Raised by the prover when the provided inputs are not a satisfying assignment of the circuit.

Raised by the prover when the provided inputs are not a satisfying assignment of the circuit when using Plookup.

Before proving and verifying, circuits go through a pre-processing step called setup. The setup takes as input a circuit_map, which associates an identifier to a circuit and the number of statements that can be proved with that circuit. This produces a set of public_parameters which are bound to the circuits and can be reused.

Set of public_parameters needed by the prover. Its size is linear in the size of the circuits.

Set of public_parameters needed by the verifier. Its size is constant w.r.t. the size of the circuits.

Succinct proof for a collection of statements.

Witness is the whole trace for the circuit, including input_commitment values first, followed by public input values and followed by the rest of the trace. This is the prover input for a single proof.

Map where each circuit identifier is bound to a list of circuit_prover_input for a list of statements.

The public inputs for one circuit & several statements

The verifier inputs, represented as a map where each circuit is binded to the verifier inputs for this circuit.

Conversion from prover_inputs to verifier_inputs.

input_commit ~shift pp secret produces a commitment to the secret array and additional prover information. This commitment is designed to be easily involved in a PlonK proof. In particular, the values of secret will be added to the arithmetic identity in such a way that secret.(i) participates in constraint number shift + i, where equality will be asserted with respect to a PlonK variable in the same constraint. This allows us to "load" the value of secret.(i) into the variable, which may be reused across the circuit. The optional argument shift has a default value of 0. The commitment is relative to a certain domain size n, included in pp, the secret will remain information-theoretically hidden as long as the commitment is involved in at most n - |secret| different proofs. If the optionnal argument size is given, the secret will be padded with zeros to have the length size (note that an error will be risen if size is smaller than the secret length).

setup ~zero_knowledge circuit_map ~srs pre-processes the circuit_map producing the public parameters. The SRSs of ZCash and Filecoin can be loaded from file using the Bls12_381_polynomial library. Activating zero_knowledge adds an overhead in proving time.

Enrich the prover_public_parameters with extra application data to prevent replay attacks. The same data must be used for updating the prover and verifier public parameters.

Enrich the verifier_public_parameters with extra application data to prevent replay attacks. The same data must be used for updating the prover and verifier public parameters.

prove public_parameters ~inputs produces a proof for the collection of statements implied by inputs and the circuits used for generating public_parameters.

• raises Rest_not_null

• raises Entry_not_in_table

verify public_parameters ~inputs proof checks the validity of the proof with regards to public_parameters and inputs.