Making Sigma-Protocols Non-interactive Without Random Oracles

Damgard, Fazio and Nicolosi (TCC 2006) gave a transformation of Sigma-protocols, 3-move honest verifier zero-knowledge proofs, into efficient non-interactive zero-knowledge arguments for a designated verifier. Their transformation uses additively homomorphic encryption to encrypt the verifier’s challenge, which the prover uses to compute an encrypted answer. The transformation does not rely on the random oracle model but proving soundness requires a complexity leveraging assumption.

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