Provably Secure Electronic Cash Based on Blind Multisignature Schemes

  • Yoshikazu Hanatani
  • Yuichi Komano
  • Kazuo Ohta
  • Noboru Kunihiro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4107)


Though various blind multisignature schemes have been proposed for secure electronic cash, the formal model of security was not discussed. This paper first formalizes the security notions for e-cash schemes based on the blind multisignature scheme. We then construct a blind multisignature scheme and propose a new untraceable e-cash scheme which is provably secure under the DDH assumption in the random oracle model applying the blind multisignature scheme. The proposed scheme can ensure the framing attack by banks where they collude to simulate the double-spending of an honest user.


Blind multisignature electronic cash provable security random oracle model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abe, M.: A secure three-move blind signature scheme for polynomially many signatures. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 136–151. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Abe, M., Okamoto, T.: Provably secure partially blind signatures. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 271–286. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: One-more-RSA-inversion problems and the security of chaum’s blind signature scheme. J. Cryptology 16(3), 185–215 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security 1993, pp. 62–73 (1993)Google Scholar
  5. 5.
    Boneh, D.: The decision diffie-hellman problem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 48–63. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  6. 6.
    Brands, S.: Untraceable off-line cash in wallet with observers (extended abstract). In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 302–318. Springer, Heidelberg (1994)Google Scholar
  7. 7.
    Chaum, D.: Blind signatures for untraceable payments. In: McCurley, K.S., Ziegler, C.D. (eds.) Advances in Cryptology 1981 - 1997. LNCS, vol. 1440, pp. 199–203. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Chaum, D., Fiat, A., Naor, M.: Untraceable electronic cash. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 319–327. Springer, Heidelberg (1990)Google Scholar
  9. 9.
    Chen, X., Zhang, F., Kim, K.: Id-based multi-proxy signature and blind multisignature from bilinear pairings. In: KIISC conference 2003, pp. 11–19 (2003)Google Scholar
  10. 10.
    Franklin, M., Yung, M.: Secure and efficient off-line digital money. In: Lingas, A., Carlsson, S., Karlsson, R. (eds.) ICALP 1993. LNCS, vol. 700, pp. 265–276. Springer, Heidelberg (1993)Google Scholar
  11. 11.
    Horster, P., Michels, M., Petersen, H.: Blind multisignature scheme based on the discrete logarithm problem. In: Proc. of 11th Annual Computer Security Applications Conference, pp. 149–155 (1995)Google Scholar
  12. 12.
    Itakura, K., Nakamura, K.: A public key cryptosystem suitable for digital multisignatures. In: NEC Research & Development, vol. 71, pp. 1–8 (1983)Google Scholar
  13. 13.
    Micali, S., Ohta, K., Reyzin, L.: Accountable-subgroup multisignatures. In: ACM Conference on Computer and Communications Security 2001, pp. 245–254 (2001)Google Scholar
  14. 14.
    Pointcheval, D., Stern, J.: Provably secure blind signature schemes. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 252–265. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  15. 15.
    Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptology 13(3), 361–396 (2000)zbMATHCrossRefGoogle Scholar
  16. 16.
    Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yoshikazu Hanatani
    • 1
  • Yuichi Komano
    • 2
  • Kazuo Ohta
    • 1
  • Noboru Kunihiro
    • 1
  1. 1.The University of Electro-CommunicationsTokyoJapan
  2. 2.TOSHIBA CorporationKawasaki-shi, KanagawaJapan

Personalised recommendations