On the Existence of 3-Round Zero-Knowledge Protocols

In this paper, we construct a 3-round zero-knowledge protocol for any NP language. Goldreich and Krawczyk proved that a 3-round black-box simulation zero-knowledge protocol exists only for BPP languages. However, there is no contradiction here. That is, our proposed protocol achieves a weaker notion of zero-knowledge: auxiliary-input non-uniform zero-knowledge. Since this notion has not been investigated in the literature, we classify several zero-knowledge notions including it and discuss the relationships among them. Our main contribution is to provide a non-black-box simulation technique. It is based on a novel computational assumption related to the Diffie-Hellman problem. Although this assumption is strong and non-standard, its non-standard nature seems essential for our simulation technique.

[1]  Rafail Ostrovsky,et al.  Perfect zero-knowledge in constant rounds , 1990, STOC '90.

[2]  Amos Fiat,et al.  Zero-knowledge proofs of identity , 1987, Journal of Cryptology.

[3]  Mihir Bellare,et al.  Random oracles are practical: a paradigm for designing efficient protocols , 1993, CCS '93.

[4]  Silvio Micali,et al.  Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems , 1991, JACM.

[5]  Ivan Damgård,et al.  Towards Practical Public Key Systems Secure Against Chosen Ciphertext Attacks , 1991, CRYPTO.

[6]  Silvio Micali,et al.  The knowledge complexity of interactive proof-systems , 1985, STOC '85.

[7]  David Chaum,et al.  Minimum Disclosure Proofs of Knowledge , 1988, J. Comput. Syst. Sci..

[8]  M. Rabin.  Probabilistic algorithm for testing primality , 1980 .

[9]  Gilles Brassard,et al.  Non-transitive transfer of confidence: A perfect zero-knowledge interactive protocol for SAT and beyond , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[10]  Adi Shamir,et al.  Zero Knowledge Proofs of Knowledge in Two Rounds , 1989, CRYPTO.

[11]  Martin Tompa,et al.  Random self-reducibility and zero knowledge interactive proofs of possession of information , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[12]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[13]  Moti Yung,et al.  Everything in NP can be Argued in Perfect Zero-Knowledge in a Bounded Number of Rounds , 1989, ICALP.

[14]  Giovanni Di Crescenzo,et al.  The Knowledge Complexity of Quadratic Residuosity Languages , 1994, Theor. Comput. Sci..

[15]  N. S. Barnett,et al.  Private communication , 1969 .

[16]  Markus Jakobsson,et al.  Round-Optimal Zero-Knowledge Arguments Based on any One-Way Function , 1997, EUROCRYPT.

[17]  Manuel Blum,et al.  How to generate cryptographically strong sequences of pseudo random bits , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[18]  Hugo Krawczyk,et al.  On the Composition of Zero-Knowledge Proof Systems , 1990, ICALP.

[19]  Oded Goldreich,et al.  Foundations of Cryptography (Fragments of a Book) , 1995 .

[20]  Mihir Bellare,et al.  On Defining Proofs of Knowledge , 1992, CRYPTO.

[21]  Adi Shamir,et al.  Witness indistinguishable and witness hiding protocols , 1990, STOC '90.

[22]  Volker Strassen,et al.  A Fast Monte-Carlo Test for Primality , 1977, SIAM J. Comput..