libsnark::kzg10_batched_2_point< ppT > Class Template Reference

#include <kzg10_batched.hpp>

Classes
class	evaluation_witness
class	evaluations

Public Types
using	Field = libff::Fr< ppT >
using	srs = typename kzg10< ppT >::srs
using	commitment = typename kzg10< ppT >::commitment

Static Public Member Functions
static evaluations	evaluate_polynomials (const std::vector< polynomial< Field >> &fs, const std::vector< polynomial< Field >> &gs, const Field &z_1, const Field &z_2)
static evaluation_witness	create_evaluation_witness (const std::vector< polynomial< Field >> &fs, const std::vector< polynomial< Field >> &gs, const Field &z_1, const Field &z_2, const evaluations &evaluations, const srs &srs, const Field &gamma_1, const Field &gamma_2)
static bool	verify_evaluations (const Field &z_1, const Field &z_2, const evaluations &evaluations, const srs &srs, const Field &gamma_1, const Field &gamma_2, const evaluation_witness &witness, const std::vector< commitment > &cm_1s, const std::vector< commitment > &cm_2s, const Field &r)

Detailed Description

template<typename ppT>
class libsnark::kzg10_batched_2_point< ppT >

Batched version of KZG10, as described in Section 3 of [GWC19]. Supports evaluation of arbitrary number of polynomials at 2 points, requiring a fixed-size witness (of 2 elements of G1), which can be verified with 2 pairings (similarly to KZG10) and a number of group operations proportional to the number of polynomials.

Note, this could be extended to the case of N evaluation points (and thereby N sets of polynomials).

Definition at line 31 of file kzg10_batched.hpp.

Member Typedef Documentation

commitment

template<typename ppT >

using libsnark::kzg10_batched_2_point< ppT >::commitment = typename kzg10<ppT>::commitment

Definition at line 40 of file kzg10_batched.hpp.

Field

template<typename ppT >

using libsnark::kzg10_batched_2_point< ppT >::Field = libff::Fr<ppT>

Definition at line 34 of file kzg10_batched.hpp.

srs

template<typename ppT >

using libsnark::kzg10_batched_2_point< ppT >::srs = typename kzg10<ppT>::srs

The srs generated by the setup step. This is denoted PK in [KZG10] section 3.2.

Definition at line 38 of file kzg10_batched.hpp.

Member Function Documentation

create_evaluation_witness()

template<typename ppT >

static evaluation_witness libsnark::kzg10_batched_2_point< ppT >::create_evaluation_witness ( const std::vector< polynomial< Field >> &  fs, const std::vector< polynomial< Field >> &  gs, const Field &  z_1, const Field &  z_2, const evaluations &  evaluations, const srs &  srs, const Field &  gamma_1, const Field &  gamma_2  )

static

Generate a witness to prove the correctness of these evaluations. Returns a multi_point_evaluation_witness object holding this data.

evaluate_polynomials()

template<typename ppT >

static evaluations libsnark::kzg10_batched_2_point< ppT >::evaluate_polynomials ( const std::vector< polynomial< Field >> &  fs, const std::vector< polynomial< Field >> &  gs, const Field &  z_1, const Field &  z_2  )

static

Evaluate the polynomials and return an evaluation object. f_s are evaluated at z_1 and g_s are evaluated at z_2.

verify_evaluations()

template<typename ppT >

static bool libsnark::kzg10_batched_2_point< ppT >::verify_evaluations ( const Field &  z_1, const Field &  z_2, const evaluations &  evaluations, const srs &  srs, const Field &  gamma_1, const Field &  gamma_2, const evaluation_witness &  witness, const std::vector< commitment > &  cm_1s, const std::vector< commitment > &  cm_2s, const Field &  r  )

static

Given an evaluation and evaluation_witness generated for polynomials with commitments cm_1s and cm_2s, verify the witnesses using randomness r. This convinces the verifier that the given polynomials attain the claimed values at the evaluation points z_1 and z_2.

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The documentation for this class was generated from the following file:

• /home/runner/work/libsnark/libsnark/libsnark/polynomial_commitments/kzg10_batched.hpp