Multisignatures as Secure as the Diffie-Hellman Problem in the Plain Public-Key Model

  • Duc-Phong Le
  • Alexis Bonnecaze
  • Alban Gabillon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5671)

Abstract

A multisignature scheme allows a group of signers to cooperate to generate a compact signature on a common document. The length of the multisignature depends only on the security parameters of the signature schemes and not on the number of signers involved. The existing state-of-the-art multisignature schemes suffer either from impractical key setup assumptions, from loose security reductions, or from inefficient signature verification. In this paper, we present two new multisignature schemes that address all of these issues, i.e., they have efficient signature verification, they are provably secure in the plain public-key model, and their security is tightly related to the computation and decisional Diffie-Hellman problems in the random oracle model. Our construction derives from variants of EDL signatures.

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References

  1. 1.
    Bagherzandi, A., Jarecki, S.: Multisignatures using proofs of secret key possession, as secure as the diffie-hellman problem. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 218–235. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 354–368. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Namprempre, C., Neven, G.: Unrestricted aggregate signatures. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 411–422. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Bellare, M., Neven, G.: Multi-signatures in the plain public-key model and a general forking lemma. In: CCS 2006: Proceedings of the 13th ACM conference on Computer and communications security, pp. 390–399. ACM Press, New York (2006)Google Scholar
  5. 5.
    Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    Boyd, C.: Digital multisignatures. In: Cryptography and Coding, pp. 241–246. Oxford University Press, Oxford (1989)Google Scholar
  8. 8.
    Chaum, D., Pedersen, T.P.: Wallet Databases with Observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  9. 9.
    Chevallier-Mames, B.: An Efficient CDH-Based Signature Scheme with a Tight Security Reduction. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 511–526. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Goh, E.-J., Jarecki, S.: A signature scheme as secure as the Diffie-Hellman problem. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 401–415. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Goh, E.-J., Jarecki, S., Katz, J., Wang, N.: Efficient signature schemes with tight security reductions to the diffie-hellman problems. Journal of Cryptology 20(4), 493–514 (2007)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Itakura, K., Nakamura, K.: A public key cryptosystem suitable for digital multisignatures. NEC Research and Development 71, 1–8 (1983)Google Scholar
  13. 13.
    Jakobsson, M., Schnorr, C.-P.: Efficient Oblivious Proofs of Correct Exponentiation. In: CMS 1999: Communications and Multimedia Security. IFIP Conference Proceedings, vol. 152, pp. 71–86. Kluwer, Dordrecht (1999)Google Scholar
  14. 14.
    Joux, A., Nguyen, K.: Separating Decision Diffie-Hellman from Computational Diffie-Hellman in cryptographic groups. J. Cryptology 16(4), 239–247 (2003)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Katz, J., Wang, N.: Efficiency improvements for signature schemes with tight security reductions. In: CCS 2003: Proceedings of the 10th ACM Conference on Computer and Communications Security, pp. 155–164 (2003)Google Scholar
  16. 16.
    Micali, S., Ohta, K., Reyzin, L.: Accountable-subgroup multisignatures. In: CCS 2001: Proceedings of the 8th ACM conference on Computer and Communications Security, pp. 245–254. ACM Press, New York (2001)Google Scholar
  17. 17.
    Micali, S., Reyzin, L.: Improving the exact security of digital signature schemes. J. Cryptology 15(1), 1–18 (2002)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Okamoto, T.: A digital multisignature scheme using bijective public-key cryptosystems. ACM Trans. Comput. Syst. 6(4), 432–441 (1988)CrossRefMATHGoogle Scholar
  19. 19.
    Ristenpart, T., Yilek, S.: The power of proofs-of-possession: Securing multiparty signatures against rogue-key attacks. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 228–245. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Duc-Phong Le
    • 1
  • Alexis Bonnecaze
    • 2
  • Alban Gabillon
    • 3
  1. 1.Laboratoire LIUPPAUniversité de Pau et des Pays de l’AdourPau CedexFrance
  2. 2.Laboratoire IMLUniversité de MéditéranéeMarseille cedex 09France
  3. 3.Laboratoire GePaSudUniversité de la Polynésie Française, 98702 FAA’A - Tahiti - Polynésie françaiseFrance

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