International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2010: Advances in Cryptology - ASIACRYPT 2010 pp 341-358

Short Non-interactive Zero-Knowledge Proofs

  • Jens Groth
Conference paper

DOI: 10.1007/978-3-642-17373-8_20

Volume 6477 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Groth J. (2010) Short Non-interactive Zero-Knowledge Proofs. In: Abe M. (eds) Advances in Cryptology - ASIACRYPT 2010. ASIACRYPT 2010. Lecture Notes in Computer Science, vol 6477. Springer, Berlin, Heidelberg

Abstract

We show that probabilistically checkable proofs can be used to shorten non-interactive zero-knowledge proofs. We obtain publicly verifiable non-interactive zero-knowledge proofs for circuit satisfiability with adaptive and unconditional soundness where the size grows quasi-linearly in the number of gates. The zero-knowledge property relies on the existence of trapdoor permutations, or it can be based on a specific number theoretic assumption related to factoring to get better efficiency. As an example of the latter, we suggest a non-interactive zero-knowledge proof for circuit satisfiability based on the Naccache-Stern cryptosystem consisting of a quasi-linear number of bits. This yields the shortest known non-interactive zero-knowledge proof for circuit satisfiability.

Keywords

Non-interactive zero-knowledge proofsadaptive soundnessprobabilistically checkable proofsNaccache-Stern encryption
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Copyright information

© International Association for Cryptologic Research 2010

Authors and Affiliations

  • Jens Groth
    • 1
  1. 1.University College LondonUK