Non-interactive zero-knowledge (NIZK) proof systems are fundamental primitives used in many cryptographic constructions, including CCA2-secure cryptosystems, digital signatures, and various cryptographic protocols. We introduce new techniques for constructing NIZK proofs based on groups with a bilinear map. In comparison with previous constructions of NIZK proofs, our techniques yield significant reductions in the length of the common reference string and the size of the proofs. The new techniques also allow us to answer long standing open questions in the theory of non-interactive zero-knowledge.
We construct the first perfect NIZK argument system for all
NP languages.
We construct the first UC-secure NIZK argument for all NP languages in the presence of an adaptive adversary.
We construct the first non-interactive zap for all NP
languages based on a standard cryptographic security assumption.
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