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third.rs
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third.rs
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// Copyright (C) 2019-2022 Aleo Systems Inc.
// This file is part of the snarkVM library.
// The snarkVM library is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// The snarkVM library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with the snarkVM library. If not, see <https://www.gnu.org/licenses/>.
use core::convert::TryInto;
use std::collections::BTreeMap;
use crate::{
fft::{
domain::{FFTPrecomputation, IFFTPrecomputation},
polynomial::PolyMultiplier,
DensePolynomial,
EvaluationDomain,
Evaluations as EvaluationsOnDomain,
},
polycommit::sonic_pc::{LabeledPolynomial, PolynomialInfo, PolynomialLabel},
snark::marlin::{
ahp::{indexer::CircuitInfo, verifier, AHPError, AHPForR1CS},
matrices::MatrixArithmetization,
prover,
MarlinMode,
},
};
use snarkvm_fields::{batch_inversion_and_mul, PrimeField};
use snarkvm_utilities::{cfg_iter, cfg_iter_mut, ExecutionPool};
use rand_core::RngCore;
#[cfg(not(feature = "parallel"))]
use itertools::Itertools;
#[cfg(feature = "parallel")]
use rayon::prelude::*;
impl<F: PrimeField, MM: MarlinMode> AHPForR1CS<F, MM> {
/// Output the number of oracles sent by the prover in the third round.
pub fn num_third_round_oracles() -> usize {
3
}
/// Output the degree bounds of oracles in the first round.
pub fn third_round_polynomial_info(info: &CircuitInfo<F>) -> BTreeMap<PolynomialLabel, PolynomialInfo> {
let non_zero_a_size = EvaluationDomain::<F>::compute_size_of_domain(info.num_non_zero_a).unwrap();
let non_zero_b_size = EvaluationDomain::<F>::compute_size_of_domain(info.num_non_zero_b).unwrap();
let non_zero_c_size = EvaluationDomain::<F>::compute_size_of_domain(info.num_non_zero_c).unwrap();
[
PolynomialInfo::new("g_a".into(), Some(non_zero_a_size - 2), None),
PolynomialInfo::new("g_b".into(), Some(non_zero_b_size - 2), None),
PolynomialInfo::new("g_c".into(), Some(non_zero_c_size - 2), None),
]
.into_iter()
.map(|info| (info.label().into(), info))
.collect()
}
/// Output the third round message and the next state.
pub fn prover_third_round<'a, R: RngCore>(
verifier_message: &verifier::SecondMessage<F>,
mut state: prover::State<'a, F, MM>,
_r: &mut R,
) -> Result<(prover::ThirdMessage<F>, prover::ThirdOracles<F>, prover::State<'a, F, MM>), AHPError> {
let round_time = start_timer!(|| "AHP::Prover::ThirdRound");
let verifier::FirstMessage { alpha, .. } = state
.verifier_first_message
.as_ref()
.expect("prover::State should include verifier_first_msg when prover_third_round is called");
let beta = verifier_message.beta;
let v_H_at_alpha = state.constraint_domain.evaluate_vanishing_polynomial(*alpha);
let v_H_at_beta = state.constraint_domain.evaluate_vanishing_polynomial(beta);
let v_H_alpha_v_H_beta = v_H_at_alpha * v_H_at_beta;
let largest_non_zero_domain_size = Self::max_non_zero_domain(&state.index.index_info).size_as_field_element;
let mut pool = ExecutionPool::with_capacity(3);
pool.add_job(|| {
Self::matrix_sumcheck_helper(
"a",
state.non_zero_a_domain,
&state.index.a_arith,
*alpha,
beta,
v_H_alpha_v_H_beta,
largest_non_zero_domain_size,
state.fft_precomputation(),
state.ifft_precomputation(),
)
});
pool.add_job(|| {
Self::matrix_sumcheck_helper(
"b",
state.non_zero_b_domain,
&state.index.b_arith,
*alpha,
beta,
v_H_alpha_v_H_beta,
largest_non_zero_domain_size,
state.fft_precomputation(),
state.ifft_precomputation(),
)
});
pool.add_job(|| {
Self::matrix_sumcheck_helper(
"c",
state.non_zero_c_domain,
&state.index.c_arith,
*alpha,
beta,
v_H_alpha_v_H_beta,
largest_non_zero_domain_size,
state.fft_precomputation(),
state.ifft_precomputation(),
)
});
let [(sum_a, lhs_a, g_a), (sum_b, lhs_b, g_b), (sum_c, lhs_c, g_c)]: [_; 3] =
pool.execute_all().try_into().unwrap();
let msg = prover::ThirdMessage { sum_a, sum_b, sum_c };
let oracles = prover::ThirdOracles { g_a, g_b, g_c };
state.lhs_polynomials = Some([lhs_a, lhs_b, lhs_c]);
state.sums = Some([sum_a, sum_b, sum_c]);
assert!(oracles.matches_info(&Self::third_round_polynomial_info(&state.index.index_info)));
end_timer!(round_time);
Ok((msg, oracles, state))
}
#[allow(clippy::too_many_arguments)]
fn matrix_sumcheck_helper(
label: &str,
non_zero_domain: EvaluationDomain<F>,
arithmetization: &MatrixArithmetization<F>,
alpha: F,
beta: F,
v_H_alpha_v_H_beta: F,
largest_non_zero_domain_size: F,
fft_precomputation: &FFTPrecomputation<F>,
ifft_precomputation: &IFFTPrecomputation<F>,
) -> (F, DensePolynomial<F>, LabeledPolynomial<F>) {
let mut job_pool = snarkvm_utilities::ExecutionPool::with_capacity(2);
job_pool.add_job(|| {
let a_poly_time = start_timer!(|| "Computing a poly");
let a_poly = {
let coeffs = cfg_iter!(arithmetization.val.as_dense().unwrap().coeffs())
.map(|a| v_H_alpha_v_H_beta * a)
.collect();
DensePolynomial::from_coefficients_vec(coeffs)
};
end_timer!(a_poly_time);
a_poly
});
let (row_on_K, col_on_K, row_col_on_K) =
(&arithmetization.evals_on_K.row, &arithmetization.evals_on_K.col, &arithmetization.evals_on_K.row_col);
job_pool.add_job(|| {
let b_poly_time = start_timer!(|| "Computing b poly");
let alpha_beta = alpha * beta;
let b_poly = {
let evals: Vec<F> = cfg_iter!(row_on_K.evaluations)
.zip_eq(&col_on_K.evaluations)
.zip_eq(&row_col_on_K.evaluations)
.map(|((r, c), r_c)| alpha_beta - alpha * r - beta * c + r_c)
.collect();
EvaluationsOnDomain::from_vec_and_domain(evals, non_zero_domain)
.interpolate_with_pc(ifft_precomputation)
};
end_timer!(b_poly_time);
b_poly
});
let [a_poly, b_poly]: [_; 2] = job_pool.execute_all().try_into().unwrap();
let f_evals_time = start_timer!(|| "Computing f evals on K");
let mut inverses: Vec<_> = cfg_iter!(row_on_K.evaluations)
.zip_eq(&col_on_K.evaluations)
.map(|(r, c)| (beta - r) * (alpha - c))
.collect();
batch_inversion_and_mul(&mut inverses, &v_H_alpha_v_H_beta);
cfg_iter_mut!(inverses).zip_eq(&arithmetization.evals_on_K.val.evaluations).for_each(|(inv, a)| *inv *= a);
let f_evals_on_K = inverses;
end_timer!(f_evals_time);
let f_poly_time = start_timer!(|| "Computing f poly");
let f = EvaluationsOnDomain::from_vec_and_domain(f_evals_on_K, non_zero_domain)
.interpolate_with_pc(ifft_precomputation);
end_timer!(f_poly_time);
let g = DensePolynomial::from_coefficients_slice(&f.coeffs[1..]);
let h = &a_poly
- &{
let mut multiplier = PolyMultiplier::new();
multiplier.add_polynomial_ref(&b_poly, "b");
multiplier.add_polynomial_ref(&f, "f");
multiplier.add_precomputation(fft_precomputation, ifft_precomputation);
multiplier.multiply().unwrap()
};
// Let K_max = largest_non_zero_domain;
// Let K = non_zero_domain;
// Let s := K_max.selector_polynomial(K) = (v_K_max / v_K) * (K.size() / K_max.size());
// Let v_K_max := K_max.vanishing_polynomial();
// Let v_K := K.vanishing_polynomial();
// Later on, we multiply `h` by s, and divide by v_K_max.
// Substituting in s, we get that h * s / v_K_max = h / v_K * (K.size() / K_max.size());
// That's what we're computing here.
let (mut h, remainder) = h.divide_by_vanishing_poly(non_zero_domain).unwrap();
assert!(remainder.is_zero());
let multiplier = non_zero_domain.size_as_field_element / largest_non_zero_domain_size;
cfg_iter_mut!(h.coeffs).for_each(|c| *c *= multiplier);
let g = LabeledPolynomial::new("g_".to_string() + label, g, Some(non_zero_domain.size() - 2), None);
assert!(h.degree() <= non_zero_domain.size() - 2);
assert!(g.degree() <= non_zero_domain.size() - 2);
(f.coeffs[0], h, g)
}
}