The type of prover public parameters.

The type of verifier public parameters.

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 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.