Randomness-eecient Non-interactive Zero Knowledge

The model of Non-Interactive Zero-Knowledge allows to obtain minimal interaction between prover and veriier in a zero-knowledge proof if a public random string is available to both parties. In this paper we investigate upper bounds for the length of the random string for proving one and many statements, obtaining the following results: { We show how to prove in non-interactive perfect zero-knowledge any polynomial number of statements using a random string of xed length, that is, not depending on the number of statements. Previously , such a result was known only in the case of computational zero-knowledge. { Under the quadratic residuosity assumption, we show how to prove any NP statement in non-interactive zero-knowledge on a random string of length (nk), where n is the size of the statement and k is the security parameter, which improves the previous best construction by a factor of (k).

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