Module to operate with polynomials in FFT evaluations form.

The type of prover public parameters.

The type of verifier public parameters.

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).

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

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.

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

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.

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).

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.

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

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

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

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.

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.

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.

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.