New Techniques for Non-interactive Zero-Knowledge

Non-interactive zero-knowledge (NIZK) proof systems are fundamental primitives used in many cryptographic constructions, including public-key encryption secure against chosen ciphertext attack, digital signatures, and various other cryptographic protocols. We introduce new techniques for constructing NIZK proofs based on groups with a bilinear map. Compared to previous constructions of NIZK proofs, our techniques yield dramatic reduction in the length of the common reference string (CRS) (our CRS is proportional to security parameter) and the size of the proofs (proportional to security parameter times the circuit size). Our novel techniques allow us to answer several long-standing open questions cryptography: • We construct the first perfect NIZK argument system for all NP; • We construct the first universally composable NIZK argument for all NP in the presence of an adaptive adversary. • We construct a non-interactive zap for all NP, which is the first that is based on a standard cryptographic security assumption. Another important contribution of this paper is the introduction of a new “parameter switching” technique in cryptography, later renamed “lossy encryption” and “dual encryption”. This technique has proven to be an important new tool for solving multiple other cryptographic problems.