Skip to main content
SpringerLink
Log in

Obfuscation-Based Non-Black-Box Extraction and Constant-Round Zero-Knowledge Arguments of Knowledge

  • Conference paper
Book cover Information Security (ISC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8783))

Included in the following conference series:

Abstract

This paper addresses the issues of constructing zero- knowledge arguments of knowledge (ZKAOK) with properties such as a small number of rounds, public-coin and strict-polynomial-time simulation and extraction, and shows the existence of the following systems for NP for the first time under some assumptions.

  • There exists a 4-round auxiliary-input ZKAOK with strict-polynomial-time simulation and extraction. Previously even combining the strict-polynomial-time simulation and extraction construction by Barak and Lindell (STOC’02) with the recent 4-round zero-knowledge argument by Pandey et al.[ePrint’13] brings such a construction using at least 6 rounds.

  • There exists a 3-round bounded-auxiliary-input ZKAOK with strict-polynomial-time simulation and extraction. Previously the extractor of the 3-round construction by Bitansky et al.[STOC’14] runs in expected-polynomial-time.

  • There exists a 2-round public-coin bounded-auxiliary-input ZKAOK with strict-polynomial-time simulation which extractor works for bounded-size provers and runs in strict-polynomial-time.

We demonstrate a new non-black-box extraction technique based on differing-input obfuscation due to Ananth et al.[ePrint’13] to achieve strict-polynomial-time extraction.

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 54.99
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. Ananth, P., Boneh, D., Garg, S., Sahai, A., Zhandry, M.: Differing-inputs obfuscation and applications. IACR Cryptology ePrint Archive 2013, 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. Barak, B., Lindell, Y.: Strict polynomial-time in simulation and extraction. In: Reif, J.H. (ed.) STOC, pp. 484–493. ACM (2002)

    Google Scholar 

  5. Barak, B., Lindell, Y., Vadhan, S.P.: Lower bounds for non-black-box zero knowledge. J. Comput. Syst. Sci. 72(2), 321–391 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Barak, B., Ong, S.J., Vadhan, S.P.: Derandomization in cryptography. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 299–315. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Bellare, M., Goldreich, O.: On defining proofs of knowledge. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 390–420. Springer, Heidelberg (1993)

    Google Scholar 

  8. Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: Recursive composition and bootstrapping for snarks and proof-carrying data. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) STOC, pp. 111–120. ACM (2013)

    Google Scholar 

  9. Bitansky, N., Canetti, R., Paneth, O., Rosen, A.: On the existence of extractable one-way functions. In: Shmoys, D.B. (ed.) STOC, pp. 505–514. ACM (2014)

    Google Scholar 

  10. 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 

  11. 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 

  12. Boyle, E., Chung, K.-M., Pass, R.: On extractability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 52–73. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Google Scholar 

  15. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS, pp. 40–49. IEEE Computer Society (2013)

    Google Scholar 

  16. 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)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  18. Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield nothing but their validity and a methodology of cryptographic protocol design (extended abstract). In: FOCS, pp. 174–187. IEEE Computer Society (1986)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  21. Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive zaps and new techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 97–111. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Hada, S., Tanaka, T.: On the existence of 3-round zero-knowledge protocols. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 408–423. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  23. Katz, J.: Which languages have 4-round zero-knowledge proofs? In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 73–88. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  25. Micali, S.: Cs proofs (extended abstracts). In: FOCS, pp. 436–453. IEEE Computer Society (1994)

    Google Scholar 

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

    Google Scholar 

  27. Pandey, O., Prabhakaran, M., Sahai, A.: Obfuscation-based non-black-box simulation and four message concurrent zero knowledge for np. Cryptology ePrint Archive, Report 2013/754 (2013), http://eprint.iacr.org/

Download references

Author information

Authors and Affiliations

  1. NTT Secure Platform Laboratories, Japan

    Ning Ding

  2. Shanghai Jiao Tong University, China

    Ning Ding

Authors
  1. Ning Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Information Engineering, Chinese University of Hong Kong, Room 808, Ho Sin Hang Engineering Building, Sha Tin, N.T., Hong Kong, China

    Sherman S. M. Chow

  2. IBM Research Zurich, Säumerstrasse 4, 8803, Rüschlikon, Switzerland

    Jan Camenisch

  3. Department of Computer Science, The University of Hong Kong, Chow Yei Ching Building, Pokfulam Road, Hong Kong, China

    Lucas C. K. Hui  & Siu Ming Yiu  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Ding, N. (2014). 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) Information Security. ISC 2014. Lecture Notes in Computer Science, vol 8783. Springer, Cham. https://doi.org/10.1007/978-3-319-13257-0_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13257-0_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13256-3

  • Online ISBN: 978-3-319-13257-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation