Skip to main content
SpringerLink
Log in

A Note on Constant-Round Concurrent Zero-Knowledge Arguments of Knowledge for NP

  • Conference paper
Internet and Distributed Computing Systems (IDCS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7646))

Included in the following conference series:

  • 731 Accesses

Abstract

This paper deals with how to construct a constant-round bounded-concurrent zero-knowledge argument of knowledge with black-box extractors for any NP language under standard complexity assumptions. It is accepted that both constant-round zero-knowledge arguments of knowledge and constant-round bound-concurrent zero-knowledge arguments exist for all NP. But the existence of constant-round bounded-concurrent zero-knowledge arguments of knowledge (with black-box extractors) for NP is still an unsolved question. In this paper, we give a positive answer to this question by constructing a constant-round bounded-concurrent zero-knowledge argument of knowledge with a black-box extractor for any NP under certain standard complexity assumptions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Google Scholar 

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

    Google Scholar 

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

  4. Barak, B., Goldreich, O.: Universal arguments and their applications, http://eprint.iacr.org/2001/063

  5. Barak, B., Lindell, Y.: Strict polynomial-time in simulation and extraction. In the SIAM Journal on Computing 33(4), 783–818 (2004); An extended abstract appeared in the 34th STOC, pp. 484–493 (2002)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  7. Barak, B., Lindell, Y., Vadhan, S.: Lower bounds for non-black-box zero knowledge. Journal of Computer and System Sciences 72(2), 321–391 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bellare, M., Jakobsson, M., Yung, M.: Round-Optimal Zero-Knowledge Arguments Based on Any One-Way Function. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 280–305. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  9. Dwork, C., Naor, M., Sahai, A.: Concurrent zero-knowledge. In: Proceedings of 30th STOC, Dallas, Texas, USA, 1998, pp. 409–418 (1998)

    Google Scholar 

  10. Feige, U., Shamir, A.: Zero Knowledge Proofs of Knowledge in Two Rounds. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 526–544. Springer, Heidelberg (1990)

    Google Scholar 

  11. Feige, U.: Alternative models for zero knowledge interactive proofs. Ph.D., Weizmann Institute of science (1990)

    Google Scholar 

  12. Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive, zero-knowledge proofs based on a single random string. In: Proc. 31th Ann. Symp. on FOCS, pp. 186–189 (1990)

    Google Scholar 

  13. Goldreich, O., Krawczyk, H.: On the composition of zero-knowledge proof systems. SIAM Journal of Computing 25(1), 169–192 (1996); Preliminary version appeared in LNCS, vol. 443, pp. 268–282 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  14. Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM Journal on Computing 18(1), 186–208 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  15. Goldreich, O., Oren, Y.: Definitions and properties of zero-knowledge proof systems. Journal of Cryptology 7(1), 1–32 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof system for NP. Journal of Cryptology 9(3), 167–189 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Goldreich, O.: Foundations of Cryptography - Basic Tools. Cambridge University Press (2001)

    Google Scholar 

  18. Li, H., Xue, H., Li, B., Feng, D.: On constant-round zero-knowledge proofs of knowledge for NP-relations. Science China Information Sciences 53(4), 788–799 (2010)

    Article  MathSciNet  Google Scholar 

  19. Jiang, S., Li, H., Li, B.: Constant-round bounded concurrent zero-knowledge arguments of knowledge for NP. In: The 7th China Conference on Information and Communications Security, CCICS 2010, pp. 174–191 (2010)

    Google Scholar 

  20. Lindell, Y.: Constant-round zero-knowledge proofs of knowledge. ECCC Reports- TR11-003, http://eccc.hpi-web.de/report/2011/003/

  21. Pass, R., Rosen, A.: New and Improved Constructions of Non-Malleable Cryptographic Protocols. SIAM Journal on Computing 38(2), 702–752 (2008); In: 37th STOC, pp. 533–542 (2005)

    Article  MathSciNet  Google Scholar 

  22. Rosen, A.: A Note on Constant-Round Zero-Knowledge Proofs for NP. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 191–202. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, China

    Hongda Li, Yang Liu & Qihua Niu

Authors
  1. Hongda Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qihua Niu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Information Technology, Deakin University, Melbourne Burwood Campus, 221 Burwood Highway, 3125, Burwood, VIC, Australia

    Yang Xiang

  2. Media Distribution, Telstra Corporation Limited, 21/35 Collins St, 3000, Melbourne, VIC, Australia

    Mukaddim Pathan

  3. Department of Mathematics and Computing, The University of Southern Queensland, Toowoomba, QLD, Australia

    Xiaohui Tao  & Hua Wang  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li, H., Liu, Y., Niu, Q. (2012). A Note on Constant-Round Concurrent Zero-Knowledge Arguments of Knowledge for NP. In: Xiang, Y., Pathan, M., Tao, X., Wang, H. (eds) Internet and Distributed Computing Systems. IDCS 2012. Lecture Notes in Computer Science, vol 7646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34883-9_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34883-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34882-2

  • Online ISBN: 978-3-642-34883-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation