An Efficient Signature Scheme from Bilinear Pairings and Its Applications

  • Fangguo Zhang
  • Reihaneh Safavi-Naini
  • Willy Susilo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2947)

Abstract

In Asiacrypt2001, Boneh, Lynn, and Shacham [8] proposed a short signature scheme (BLS scheme) using bilinear pairing on certain elliptic and hyperelliptic curves. Subsequently numerous cryptographic schemes based on BLS signature scheme were proposed. BLS short signature needs a special hash function [6,1,8]. This hash function is probabilistic and generally inefficient. In this paper, we propose a new short signature scheme from the bilinear pairings that unlike BLS, uses general cryptographic hash functions such as SHA-1 or MD5, and does not require special hash functions. Furthermore, the scheme requires less pairing operations than BLS scheme and so is more efficient than BLS scheme. We use this signature scheme to construct a ring signature scheme and a new method for delegation. We give the security proofs for the new signature scheme and the ring signature scheme in the random oracle model.

Keywords

Short signature Bilinear pairings ID-based cryptography Ring signature Proxy signature 
Download to read the full conference paper text

References

  1. 1.
    Barreto, P.S.L.M., Kim, H.Y.: Fast hashing onto elliptic curves over fields of characteristic 3. Cryptology ePrint Archive, Report 2001/098Google 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.
    Barreto, P.S.L.M., Lynn, B., Scott, M.: On the selection of pairing-friendly groups. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol. 3006. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Bellare, M., Rogaway, P.: The exact security of digital signatures - How to sign with RSA and Rabin. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 399–416. Springer, Heidelberg (1996)Google Scholar
  5. 5.
    Boldyreva, A.: Efficient threshold signature, multisignature and blind signature schemes based on the Gap-Diffie-Hellman -group signature scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 31–46. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    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. 272–293. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Cha, J.C., Cheon, J.H.: An identity-based signature from gap Diffie-Hellman groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18–30. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Courtois, N.T., Finiasz, M., Sendrier, N.: How to achieve a McEliece-based Digital Signature Scheme. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 157–174. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Galbraith, S.D., Harrison, K., Soldera, D.: Implementing the Tate pairing. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 324–337. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Goldwasser, S., Micali, S., Rivest, R.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal of computing 17(2), 281–308 (1988)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hess, F.: Efficient identity based signature schemes based on pairings. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 310–324. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Kim, S., Park, S., Won, D.: Proxy signatures, revisited. In: Han, Y., Quing, S. (eds.) ICICS 1997. LNCS, vol. 1334, pp. 223–232. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  16. 16.
    Mambo, M., Usuda, K., Okamoto, E.: Proxy signature: Delegation of the power to sign messages. IEICE Trans. Fundamentals E79-A(9), 1338–1353 (1996)Google Scholar
  17. 17.
    Maurer, U.: Towards the equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 271–281. Springer, Heidelberg (1994)Google Scholar
  18. 18.
    Mitsunari, S., Sakai, R., Kasahara, M.: A new traitor tracing. IEICE Trans. E85-A(2), 481–484 (2002)Google Scholar
  19. 19.
    Patarin, J., Courtois, N., Goubin, L.: QUARTZ, 128-bit long digital signatures. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 282–297. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  20. 20.
    Paterson, K.G.: ID-based signatures from pairings on elliptic curves. Electron. Lett. 38(18), 1025–1026 (2002)CrossRefGoogle Scholar
  21. 21.
    Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    Sadeghi, A.R., Steiner, M.: Assumptions related to discrete logarithms: why subtleties make a real difference. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 243–260. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  23. 23.
    Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: SCIS 2000-C20, Okinawa, Japan (January 2000)Google Scholar
  24. 24.
    Sakai, R., Kasahara, M.: Cryptosystems based on pairing over elliptic curve. In: SCIS 2003, 8C-1, January 2003, Japan (2003)Google Scholar
  25. 25.
    Sakai, R., Kasahara, M.: ID based cryptosystems with pairing on elliptic curve, Cryptology ePrint Archive, Report 2003/054Google Scholar
  26. 26.
    Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  27. 27.
    Smart, N.P.: An identity based authenticated key agreement protocol based on the Weil pairing. Electron. Lett. 38(13), 630–632 (2002)MATHCrossRefGoogle Scholar
  28. 28.
    Zhang, F., Kim, K.: ID-based blind signature and ring signature from pairings. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 533–547. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Fangguo Zhang
    • 1
  • Reihaneh Safavi-Naini
    • 1
  • Willy Susilo
    • 1
  1. 1.School of Information Technology and Computer ScienceUniversity of WollongongAustralia

Personalised recommendations