p3_commit/pcs/

univariate.rs

//! Traits for univariate polynomial commitment schemes.

use alloc::vec::Vec;
use core::fmt::Debug;

use p3_field::ExtensionField;
use p3_matrix::Matrix;
use p3_matrix::dense::RowMajorMatrix;
use serde::Serialize;
use serde::de::DeserializeOwned;

use crate::{PeriodicLdeTable, PolynomialSpace};

pub type Val<D> = <D as PolynomialSpace>::Val;

/// A polynomial commitment scheme, for committing to batches of polynomials defined by their evaluations
/// over some domain.
///
/// In general this does not have to be a hiding commitment scheme but it might be for some implementations.
// TODO: Should we have a super-trait for weakly-binding PCSs, like FRI outside unique decoding radius?
pub trait Pcs<Challenge, Challenger>
where
    Challenge: ExtensionField<Val<Self::Domain>>,
{
    /// The class of evaluation domains that this commitment scheme works over.
    type Domain: PolynomialSpace;

    /// The commitment that's sent to the verifier.
    type Commitment: Clone + Serialize + DeserializeOwned;

    /// Data that the prover stores for committed polynomials, to help the prover with opening.
    type ProverData;

    /// Type of the output of `get_evaluations_on_domain`.
    type EvaluationsOnDomain<'a>: Matrix<Val<Self::Domain>> + 'a;

    /// The opening argument.
    type Proof: Clone + Serialize + DeserializeOwned;

    /// The type of a proof verification error.
    type Error: Debug;

    /// Set to true to activate randomization and achieve zero-knowledge.
    const ZK: bool;

    /// Index of the trace commitment in the computed opened values.
    const TRACE_IDX: usize = Self::ZK as usize;

    /// Index of the quotient commitments in the computed opened values.
    const QUOTIENT_IDX: usize = Self::TRACE_IDX + 1;

    /// Index of the preprocessed trace commitment in the computed opened values.
    const PREPROCESSED_TRACE_IDX: usize = Self::QUOTIENT_IDX + 1; // Note: not always present

    /// This should return a domain such that `Domain::next_point` returns `Some`.
    fn natural_domain_for_degree(&self, degree: usize) -> Self::Domain;

    /// The base-2 logarithm of the largest evaluation domain this PCS can construct.
    fn log_max_lde_height(&self) -> usize;

    /// Given a collection of evaluation matrices, produce a binding commitment to
    /// the polynomials defined by those evaluations. If `zk` is enabled, the evaluations are
    /// first randomized as explained in Section 3 of <https://eprint.iacr.org/2024/1037.pdf>.
    ///
    /// Returns both the commitment which should be sent to the verifier
    /// and the prover data which can be used to produce opening proofs.
    #[allow(clippy::type_complexity)]
    fn commit(
        &self,
        evaluations: impl IntoIterator<Item = (Self::Domain, RowMajorMatrix<Val<Self::Domain>>)>,
    ) -> (Self::Commitment, Self::ProverData);

    /// Same as `commit` but without randomization. This is used for preprocessed columns
    /// which do not have to be randomized even when ZK is enabled. Note that the preprocessed columns still
    /// need to be padded to the extended domain height.
    ///
    /// Returns both the commitment which should be sent to the verifier
    /// and the prover data which can be used to produce opening proofs.
    fn commit_preprocessing(
        &self,
        evaluations: impl IntoIterator<Item = (Self::Domain, RowMajorMatrix<Val<Self::Domain>>)>,
    ) -> (Self::Commitment, Self::ProverData) {
        self.commit(evaluations)
    }

    /// Commit to the quotient polynomial. We first decompose the quotient polynomial into
    /// `num_chunks` many smaller polynomials each of degree `degree / num_chunks`.
    /// This can have minor performance benefits, but is not strictly necessary in the non `zk` case.
    /// When `zk` is enabled, this commitment will additionally include some randomization process
    /// to hide the inputs.
    ///
    /// ### Arguments
    /// - `quotient_domain` the domain of the quotient polynomial.
    /// - `quotient_evaluations` the evaluations of the quotient polynomial over the domain. This should be in
    ///   standard (not bit-reversed) order.
    /// - `num_chunks` the number of smaller polynomials to decompose the quotient polynomial into.
    #[allow(clippy::type_complexity)]
    fn commit_quotient(
        &self,
        quotient_domain: Self::Domain,
        quotient_evaluations: RowMajorMatrix<Val<Self::Domain>>,
        num_chunks: usize,
    ) -> (Self::Commitment, Self::ProverData) {
        // Given the evaluation vector of `Q_i(x)` over a domain, split it into evaluation vectors
        // of `q_{i0}(x), ...` over subdomains and commit to these `q`'s.
        // TODO: Currently, split_evals involves copying the data to a new matrix.
        //       We may be able to avoid this copy making use of bit-reversals.
        let quotient_sub_evaluations =
            quotient_domain.split_evals(num_chunks, quotient_evaluations);
        let quotient_sub_domains = quotient_domain.split_domains(num_chunks);

        let ldes = self.get_quotient_ldes(
            quotient_sub_domains
                .into_iter()
                .zip(quotient_sub_evaluations),
            num_chunks,
        );
        self.commit_ldes(ldes)
    }

    /// When committing to quotient polynomials in batch-STARK,
    /// it is simpler to first compute the LDE evaluations before batch-committing to them.
    ///
    /// This corresponds to the first step of `commit_quotient`. When `zk` is enabled,
    /// this will additionally add randomization.
    fn get_quotient_ldes(
        &self,
        evaluations: impl IntoIterator<Item = (Self::Domain, RowMajorMatrix<Val<Self::Domain>>)>,
        num_chunks: usize,
    ) -> Vec<RowMajorMatrix<Val<Self::Domain>>>;

    /// Commits to a collection of LDE evaluation matrices.
    fn commit_ldes(
        &self,
        ldes: Vec<RowMajorMatrix<Val<Self::Domain>>>,
    ) -> (Self::Commitment, Self::ProverData);

    /// Given prover data corresponding to a commitment to a collection of evaluation matrices,
    /// return the evaluations of those matrices on the given domain.
    ///
    /// This is essentially a no-op when called with a `domain` which is a subset of the evaluation domain
    /// on which the evaluation matrices are defined.
    fn get_evaluations_on_domain<'a>(
        &self,
        prover_data: &'a Self::ProverData,
        idx: usize,
        domain: Self::Domain,
    ) -> Self::EvaluationsOnDomain<'a>;

    /// This is the same as `get_evaluations_on_domain` but without randomization.
    /// This is used for preprocessed columns which do not have to be randomized even when ZK is enabled.
    fn get_evaluations_on_domain_no_random<'a>(
        &self,
        prover_data: &'a Self::ProverData,
        idx: usize,
        domain: Self::Domain,
    ) -> Self::EvaluationsOnDomain<'a> {
        self.get_evaluations_on_domain(prover_data, idx, domain)
    }

    /// Open a collection of polynomial commitments at a set of points. Produce the values at those points along with a proof
    /// of correctness.
    ///
    /// Arguments:
    /// - `commitment_data_with_opening_points`: A vector whose elements are a pair:
    ///     - `data`: The prover data corresponding to a multi-matrix commitment.
    ///     - `opening_points`: A vector containing, for each matrix committed to, a vector of opening points.
    /// - `fiat_shamir_challenger`: The challenger that will be used to generate the proof.
    ///
    /// Unwrapping the arguments further, each `data` contains a vector of the committed matrices (`matrices = Vec<M>`).
    /// If the length of `matrices` is not equal to the length of `opening_points` the function will error. Otherwise, for
    /// each index `i`, the matrix `M = matrices[i]` will be opened at the points `opening_points[i]`.
    ///
    /// This means that each column of `M` will be interpreted as the evaluation vector of some polynomial
    /// and we will compute the value of all of those polynomials at `opening_points[i]`.
    ///
    /// The domains on which the evaluation vectors are defined is not part of the arguments here
    /// but should be public information known to both the prover and verifier.
    fn open(
        &self,
        // For each multi-matrix commitment,
        commitment_data_with_opening_points: Vec<(
            // The matrices and auxiliary prover data
            &Self::ProverData,
            // for each matrix,
            Vec<
                // the points to open
                Vec<Challenge>,
            >,
        )>,
        fiat_shamir_challenger: &mut Challenger,
    ) -> (OpenedValues<Challenge>, Self::Proof);

    /// Open a collection of polynomial commitments at a set of points, when there is preprocessing data.
    /// It is the same as `open` when `ZK` is disabled.
    /// Produce the values at those points along with a proof of correctness.
    ///
    /// Arguments:
    /// - `commitment_data_with_opening_points`: A vector whose elements are a pair:
    ///     - `data`: The prover data corresponding to a multi-matrix commitment.
    ///     - `opening_points`: A vector containing, for each matrix committed to, a vector of opening points.
    /// - `fiat_shamir_challenger`: The challenger that will be used to generate the proof.
    /// - `is_preprocessing`: If one of the committed matrices corresponds to preprocessed columns, this is the index of that matrix.
    ///
    /// Unwrapping the arguments further, each `data` contains a vector of the committed matrices (`matrices = Vec<M>`).
    /// If the length of `matrices` is not equal to the length of `opening_points` the function will error. Otherwise, for
    /// each index `i`, the matrix `M = matrices[i]` will be opened at the points `opening_points[i]`.
    ///
    /// This means that each column of `M` will be interpreted as the evaluation vector of some polynomial
    /// and we will compute the value of all of those polynomials at `opening_points[i]`.
    ///
    /// The domains on which the evaluation vectors are defined is not part of the arguments here
    /// but should be public information known to both the prover and verifier.
    fn open_with_preprocessing(
        &self,
        // For each multi-matrix commitment,
        commitment_data_with_opening_points: Vec<(
            // The matrices and auxiliary prover data
            &Self::ProverData,
            // for each matrix,
            Vec<
                // the points to open
                Vec<Challenge>,
            >,
        )>,
        fiat_shamir_challenger: &mut Challenger,
        _is_preprocessing: bool,
    ) -> (OpenedValues<Challenge>, Self::Proof) {
        assert!(
            !Self::ZK,
            "open_with_preprocessing should have a different implementation when ZK is enabled"
        );
        self.open(commitment_data_with_opening_points, fiat_shamir_challenger)
    }

    /// Verify that a collection of opened values is correct.
    ///
    /// Arguments:
    /// - `commitments_with_opening_points`: A vector whose elements are a pair:
    ///     - `commitment`: A multi matrix commitment.
    ///     - `opening_points`: A vector containing, for each matrix committed to, a vector of opening points and claimed evaluations.
    /// - `proof`: A claimed proof of correctness for the opened values.
    /// - `fiat_shamir_challenger`: The challenger that will be used to generate the proof.
    #[allow(clippy::type_complexity)]
    fn verify(
        &self,
        // For each commitment:
        commitments_with_opening_points: Vec<(
            // The commitment
            Self::Commitment,
            // for each matrix in the commitment:
            Vec<(
                // its domain,
                Self::Domain,
                // A vector of (point, claimed_evaluation) pairs
                Vec<(
                    // the point the matrix was opened at,
                    Challenge,
                    // the claimed evaluations at that point
                    Vec<Challenge>,
                )>,
            )>,
        )>,
        // The opening proof for all claimed evaluations.
        proof: &Self::Proof,
        fiat_shamir_challenger: &mut Challenger,
    ) -> Result<(), Self::Error>;

    fn get_opt_randomization_poly_commitment(
        &self,
        _domain: impl IntoIterator<Item = Self::Domain>,
    ) -> Option<(Self::Commitment, Self::ProverData)> {
        None
    }

    /// Build the compact periodic LDE table (height = max_period × blowup, width = num periodic columns).
    ///
    /// Default: evaluate each column at the first `extended_height` quotient points. Backends that
    /// can compute this faster (e.g. via coset LDE) should override this method.
    fn build_periodic_lde_table(
        &self,
        periodic_cols: &[Vec<Val<Self::Domain>>],
        trace_domain: Self::Domain,
        quotient_domain: Self::Domain,
    ) -> PeriodicLdeTable<Val<Self::Domain>>
    where
        Self::Domain: Clone,
        Val<Self::Domain>: Clone,
    {
        if periodic_cols.is_empty() {
            return PeriodicLdeTable::empty();
        }
        let trace_size = trace_domain.size();
        let quotient_size = quotient_domain.size();
        assert!(
            quotient_size >= trace_size,
            "quotient domain size ({quotient_size}) must be >= trace domain size ({trace_size})",
        );
        assert!(
            quotient_size.is_multiple_of(trace_size),
            "quotient domain size ({quotient_size}) must be divisible by trace domain size ({trace_size})",
        );
        let blowup = quotient_size / trace_size;

        for col in periodic_cols {
            let period = col.len();
            assert!(
                period > 0 && period.is_power_of_two(),
                "periodic column length must be a non-zero power of 2, got {period}",
            );
            assert!(
                trace_size.is_multiple_of(period),
                "trace domain size ({trace_size}) must be divisible by periodic column length ({period})",
            );
        }
        let max_period = periodic_cols.iter().map(|c| c.len()).max().unwrap();
        let extended_height = max_period
            .checked_mul(blowup)
            .expect("extended height overflow when computing max_period * blowup");
        // Implied by the column checks above.
        // Each period divides the trace size, so max_period <= trace_size.
        // Therefore extended_height = max_period * blowup <= trace_size * blowup = quotient_size.
        debug_assert!(extended_height <= quotient_size);
        let num_cols = periodic_cols.len();
        let row_major_capacity = extended_height
            .checked_mul(num_cols)
            .expect("row-major periodic table capacity overflow");

        let mut quotient_pts = Vec::with_capacity(extended_height);
        let mut pt = quotient_domain.first_point();
        for _ in 0..extended_height {
            quotient_pts.push(pt);
            pt = quotient_domain
                .next_point(pt)
                .expect("quotient domain must support next_point");
        }

        let padded_cols: Vec<Vec<Val<Self::Domain>>> = periodic_cols
            .iter()
            .map(|col| (0..max_period).map(|i| col[i % col.len()]).collect())
            .collect();

        let mut row_major = Vec::with_capacity(row_major_capacity);
        for point in quotient_pts.iter().take(extended_height) {
            for padded in &padded_cols {
                row_major.push(trace_domain.evaluate_periodic_column_at(padded, *point));
            }
        }
        PeriodicLdeTable::new(RowMajorMatrix::new(row_major, num_cols))
    }
}

pub type OpenedValues<F> = Vec<OpenedValuesForRound<F>>;
pub type OpenedValuesForRound<F> = Vec<OpenedValuesForMatrix<F>>;
pub type OpenedValuesForMatrix<F> = Vec<OpenedValuesForPoint<F>>;
pub type OpenedValuesForPoint<F> = Vec<F>;