On constant-round zero-knowledge proofs of knowledge for NP-relations

This paper considers the existence of constant-round zero-knowledge proofs of knowledge for NP under standard assumptions. By introducing a new interactive proof model, we construct a 3-round zero-knowledge proof of knowledge system for the NP-relation under the assumption that factoring is intractable. Our construction not only shows the existence of constant-round zero-knowledge proofs of knowledge, but also gives a positive answer to the open problem of the existence of 3-round zero-knowledge proofs for NP.

[1]  Alon Rosen,et al.  A Note on Constant-Round Zero-Knowledge Proofs for NP , 2004, TCC.

[2]  Matthew Lepinski,et al.  On the Existence of 3-Round Zero-Knowledge Proofs , 2002 .

[3]  Moni Naor,et al.  On Cryptographic Assumptions and Challenges , 2003, CRYPTO.

[4]  Mihir Bellare,et al.  On Probabilistic versus Deterministic Provers in the Definition of Proofs Of Knowledge , 2006, IACR Cryptol. ePrint Arch..

[5]  Boaz Barak,et al.  Non-black-box Techniques in Cryptography , 2006, CSR.

[6]  Kouichi Sakurai,et al.  On the Complexity of Constant Round ZKIP of Possession of Knowledge , 1991, ASIACRYPT.

[7]  Bao Li,et al.  Existence of 3-round zero-knowledge proof systems for NP , 2008, Science in China Series F: Information Sciences.

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

[9]  Oded Goldreich,et al.  Foundations of Cryptography: List of Figures , 2001 .

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

[11]  Jonathan Katz.  Which Languages Have 4-Round Zero-Knowledge Proofs? , 2008, TCC.

[12]  Yehuda Lindell,et al.  Strict Polynomial-Time in Simulation and Extraction , 2004, SIAM J. Comput..

[13]  Toshiaki Tanaka,et al.  On the Existence of 3-Round Zero-Knowledge Protocols , 1998, CRYPTO.

[14]  Oded Goldreich.  Foundations of Cryptography: Index , 2001 .

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

[16]  Oded Goldreich,et al.  How to construct constant-round zero-knowledge proof systems for NP , 1996, Journal of Cryptology.

[17]  Oded Goldreich,et al.  Definitions and properties of zero-knowledge proof systems , 1994, Journal of Cryptology.

[18]  Boaz Barak,et al.  How to go beyond the black-box simulation barrier , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[19]  Yehuda Lindell,et al.  Lower bounds for non-black-box zero knowledge , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

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

[21]  Mihir Bellare,et al.  The Knowledge-of-Exponent Assumptions and 3-Round Zero-Knowledge Protocols , 2004, CRYPTO.

[22]  Silvio Micali,et al.  More on Proofs of Knowledge , 1998, IACR Cryptol. ePrint Arch..

[23]  Oded Goldreich,et al.  Foundations of Cryptography: Basic Tools , 2000 .

[24]  Manuel Blum,et al.  How to Prove a Theorem So No One Else Can Claim It , 2010 .

[25]  Li HongDa,et al.  Existence of 3-round zero-knowledge proof systems for NP , 2008 .