snarkvm_algorithms/polycommit/sonic_pc/

mod.rs

// Copyright (c) 2019-2025 Provable 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::{
    AlgebraicSponge,
    fft::DensePolynomial,
    msm::variable_base::VariableBase,
    polycommit::{PCError, kzg10, optional_rng::OptionalRng},
    srs::{UniversalProver, UniversalVerifier},
};
use hashbrown::HashMap;
use itertools::Itertools;
use snarkvm_curves::traits::{AffineCurve, PairingCurve, PairingEngine, ProjectiveCurve};
use snarkvm_fields::{One, Zero};

use anyhow::{Result, bail, ensure};
use rand::{RngCore, SeedableRng};
use std::{
    borrow::Borrow,
    collections::{BTreeMap, BTreeSet},
    convert::TryInto,
    marker::PhantomData,
    ops::Mul,
};

mod data_structures;
pub use data_structures::*;

mod polynomial;
pub use polynomial::*;

/// Polynomial commitment based on [\[KZG10\]][kzg], with degree enforcement and
/// batching taken from [[MBKM19, “Sonic”]][sonic] (more precisely, their
/// counterparts in [[Gabizon19, “AuroraLight”]][al] that avoid negative G1
/// powers). The (optional) hiding property of the commitment scheme follows the
/// approach described in [[CHMMVW20, “Marlin”]][marlin].
///
/// [kzg]: http://cacr.uwaterloo.ca/techreports/2010/cacr2010-10.pdf
/// [sonic]: https://eprint.iacr.org/2019/099
/// [al]: https://eprint.iacr.org/2019/601
/// [marlin]: https://eprint.iacr.org/2019/1047
#[derive(Clone, Debug)]
pub struct SonicKZG10<E: PairingEngine, S: AlgebraicSponge<E::Fq, 2>> {
    _engine: PhantomData<(E, S)>,
}

impl<E: PairingEngine, S: AlgebraicSponge<E::Fq, 2>> SonicKZG10<E, S> {
    pub fn load_srs(max_degree: usize) -> Result<UniversalParams<E>, PCError> {
        kzg10::KZG10::load_srs(max_degree)
    }

    pub fn trim(
        pp: &UniversalParams<E>,
        supported_degree: usize,
        supported_lagrange_sizes: impl IntoIterator<Item = usize>,
        supported_hiding_bound: usize,
        enforced_degree_bounds: Option<&[usize]>,
    ) -> Result<(CommitterKey<E>, UniversalVerifier<E>)> {
        let trim_time = start_timer!(|| "Trimming public parameters");
        let max_degree = pp.max_degree();

        let enforced_degree_bounds = enforced_degree_bounds.map(|bounds| {
            let mut v = bounds.to_vec();
            v.sort_unstable();
            v.dedup();
            v
        });

        let (shifted_powers_of_beta_g, shifted_powers_of_beta_times_gamma_g) = if let Some(enforced_degree_bounds) =
            enforced_degree_bounds.as_ref()
        {
            if enforced_degree_bounds.is_empty() {
                (None, None)
            } else {
                let highest_enforced_degree_bound = *enforced_degree_bounds.last().unwrap();
                if highest_enforced_degree_bound > supported_degree {
                    bail!(
                        "The highest enforced degree bound {highest_enforced_degree_bound} is larger than the supported degree {supported_degree}"
                    );
                }

                let lowest_shift_degree = max_degree - highest_enforced_degree_bound;

                let shifted_ck_time = start_timer!(|| format!(
                    "Constructing `shifted_powers_of_beta_g` of size {}",
                    max_degree - lowest_shift_degree + 1
                ));

                let shifted_powers_of_beta_g = pp.powers_of_beta_g(lowest_shift_degree, pp.max_degree() + 1)?;
                let mut shifted_powers_of_beta_times_gamma_g = BTreeMap::new();
                // Also add degree 0.
                for degree_bound in enforced_degree_bounds {
                    let shift_degree = max_degree - degree_bound;
                    // We have an additional degree in `powers_of_beta_times_gamma_g` beyond
                    // `powers_of_beta_g`.
                    let powers_for_degree_bound = pp
                        .powers_of_beta_times_gamma_g()
                        .range(shift_degree..max_degree.min(shift_degree + supported_hiding_bound) + 2)
                        .map(|(_k, v)| *v)
                        .collect();
                    shifted_powers_of_beta_times_gamma_g.insert(*degree_bound, powers_for_degree_bound);
                }

                end_timer!(shifted_ck_time);

                (Some(shifted_powers_of_beta_g), Some(shifted_powers_of_beta_times_gamma_g))
            }
        } else {
            (None, None)
        };

        let powers_of_beta_g = pp.powers_of_beta_g(0, supported_degree + 1)?;
        let powers_of_beta_times_gamma_g = pp
            .powers_of_beta_times_gamma_g()
            .range(0..=(supported_hiding_bound + 1))
            .map(|(_k, v)| *v)
            .collect::<Vec<_>>();
        if powers_of_beta_times_gamma_g.len() != supported_hiding_bound + 2 {
            return Err(
                PCError::HidingBoundToolarge { hiding_poly_degree: supported_hiding_bound, num_powers: 0 }.into()
            );
        }

        let mut lagrange_bases_at_beta_g = BTreeMap::new();
        for size in supported_lagrange_sizes {
            let lagrange_time = start_timer!(|| format!("Constructing `lagrange_bases` of size {size}"));
            if !size.is_power_of_two() {
                bail!("The Lagrange basis size ({size}) is not a power of two")
            }
            if size > pp.max_degree() + 1 {
                bail!("The Lagrange basis size ({size}) is larger than the supported degree ({})", pp.max_degree() + 1)
            }
            let domain = crate::fft::EvaluationDomain::new(size).unwrap();
            let lagrange_basis_at_beta_g = pp.lagrange_basis(domain)?;
            assert!(lagrange_basis_at_beta_g.len().is_power_of_two());
            lagrange_bases_at_beta_g.insert(domain.size(), lagrange_basis_at_beta_g);
            end_timer!(lagrange_time);
        }

        let ck = CommitterKey {
            powers_of_beta_g,
            lagrange_bases_at_beta_g,
            powers_of_beta_times_gamma_g,
            shifted_powers_of_beta_g,
            shifted_powers_of_beta_times_gamma_g,
            enforced_degree_bounds,
        };

        let vk = pp.to_universal_verifier()?;

        end_timer!(trim_time);
        Ok((ck, vk))
    }

    /// Outputs commitments to `polynomials`.
    ///
    /// If `polynomials[i].is_hiding()`, then the `i`-th commitment is hiding
    /// up to `polynomials.hiding_bound()` queries.
    ///
    /// `rng` should not be `None` if `polynomials[i].is_hiding() == true` for
    /// any `i`.
    ///
    /// If for some `i`, `polynomials[i].is_hiding() == false`, then the
    /// corresponding randomness is `Randomness<E>::empty()`.
    ///
    /// If for some `i`, `polynomials[i].degree_bound().is_some()`, then that
    /// polynomial will have the corresponding degree bound enforced.
    #[allow(clippy::format_push_string)]
    pub fn commit<'b>(
        universal_prover: &UniversalProver<E>,
        ck: &CommitterUnionKey<E>,
        polynomials: impl IntoIterator<Item = LabeledPolynomialWithBasis<'b, E::Fr>>,
        rng: Option<&mut dyn RngCore>,
    ) -> Result<(Vec<LabeledCommitment<Commitment<E>>>, Vec<Randomness<E>>), PCError> {
        let rng = &mut OptionalRng(rng);
        let commit_time = start_timer!(|| "Committing to polynomials");

        let mut pool = snarkvm_utilities::ExecutionPool::<Result<_, _>>::new();
        for p in polynomials {
            let seed = rng.0.as_mut().map(|r| {
                let mut seed = [0u8; 32];
                r.fill_bytes(&mut seed);
                seed
            });

            kzg10::KZG10::<E>::check_degrees_and_bounds(
                universal_prover.max_degree,
                ck.enforced_degree_bounds.as_deref(),
                p.clone(),
            )?;
            let degree_bound = p.degree_bound();
            let hiding_bound = p.hiding_bound();
            let label = p.label().to_string();

            pool.add_job(move || {
                let mut rng = seed.map(rand::rngs::StdRng::from_seed);
                add_to_trace!(|| "PC::Commit", || format!(
                    "Polynomial {} of degree {}, degree bound {:?}, and hiding bound {:?}",
                    label,
                    p.degree(),
                    degree_bound,
                    hiding_bound,
                ));

                let (comm, rand) = {
                    let rng_ref = rng.as_mut().map(|s| s as _);
                    match p.polynomial {
                        PolynomialWithBasis::Lagrange { evaluations } => {
                            let domain = crate::fft::EvaluationDomain::new(evaluations.evaluations.len()).unwrap();
                            let lagrange_basis = ck
                                .lagrange_basis(domain)
                                .ok_or(PCError::UnsupportedLagrangeBasisSize(domain.size()))?;
                            assert!(domain.size().is_power_of_two());
                            assert!(lagrange_basis.size().is_power_of_two());
                            kzg10::KZG10::commit_lagrange(
                                &lagrange_basis,
                                &evaluations.evaluations,
                                hiding_bound,
                                rng_ref,
                            )?
                        }
                        PolynomialWithBasis::Monomial { polynomial, degree_bound } => {
                            let powers = if let Some(degree_bound) = degree_bound {
                                ck.shifted_powers_of_beta_g(degree_bound).unwrap()
                            } else {
                                ck.powers()
                            };

                            kzg10::KZG10::commit(&powers, &polynomial, hiding_bound, rng_ref)?
                        }
                    }
                };

                Ok((LabeledCommitment::new(label.to_string(), comm, degree_bound), rand))
            });
        }
        let results: Vec<Result<_, PCError>> = pool.execute_all();

        let mut labeled_comms = Vec::with_capacity(results.len());
        let mut randomness = Vec::with_capacity(results.len());
        for result in results {
            let (comm, rand) = result?;
            labeled_comms.push(comm);
            randomness.push(rand);
        }

        end_timer!(commit_time);
        Ok((labeled_comms, randomness))
    }

    pub fn combine_for_open<'a>(
        universal_prover: &UniversalProver<E>,
        ck: &CommitterUnionKey<E>,
        labeled_polynomials: impl ExactSizeIterator<Item = &'a LabeledPolynomial<E::Fr>>,
        rands: impl ExactSizeIterator<Item = &'a Randomness<E>>,
        fs_rng: &mut S,
    ) -> Result<(DensePolynomial<E::Fr>, Randomness<E>)>
    where
        Randomness<E>: 'a,
        Commitment<E>: 'a,
    {
        ensure!(labeled_polynomials.len() == rands.len());
        let mut to_combine = Vec::with_capacity(labeled_polynomials.len());

        for (p, r) in labeled_polynomials.zip_eq(rands) {
            let enforced_degree_bounds: Option<&[usize]> = ck.enforced_degree_bounds.as_deref();

            kzg10::KZG10::<E>::check_degrees_and_bounds(universal_prover.max_degree, enforced_degree_bounds, p)?;
            let challenge = fs_rng.squeeze_short_nonnative_field_element::<E::Fr>();
            to_combine.push((challenge, p.polynomial().to_dense(), r));
        }

        Ok(Self::combine_polynomials(to_combine))
    }

    /// On input a list of labeled polynomials and a query set, `open` outputs a
    /// proof of evaluation of the polynomials at the points in the query
    /// set.
    pub fn batch_open<'a>(
        universal_prover: &UniversalProver<E>,
        ck: &CommitterUnionKey<E>,
        labeled_polynomials: impl ExactSizeIterator<Item = &'a LabeledPolynomial<E::Fr>>,
        query_set: &QuerySet<E::Fr>,
        rands: impl ExactSizeIterator<Item = &'a Randomness<E>>,
        fs_rng: &mut S,
    ) -> Result<BatchProof<E>>
    where
        Randomness<E>: 'a,
        Commitment<E>: 'a,
    {
        ensure!(labeled_polynomials.len() == rands.len());
        let poly_rand: HashMap<_, _> =
            labeled_polynomials.into_iter().zip_eq(rands).map(|(poly, r)| (poly.label(), (poly, r))).collect();

        let open_time = start_timer!(|| format!(
            "Opening {} polynomials at query set of size {}",
            poly_rand.len(),
            query_set.len(),
        ));

        let mut query_to_labels_map = BTreeMap::new();

        for (label, (point_name, point)) in query_set.iter() {
            let labels = query_to_labels_map.entry(point_name).or_insert((point, BTreeSet::new()));
            labels.1.insert(label);
        }

        let mut pool = snarkvm_utilities::ExecutionPool::<_>::with_capacity(query_to_labels_map.len());
        for (_point_name, (&query, labels)) in query_to_labels_map.into_iter() {
            let mut query_polys = Vec::with_capacity(labels.len());
            let mut query_rands = Vec::with_capacity(labels.len());

            for label in labels {
                let (polynomial, rand) =
                    poly_rand.get(label as &str).ok_or(PCError::MissingPolynomial { label: label.to_string() })?;

                query_polys.push(*polynomial);
                query_rands.push(*rand);
            }
            let (polynomial, rand) =
                Self::combine_for_open(universal_prover, ck, query_polys.into_iter(), query_rands.into_iter(), fs_rng)?;
            let _randomizer = fs_rng.squeeze_short_nonnative_field_element::<E::Fr>();

            pool.add_job(move || {
                let proof_time = start_timer!(|| "Creating proof");
                let proof = kzg10::KZG10::open(&ck.powers(), &polynomial, query, &rand);
                end_timer!(proof_time);
                proof
            });
        }
        let batch_proof = pool.execute_all().into_iter().collect::<Result<_, _>>().map(BatchProof).map_err(Into::into);
        end_timer!(open_time);

        batch_proof
    }

    pub fn batch_check<'a>(
        vk: &UniversalVerifier<E>,
        commitments: impl IntoIterator<Item = &'a LabeledCommitment<Commitment<E>>>,
        query_set: &QuerySet<E::Fr>,
        values: &Evaluations<E::Fr>,
        proof: &BatchProof<E>,
        fs_rng: &mut S,
    ) -> Result<bool>
    where
        Commitment<E>: 'a,
    {
        let commitments: BTreeMap<_, _> = commitments.into_iter().map(|c| (c.label().to_owned(), c)).collect();
        let batch_check_time = start_timer!(|| format!(
            "Checking {} commitments at query set of size {}",
            commitments.len(),
            query_set.len(),
        ));
        let mut query_to_labels_map = BTreeMap::new();

        for (label, (point_name, point)) in query_set.iter() {
            let labels = query_to_labels_map.entry(point_name).or_insert((point, BTreeSet::new()));
            labels.1.insert(label);
        }

        assert_eq!(proof.0.len(), query_to_labels_map.len());

        let mut randomizer = E::Fr::one();

        let mut combined_comms = BTreeMap::new();
        let mut combined_witness = E::G1Projective::zero();
        let mut combined_adjusted_witness = E::G1Projective::zero();

        ensure!(query_to_labels_map.len() == proof.0.len());
        for ((_query_name, (query, labels)), p) in query_to_labels_map.into_iter().zip_eq(&proof.0) {
            let mut comms_to_combine: Vec<&'_ LabeledCommitment<_>> = Vec::new();
            let mut values_to_combine = Vec::new();
            for label in labels.into_iter() {
                let commitment =
                    commitments.get(label).ok_or(PCError::MissingPolynomial { label: label.to_string() })?;

                let v_i = values
                    .get(&(label.clone(), *query))
                    .ok_or(PCError::MissingEvaluation { label: label.to_string() })?;

                comms_to_combine.push(commitment);
                values_to_combine.push(*v_i);
            }

            Self::accumulate_elems(
                &mut combined_comms,
                &mut combined_witness,
                &mut combined_adjusted_witness,
                vk,
                comms_to_combine.into_iter(),
                *query,
                values_to_combine.into_iter(),
                p,
                Some(randomizer),
                fs_rng,
            )?;

            randomizer = fs_rng.squeeze_short_nonnative_field_element::<E::Fr>();
        }

        let result = Self::check_elems(vk, combined_comms, combined_witness, combined_adjusted_witness);
        end_timer!(batch_check_time);
        result
    }

    pub fn open_combinations<'a>(
        universal_prover: &UniversalProver<E>,
        ck: &CommitterUnionKey<E>,
        linear_combinations: impl IntoIterator<Item = &'a LinearCombination<E::Fr>>,
        polynomials: impl IntoIterator<Item = LabeledPolynomial<E::Fr>>,
        rands: impl IntoIterator<Item = &'a Randomness<E>>,
        query_set: &QuerySet<E::Fr>,
        fs_rng: &mut S,
    ) -> Result<BatchLCProof<E>>
    where
        Randomness<E>: 'a,
        Commitment<E>: 'a,
    {
        let label_map =
            polynomials.into_iter().zip_eq(rands).map(|(p, r)| (p.to_label(), (p, r))).collect::<BTreeMap<_, _>>();

        let mut lc_polynomials = Vec::new();
        let mut lc_randomness = Vec::new();
        let mut lc_info = Vec::new();

        for lc in linear_combinations {
            let lc_label = lc.label().to_string();
            let mut poly = DensePolynomial::zero();
            let mut randomness = Randomness::empty();
            let mut degree_bound = None;
            let mut hiding_bound = None;

            let num_polys = lc.len();
            // We filter out l.is_one() entries because those constants are not committed to
            // and used directly by the verifier.
            for (coeff, label) in lc.iter().filter(|(_, l)| !l.is_one()) {
                let label: &String = label.try_into().expect("cannot be one!");
                let (cur_poly, cur_rand) =
                    label_map.get(label as &str).ok_or(PCError::MissingPolynomial { label: label.to_string() })?;
                if let Some(cur_degree_bound) = cur_poly.degree_bound() {
                    if num_polys != 1 {
                        bail!(PCError::EquationHasDegreeBounds(lc_label));
                    }
                    assert!(coeff.is_one(), "Coefficient must be one for degree-bounded equations");
                    if let Some(old_degree_bound) = degree_bound {
                        assert_eq!(old_degree_bound, cur_degree_bound)
                    } else {
                        degree_bound = cur_poly.degree_bound();
                    }
                }
                // Some(_) > None, always.
                hiding_bound = core::cmp::max(hiding_bound, cur_poly.hiding_bound());
                poly += (*coeff, cur_poly.polynomial());
                randomness += (*coeff, *cur_rand);
            }

            let lc_poly = LabeledPolynomial::new(lc_label.clone(), poly, degree_bound, hiding_bound);
            lc_polynomials.push(lc_poly);
            lc_randomness.push(randomness);
            lc_info.push((lc_label, degree_bound));
        }

        let proof =
            Self::batch_open(universal_prover, ck, lc_polynomials.iter(), query_set, lc_randomness.iter(), fs_rng)?;

        Ok(BatchLCProof { proof })
    }

    /// Checks that `values` are the true evaluations at `query_set` of the
    /// polynomials committed in `labeled_commitments`.
    pub fn check_combinations<'a>(
        vk: &UniversalVerifier<E>,
        linear_combinations: impl IntoIterator<Item = &'a LinearCombination<E::Fr>>,
        commitments: impl IntoIterator<Item = &'a LabeledCommitment<Commitment<E>>>,
        query_set: &QuerySet<E::Fr>,
        evaluations: &Evaluations<E::Fr>,
        proof: &BatchLCProof<E>,
        fs_rng: &mut S,
    ) -> Result<bool>
    where
        Commitment<E>: 'a,
    {
        let BatchLCProof { proof } = proof;
        let label_comm_map = commitments.into_iter().map(|c| (c.label(), c)).collect::<BTreeMap<_, _>>();

        let mut lc_commitments = Vec::new();
        let mut lc_info = Vec::new();
        let mut evaluations = evaluations.clone();

        let lc_processing_time = start_timer!(|| "Combining commitments");
        for lc in linear_combinations {
            let lc_label = lc.label().to_string();
            let num_polys = lc.len();

            let mut degree_bound = None;
            let mut coeffs_and_comms = Vec::new();

            for (coeff, label) in lc.iter() {
                if label.is_one() {
                    for ((label, _), ref mut eval) in evaluations.iter_mut() {
                        if label == &lc_label {
                            **eval -= coeff;
                        }
                    }
                } else {
                    let label: &String = label.try_into().unwrap();
                    let &cur_comm = label_comm_map
                        .get(label as &str)
                        .ok_or(PCError::MissingPolynomial { label: label.to_string() })?;

                    if cur_comm.degree_bound().is_some() {
                        if num_polys != 1 || !coeff.is_one() {
                            bail!(PCError::EquationHasDegreeBounds(lc_label));
                        }
                        degree_bound = cur_comm.degree_bound();
                    }
                    coeffs_and_comms.push((*coeff, cur_comm.commitment()));
                }
            }
            let lc_time = start_timer!(|| format!("Combining {num_polys} commitments for {lc_label}"));
            lc_commitments.push(Self::combine_commitments(coeffs_and_comms));
            end_timer!(lc_time);
            lc_info.push((lc_label, degree_bound));
        }
        end_timer!(lc_processing_time);

        let combined_comms_norm_time = start_timer!(|| "Normalizing commitments");
        let comms = Self::normalize_commitments(lc_commitments);
        ensure!(lc_info.len() == comms.len());
        let lc_commitments = lc_info
            .into_iter()
            .zip_eq(comms)
            .map(|((label, d), c)| LabeledCommitment::new(label, c, d))
            .collect::<Vec<_>>();
        end_timer!(combined_comms_norm_time);

        Self::batch_check(vk, &lc_commitments, query_set, &evaluations, proof, fs_rng)
    }
}

impl<E: PairingEngine, S: AlgebraicSponge<E::Fq, 2>> SonicKZG10<E, S> {
    fn combine_polynomials<'a, B: Borrow<DensePolynomial<E::Fr>>>(
        coeffs_polys_rands: impl IntoIterator<Item = (E::Fr, B, &'a Randomness<E>)>,
    ) -> (DensePolynomial<E::Fr>, Randomness<E>) {
        let mut combined_poly = DensePolynomial::zero();
        let mut combined_rand = Randomness::empty();
        for (coeff, poly, rand) in coeffs_polys_rands {
            let poly = poly.borrow();
            if coeff.is_one() {
                combined_poly += poly;
                combined_rand += rand;
            } else {
                combined_poly += (coeff, poly);
                combined_rand += (coeff, rand);
            }
        }
        (combined_poly, combined_rand)
    }

    /// MSM for `commitments` and `coeffs`
    fn combine_commitments<'a>(
        coeffs_and_comms: impl IntoIterator<Item = (E::Fr, &'a Commitment<E>)>,
    ) -> E::G1Projective {
        let (scalars, bases): (Vec<_>, Vec<_>) = coeffs_and_comms.into_iter().map(|(f, c)| (f.into(), c.0)).unzip();
        VariableBase::msm(&bases, &scalars)
    }

    fn normalize_commitments(commitments: Vec<E::G1Projective>) -> impl ExactSizeIterator<Item = Commitment<E>> {
        let comms = E::G1Projective::batch_normalization_into_affine(commitments);
        comms.into_iter().map(|c| kzg10::KZGCommitment(c))
    }
}

impl<E: PairingEngine, S: AlgebraicSponge<E::Fq, 2>> SonicKZG10<E, S> {
    #[allow(clippy::too_many_arguments)]
    fn accumulate_elems<'a>(
        combined_comms: &mut BTreeMap<Option<usize>, E::G1Projective>,
        combined_witness: &mut E::G1Projective,
        combined_adjusted_witness: &mut E::G1Projective,
        vk: &UniversalVerifier<E>,
        commitments: impl ExactSizeIterator<Item = &'a LabeledCommitment<Commitment<E>>>,
        point: E::Fr,
        values: impl ExactSizeIterator<Item = E::Fr>,
        proof: &kzg10::KZGProof<E>,
        randomizer: Option<E::Fr>,
        fs_rng: &mut S,
    ) -> Result<()> {
        let acc_time = start_timer!(|| "Accumulating elements");
        // Keeps track of running combination of values
        let mut combined_values = E::Fr::zero();

        // Iterates through all of the commitments and accumulates common degree_bound
        // elements in a BTreeMap
        ensure!(commitments.len() == values.len());
        for (labeled_comm, value) in commitments.into_iter().zip_eq(values) {
            let acc_timer = start_timer!(|| format!("Accumulating {}", labeled_comm.label()));
            let curr_challenge = fs_rng.squeeze_short_nonnative_field_element::<E::Fr>();

            combined_values += &(value * curr_challenge);

            let comm = labeled_comm.commitment();
            let degree_bound = labeled_comm.degree_bound();

            // Applying opening challenge and randomness (used in batch_checking)
            let coeff = randomizer.unwrap_or_else(E::Fr::one) * curr_challenge;
            let comm_with_challenge: E::G1Projective = comm.0.mul(coeff);

            // Accumulate values in the BTreeMap
            *combined_comms.entry(degree_bound).or_insert_with(E::G1Projective::zero) += &comm_with_challenge;
            end_timer!(acc_timer);
        }

        // Push expected results into list of elems. Power will be the negative of the
        // expected power
        let mut bases = vec![vk.vk.g, -proof.w];
        let mut coeffs = vec![combined_values, point];
        if let Some(random_v) = proof.random_v {
            bases.push(vk.vk.gamma_g);
            coeffs.push(random_v);
        }
        *combined_witness += if let Some(randomizer) = randomizer {
            coeffs.iter_mut().for_each(|c| *c *= randomizer);
            proof.w.mul(randomizer)
        } else {
            proof.w.to_projective()
        };
        let coeffs = coeffs.into_iter().map(|c| c.into()).collect::<Vec<_>>();
        *combined_adjusted_witness += VariableBase::msm(&bases, &coeffs);
        end_timer!(acc_time);
        Ok(())
    }

    fn check_elems(
        vk: &UniversalVerifier<E>,
        combined_comms: BTreeMap<Option<usize>, E::G1Projective>,
        combined_witness: E::G1Projective,
        combined_adjusted_witness: E::G1Projective,
    ) -> Result<bool> {
        let check_time = start_timer!(|| "Checking elems");
        let mut g1_projective_elems = Vec::with_capacity(combined_comms.len() + 2);
        let mut g2_prepared_elems = Vec::with_capacity(combined_comms.len() + 2);

        for (degree_bound, comm) in combined_comms.into_iter() {
            let shift_power = if let Some(degree_bound) = degree_bound {
                // Find the appropriate prepared shift for the degree bound.
                vk.prepared_negative_powers_of_beta_h
                    .get(&degree_bound)
                    .cloned()
                    .ok_or(PCError::UnsupportedDegreeBound(degree_bound))?
            } else {
                vk.vk.prepared_h.clone()
            };

            g1_projective_elems.push(comm);
            g2_prepared_elems.push(shift_power);
        }

        g1_projective_elems.push(-combined_adjusted_witness);
        g2_prepared_elems.push(vk.vk.prepared_h.clone());

        g1_projective_elems.push(-combined_witness);
        g2_prepared_elems.push(vk.vk.prepared_beta_h.clone());

        let g1_prepared_elems_iter = E::G1Projective::batch_normalization_into_affine(g1_projective_elems)
            .into_iter()
            .map(|a| a.prepare())
            .collect::<Vec<_>>();

        ensure!(g1_prepared_elems_iter.len() == g2_prepared_elems.len());
        let g1_g2_prepared = g1_prepared_elems_iter.iter().zip_eq(g2_prepared_elems.iter());
        let is_one: bool = E::product_of_pairings(g1_g2_prepared).is_one();
        end_timer!(check_time);
        Ok(is_one)
    }
}

#[cfg(test)]
mod tests {
    #![allow(non_camel_case_types)]

    use super::{CommitterKey, SonicKZG10};
    use crate::{crypto_hash::PoseidonSponge, polycommit::test_templates::*};
    use snarkvm_curves::bls12_377::{Bls12_377, Fq};
    use snarkvm_utilities::{FromBytes, ToBytes, rand::TestRng};

    use rand::distributions::Distribution;

    type Sponge = PoseidonSponge<Fq, 2, 1>;
    type PC_Bls12_377 = SonicKZG10<Bls12_377, Sponge>;

    #[test]
    fn test_committer_key_serialization() {
        let rng = &mut TestRng::default();
        let max_degree = rand::distributions::Uniform::from(8..=64).sample(rng);
        let supported_degree = rand::distributions::Uniform::from(1..=max_degree).sample(rng);

        let lagrange_size = |d: usize| if d.is_power_of_two() { d } else { d.next_power_of_two() >> 1 };

        let pp = PC_Bls12_377::load_srs(max_degree).unwrap();

        let (ck, _vk) = PC_Bls12_377::trim(&pp, supported_degree, [lagrange_size(supported_degree)], 0, None).unwrap();

        let ck_bytes = ck.to_bytes_le().unwrap();
        let ck_recovered: CommitterKey<Bls12_377> = FromBytes::read_le(&ck_bytes[..]).unwrap();
        let ck_recovered_bytes = ck_recovered.to_bytes_le().unwrap();

        assert_eq!(&ck_bytes, &ck_recovered_bytes);
    }

    #[test]
    fn test_single_poly() {
        single_poly_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
    }

    #[test]
    fn test_quadratic_poly_degree_bound_multiple_queries() {
        quadratic_poly_degree_bound_multiple_queries_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
    }

    #[test]
    fn test_linear_poly_degree_bound() {
        linear_poly_degree_bound_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
    }

    #[test]
    fn test_single_poly_degree_bound() {
        single_poly_degree_bound_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
    }

    #[test]
    fn test_single_poly_degree_bound_multiple_queries() {
        single_poly_degree_bound_multiple_queries_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
    }

    #[test]
    fn test_two_polys_degree_bound_single_query() {
        two_polys_degree_bound_single_query_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
    }

    #[test]
    fn test_full_end_to_end() {
        full_end_to_end_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
        println!("Finished bls12-377");
    }

    #[test]
    fn test_single_equation() {
        single_equation_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
        println!("Finished bls12-377");
    }

    #[test]
    fn test_two_equation() {
        two_equation_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
        println!("Finished bls12-377");
    }

    #[test]
    fn test_two_equation_degree_bound() {
        two_equation_degree_bound_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
        println!("Finished bls12-377");
    }

    #[test]
    fn test_full_end_to_end_equation() {
        full_end_to_end_equation_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
        println!("Finished bls12-377");
    }

    #[test]
    #[should_panic]
    fn test_bad_degree_bound() {
        bad_degree_bound_test::<Bls12_377, Sponge>().expect("test failed for bls12-377");
        println!("Finished bls12-377");
    }

    #[test]
    fn test_lagrange_commitment() {
        crate::polycommit::test_templates::lagrange_test_template::<Bls12_377, Sponge>()
            .expect("test failed for bls12-377");
        println!("Finished bls12-377");
    }
}