ID-Based Blind Signature and Ring Signature from Pairings

  • Fangguo Zhang
  • Kwangjo Kim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2501)


Recently the bilinear pairing such as Weil pairing or Tate pairing on elliptic curves and hyperelliptic curves have been found various applications in cryptography. Several identity-based (simply ID-based) cryptosystems using bilinear pairings of elliptic curves or hyperelliptic curves were presented. Blind signature and ring signature are very useful to provide the user’s anonymity and the signer’s privacy. They are playing an important role in building e-commerce. In this paper, we firstly propose an ID-based blind signature scheme and an ID-based ring signature scheme, both of which are based on the bilinear pairings. Also we analyze their security and efficiency.


Blind signature Ring signature Bilinear pairings ID-based cryptography Provably security 


  1. 1.
    M. Abe, M. Ohkubo, and K. Suzuki, 1-out-of-n signatures from a variety of keys, To appear in Advances in Cryptology-Asiacrypt 2002, 2002.Google Scholar
  2. 2.
    M. Abe and T. Okamoto, Provably secure partially blind signatures, Advances in Cryptology-Crypto 2000, LNCS 1880, pp. 271–286, Springer-Verlag, 2000.CrossRefGoogle Scholar
  3. 3.
    P.S.L.M. Barreto, H.Y. Kim, B. Lynn, and M. Scott, Efficient algorithms for pairing-based cryptosystems, Advances in Cryptology-Crypto 2002, LNCS 2442, pp. 354–368, Springer-Verlag, 2002.CrossRefGoogle Scholar
  4. 4.
    D. Boneh and M. Franklin, Identity-based encryption from the Weil pairing, Advances in Cryptology-Crypto 2001, LNCS 2139, pp. 213–229, Springer-Verlag, 2001.CrossRefGoogle Scholar
  5. 5.
    D. Boneh, B. Lynn, and H. Shacham, Short signatures from the Weil pairing, Advances in Cryptology-Asiacrypt 2001, LNCS 2248, pp. 514–532, Springer-Verlag, 2001.CrossRefGoogle Scholar
  6. 6.
    J.C. Cha and J.H. Cheon, An identity-based signature from gap Diffie-Hellman groups, Cryptology ePrint Archive, Report 2002/018, available at
  7. 7.
    D. Chaum, Blind signatures for untraceable payments, Advances in Cryptology-Crypto 82, Plenum, NY, pp. 199–203, 1983.Google Scholar
  8. 8.
    C. Cocks, An identity based encryption scheme based on quadratic residues, In Cryptography and Coding, LNCS 2260, pp. 360–363, Springer-Verlag, 2001.CrossRefGoogle Scholar
  9. 9.
    G. Frey and H. Rück, A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Mathematics of Computation, 62, pp. 865–874, 1994.CrossRefMathSciNetGoogle Scholar
  10. 10.
    S. D. Galbraith, K. Harrison, and D. Soldera, Implementing the Tate pairing, ANTS 2002, LNCS 2369, pp. 324–337, Springer-Verlag, 2002.Google Scholar
  11. 11.
    F. Hess, Exponent group signature schemes and efficient identity based signatureschemes based on pairings, Cryptology ePrint Archive, Report 2002/012, available at
  12. 12.
    F. Hess G. Seroussi and N. Smart, Two topics in hyperelliptic cryptography, SAC (Selected Areas in Cryptography) 2001, LNCS 2259, pp. 181–189, Springer-Verlag, 2001.CrossRefGoogle Scholar
  13. 13.
    IEEE Std 2000-1363, Standard specifications for public key cryptography, 2000.Google Scholar
  14. 14.
    A. Joux, A one round protocol for tripartite Diffie-Hellman, ANTS IV, LNCS 1838, pp. 385–394, Springer-Verlag, 2000.Google Scholar
  15. 15.
    A. Joux, The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems, ANTS 2002, LNCS 2369, pp. 20–32, Springer-Verlag, 2002.Google Scholar
  16. 16.
    A. Juels, M. Luby and R. Ostrovsky, Security of blind digital signatures, Advances in Cryptology-Crypto 97, LNCS 1294, pp. 150–164, Springer-Verlag, 1997.CrossRefGoogle Scholar
  17. 17.
    M.S. Kim and K. Kim, A new identification scheme based on the bilinear Diffie-Hellman problem, Proc. of ACISP(The 7th Australasian Conference on Information Security and Privacy) 2002, LNCS 2384, pp. 464–481, Springer-Verlag, 2002.Google Scholar
  18. 18.
    A. Menezes, T. Okamoto, and S. Vanstone, Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Transaction on Information Theory, Vol. 39, pp. 1639–1646, 1993.zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    M. Naor, Deniable Ring Authentication, Advances in Cryptology-Crypto 2002, LNCS 2442, pp. 481–498, Springer-Verlag, 2002.CrossRefGoogle Scholar
  20. 20.
    K.G. Paterson, ID-based signatures from pairings on elliptic curves, Cryptology ePrint Archive, Report 2002/004, available at
  21. 21.
    D. Pointcheval and J. Stern, Security arguments for digital signatures and blind signatures, Journal of Cryptology, Vol. 13, No. 3, pp. 361–396, 2000.zbMATHCrossRefGoogle Scholar
  22. 22.
    R.L. Rivest, A. Shamir and Y. Tauman, How to leak a secret, Advances in Cryptology-Asiacrypt 2001, LNCS 2248, pp. 552–565, Springer-Verlag, 2001.CrossRefGoogle Scholar
  23. 23.
    R. Sakai, K. Ohgishi, M. Kasahara, Cryptosystems based on pairing, SCIS 2000-C20, Okinawa, Japan. Jan. 2000.Google Scholar
  24. 24.
    C. P. Schnorr, Security of blind discrete log signatures against interactive attacks, ICICS 2001, LNCS 2229, pp. 1–12, Springer-Verlag, 2001.Google Scholar
  25. 25.
    A. Shamir, Identity-based cryptosystems and signature schemes, Advances in Cryptology-Crypto 84, LNCS 196, pp. 47–53, Springer-Verlag, 1984.CrossRefGoogle Scholar
  26. 26.
    N.P. Smart, Identity-based authenticated key agreement protocol based on Weil pairing, Electron. Lett., Vol. 38, No. 13, pp. 630–632, 2002.CrossRefGoogle Scholar
  27. 27.
    S. Tsuji and T. Itoh, An ID-based cryptosystem based on the discrete logarithm problem, IEEE Journal of Selected Areas in Communications, Vol. 7, No. 4, pp. 467–473, 1989.CrossRefGoogle Scholar
  28. 28.
    D. Wagner, A generalized birthday problem, Advances in Cryptology-Crypto 2002, LNCS 2442, pp. 288–303, Springer-Verlag, 2002.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Fangguo Zhang
    • 1
  • Kwangjo Kim
    • 1
  1. 1.International Research center for Information Security (IRIS)Information and Communications University(ICU)TaejonKorea

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