Efficient Non-interactive Proof Systems for Bilinear Groups

  • Jens Groth
  • Amit Sahai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4965)

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 

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jens Groth
    • 1
  • Amit Sahai
    • 2
  1. 1.University College London 
  2. 2.University of California Los Angeles 

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