Skip to main content
SpringerLink
Log in

Complex Zero-Knowledge Proofs of Knowledge Are Easy to Use

  • Conference paper
Book cover Provable Security (ProvSec 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4784))

Included in the following conference series:

Abstract

Since 1985 and their introduction by Goldwasser, Micali and Rackoff, followed in 1988 by Feige, Fiat and Shamir, zero-knowledge proofs of knowledge have become a central tool in modern cryptography. Many articles use them as building blocks to construct more complex protocols, for which security is often hard to prove. The aim of this paper is to simplify analysis of many of these protocols, by providing the cryptographers with a theorem which will save them from stating explicit security proofs. Kiayias, Tsiounis and Yung made a first step in this direction at Eurocrypt’04, but they only addressed the case of so-called “triangular set of discrete-log relations”. By generalizing their result to any set of discrete-log relations, we greatly extend the range of protocols it can be applied to.

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. Ateniese, G., Camenisch, J., Joye, M., Tsudik, G.: A Practical and Provably Secure Coalition-Resistant Group Signature Scheme. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 255–270. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  2. Barić, N., Pfitzmann, B.: Collision-Free Accumulators and Fail-Stop Signature Schemes Without Trees. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 480–484. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  3. Bellare, M., Goldwasser, S.: Verifiable Partial Key Escrow. In: ACM CCS 1997, pp. 78–91. ACM Press, New York (1997)

    Chapter  Google Scholar 

  4. Boudot, F.: Efficient Proofs that a Committed Number Lies in an Interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Camenisch, J., Lysyanskaya, A.: Dynamic Accumulators and Application to Efficient Revocation of Anonymous Credentials. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 61–76. Springer, Heidelberg (2002)

    Google Scholar 

  6. Camenisch, J., Michels, M.: A Group Signature Scheme Based on an RSA-Variant. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 160–174. Springer, Heidelberg (1998)

    Google Scholar 

  7. Camenisch, J., Michels, M.: Proving in Zero-Knowledge that a Number is the Product of Two Safe Primes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 107–122. Springer, Heidelberg (1999)

    Google Scholar 

  8. Canard, S., Gouget, A., Hufschmitt, E.: A Handy Muti-Coupon System. In: Jakobsson, M., Yung, M., Zhou, J. (eds.) ACNS 2004. LNCS, vol. 3089, pp. 66–81. Springer, Heidelberg (2004)

    Google Scholar 

  9. Canard, S., Traoré, J.: On Fair E-cash Systems based on Group Signature Schemes. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 237–248. Springer, Heidelberg (2003)

    Google Scholar 

  10. Chan, A.H., Frankel, Y., Tsiounis, Y.: Easy Come - Easy Go Divisible Cash. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 561–575. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  11. Chaum, D., Pedersen, T.: Transferred Cash Grows in Size. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 390–407. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  12. Cramer, R., Shoup, V.: Signature Schemes Based on the Strong RSA Assumption. ACM TISSEC 3(3), 161–185 (2000)

    Article  Google Scholar 

  13. Damgård, I., Fujisaki, E.: A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 143–159. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. Feige, U., Fiat, A., Shamir, A.: Zero-knowledge Proofs of Identity. Journal of Cryptology 1(2), 77–94 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  15. Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)

    Google Scholar 

  16. Fujisaki, E., Okamoto, T.: Statistical Zero-Knowledge Protocols Solution to Identification and Signature Problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 16–30. Springer, Heidelberg (1997)

    Google Scholar 

  17. Gennaro, R., Rabin, T., Krawczyk, H.: RSA-Based Undeniable Signatures. Journal of Cryptology 13(4), 397–416 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. Girault, M., Poupard, G., Stern, J.: On the Fly Authentication and Signature Schemes Based on Groups of Unknown Order. Journal of Cryptology 19(4), 463–487 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  19. Goldwasser, S., Micali, S., Rackoff, C.W.: The Knowledge Complexity of Interactive Proof Systems. SIAM Journal of Computing 18(1), 186–208 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  20. Kiayias, A., Tsiounis, Y., Yung, M.: Traceable Signatures. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 571–589. Springer, Heidelberg (2004), http://eprint.iacr.org/

    Google Scholar 

  21. Pointcheval, D., Stern, J.: Security Arguments for Digital Signatures and Blind Signatures. Journal of Cryptology 13(3), 361–396 (2000)

    Article  MATH  Google Scholar 

  22. Schnorr, C.P.: Efficient Signature Generation for Smart Cards. Journal of Cryptology 4(3), 239–252 (1991)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Orange Labs, 42 rue des Coutures, 14000 Caen, France

    Sébastien Canard, Iwen Coisel & Jacques Traoré

Authors
  1. Sébastien Canard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iwen Coisel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jacques Traoré
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Willy Susilo Joseph K. Liu Yi Mu

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Canard, S., Coisel, I., Traoré, J. (2007). Complex Zero-Knowledge Proofs of Knowledge Are Easy to Use. In: Susilo, W., Liu, J.K., Mu, Y. (eds) Provable Security. ProvSec 2007. Lecture Notes in Computer Science, vol 4784. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75670-5_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-75670-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75669-9

  • Online ISBN: 978-3-540-75670-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation