Cryptology ePrint Archive: Report 2017/540

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

Jens Groth and Mary Maller

Abstract: We construct a pairing based simulation-extractable SNARK (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) zero-knowledge - 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-NIZK argument 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.

Category / Keywords: signatures of knowledge, SNARKs, simulation soundness

Original Publication (in the same form): IACR-CRYPTO-2017

Date: received 5 Jun 2017, last revised 5 Jun 2017

Contact author: mary maller 15 at ucl ac uk, j groth@ucl ac uk

Available format(s): PDF | BibTeX Citation

Version: 20170608:155147 (All versions of this report)

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