Perfect Zero-Knowledge Arguments for NP Using Any One-Way Permutation

Abstract

``Perfect zero-knowledge arguments'' is a cryptographic primitive which allows one polynomial-time player to convince another polynomial-time player of the validity of an NP statement, without revealing any additional information (in the information-theoretic sense). Here the security achieved is on-line: in order to cheat and validate a false theorem, the prover must break a cryptographic assumption on-line during the conversation, while the verifier cannot find (ever) any information unconditionally. Despite their practical and theoretical importance, it was only known how to implement zero-knowledge arguments based on specific algebraic assumptions. In this paper we show a general construction which can be based on any one-way permutation. The result is obtained by a construction of an information-theoretic secure bit-commitment protocol. The protocol is efficient (both parties are polynomial time) and can be based on any one-way permutation.