Snarky Signatures: Minimal Signatures of Knowledge from Simulation-Extractable SNARKs

We construct a pairing-based simulation-extractable succinct non-interactive argument of knowledge (SE-SNARK) that consists of only 3 group elements and has highly efficient verification. By formally linking SE-SNARKs to signatures of knowledge, we then obtain a succinct signature of knowledge consisting of only 3 group elements. SE-SNARKs enable a prover to give a proof that they know a witness to an instance in a manner which is: (1) succinct proofs are short and verifier computation is small; (2) zeroknowledge proofs do not reveal the witness; (3) simulation-extractable it is only possible to prove instances to which you know a witness, even when you have already seen a number of simulated proofs. We also prove that any pairing-based signature of knowledge or SE-SNARK must have at least 3 group elements and 2 verification equations. Since our constructions match these lower bounds, we have the smallest size signature of knowledge and the smallest size SE-SNARK possible.