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

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Abstract

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.

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References

  1. Goldwasser S, Micali S, Rackoff C. The knowledge complexity of interactive proof systems. SIAM J Comput, 1989, 18: 186–208

    Article  MATH  MathSciNet  Google Scholar 

  2. Bellare M, Goldreich O. On defining proofs of knowledge. Advances in Cryptology-CRYPT’92, LNCS, Vol. 740. Berlin: Springer-Verlag, 1992. 390–420

    Google Scholar 

  3. Halevi S, Micali S. More on proofs of knowledge. http://eprint.iacr.org/1998/015

  4. Goldreich O. Foundations of Cryptography-Basic Tools. Cambridge: Cambridge University Press, 2001

    Book  MATH  Google Scholar 

  5. Bellare M, Goldreich O. On probabilistic versus deterministic provers in the definition of proofs of knowledge. Electronic Colloquimon Computational Complexity, 2006, 13(136). Available also from http://eprint.iacr.org/2006/359.ps

  6. Barak B, Lindell Y, Vadhan S. Lower bounds for non-black-box zero knowledge. In: 44th Annual IEEE Symposium Foundations of Computer Science. IEEE Computer Society, 2003. 384–393

  7. Barak B, Lindell Y, Vadhan S. Lower bounds for non-black-box zero knowledge. J Comput Sys Sci, 2006, 72: 321–391

    Article  MATH  MathSciNet  Google Scholar 

  8. Bellare M, Jakobsson M, Yung M. Round-optimal zero-knowledge arguments base on any one-way function. In: EUROCRPT’ 97, LNCS, Vol.1233. Berlin: Spring-Verlag, 1997. 280–305

    Google Scholar 

  9. Feige U, Shamir A. Zero knowledge proofs of knowledge in two rounds. In: Proceedings of CRYPTO’89. Berlin: Springer-Verlag, 1989. 526–545

    Google Scholar 

  10. Goldreich O, Oren Y. Definitions and properties of zero-knowledge proof systems. J Crypt, 1994, 7: 1–32

    MATH  MathSciNet  Google Scholar 

  11. Goldreich O, Krawczyk H. On the composition of zero-knowledge proof systems. SIAM J Comput, 1996, 25: 169–192

    Article  MATH  MathSciNet  Google Scholar 

  12. Katz J. Which languages have 4-round zero-knowledge proofs. In: Fifth Theory of Cryptography Conference, LNCS Vol. 4948. Berlin: Spring-Verlag, 2008. 73–88

    Google Scholar 

  13. Goldreich O, Kahan A. How to construct constant-round zero-knowledge proof system for NP. J Crypt, 1996, 9: 167–189

    Article  MATH  MathSciNet  Google Scholar 

  14. Rosen A. A note on constant-round zero-knowledge proofs for NP. In: First Theory of Cryptography Conference (TCC), LNCS 2951. Berlin: Spring-Verlag, 2004. 191–202

    Google Scholar 

  15. Toshiya I, Kouichi S. On the complexity of constant round ZKIP of possession of knowledge. IEICE Trans Fundam, 1993, E76-A: 31–39

    Google Scholar 

  16. Barak B. How to go beyond the black-box simulation barrier. In: 42th Annual Syposium on Foundation of Computing Science. IEEE Computer Society, 2001. 106–115

  17. Barak B. Non-black-box techniques in cryptography. Thesis for the Ph. D. Degree. Weizmann Institute of Science, 2004, 53–102 (http://www.math.ias.edu/boaz/index.html)

  18. Hada S, Tanaka T. On the existence of 3-round zero-knowledge protocol. http://eprint.iacr.org/1999/009. (Final version of [22])

  19. Bellare M, Palacio A. The knowledge-of-exponent assumptions and 3-round zero-knowledge protocol. http://eprint.iacr.org/2003

  20. Lepinski M. On the existence of 3-round zero-knowledge proofs. Thesis for the Degree of Master, Massachusetts Institute of Technology, 2002. (http://citeseer.ist.psu.edu/lepinski01existence.html)

  21. Barak B, Lindell Y. Strict polynomial-time in simulation and extraction. In: 34th STOC, Montréal, Québec, Canada, 2002. 484–493

  22. Li H D, Li B. The existence of 3-round zero-knowledge proof systems for NP. Sci China Ser F-Inf Sci, 2008, 51: 273–282

    Article  Google Scholar 

  23. Blum M. How to prove a theorem so no one else can claim it. In: Proceedings of the International Congress of Mathematicians, California, USA, 1986. 1444–1451

  24. Naor M. On cryptographic assumptions and challenges. In: Proceedings of Advances in Cryptology-CRYPT’2003, LNCS, Vol. 2729. Berlin: Springer, 2003. 96–109

    Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing, 100049, China

    HongDa Li, HaiXia Xu & Bao Li

  2. State Key Laboratory of Information Security, Institute of Software of Chinese Academy of Sciences, Beijing, 100080, China

    DengGuo Feng

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  1. HongDa Li
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Correspondence to HongDa Li.

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Li, H., Xu, H., Li, B. et al. On constant-round zero-knowledge proofs of knowledge for NP-relations. Sci. China Inf. Sci. 53, 788–799 (2010). https://doi.org/10.1007/s11432-010-0071-3

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