Chapter

Advances in Cryptology – EUROCRYPT 2008

Volume 4965 of the series Lecture Notes in Computer Science pp 415-432

Efficient Non-interactive Proof Systems for Bilinear Groups

  • Jens GrothAffiliated withUniversity College London
  • , Amit SahaiAffiliated withUniversity of California Los Angeles

Abstract

Non-interactive zero-knowledge proofs and non-interactive witness-indistinguishable proofs have played a significant role in the theory of cryptography. However, lack of efficiency has prevented them from being used in practice. One of the roots of this inefficiency is that non-interactive zero-knowledge proofs have been constructed for general NP-complete languages such as Circuit Satisfiability, causing an expensive blowup in the size of the statement when reducing it to a circuit. The contribution of this paper is a general methodology for constructing very simple and efficient non-interactive zero-knowledge proofs and non-interactive witness-indistinguishable proofs that work directly for groups with a bilinear map, without needing a reduction to Circuit Satisfiability.

Groups with bilinear maps have enjoyed tremendous success in the field of cryptography in recent years and have been used to construct a plethora of protocols. This paper provides non-interactive witness-indistinguishable proofs and non-interactive zero-knowledge proofs that can be used in connection with these protocols. Our goal is to spread the use of non-interactive cryptographic proofs from mainly theoretical purposes to the large class of practical cryptographic protocols based on bilinear groups.

Keywords

Non-interactive witness-indistinguishability non-interactive zero-knowledge common reference string bilinear groups