Skip to main content
Springer Nature Link
Log in

Four-Round Zero-Knowledge Arguments of Knowledge with Strict Polynomial-Time Simulation from Differing-Input Obfuscation for Circuits

  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9797))

Included in the following conference series:

  • 898 Accesses

Abstract

In this paper we present a 4-round zero-knowledge argument of knowledge for \(\mathbf {NP}\) with strict-polynomial-time simulation and expected polynomial-time extraction based on differing-input obfuscation for some circuit samplers and other reasonable assumptions.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ananth, P., Boneh, D., Garg, S., Sahai, A., Zhandry, M.: Differing-inputs obfuscation and applications. In: IACR Cryptology ePrint Archive 2013, p. 689 (2013)

    Google Scholar 

  2. Barak, B.: How to go beyond the black-box simulation barrier. In: FOCS, pp. 106–115 (2001)

    Google Scholar 

  3. Barak, B., Goldreich, O.: Universal arguments and their applications. In: IEEE Conference on Computational Complexity, pp. 194–203 (2002)

    Google Scholar 

  4. Blum, M.: Coin flipping by telephone. In: Gersho, A. (ed.) CRYPTO, pp. 11–15, U. C. Santa Barbara, Dept. of Elec. and Computer Eng., ECE Report No. 82-04 (1981)

    Google Scholar 

  5. Blum, M.: How to prove a theorem so no one else can claim it. In: Proceedings of the International Congress of Mathematicians, pp. 1444–1451 (1987)

    Google Scholar 

  6. Brassard, G., Chaum, D., Crépeau, C.: Minimum disclosure proofs of knowledge. J. Comput. Syst. Sci. 37(2), 156–189 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  7. van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010). http://dx.doi.org/10.1007/978-3-642-13190-5

    Chapter  Google Scholar 

  8. Ding, N.: Obfuscation-based non-black-box extraction and constant-round zero-knowledge arguments of knowledge. In: Chow, S.S.M., Camenisch, J., Hui, L.C.K., Yiu, S.M. (eds.) ISC 2014. LNCS, vol. 8783, pp. 120–139. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-319-13257-0_8

    Google Scholar 

  9. Ding, N.: On zero-knowledge with strict polynomial-time simulation and extraction from differing-input obfuscation for circuits. In: Lehmann, A., Wolf, S. (eds.) Information Theoretic Security. LNCS, vol. 9063, pp. 51–68. Springer, Heidelberg (2015). http://dx.doi.org/10.1007/978-3-319-17470-9_4

    Google Scholar 

  10. Dodis, Y., Nielsen, J.B. (eds.): TCC 2015. LNCS, vol. 9015. Springer, Heidelberg (2015). http://dx.doi.org/10.1007/978-3-662-46497-7

    MATH  Google Scholar 

  11. Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: STOC, pp. 416–426. ACM (1990)

    Google Scholar 

  12. Fischlin, M.: Trapdoor commitment schemes and their applications. Ph.D. thesis, Fachbereich Mathematik Johann Wolfgang Goethe-Universit at Frankfurt am Main (2001)

    Google Scholar 

  13. Garg, S., Gentry, C., Halevi, S., Wichs, D.: On the implausibility of differing-inputs obfuscation and extractable witness encryption with auxiliary input. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 518–535. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-662-44371-2_29

    Chapter  Google Scholar 

  14. Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for NP. J. Cryptol. 9(3), 167–190 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Ishai, Y., Pandey, O., Sahai, A.: Public-coin differing-inputs obfuscation and its applications. In: Dodis and Nielsen [10], pp. 668–697. http://dx.doi.org/10.1007/978-3-662-46497-7_26

    Google Scholar 

  17. Lapidot, D., Shamir, A.: Publicly verifiable non-interactive zero-knowledge proofs. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 353–365. Springer, Heidelberg (1991)

    Google Scholar 

  18. Lindell, Y.: A note on constant-round zero-knowledge proofs of knowledge. J. Cryptol. 26(4), 638–654 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Ostrovsky, R., Visconti, I.: Simultaneous resettability from collision resistance. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 19, p. 164 (2012). http://dblp.uni-trier.de/db/journals/eccc/eccc19.html#OstrovskyV12

  20. Pandey, O., Prabhakaran, M., Sahai, A.: Obfuscation-based non-black-box simulation and four message concurrent zero knowledge for NP. In: Dodis and Nielsen [10], pp. 638–667. http://dx.doi.org/10.1007/978-3-662-46497-7_25

    Google Scholar 

Download references

Acknowledgments

We are grateful to the reviewers of COCOON 2016 for their useful comments. This work is supported by the National Natural Science Foundation of China (Grant No. 61572309) and Major State Basic Research Development Program (973 Plan) of China (Grant No. 2013CB338004) and Research Fund of Ministry of Education of China and China Mobile (Grant No. MCM20150301).

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

    Ning Ding & Dawu Gu

  2. State Key Laboratory of Cryptology, Beijing, China

    Ning Ding

  3. School of Communication and Information Engineering, Shanghai University, Shanghai, China

    Yanli Ren

Authors
  1. Ning Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanli Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dawu Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ning Ding .

Editor information

Editors and Affiliations

  1. Virginia Commonwealth Univ , Richmond, Virginia, USA

    Thang N. Dinh

  2. University of Florida , Gainesville, Alabama, USA

    My T. Thai

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Ding, N., Ren, Y., Gu, D. (2016). Four-Round Zero-Knowledge Arguments of Knowledge with Strict Polynomial-Time Simulation from Differing-Input Obfuscation for Circuits. In: Dinh, T., Thai, M. (eds) Computing and Combinatorics . COCOON 2016. Lecture Notes in Computer Science(), vol 9797. Springer, Cham. https://doi.org/10.1007/978-3-319-42634-1_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-42634-1_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42633-4

  • Online ISBN: 978-3-319-42634-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics