Skip to main content
Springer Nature Link
Log in

Fair Exchange of Short Signatures without Trusted Third Party

  • Conference paper
Topics in Cryptology – CT-RSA 2013 (CT-RSA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7779))

Included in the following conference series:

  • 2432 Accesses

Abstract

We propose a protocol to exchange Boneh-Boyen short signatures in a fair way and without relying on a trusted third party. Our protocol is quite practical and is the first of the sort to the best of our knowledge. Our construction uses a new non-interactive zero-knowledge (NIZK) argument to prove that a commitment is the encryption of a bit vector. We also design a NIZK argument to prove that a commitment to a bit vector v = (b 1,b 2,...,b κ ) is such that ∑  i ∈ [κ] b i 2i − 1 = θ where θ is the discrete logarithm of some public value D = g θ. These arguments may be of independent interest.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Asokan, N., Schunter, M., Waidner, M.: Optimistic protocols for fair exchange. In: CCS, pp. 7–17. ACM Press (April 1997)

    Google Scholar 

  2. Blum, M.: How to exchange (secret) keys. ACM Transactions on Computer Systems 1(2), 175–193 (1983)

    Article  Google Scholar 

  3. Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Boneh, D., Boyen, X.: Short Signatures Without Random Oracles and the SDH Assumption in Bilinear Groups. Journal of Cryptology 21(2), 149–177 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Boneh, D., Naor, M.: Timed Commitments. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 236–254. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Brickell, E.F., Chaum, D., Damgård, I.B., van de Graaf, J.: Gradual and Verifiable Release of a Secret. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 156–166. Springer, Heidelberg (1988)

    Google Scholar 

  7. Camacho, P.: Fair Exchange of Short Signatures Without Trusted Third Party (2012), http://eprint.iacr.org/2012/288

  8. Camenisch, J., Stadler, M.: Proof Systems for General Statements about Discrete Logarithms (1997), ftp://ftp.inf.ethz.ch/pub/crypto/publications/CamSta97b.ps

  9. Choi, S.G., Hwang, K.-W., Katz, J., Malkin, T., Rubenstein, D.: Secure Multi-Party Computation of Boolean Circuits with Applications to Privacy in On-Line Marketplaces. In: Dunkelman, O. (ed.) CT-RSA 2012. LNCS, vol. 7178, pp. 416–432. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  10. Cleve, R.: Limits on the security of coin flips when half the processors are faulty. In: STOC, pp. 364–369. ACM Press (November 1986)

    Google Scholar 

  11. Cleve, R.: Controlled Gradual Disclosure Schemes for Random Bits and Their Applications. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 573–588. Springer, Heidelberg (1990)

    Google Scholar 

  12. Damgård, I.: Practical and Provably Secure Release of a Secret and Exchange of Signatures. Journal of Cryptology 8(4), 201–222 (1995)

    Article  MATH  Google Scholar 

  13. Duc, A., Jetchev, D.: Hardness of Computing Individual Bits for One-Way Functions on Elliptic Curves. In: Safavi-Naini, R. (ed.) CRYPTO 2012. LNCS, vol. 7417, pp. 832–849. Springer, Heidelberg (2012)

    Google Scholar 

  14. Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Communications of the ACM 28(6), 637–647 (1985)

    Article  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)

    Chapter  Google Scholar 

  16. Garay, J.A., MacKenzie, P.D., Prabhakaran, M., Yang, K.: Resource Fairness and Composability of Cryptographic Protocols. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 404–428. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  17. Goldwasser, S., Micali, S., Rivest, R.L.: A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks. SIAM Journal on Computing 17(2), 281 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  18. Gordon, S.D., Hazay, C., Katz, J., Lindell, Y.: Complete Fairness in Secure Two-Party Computation. Journal of the ACM 58(6), 1–37 (2011)

    Article  MathSciNet  Google Scholar 

  19. Gordon, S.D., Katz, J.: Partial Fairness in Secure Two-Party Computation. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 157–176. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  20. Groth, J.: Short Pairing-Based Non-interactive Zero-Knowledge Arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  21. Groth, J., Ostrovsky, R., Sahai, A.: Perfect Non-interactive Zero Knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339–358. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Huang, Q., Wong, D.S., Susilo, W.: The Construction of Ambiguous Optimistic Fair Exchange from Designated Confirmer Signature without Random Oracles. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 120–137. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-Size Commitments to Polynomials and Their Applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  24. MacKenzie, P.D., Patel, S.: Hard Bits of the Discrete Log with Applications to Password Authentication. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 209–226. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Micali, S.: Simple and fast optimistic protocols for fair electronic exchange. In: PODC, pp. 12–19. ACM Press, New York (2003)

    Google Scholar 

  26. Mitsunari, S., Sakai, R., Kasahara, M.: A New Traitor Tracing. In: EICE, vol. E 85-A, pp. 481–484 (2002)

    Google Scholar 

  27. Patel, S., Sundaram, G.S.: An Efficient Discrete Log Pseudo Random Generator. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 304–317. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  28. Pedersen, T.P.: Non-interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)

    Google Scholar 

  29. Schnorr, C.P.: Security of Almost ALL Discrete Log Bits. Electronic Colloquium on Computational Complexity (1998)

    Google Scholar 

  30. Zhang, F., Safavi-Naini, R., Susilo, W.: An Efficient Signature Scheme from Bilinear Pairings and Its Applications. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 277–290. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computer Science, University of Chile, Blanco Encalada 2120, 4to piso, Santiago, Chile

    Philippe Camacho

Authors
  1. Philippe Camacho
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Future Enviroments, Queensland University of Technology, GPO Box 2434, 4000, Brisbane, QLD, Australia

    Ed Dawson

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Camacho, P. (2013). Fair Exchange of Short Signatures without Trusted Third Party. In: Dawson, E. (eds) Topics in Cryptology – CT-RSA 2013. CT-RSA 2013. Lecture Notes in Computer Science, vol 7779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36095-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36095-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36094-7

  • Online ISBN: 978-3-642-36095-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics