Victor Shoup

Efficient Non-interactive Proof Systems for Bilinear Groups

Jens Groth and Amit Sahai (Proc. of Eurocrypt 2008)

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 

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.