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third.rs
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third.rs
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// Copyright (C) 2019-2023 Aleo Systems Inc.
// This file is part of the snarkVM library.
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at:
// http://www.apache.org/licenses/LICENSE-2.0
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
use crate::{
fft::{
domain::{FFTPrecomputation, IFFTPrecomputation},
polynomial::PolyMultiplier,
DensePolynomial,
EvaluationDomain,
Evaluations,
},
polycommit::sonic_pc::{LabeledPolynomial, PolynomialInfo, PolynomialLabel},
snark::varuna::{
ahp::{indexer::CircuitId, verifier, AHPForR1CS},
matrices::transpose,
prover::{self, MatrixSums, ThirdMessage},
selectors::apply_randomized_selector,
AHPError,
Matrix,
SNARKMode,
},
};
use snarkvm_fields::PrimeField;
use snarkvm_utilities::{cfg_iter, ExecutionPool};
use anyhow::{ensure, Result};
use itertools::Itertools;
use rand_core::RngCore;
use std::collections::BTreeMap;
#[cfg(not(feature = "serial"))]
use rayon::prelude::*;
struct LinevalInstance<F: PrimeField> {
h_1_i: DensePolynomial<F>,
xg_1_i: DensePolynomial<F>,
sum: F,
}
impl<F: PrimeField, SM: SNARKMode> AHPForR1CS<F, SM> {
/// Output the number of oracles sent by the prover in the third round.
pub const fn num_third_round_oracles() -> usize {
2
}
/// Output the degree bounds of oracles in the first round.
pub fn third_round_polynomial_info(variable_domain_size: usize) -> BTreeMap<PolynomialLabel, PolynomialInfo> {
[
PolynomialInfo::new("g_1".into(), Some(variable_domain_size - 2), Self::zk_bound()),
PolynomialInfo::new("h_1".into(), None, 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::FirstMessage<F>,
verifier_second_message: &verifier::SecondMessage<F>,
mut state: prover::State<'a, F, SM>,
_r: &mut R,
) -> Result<(prover::ThirdMessage<F>, prover::ThirdOracles<F>, prover::State<'a, F, SM>), AHPError> {
let round_time = start_timer!(|| "AHP::Prover::ThirdRound");
let zk_bound = Self::zk_bound();
let max_variable_domain = state.max_variable_domain;
let verifier::FirstMessage { batch_combiners } = verifier_message;
let verifier::SecondMessage { alpha, eta_b, eta_c } = verifier_second_message;
let assignments = Self::calculate_assignments(&mut state)?;
let matrix_transposes = Self::calculate_matrix_transpose(&mut state)?;
let (h_1, x_g_1_sum, msg) = Self::calculate_lineval_sumcheck_witness(
&mut state,
batch_combiners,
assignments,
matrix_transposes,
alpha,
eta_b,
eta_c,
)?;
#[cfg(debug_assertions)]
{
let mut sumcheck_lhs = h_1.mul_by_vanishing_poly(max_variable_domain);
sumcheck_lhs += &x_g_1_sum;
debug_assert!(
sumcheck_lhs.evaluate_over_domain_by_ref(max_variable_domain).evaluations.into_iter().sum::<F>()
== msg.sum(batch_combiners, *eta_b, *eta_c)
);
}
let g_1 = DensePolynomial::from_coefficients_slice(&x_g_1_sum.coeffs[1..]);
drop(x_g_1_sum); // Be assured we don't use x_g_1_sum anymore
assert!(g_1.degree() <= max_variable_domain.size() - 2);
assert!(h_1.degree() <= 2 * max_variable_domain.size() + 2 * zk_bound.unwrap_or(0) - 2);
let oracles = prover::ThirdOracles {
g_1: LabeledPolynomial::new("g_1", g_1, max_variable_domain.size() - 2, zk_bound),
h_1: LabeledPolynomial::new("h_1", h_1, None, None),
};
assert!(oracles.matches_info(&Self::third_round_polynomial_info(state.max_variable_domain.size())));
end_timer!(round_time);
Ok((msg, oracles, state))
}
fn calculate_lineval_sumcheck_witness(
state: &mut prover::State<F, SM>,
batch_combiners: &BTreeMap<CircuitId, verifier::BatchCombiners<F>>,
assignments: BTreeMap<CircuitId, Vec<DensePolynomial<F>>>,
matrix_transposes: BTreeMap<CircuitId, BTreeMap<String, Matrix<F>>>,
alpha: &F,
eta_b: &F,
eta_c: &F,
) -> Result<(DensePolynomial<F>, DensePolynomial<F>, ThirdMessage<F>)> {
let num_instances = batch_combiners.values().map(|c| c.instance_combiners.len()).collect_vec();
let total_instances = num_instances.iter().sum::<usize>();
let max_variable_domain = &state.max_variable_domain;
let matrix_labels = ["a", "b", "c"];
let matrix_combiners = [F::one(), *eta_b, *eta_c];
// Compute lineval sumcheck witnesses
let mut job_pool = ExecutionPool::with_capacity(total_instances * 3);
for ((((circuit, circuit_specific_state), batch_combiner), assignments_i), matrix_transposes_i) in state
.circuit_specific_states
.iter_mut()
.zip_eq(batch_combiners.values())
.zip_eq(assignments.values())
.zip_eq(matrix_transposes.values())
{
let circuit_combiner = batch_combiner.circuit_combiner;
let instance_combiners = &batch_combiner.instance_combiners;
let constraint_domain = &circuit_specific_state.constraint_domain;
let variable_domain = &circuit_specific_state.variable_domain;
let fft_precomputation = &circuit.fft_precomputation;
let ifft_precomputation = &circuit.ifft_precomputation;
for (&instance_combiner, assignment) in itertools::izip!(instance_combiners, assignments_i) {
for (label, matrix_combiner) in itertools::izip!(matrix_labels, matrix_combiners) {
let matrix_transpose = &matrix_transposes_i[label];
let combiner = circuit_combiner * instance_combiner * matrix_combiner;
job_pool.add_job(move || {
Self::calculate_lineval_sumcheck_instance_witness(
label,
constraint_domain,
variable_domain,
max_variable_domain,
fft_precomputation,
ifft_precomputation,
assignment,
matrix_transpose,
*alpha,
combiner,
)
});
}
}
}
let mut sums = num_instances.iter().map(|n| Vec::with_capacity(*n)).collect_vec();
let mut h_1_sum = DensePolynomial::zero();
let mut xg_1_sum = DensePolynomial::zero();
let mut circuit_index = 0;
let mut instances_seen = 0;
for (i, linevals) in job_pool.execute_all().chunks_exact_mut(3).enumerate() {
if linevals[0].is_ok() && linevals[1].is_ok() && linevals[2].is_ok() {
let lineval_a = linevals[0].as_ref().unwrap();
let lineval_b = linevals[1].as_ref().unwrap();
let lineval_c = linevals[2].as_ref().unwrap();
h_1_sum += &lineval_a.h_1_i;
h_1_sum += &lineval_b.h_1_i;
h_1_sum += &lineval_c.h_1_i;
xg_1_sum += &lineval_a.xg_1_i;
xg_1_sum += &lineval_b.xg_1_i;
xg_1_sum += &lineval_c.xg_1_i;
sums[circuit_index].push(MatrixSums {
sum_a: lineval_a.sum,
sum_b: lineval_b.sum,
sum_c: lineval_c.sum,
});
if 1 + i - instances_seen == num_instances[circuit_index] {
instances_seen += num_instances[circuit_index];
circuit_index += 1;
}
}
}
let mask_poly = state.first_round_oracles.as_ref().unwrap().mask_poly.as_ref();
assert_eq!(SM::ZK, mask_poly.is_some());
assert_eq!(!SM::ZK, mask_poly.is_none());
let mask_poly = &mask_poly.map_or(DensePolynomial::zero(), |p| p.polynomial().into_dense());
let (mut h_1_mask, mut xg_1_mask) = mask_poly.divide_by_vanishing_poly(*max_variable_domain).unwrap();
h_1_sum += &core::mem::take(&mut h_1_mask);
xg_1_sum += &core::mem::take(&mut xg_1_mask);
let msg = ThirdMessage { sums };
Ok((h_1_sum, xg_1_sum, msg))
}
pub(in crate::snark::varuna) fn calculate_assignments(
state: &mut prover::State<F, SM>,
) -> Result<BTreeMap<CircuitId, Vec<DensePolynomial<F>>>> {
let assignments_time = start_timer!(|| "Calculate assignments");
let assignments: BTreeMap<_, _> = state
.circuit_specific_states
.iter()
.zip_eq(state.first_round_oracles.as_ref().unwrap().batches.values())
.map(|((circuit, circuit_specific_state), w_polys)| {
let x_polys = &circuit_specific_state.x_polys;
let input_domain = &circuit_specific_state.input_domain;
let assignments_i: Vec<_> = cfg_iter!(w_polys)
.zip_eq(x_polys)
.enumerate()
.map(|(_j, (w_poly, x_poly))| {
let z_time = start_timer!(move || format!("Compute z poly for circuit {} {}", circuit.id, _j));
let mut assignment =
w_poly.0.polynomial().as_dense().unwrap().mul_by_vanishing_poly(*input_domain);
// Zip safety: `x_poly` is smaller than `z_poly`.
assignment.coeffs.iter_mut().zip(&x_poly.coeffs).for_each(|(z, x)| *z += x);
end_timer!(z_time);
assignment
})
.collect();
(circuit.id, assignments_i)
})
.collect();
end_timer!(assignments_time);
Ok(assignments)
}
fn calculate_matrix_transpose(
state: &mut prover::State<F, SM>,
) -> Result<BTreeMap<CircuitId, BTreeMap<String, Matrix<F>>>> {
let transpose_time = start_timer!(|| "Transpose of matrices");
let mut job_pool = ExecutionPool::with_capacity(state.circuit_specific_states.len() * 3);
state.circuit_specific_states.iter().for_each(|(circuit, circuit_specific_state)| {
let variable_domain = &circuit_specific_state.variable_domain;
let input_domain = &circuit_specific_state.input_domain;
let matrices = [&circuit.a, &circuit.b, &circuit.c];
let circuit_id = circuit.id;
for matrix in matrices.into_iter() {
job_pool.add_job(move || (circuit_id, transpose(matrix, variable_domain, input_domain)));
}
});
let mut matrix_transposes = BTreeMap::new();
for ((id_a, matrix_a), (id_b, matrix_b), (id_c, matrix_c)) in job_pool.execute_all().into_iter().tuples() {
ensure!(id_a == id_b);
ensure!(id_a == id_c);
let mut matrix_transposes_i = BTreeMap::new();
matrix_transposes_i.insert("a".into(), matrix_a?);
matrix_transposes_i.insert("b".into(), matrix_b?);
matrix_transposes_i.insert("c".into(), matrix_c?);
matrix_transposes.insert(id_a, matrix_transposes_i);
}
end_timer!(transpose_time);
Ok(matrix_transposes)
}
#[allow(clippy::too_many_arguments)]
fn calculate_lineval_sumcheck_instance_witness(
_label: &str,
constraint_domain: &EvaluationDomain<F>,
variable_domain: &EvaluationDomain<F>,
max_variable_domain: &EvaluationDomain<F>,
fft_precomputation: &FFTPrecomputation<F>,
ifft_precomputation: &IFFTPrecomputation<F>,
assignment: &DensePolynomial<F>,
matrix_transpose: &Matrix<F>,
alpha: F,
combiner: F,
) -> Result<LinevalInstance<F>> {
let sumcheck_time = start_timer!(|| format!("Compute LHS of sumcheck for {_label}"));
// Let C = variable_domain
// Let R = constraint_domain
// Let K = non_zero_domain
// Let L^S_t(X) = Lagrange polynomial evaluating to 1 on S when any X∈S==t
// Compute for each c∈C: M(α,c) = \sum_{κ∈K} val(κ)·L^R_row(κ)(α)·L^C_col(κ)(c)
// We do this by iterating over the sparse transpose of matrix M
// Instead of calculating L^C_col(κ)(c), we add val(k)*L^R_row(α) where we know L^C_col(k)(X) will be 1
let m_at_alpha_evals_time = start_timer!(|| format!("Compute m_at_alpha_evals parallel for {_label}"));
let l_at_alpha = constraint_domain.evaluate_all_lagrange_coefficients(alpha);
let m_at_alpha_evals: Vec<_> = cfg_iter!(matrix_transpose)
.map(|col| col.iter().map(|(val, row_index)| *val * l_at_alpha[*row_index]).sum::<F>())
.collect();
end_timer!(m_at_alpha_evals_time);
let z_m_at_alpha_time = start_timer!(|| format!("Compute z_m_at_alpha_time for {_label}"));
let m_at_alpha = Evaluations::from_vec_and_domain(m_at_alpha_evals, *variable_domain)
.interpolate_with_pc(ifft_precomputation);
let mut multiplier = PolyMultiplier::new();
multiplier.add_precomputation(fft_precomputation, ifft_precomputation);
multiplier.add_polynomial(m_at_alpha, "m_at_alpha");
multiplier.add_polynomial_ref(assignment, "assignment");
let mut z_m_at_alpha = multiplier.multiply().unwrap();
let sum = z_m_at_alpha.evaluate_over_domain_by_ref(*variable_domain).evaluations.into_iter().sum::<F>();
end_timer!(z_m_at_alpha_time);
let (h_1_i, xg_1_i) =
apply_randomized_selector(&mut z_m_at_alpha, combiner, max_variable_domain, variable_domain, true)?;
let xg_1_i = xg_1_i.ok_or(anyhow::anyhow!("Expected remainder when applying selector"))?;
end_timer!(sumcheck_time);
Ok(LinevalInstance { h_1_i, xg_1_i, sum })
}
}