Module commitment

This module implements Dlog-based polynomial commitment schema. The following functionality is implemented

1. Commit to polynomial with its max degree
2. Open polynomial commitment batch at the given evaluation point and scaling factor scalar producing the batched opening proof
3. Verify batch of batched opening proofs

Modules

caml

Structs

BatchEvaluationProof

Contains the batch evaluation

BlindedCommitment

A commitment to a polynomial with some blinding factors.

Evaluation

Contains the evaluation of a polynomial commitment at a set of points.

PolyComm

Represent a polynomial commitment when the type is instantiated with a curve.

Traits

CommitmentCurve

A useful trait extending AffineRepr for commitments. Unfortunately, we can’t specify that AffineRepr<BaseField : PrimeField>, so usage of this traits must manually bind G::BaseField: PrimeField.

EndoCurve

A trait extending CommitmentCurve for endomorphisms. Unfortunately, we can’t specify that AffineRepr<BaseField : PrimeField>, so usage of this traits must manually bind G::BaseField: PrimeField.

Functions

absorb_commitment

b_poly

Returns (1 + chal[-1] x)(1 + chal[-2] x^2)(1 + chal[-3] x^4) … It’s “step 8: Define the univariate polynomial” of appendix A.2 of https://eprint.iacr.org/2020/499

b_poly_coefficients

combine_commitments

This function populates the parameters scalars and points. It iterates over the evaluations and adds each commitment to the vector points. The parameter scalars is populated with the values: rand_base * polyscale^i for each commitment. For instance, if we have 3 commitments, the scalars vector will contain the values

combined_inner_product

Computes the linearization of the evaluations of a (potentially split) polynomial.

shift_scalar

Inside the circuit, we have a specialized scalar multiplication which computes either

squeeze_challenge

squeeze_prechallenge