenseMVPolynomial<F>,
> SumCheck<F, C, UV, MV>
where
<C as CurveGroup>::BaseField: Absorb,
{
fn partial_evaluate(g: &MV, point: &[Option<F>]) -> UV {
assert!(point.len() >= g.num_vars(), "Invalid evaluation domain");
// TODO: add check: there can only be 1 'None' value in point
if g.is_zero() {
return UV::from_coefficients_vec(vec![F::zero()]);
}
// note: this can be parallelized with cfg_into_iter
let mut univ_terms: Vec<(F, SparseTerm)> = vec![];
for (coef, term) in g.terms().iter() {
// partial_evaluate each term
let mut new_coef = F::one();
let mut new_term = Vec::new();
for (var, power) in term.iter() {
match point[*var] {
Some(v) => {
if v.is_zero() {
new_coef = F::zero();
new_term = vec![];
break;
} else {
new_coef *= v.pow([(*power) as u64]);
}
}
_ => {
new_term.push((*var, *power));
}
};
}
let new_term = SparseTerm::new(new_term);
let new_coef = new_coef * coef;
univ_terms.push((new_coef, new_term));
}
let mv_poly: SparsePolynomial<F, SparseTerm> =
DenseMVPolynomial::<F>::from_coefficients_vec(g.num_vars(), univ_terms.clone());
let mut univ_coeffs: Vec<F> = vec![F::zero(); mv_poly.degree() + 1];
for (coef, term) in univ_terms {
if term.is_empty() {
univ_coeffs[0] += coef;
continue;
}
for (_, power) in term.iter() {
univ_coeffs[*power] += coef;
}
}
UV::from_coefficients_vec(univ_coeffs)
}
fn point_complete(challenges: Vec<F>, n_elems: usize, iter_num: usize) -> Vec<F> {
let p = Self::point(challenges, false, n_elems, iter_num);
let mut r = vec![F::zero(); n_elems];
for i in 0..n_elems {
r[i] = p[i].unwrap();
}
r
}
fn point(challenges: Vec<F>, none: bool, n_elems: usize, iter_num: usize) -> Vec<Option<F>> {
let mut n_vars = n_elems - challenges.len();
assert!(n_vars >= log2(iter_num + 1) as usize);
if none {
// WIP
if n_vars == 0 {
panic!("err"); // or return directly challenges vector
}
n_vars -= 1;
}
let none_pos = if none {
challenges.len() + 1
} else {
challenges.len()
};
let mut p: Vec<Option<F>> = vec![None; n_elems];
for i in 0..challenges.len() {
p[i] = Some(challenges[i]);
}
for i in 0..n_vars {
let k = F::from(iter_num as u64).into_bigint().to_bytes_le();
let bit = k[i / 8] & (1 << (i % 8));
if bit == 0 {
p[none_pos + i] = Some(F::zero());
} else {
p[none_pos + i] = Some(F::one());
}
}
p
}
pub fn prove(poseidon_config: &PoseidonConfig<F>, g: MV) -> (F, Vec<UV>, F)
where
<MV as Polynomial<F>>::Point: From<Vec<F>>,
{
// init transcript
let mut transcript = Transcript::<F, C>::new(poseidon_config);
let v = g.num_vars();
// compute H
let mut H = F::zero();
for i in 0..(2_u64.pow(v as u32) as usize) {
let p = Self::point_complete(vec![], v, i);
H += g.evaluate(&p.into());
}
transcript.add(&H);
let mut ss: Vec<UV> = Vec::new();
let mut r: Vec<F> = vec![];
for i in 0..v {
let r_i = transcript.get_challenge();
r.push(r_i);
let var_slots = v - 1 - i;
let n_points = 2_u64.pow(var_slots as u32) as usize;
let mut s_i = UV::zero();
for j in 0..n_points {
let point = Self::point(r[..i].to_vec(), true, v, j);
s_i = s_i + Self::partial_evaluate(&g, &point);
}
transcript.add_vec(s_i.coeffs());
ss.push(s_i);
}
let last_g_eval = g.evaluate(&r.into());
(H, ss, last_g_eval)
}
pub fn verify(poseidon_config: &PoseidonConfig<F>, proof: (F, Vec<UV>, F)) -> bool {
// init transcript
let mut transcript = Transcript::<F, C>::new(poseidon_config);
transcript.add(&proof.0);
let (c, ss, last_g_eval) = proof;
let mut r: Vec<F> = vec![];
for (i, s) in ss.iter().enumerate() {
// TODO check degree
if i == 0 {
if c != s.evaluate(&F::zero()) + s.evaluate(&F::one()) {
return false;
}
let r_i = transcript.get_challenge();
r.push(r_i);
transcript.add_vec(s.coeffs());
continue;
}
let r_i = transcript.get_challenge();
r.push(r_i);
if ss[i - 1].evaluate(&r[i - 1]) != s.evaluate(&F::zero()) + s.evaluate(&F::one()) {
return false;
}
transcript.add_vec(s.coeffs());
}
// last round
if ss[ss.len() - 1].evaluate(&r[r.len() - 1]) != last_g_eval {
return false;
}
true
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::transcript::poseidon_test_config;
use ark_mnt4_298::{Fr, G1Projective}; // scalar field
use ark_poly::{
multivariate::{SparsePolynomial, SparseTerm, Term},
univariate::DensePolynomial,
DenseMVPolynomial, DenseUVPolynomial,
};
use ark_std::{rand::Rng, UniformRand};
#[test]
fn test_new_point() {
let f4 = Fr::from(4_u32);
let f1 = Fr::from(1);
let f0 = Fr::from(0);
type SC = SumCheck<Fr, G1Projective, DensePolynomial<Fr>, SparsePolynomial<Fr, SparseTerm>>;
let p = SC::point(vec![Fr::from(4_u32)], true, 5, 0);
assert_eq!(vec![Some(f4), None, Some(f0), Some(f0), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], true, 5, 1);
assert_eq!(vec![Some(f4), None, Some(f1), Some(f0), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], true, 5, 2);
assert_eq!(vec![Some(f4), None, Some(f0), Some(f1), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], true, 5, 3);
assert_eq!(vec![Some(f4), None, Some(f1), Some(f1), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], true, 5, 4);
assert_eq!(vec![Some(f4), None, Some(f0), Some(f0), Some(f1),], p);
// without None
let p = SC::point(vec![], false, 4, 0);
assert_eq!(vec![Some(f0), Some(f0), Some(f0), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], false, 5, 0);
assert_eq!(vec![Some(f4), Some(f0), Some(f0), Some(f0), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], false, 5, 1);
assert_eq!(vec![Some(f4), Some(f1), Some(f0), Some(f0), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], false, 5, 3);
assert_eq!(vec![Some(f4), Some(f1), Some(f1), Some(f0), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], false, 5, 4);
assert_eq!(vec![Some(f4), Some(f0), Some(f0), Some(f1), Some(f0),], p);
let p = SC::point(vec![Fr::from(4_u32)], false, 5, 10);
assert_eq!(vec![Some(f4), Some(f0), Some(f1), Some(f0), Some(f1),], p);
let p = SC::point(vec![Fr::from(4_u32)], false, 5, 15);
assert_eq!(vec![Some(f4), Some(f1), Some(f1), Some(f1), Some(f1),], p);
// let p = SC::point(vec![Fr::from(4_u32)], false, 4, 16); // TODO expect error
}
#[test]
fn test_partial_evaluate() {
// g(X_0, X_1, X_2) = 2 X_0^3 + X_0 X_2 + X_1 X_2
let terms = vec![
(Fr::from(2u32), SparseTerm::new(vec![(0_usize, 3)])),
(
Fr::from(1u32),
SparseTerm::new(vec![(0_usize, 1), (2_usize, 1)]),
),
(
Fr::from(1u32),
SparseTerm::new(vec![(1_usize, 1), (2_usize, 1)]),
),
];
let p = SparsePolynomial::from_coefficients_slice(3, &terms);
type SC = SumCheck<Fr, G1Projective, DensePolynomial<Fr>, SparsePolynomial<Fr, SparseTerm>>;
let e0 = SC::partial_evaluate(&p, &[Some(Fr::from(2_u32)), None, Some(Fr::from(0_u32))]);
assert_eq!(e0.coeffs(), vec![Fr::from(16_u32)]);
let e1 = SC::partial_evaluate(&p, &[Some(Fr::from(2_u32)), None, Some(Fr::from(1_u32))]);
assert_eq!(e1.coeffs(), vec![Fr::from(18_u32), Fr::from(1)]);
assert_eq!((e0 + e1).coeffs(), vec![Fr::from(34_u32), Fr::from(1)]);
}
#[test]
fn test_flow_hardcoded_values() {
// g(X_0, X_1, X_2) = 2 X_0^3 + X_0 X_2 + X_1 X_2
let terms = vec![
(Fr::from(2u32), SparseTerm::new(vec![(0_usize, 3)])),
(
Fr::from(1u32),
SparseTerm::new(vec![(0_usize, 1), (2_usize, 1)]),
),
(
Fr::from(1u32),
SparseTerm::new(vec![(1_usize, 1), (2_usize, 1)]),
),
];
let p = SparsePolynomial::from_coefficients_slice(3, &terms);
// println!("p {:?}", p);
let poseidon_config = poseidon_test_config::<Fr>();
type SC = SumCheck<Fr, G1Projective, DensePolynomial<Fr>, SparsePolynomial<Fr, SparseTerm>>;
let proof = SC::prove(&poseidon_config, p);
assert_eq!(proof.0, Fr::from(12_u32));
// println!("proof {:?}", proof);
let v = SC::verify(&poseidon_config, proof);
assert!(v);
}
fn rand_poly<R: Rng>(l: usize, d: usize, rng: &mut R) -> SparsePolynomial<Fr, SparseTerm> {
// This method is from the arkworks/algebra/poly/multivariate test:
// https://github.com/arkworks-rs/algebra/blob/bc991d44c5e579025b7ed56df3d30267a7b9acac/poly/src/polynomial/multivariate/sparse.rs#L303
let mut random_terms = Vec::new();
let num_terms = rng.gen_range(1..1000);
// For each term, randomly select up to `l` variables with degree
// in [1,d] and random coefficient
random_terms.push((Fr::rand(rng), SparseTerm::new(vec![])));
for _ in 1..num_terms {
let term = (0..l)
.map(|i| {
if rng.gen_bool(0.5) {
Some((i, rng.gen_range(1..(d + 1))))
} else {
None
}
})
.flatten()
.collect();
let coeff = Fr::rand(rng);
random_terms.push((coeff, SparseTerm::new(term)));
}
SparsePolynomial::from_coefficients_slice(l, &random_terms)
}
#[test]
fn test_flow_rng() {
let mut rng = ark_std::test_rng();
// let p = SparsePolynomial::<Fr, SparseTerm>::rand(3, 3, &mut rng);
let p = rand_poly(3, 3, &mut rng);
// println!("p {:?}", p);
let poseidon_config = poseidon_test_config::<Fr>();
type SC = SumCheck<Fr, G1Projective, DensePolynomial<Fr>, SparsePolynomial<Fr, SparseTerm>>;
let proof = SC::prove(&poseidon_config, p);
// println!("proof.s len {:?}", proof.1.len());
let v = SC::verify(&poseidon_config, proof);
assert!(v);
}
}
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