tezos-plonk 1.0.1 · OCaml Package

Parameters

module PC : Polynomial_commitment.S

Signature

module PC = PC

Underlying polynomial commitment scheme on which the polynomial protocol is based. Input of the functor Polynomial_protocol.Make.

module Evaluations : 
  Evaluations_map.Evaluations_sig
    with type scalar := PC.Scalar.t
     and type domain = PC.Polynomial.Domain.t
     and type polynomial = PC.Polynomial.Polynomial.t
     and type t = PC.Polynomial.Evaluations.t

Module to operate with polynomials in FFT evaluations form.

type prover_public_parameters = PC.Public_parameters.prover

The type of prover public parameters.

val prover_public_parameters_t : prover_public_parameters Repr.t

type verifier_public_parameters = PC.Public_parameters.verifier

The type of verifier public parameters.

val verifier_public_parameters_t : verifier_public_parameters Repr.t

type prover_identities = Evaluations.t SMap.t -> Evaluations.t SMap.t

The type for prover identities: functions from a (string) map of polynomials in FFT evaluations form to a (string) map of evaluated identities (also polynomials in FFT evaluations form).

type verifier_identities =
  PC.Scalar.t ->
  PC.Scalar.t SMap.t SMap.t ->
  PC.Scalar.t SMap.t

The type for verifier identities: functions which map an evaluation point ξ an a PC.answer into a (string) map of evaluated identities.

type non_committed =
  PC.Scalar.t ->
  PC.Scalar.t SMap.t SMap.t ->
  PC.Scalar.t SMap.t

A type to involve in the identities computations corresponding to (public) polynomials that have not been committed by the prover. It maps an evaluation point ξ and a PC.answer into a (string) map of evaluated (non-committed) polynomials.

type transcript = PC.transcript

The type for transcripts, used for applying the Fiat-Shamir heuristic

val transcript_t : transcript Repr.t

type proof = {

cm_t : PC.Commitment.t;
pc_proof : PC.proof;
pc_answers : PC.answer list;

}

The type for proofs, containing a commitment to the polynomial T that asserts the satisfiability of the identities over the subset of interest, as well as a PC proof and a list of PC answers.

val proof_t : proof Repr.t

type eval_point =

| X
| GX
| Custom of string * PC.Scalar.t -> PC.Scalar.t

The type for evaluation points. Either X, GX, or a custom point, which must be specified by an evaluation point name paired with a function that computes it from ξ. For example:

X could be implemented as Custom ("x", Fun.id)
GX could be implemented as Custom ("gx", fun x -> Scalar.mul generator x).

val convert_eval_points : 
  generator:PC.Scalar.t ->
  x:PC.Scalar.t ->
  eval_point list ->
  PC.Scalar.t SMap.t

convert_eval_points gen x points maps the polynomial protocol points : eval_point list into scalars, by evaluating the underlying "composition" polynomial at x. The generator gen is used in case the eval_point equals GX, in which case the resulting scalar is x * gen.

val get_answer : PC.answer -> eval_point -> string -> PC.Scalar.t

get_answer answers p name extracts the evaluation of polynomial name at point p from the given answers.

val merge_prover_identities : prover_identities list -> prover_identities

A function to merge a list of prover identities into one.

val merge_verifier_identities : verifier_identities list -> verifier_identities

A function to merge a list of verifier identities into one.

val compute_t : 
  n:int ->
  alpha:PC.Scalar.t ->
  nb_of_t_chunks:int ->
  Evaluations.t SMap.t ->
  Evaluations.polynomial SMap.t

compute_t ~n ~alpha evaluations returns a polynomial T splitted in chunks, where T(X) = (sum_i alpha^i evaluations[i]) / (X^n - 1) and the returned chunks { 'T_0' -> T0; 'T_1' -> T1; 'T_2' -> T2 } are such that T = T0 + X^n T1 + X^{2n} T2.

val setup : 
  setup_params:PC.Public_parameters.setup_params ->
  srs:(Bls12_381_polynomial.Srs.t * Bls12_381_polynomial.Srs.t) ->
  prover_public_parameters * verifier_public_parameters

The polynomial commitment setup function, requires a labeled argument of setup parameters for the underlying PC and a labeled argument containing the path location of a set of SRS files.

val prove : 
  prover_public_parameters ->
  transcript ->
  n:int ->
  generator:PC.Scalar.t ->
  secrets:(PC.Polynomial.Polynomial.t SMap.t * PC.Commitment.prover_aux) list ->
  eval_points:eval_point list list ->
  evaluations:Evaluations.t SMap.t ->
  identities:prover_identities ->
  nb_of_t_chunks:int ->
  proof * transcript

The prover function. Takes as input the prover_public_parameters, an initial transcript (possibly including a context if this prove is used as a building block of a bigger protocol), the size n of subgroup H, the canonical generator of subgroup H, a list of secrets including polynomials that have supposedly been committed (and a verifier received such commitments) as well as prover auxiliary information generated during the committing process, a list of evaluation point lists specifying the evaluation points where each secret needs to be evaluated at, a map of the above-mentioned polynomials this time in FFT evaluations form, for efficient polynomial multiplication, and some prover_identities that are supposedly satisfied by the secret polynomials. Outputs a proof and an updated transcript.

val verify : 
  verifier_public_parameters ->
  transcript ->
  n:int ->
  generator:PC.Scalar.t ->
  commitments:PC.Commitment.t list ->
  eval_points:eval_point list list ->
  ?non_committed:non_committed ->
  identities:verifier_identities ->
  proof ->
  bool * transcript

The verifier function. Takes as input the verifier_public_parameters, an initial transcript (that should coincide with the initial transcript used by prove), the size n of subgroup H, the canonical generator of subgroup H, a list of commitments to the secret polynomials by the prover, a list of evaluation points as in prove, some verifier_identities, and a proof. Outputs a bool value representing acceptance or rejection.

package tezos-plonk

Parameters

Signature