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mod.rs
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mod.rs
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//! Implementation of GKR Round Sumcheck algorithm as described in [XZZPS19](https://eprint.iacr.org/2019/317.pdf#subsection.3.3) (Section 3.3)
//!
//! GKR Round Sumcheck will use `ml_sumcheck` as a subroutine.
pub mod data_structures;
#[cfg(test)]
mod test;
use crate::gkr_round_sumcheck::data_structures::{GKRProof, GKRRoundSumcheckSubClaim};
use crate::ml_sumcheck::protocol::prover::ProverState;
use crate::ml_sumcheck::protocol::{IPForMLSumcheck, ListOfProductsOfPolynomials, PolynomialInfo};
use crate::rng::FeedableRNG;
use ark_ff::{Field, Zero};
use ark_poly::{DenseMultilinearExtension, MultilinearExtension, SparseMultilinearExtension};
use ark_std::marker::PhantomData;
use ark_std::rc::Rc;
use ark_std::vec::Vec;
/// Takes multilinear f1, f3, and input g = g1,...,gl. Returns h_g, and f1 fixed at g.
pub fn initialize_phase_one<F: Field>(
f1: &SparseMultilinearExtension<F>,
f3: &DenseMultilinearExtension<F>,
g: &[F],
) -> (DenseMultilinearExtension<F>, SparseMultilinearExtension<F>) {
let dim = f3.num_vars; // 'l` in paper
assert_eq!(f1.num_vars, dim * 3);
assert_eq!(g.len(), dim);
let mut a_hg: Vec<_> = (0..(1 << dim)).map(|_| F::zero()).collect();
let f1_at_g = f1.fix_variables(g);
for (xy, v) in f1_at_g.evaluations.iter() {
if v != &F::zero() {
let x = xy & ((1 << dim) - 1);
let y = xy >> dim;
a_hg[x] += *v * f3[y];
}
}
let hg = DenseMultilinearExtension::from_evaluations_vec(dim, a_hg);
(hg, f1_at_g)
}
/// Takes h_g and returns a sumcheck state
pub fn start_phase1_sumcheck<F: Field>(
h_g: &DenseMultilinearExtension<F>,
f2: &DenseMultilinearExtension<F>,
) -> ProverState<F> {
let dim = h_g.num_vars;
assert_eq!(f2.num_vars, dim);
let mut poly = ListOfProductsOfPolynomials::new(dim);
poly.add_product(vec![Rc::new(h_g.clone()), Rc::new(f2.clone())], F::one());
IPForMLSumcheck::prover_init(&poly)
}
/// Takes multilinear f1 fixed at g, phase one randomness u. Returns f1 fixed at g||u
pub fn initialize_phase_two<F: Field>(
f1_g: &SparseMultilinearExtension<F>,
u: &[F],
) -> DenseMultilinearExtension<F> {
assert_eq!(u.len() * 2, f1_g.num_vars);
f1_g.fix_variables(u).to_dense_multilinear_extension()
}
/// Takes f1 fixed at g||u, f3, and f2 evaluated at u.
pub fn start_phase2_sumcheck<F: Field>(
f1_gu: &DenseMultilinearExtension<F>,
f3: &DenseMultilinearExtension<F>,
f2_u: F,
) -> ProverState<F> {
let f3_f2u = {
let mut zero = DenseMultilinearExtension::zero();
zero += (f2_u, f3);
zero
};
let dim = f1_gu.num_vars;
assert_eq!(f3.num_vars, dim);
let mut poly = ListOfProductsOfPolynomials::new(dim);
poly.add_product(vec![Rc::new(f1_gu.clone()), Rc::new(f3_f2u)], F::one());
IPForMLSumcheck::prover_init(&poly)
}
/// Sumcheck Argument for GKR Round Function
pub struct GKRRoundSumcheck<F: Field> {
_marker: PhantomData<F>,
}
impl<F: Field> GKRRoundSumcheck<F> {
/// Takes a GKR Round Function and input, prove the sum.
/// * `f1`,`f2`,`f3`: represents the GKR round function
/// * `g`: represents the fixed input.
pub fn prove<R: FeedableRNG>(
rng: &mut R,
f1: &SparseMultilinearExtension<F>,
f2: &DenseMultilinearExtension<F>,
f3: &DenseMultilinearExtension<F>,
g: &[F],
) -> GKRProof<F> {
assert_eq!(f1.num_vars, 3 * f2.num_vars);
assert_eq!(f1.num_vars, 3 * f3.num_vars);
let dim = f2.num_vars;
let g = g.to_vec();
let (h_g, f1_g) = initialize_phase_one(f1, f3, &g);
let mut phase1_ps = start_phase1_sumcheck(&h_g, f2);
let mut phase1_vm = None;
let mut phase1_prover_msgs = Vec::with_capacity(dim);
let mut u = Vec::with_capacity(dim);
for _ in 0..dim {
let pm = IPForMLSumcheck::prove_round(&mut phase1_ps, &phase1_vm);
rng.feed(&pm).unwrap();
phase1_prover_msgs.push(pm);
let vm = IPForMLSumcheck::sample_round(rng);
phase1_vm = Some(vm.clone());
u.push(vm.randomness);
}
let f1_gu = initialize_phase_two(&f1_g, &u);
let mut phase2_ps = start_phase2_sumcheck(&f1_gu, f3, f2.evaluate(&u).unwrap());
let mut phase2_vm = None;
let mut phase2_prover_msgs = Vec::with_capacity(dim);
let mut v = Vec::with_capacity(dim);
for _ in 0..dim {
let pm = IPForMLSumcheck::prove_round(&mut phase2_ps, &phase2_vm);
rng.feed(&pm).unwrap();
phase2_prover_msgs.push(pm);
let vm = IPForMLSumcheck::sample_round(rng);
phase2_vm = Some(vm.clone());
v.push(vm.randomness);
}
GKRProof {
phase1_sumcheck_msgs: phase1_prover_msgs,
phase2_sumcheck_msgs: phase2_prover_msgs,
}
}
/// Takes a GKR Round Function, input, and proof, and returns a subclaim.
///
/// If the `claimed_sum` is correct, then it is `subclaim.verify_subclaim` will return true.
/// Otherwise, it is very likely that `subclaim.verify_subclaim` will return false.
/// Larger field size guarantees smaller soundness error.
/// * `f2_num_vars`: represents number of variables of f2
pub fn verify<R: FeedableRNG>(
rng: &mut R,
f2_num_vars: usize,
proof: &GKRProof<F>,
claimed_sum: F,
) -> Result<GKRRoundSumcheckSubClaim<F>, crate::Error> {
// verify first sumcheck
let dim = f2_num_vars;
let mut phase1_vs = IPForMLSumcheck::verifier_init(&PolynomialInfo {
max_multiplicands: 2,
num_variables: dim,
});
for i in 0..dim {
let pm = &proof.phase1_sumcheck_msgs[i];
rng.feed(pm).unwrap();
let _result = IPForMLSumcheck::verify_round((*pm).clone(), &mut phase1_vs, rng);
}
let phase1_subclaim = IPForMLSumcheck::check_and_generate_subclaim(phase1_vs, claimed_sum)?;
let u = phase1_subclaim.point;
let mut phase2_vs = IPForMLSumcheck::verifier_init(&PolynomialInfo {
max_multiplicands: 2,
num_variables: dim,
});
for i in 0..dim {
let pm = &proof.phase2_sumcheck_msgs[i];
rng.feed(pm).unwrap();
let _result = IPForMLSumcheck::verify_round((*pm).clone(), &mut phase2_vs, rng);
}
let phase2_subclaim = IPForMLSumcheck::check_and_generate_subclaim(
phase2_vs,
phase1_subclaim.expected_evaluation,
)?;
let v = phase2_subclaim.point;
let expected_evaluation = phase2_subclaim.expected_evaluation;
Ok(GKRRoundSumcheckSubClaim {
u,
v,
expected_evaluation,
})
}
}