Struct MixComposition

pub struct MixComposition<P: PackedField, IC> { /* private fields */ }

A composition polynomial that securely batches several underlying multivariate polynomials.

Given several sumcheck instances over different multivariate polynomials, it is a useful optimization to batch them together by taking a linear combination. Since sumcheck verifies the sum of the values of a multivariate’s evaluations, the summation over the hypercube commutes with a linear combination of the polynomials.

The MixComposition chooses the multiplicative coefficients so that a batched sumcheck on the composed polynomial succeeds if and only if all of the underlying sumcheck statements would also succeed (with high probability). The current implementation uses powers of an interactively verifier-sampled challenge as mixing coefficients, and soundness of the batching technique holds following the Schwartz-Zippel lemma.

Implementations

impl<P: PackedField, IC> MixComposition<P, IC>

pub fn include<Q>( self, compositions: Q, ) -> Result<MixComposition<P, (Vec<Q::Item>, IC)>, Error>

where Q: IntoIterator, Q::Item: CompositionPolyOS<P>,

impl<P: PackedField, IC: HornerCompositions<P>> MixComposition<P, IC>

pub fn evaluate_with_inner_evals( &self, inner_evals: &[P::Scalar], ) -> Result<P::Scalar, Error>

Trait Implementations

impl<P: Clone + PackedField, IC: Clone> Clone for MixComposition<P, IC>

where P::Scalar: Clone,

fn clone(&self) -> MixComposition<P, IC>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<P, IC> CompositionPolyOS<P> for MixComposition<P, IC>

where P: PackedField<Scalar: TowerField>, IC: HornerCompositions<P> + Clone + Debug + Send + Sync,

fn n_vars(&self) -> usize

The number of variables.

fn degree(&self) -> usize

Total degree of the polynomial.

fn evaluate(&self, query: &[P]) -> Result<P, Error>

Evaluates the polynomial using packed values, where each packed value may contain multiple scalar values. The evaluation follows SIMD semantics, meaning that operations are performed element-wise across corresponding scalar values in the packed values.

fn binary_tower_level(&self) -> usize

Returns the maximum binary tower level of all constants in the arithmetic expression.

fn batch_evaluate( &self, batch_query: &[&[P]], evals: &mut [P], ) -> Result<(), Error>

Batch evaluation that admits non-strided argument layout. batch_query is a slice of slice references of equal length, which furthermore should equal the length of evals parameter.

impl<P: Debug + PackedField, IC: Debug> Debug for MixComposition<P, IC>

where P::Scalar: Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.