Noninteractive Zero-Knowledge

We investigate the possibility of disposing of interaction between Prover and Veriier in a zero-knowledge proof if they share beforehand a short random string. Without any assumption, we prove that non-interactive zero-knowledge proofs exist for some number theoretic languages for which no eecient algorithm is known. If deciding quadratic residuosity (modulo composite integers whose factorization is not known) is computationally hard, we show that the NP-complete language of satissability also possesses non-interactive zero-knowledge proofs.