Skip to main content
SpringerLink
Log in

Provably Secure Pairing-Based Convertible Undeniable Signature with Short Signature Length

  • Conference paper
Pairing-Based Cryptography – Pairing 2007 (Pairing 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4575))

Included in the following conference series:

Abstract

Undeniable signatures, introduced by Chaum and van Antwerpen, is a useful cryptography primitive to limit the publicly verifiable property of ordinary digital signatures. In an undeniable signature scheme, the validity or invalidity of the signature can only be verified via the confirmation/disavowal protocol with the help of the signer. An extended concept, convertible undeniable signatures, was introduced by Boyar, Chaum, Damgård and Pedersen. In the new concept, the signer can publish some selective proofs to convert one or more undeniable signatures into publicly verifiable ones, or issue a universal proof to make all his undeniable signatures publicly verifiable. In this paper, we first present a security model for convertible undeniable signature schemes, and then propose a new construction from bilinear pairings. Compared with the other schemes in the literature, the new construction has three advantages: Our scheme is both selectively and universally convertible; the signature length of our scheme is as short as BLS signature; meanwhile, all the security properties are formally proven under some conventional assumptions in the random oracle model.

Supported by ARC Discovery Grant DP0557493 and DP0663306.

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. Boyar, J., Chaum, D., Damgård, I.B., Pedersen, T.P.: Convertible Undeniable Signatures. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 189–205. Springer, Heidelberg (1991)

    Google Scholar 

  2. Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Biehl, I., Paulus, S., Takagi, T.: Efficient Undeniable Signature Schemes Based on Ideal Arithmetic in Quadratic Orders. In: Designs, Codes and Cryptography, vol. 31(2), pp. 99–123. Springer, Netherlands (2004)

    Google Scholar 

  4. Chaum, D., Antwerpen, H.v.: Undeniable Signatures. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 212–216. Springer, Heidelberg (1990)

    Google Scholar 

  5. Chaum, D.: Zero-Knowledge Undeniable Signatures (Extended Abstract). In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 458–464. Springer, Heidelberg (1991)

    Google Scholar 

  6. Chaum, D., Heijst, E.v., Pfitzmann, B.: Cryptographically Strong Undeniable Signatures, Unconditionally Secure for the Signer. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 470–484. Springer, Heidelberg (1992)

    Google Scholar 

  7. Diffie, W., Hellman, M.: New directions in cryptography. IEEE IT 22, 644–654 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  8. Damgård, I.B., Pedersen, T.P.: New Convertible Undeniable Signature Schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 372–386. Springer, Heidelberg (1996)

    Google Scholar 

  9. Desmedt, Y., Yung, M.: Weaknesses of Undeniable Signature Schemes (Extended Abstract). In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 205–220. Springer, Heidelberg (1991)

    Google Scholar 

  10. Fujioka, A., Okamotoa, T., Ohta, K.: Interactive Bi-Proof Systems and Undeniable Signature Schemes. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 243–256. Springer, Heidelberg (1991)

    Google Scholar 

  11. Goldwasser, S., Micali, S., Rivest, R.: A Digital Signature Scheme Secure Against Adaptively Chosen Message Attacks. SIAM Journal on Computing 17(2), 281–308 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  12. Galbraith, S.D., Mao, W., Paterson, K.G.: RSA-Based Undeniable Signatures for General Moduli. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 200–217. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  13. Galbraith, S.D., Mao, W.: Invisibility and Anonymity of Undeniable and Confirmer Signatures. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 80–97. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Gennaro, R., Krawczyk, H., Rabin, T.: RSA-Based Undeniable Signatures. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 132–149. Springer, Heidelberg (1997)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  16. Jakobsson, M., Sako, K., Impagliazzo, R.: Designated Verifier Proofs and Their Applications. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 143–154. Springer, Heidelberg (1996)

    Google Scholar 

  17. Jongkook, L., Shiryong, R., Jeungseop, K., Keeyoung, Y.: A New Undeniable Signature Scheme Using Smart Cards. In: Honary, B. (ed.) Cryptography and Coding. LNCS, vol. 2260, pp. 387–394. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  18. Jakobsson, M.: Blackmailing Using Undeniable Signatures. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 425–427. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  19. Furukawa, J., Kurosawa, K., Imai, H.: An Efficient Compiler from Σ-Protocol to 2-Move Deniable Zero-Knowledge. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 46–57. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  20. Kudla, C., Paterson, K.G.: Non-interactive Designated Verifier Proofs and Undeniable Signatures. In: Smart, N.P. (ed.) Cryptography and Coding. LNCS, vol. 3796, pp. 136–154. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Kim, S., Won, D.: Threshold Entrusted Undeniable Signature. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 195–203. Springer, Heidelberg (2005)

    Google Scholar 

  22. Kurosawa, K., Heng, S.-H.: 3-Move Undeniable Signature Scheme. In: Fuhr, N., Lalmas, M., Malik, S., Szlávik, Z. (eds.) INEX 2004. LNCS, vol. 3493, pp. 181–197. Springer, Heidelberg (2005)

    Google Scholar 

  23. Kurosawa, K., Takagi, T.: New Approach for Selectively Convertible Undeniable Signature Schemes. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 428–443. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  24. Laguillaumie, F., Paillier, P., Vergnaud, D.: Universally Convertible Directed Signatures. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 682–701. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  25. Libert, B., Quisquater, J.J.: Identity Based Undeniable Signatures. In: Okamoto, T. (ed.) CT-RSA 2004. LNCS, vol. 2964, pp. 112–125. Springer, Heidelberg (2004)

    Google Scholar 

  26. Lyuu, Y.-D., Wu, M.-L.: Convertible Group Undeniable Signatures. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 48–61. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  27. Laguillaumie, F., Vergnaud, D.: Time-Selective Convertible Undeniable Signatures. In: Menezes, A.J. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 154–171. Springer, Heidelberg (2005)

    Google Scholar 

  28. Laguillaumie, F., Vergnaud, D.: Short Undeniable Signatures Without Random Oracles: The Missing Link. In: Maitra, S., Madhavan, C.E.V., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 283–296. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  29. Miyazaki, T.: An Improved Scheme of the Gennaro-Krawczyk-Rabin Undeniable Signature System Based on RSA. In: Won, D. (ed.) ICISC 2000. LNCS, vol. 2015, pp. 135–149. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  30. Michels, M., Petersen, H., Horster, P.: Breaking and Repairing a Convertible Undeniable Signature Scheme. In: Third ACM Conference on Computer and Communications Security, pp. 148–152. ACM Press, New York (1996)

    Google Scholar 

  31. Michels, M., Stadler, M.: Efficient Convertible Undeniable Signature Schemes. In: The 4th International Workshop on Selected Areas in Cryptography - SAC 1997. pp. 231–244 (1997)

    Google Scholar 

  32. Monnerat, J., Vaudenay, S.: Undeniable Signatures Based on Characters: How to Sign with One Bit. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 69–85. Springer, Heidelberg (2004)

    Google Scholar 

  33. Monnerat, J., Vaudenay, S.: Generic Homomorphic Undeniable Signatures. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 354–371. Springer, Heidelberg (2004)

    Google Scholar 

  34. Monnerat, J., Vaudenay, S.: Optimization of the MOVA Undeniable Signature Scheme. In: Dawson, E., Vaudenay, S. (eds.) Mycrypt 2005. LNCS, vol. 3715, pp. 196–209. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  35. Monnerat, J., Vaudenay, S.: Short 2-Move Undeniable Signatures. In: Nguyen, P.Q. (ed.) VIETCRYPT 2006. LNCS, vol. 4341, pp. 19–36. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  36. Ogata, W., Kurosawa, K., Heng, S.-H.: The Security of the FDH Variant of Chaum Undeniable Signature Scheme. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 328–345. Springer, Heidelberg (2005)

    Google Scholar 

  37. Okamoto, T., Pointcheval, D.: The Gap-Problems: A New Class of Problems for the Security of Cryptographic Schemes. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 104–118. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

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

    Article  MATH  Google Scholar 

  39. Vergnaud, D., Aimani, L. E.: Gradually Convertible Undeniable Signatures. In: Applied Cryptography and Network Security. 5th International Conference, ACNS 2007. LNCS, Springer, Heidelberg (to appear, 2007)

    Google Scholar 

  40. Wang, G.: An Attack on Not-interactive Designated Verifier Proofs for Undeniable Signatures. Available online: http://eprint.iacr.org/2003/243

  41. Wang, G., Qing, S., Wang, M., Zhou, Z.: Threshold Undeniable RSA Signature Scheme. In: Qing, S., Okamoto, T., Zhou, J. (eds.) ICICS 2001. LNCS, vol. 2229, pp. 221–232. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  42. Wang, G., Zhou, J., Deng, R.H.: On the Security of the Lee-Hwang Group-Oriented Undeniable Signature Schemes. In: Katsikas, S.K., Lopez, J., Pernul, G. (eds.) TrustBus 2004. LNCS, vol. 3184, pp. 289–298. Springer, Heidelberg (2004), Avaliable online: http://eprint.iacr.org/2002/150

    Google Scholar 

  43. Zhang, F., Safavi-Naini, R., Susilo, W.: Attack on Han et al.’s ID-based Confirmer (Undeniable) Signature at ACM-EC 2003. Available online: http://eprint.iacr.org/2003/129

Download references

Author information

Authors and Affiliations

  1. Centre for Computer and Information Security Research, School of Computer Science & Software Engineering, University of Wollongong, Australia

    Xinyi Huang, Yi Mu, Willy Susilo & Wei Wu

Authors
  1. Xinyi Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Mu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Willy Susilo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Tsuyoshi Takagi Tatsuaki Okamoto Eiji Okamoto Takeshi Okamoto

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Huang, X., Mu, Y., Susilo, W., Wu, W. (2007). Provably Secure Pairing-Based Convertible Undeniable Signature with Short Signature Length. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds) Pairing-Based Cryptography – Pairing 2007. Pairing 2007. Lecture Notes in Computer Science, vol 4575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73489-5_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73489-5_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73488-8

  • Online ISBN: 978-3-540-73489-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation