Short Pairing-based Non-interactive Zero-Knowledge Arguments

Jens Groth

Paper 2009/390

Short Pairing-based Non-interactive Zero-Knowledge Arguments

Jens Groth

, University College London

Abstract

We construct non-interactive zero-knowledge arguments for circuit satisfiability with perfect completeness, perfect zero knowledge and computational soundness. The non-interactive zero-knowledge arguments have sublinear size and very efficient public verification. Their size can even be reduced to a constant number of group elements if we allow the common reference string to be large. Our constructions rely on groups with pairings, and security is based on two new cryptographic assumptions; we do not use the Fiat-Shamir heuristic or random oracles.

Note: First pairing-based zk-SNARK, first non-Fiat-Shamir SNARK, published at ASIACRYPT 2010 This revision: polished and fixed typos, added context on relation to later zk-SNARKs Lipmaa12, GGPR13 and on universal and updatable CRS from GKMMM18, addendum on preprocessing for fixed circuit

Metadata

Available format(s): PDF
Category: Foundations
Publication info: A minor revision of an IACR publication in ASIACRYPT 2010
Keywords: SNARK NIZK pairing
Contact author(s): j groth @ ucl ac uk
History: 2026-04-19: revised; 2009-08-15: received; See all versions
Short URL: https://ia.cr/2009/390
License: CC BY

BibTeX

@misc{cryptoeprint:2009/390,
      author = {Jens Groth},
      title = {Short Pairing-based Non-interactive Zero-Knowledge Arguments},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/390},
      year = {2009},
      url = {https://eprint.iacr.org/2009/390}
}