Constant-Round Zero-Knowledge Proofs of Knowledge

In this note, we show the existence of constant-round computational zero-knowledge proofs of knowledge for all N P. The existence of constant-round zero-knowledge proofs was proven by Goldreich and Kahan (Journal of Cryptology, 1996), and the existence of constant-round zeroknowledge arguments of knowledge was proven by Feige and Shamir (CRYPTO 1989). Although it is widely believed that there exist constant-round zero-knowledge proofs of knowledge for all N P, to the best of our knowledge, no proof of this fact has been published.

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

[3]  Oded Goldreich,et al.  The Foundations of Cryptography - Volume 2: Basic Applications , 2001 .

[4]  Silvio Micali,et al.  The Knowledge Complexity of Interactive Proof Systems , 1989, SIAM J. Comput..

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

[6]  Ran Canetti,et al.  Security and Composition of Multiparty Cryptographic Protocols , 2000, Journal of Cryptology.

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

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

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

[10]  I. Damgård,et al.  The protocols. , 1989, The New Zealand nursing journal. Kai tiaki.

[11]  Oded Goldreich,et al.  Foundations of Cryptography: Volume 2, Basic Applications , 2004 .

[12]  Jonathan Katz,et al.  Which Languages Have 4-Round Zero-Knowledge Proofs? , 2008, Journal of Cryptology.

[13]  Oded Goldreich,et al.  Foundations of Cryptography: Volume 1, Basic Tools , 2001 .

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

[15]  Yehuda Lindell,et al.  Parallel Coin-Tossing and Constant-Round Secure Two-Party Computation , 2001, Journal of Cryptology.

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