Struct ark_poly_commit::ipa_pc::InnerProductArgPC

pub struct InnerProductArgPC<G: AffineCurve, D: Digest, P: UVPolynomial<G::ScalarField>> { /* fields omitted */ }

A polynomial commitment scheme based on the hardness of the discrete logarithm problem in prime-order groups. The construction is described in detail in [BCMS20].

Degree bound enforcement requires that (at least one of) the points at which a committed polynomial is evaluated are from a distribution that is random conditioned on the polynomial. This is because degree bound enforcement relies on checking a polynomial identity at this point. More formally, the points must be sampled from an admissible query sampler, as detailed in [CHMMVW20].

Implementations

impl<G: AffineCurve, D: Digest, P: UVPolynomial<G::ScalarField>> InnerProductArgPC<G, D, P>

pub const PROTOCOL_NAME: &'static [u8]

PROTOCOL_NAME is used as a seed for the setup function.

Trait Implementations

impl<G, D, P> PolynomialCommitment<<G as AffineCurve>::ScalarField, P> for InnerProductArgPC<G, D, P> where
    G: AffineCurve,
    D: Digest,
    P: UVPolynomial<G::ScalarField, Point = G::ScalarField>, 

type UniversalParams = UniversalParams<G>

The universal parameters for the commitment scheme. These are “trimmed” down to Self::CommitterKey and Self::VerifierKey by Self::trim.

type CommitterKey = CommitterKey<G>

The committer key for the scheme; used to commit to a polynomial and then open the commitment to produce an evaluation proof.

type VerifierKey = VerifierKey<G>

The verifier key for the scheme; used to check an evaluation proof.

type PreparedVerifierKey = PreparedVerifierKey<G>

The prepared verifier key for the scheme; used to check an evaluation proof.

type Commitment = Commitment<G>

The commitment to a polynomial.

type PreparedCommitment = PreparedCommitment<G>

The prepared commitment to a polynomial.

type Randomness = Randomness<G>

The commitment randomness.

type Proof = Proof<G>

The evaluation proof for a single point.

type BatchProof = Vec<Self::Proof>

The evaluation proof for a query set.

type Error = Error

The error type for the scheme.

fn setup<R: RngCore>(
    max_degree: usize,
    _: Option<usize>,
    _rng: &mut R
) -> Result<Self::UniversalParams, Self::Error>

Constructs public parameters when given as input the maximum degree degree for the polynomial commitment scheme. num_vars specifies the number of variables for multivariate setup

fn trim(
    pp: &Self::UniversalParams,
    supported_degree: usize,
    _supported_hiding_bound: usize,
    _enforced_degree_bounds: Option<&[usize]>
) -> Result<(Self::CommitterKey, Self::VerifierKey), Self::Error>

Specializes the public parameters for polynomials up to the given supported_degree and for enforcing degree bounds in the range 1..=supported_degree.

fn commit<'a>(
    ck: &Self::CommitterKey,
    polynomials: impl IntoIterator<Item = &'a LabeledPolynomial<G::ScalarField, P>>,
    rng: Option<&mut dyn RngCore>
) -> Result<(Vec<LabeledCommitment<Self::Commitment>>, Vec<Self::Randomness>), Self::Error> where
    P: 'a, 

Outputs a commitment to polynomial.

fn open_individual_opening_challenges<'a>(
    ck: &Self::CommitterKey,
    labeled_polynomials: impl IntoIterator<Item = &'a LabeledPolynomial<G::ScalarField, P>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    point: &'a P::Point,
    opening_challenges: &dyn Fn(u64) -> G::ScalarField,
    rands: impl IntoIterator<Item = &'a Self::Randomness>,
    rng: Option<&mut dyn RngCore>
) -> Result<Self::Proof, Self::Error> where
    Self::Commitment: 'a,
    Self::Randomness: 'a,
    P: 'a, 

open but with individual challenges

fn check_individual_opening_challenges<'a>(
    vk: &Self::VerifierKey,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    point: &'a P::Point,
    values: impl IntoIterator<Item = G::ScalarField>,
    proof: &Self::Proof,
    opening_challenges: &dyn Fn(u64) -> G::ScalarField,
    _rng: Option<&mut dyn RngCore>
) -> Result<bool, Self::Error> where
    Self::Commitment: 'a, 

check but with individual challenges

fn batch_check_individual_opening_challenges<'a, R: RngCore>(
    vk: &Self::VerifierKey,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    query_set: &QuerySet<P::Point>,
    values: &Evaluations<G::ScalarField, P::Point>,
    proof: &Self::BatchProof,
    opening_challenges: &dyn Fn(u64) -> G::ScalarField,
    rng: &mut R
) -> Result<bool, Self::Error> where
    Self::Commitment: 'a, 

batch_check but with individual challenges

fn open_combinations_individual_opening_challenges<'a>(
    ck: &Self::CommitterKey,
    lc_s: impl IntoIterator<Item = &'a LinearCombination<G::ScalarField>>,
    polynomials: impl IntoIterator<Item = &'a LabeledPolynomial<G::ScalarField, P>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    query_set: &QuerySet<P::Point>,
    opening_challenges: &dyn Fn(u64) -> G::ScalarField,
    rands: impl IntoIterator<Item = &'a Self::Randomness>,
    rng: Option<&mut dyn RngCore>
) -> Result<BatchLCProof<G::ScalarField, P, Self>, Self::Error> where
    Self::Randomness: 'a,
    Self::Commitment: 'a,
    P: 'a, 

open_combinations but with individual challenges

fn check_combinations_individual_opening_challenges<'a, R: RngCore>(
    vk: &Self::VerifierKey,
    lc_s: impl IntoIterator<Item = &'a LinearCombination<G::ScalarField>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    query_set: &QuerySet<G::ScalarField>,
    evaluations: &Evaluations<G::ScalarField, P::Point>,
    proof: &BatchLCProof<G::ScalarField, P, Self>,
    opening_challenges: &dyn Fn(u64) -> G::ScalarField,
    rng: &mut R
) -> Result<bool, Self::Error> where
    Self::Commitment: 'a, 

Checks that values are the true evaluations at query_set of the polynomials committed in labeled_commitments.

fn open<'a>(
    ck: &Self::CommitterKey,
    labeled_polynomials: impl IntoIterator<Item = &'a LabeledPolynomial<F, P>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    point: &'a P::Point,
    opening_challenge: F,
    rands: impl IntoIterator<Item = &'a Self::Randomness>,
    rng: Option<&mut dyn RngCore>
) -> Result<Self::Proof, Self::Error> where
    P: 'a,
    Self::Randomness: 'a,
    Self::Commitment: 'a, 

On input a list of labeled polynomials and a query point, open outputs a proof of evaluation of the polynomials at the query point.

fn batch_open<'a>(
    ck: &Self::CommitterKey,
    labeled_polynomials: impl IntoIterator<Item = &'a LabeledPolynomial<F, P>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    query_set: &QuerySet<P::Point>,
    opening_challenge: F,
    rands: impl IntoIterator<Item = &'a Self::Randomness>,
    rng: Option<&mut dyn RngCore>
) -> Result<Self::BatchProof, Self::Error> where
    Self::Randomness: 'a,
    Self::Commitment: 'a,
    P: 'a, 

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.

fn check<'a>(
    vk: &Self::VerifierKey,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    point: &'a P::Point,
    values: impl IntoIterator<Item = F>,
    proof: &Self::Proof,
    opening_challenge: F,
    rng: Option<&mut dyn RngCore>
) -> Result<bool, Self::Error> where
    Self::Commitment: 'a, 

Verifies that values are the evaluations at point of the polynomials committed inside commitments.

fn batch_check<'a, R: RngCore>(
    vk: &Self::VerifierKey,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    query_set: &QuerySet<P::Point>,
    evaluations: &Evaluations<P::Point, F>,
    proof: &Self::BatchProof,
    opening_challenge: F,
    rng: &mut R
) -> Result<bool, Self::Error> where
    Self::Commitment: 'a, 

Checks that values are the true evaluations at query_set of the polynomials committed in labeled_commitments.

fn open_combinations<'a>(
    ck: &Self::CommitterKey,
    linear_combinations: impl IntoIterator<Item = &'a LinearCombination<F>>,
    polynomials: impl IntoIterator<Item = &'a LabeledPolynomial<F, P>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    query_set: &QuerySet<P::Point>,
    opening_challenge: F,
    rands: impl IntoIterator<Item = &'a Self::Randomness>,
    rng: Option<&mut dyn RngCore>
) -> Result<BatchLCProof<F, P, Self>, Self::Error> where
    P: 'a,
    Self::Randomness: 'a,
    Self::Commitment: 'a, 

On input a list of polynomials, linear combinations of those polynomials, and a query set, open_combination outputs a proof of evaluation of the combinations at the points in the query set.

fn check_combinations<'a, R: RngCore>(
    vk: &Self::VerifierKey,
    linear_combinations: impl IntoIterator<Item = &'a LinearCombination<F>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    eqn_query_set: &QuerySet<P::Point>,
    eqn_evaluations: &Evaluations<P::Point, F>,
    proof: &BatchLCProof<F, P, Self>,
    opening_challenge: F,
    rng: &mut R
) -> Result<bool, Self::Error> where
    Self::Commitment: 'a, 

Checks that evaluations are the true evaluations at query_set of the linear combinations of polynomials committed in commitments.

fn batch_open_individual_opening_challenges<'a>(
    ck: &Self::CommitterKey,
    labeled_polynomials: impl IntoIterator<Item = &'a LabeledPolynomial<F, P>>,
    commitments: impl IntoIterator<Item = &'a LabeledCommitment<Self::Commitment>>,
    query_set: &QuerySet<P::Point>,
    opening_challenges: &dyn Fn(u64) -> F,
    rands: impl IntoIterator<Item = &'a Self::Randomness>,
    rng: Option<&mut dyn RngCore>
) -> Result<Self::BatchProof, Self::Error> where
    P: 'a,
    Self::Randomness: 'a,
    Self::Commitment: 'a, 

batch_open with individual challenges