A Practical and Provably Secure Coalition-Resistant Group Signature Scheme

  • Giuseppe Ateniese
  • Jan Camenisch
  • Marc Joye
  • Gene Tsudik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1880)

Abstract

A group signature scheme allows a group member to sign messages anonymously on behalf of the group. However, in the case of a dispute, the identity of a signature’s originator can be revealed (only) by a designated entity. The interactive counterparts of group signatures are identity escrow schemes or group identification scheme with revocable anonymity. This work introduces a new provably secure group signature and a companion identity escrow scheme that are significantly more efficient than the state of the art. In its interactive, identity escrow form, our scheme is proven secure and coalition-resistant under the strong RSA and the decisional Diffie-Hellman assumptions. The security of the non-interactive variant, i.e., the group signature scheme, relies additionally on the Fiat-Shamir heuristic (also known as the random oracle model).

Keywords

Group signature schemes revocable anonymity coalition-resistance strong RSA assumption identity escrow provable security 

References

  1. BF97.
    N. Barić and B. Pfitzmann. Collision-free accumulators and fail-stop signature schemes without trees. In Advances in Cryptology — EUROCRYPT’ 97, vol. 1233 of LNCS, pp. 480–494, Springer-Verlag, 1997.Google Scholar
  2. BR93.
    M. Bellare and P. Rogaway. Random oracles are practical: A paradigm for designing efficient protocols. In 1st ACM Conference on Computer and Communication Security, pp. 62–73, ACM Press, 1993.Google Scholar
  3. Bon98.
    D. Boneh. The decision Diffie-Hellman problem. In Algorithmic Number Theory (ANTS-III), vol. 1423 of LNCS, pp. 48–63, Springer-Verlag, 1998.CrossRefGoogle Scholar
  4. Bra93.
    S. Brands. An efficient off-line electronic cash system based on the representation problem. Technical Report CS-R9323, Centrum voor Wiskunde en Informatica, April 1993.Google Scholar
  5. CM98a.
    J. Camenisch and M. Michels. A group signature scheme with improved efficiency. In Advances in Cryptology — ASIACRYPT’ 98, vol. 1514 of LNCS, pp. 160–174, Springer-Verlag, 1998.CrossRefGoogle Scholar
  6. CM98b.
    -. A group signature scheme based on an RSA-variant. Technical Report RS-98-27, BRICS, University of Aarhus, November 1998. An earlier version appears in [CM98a].Google Scholar
  7. CM99a.
    -. Proving in zero-knowledge that a number is the product of two safe primes. In Advances in Cryptology — EUROCRYPT’ 99, vol. 1592 of LNCS, pp. 107–122, Springer-Verlag, 1999.Google Scholar
  8. CM99b.
    -. Separability and efficiency for generic group signature schemes. In Advances in Cryptology — CRYPTO’ 99, vol. 1666 of LNCS, pp. 413–430, Springer-Verlag, 1999.Google Scholar
  9. CP95.
    L. Chen and T. P. Pedersen. New group signature schemes. In Advances in Cryptology — EUROCRYPT’ 94, vol. 950 of LNCS, pp. 171–181, 1995.CrossRefGoogle Scholar
  10. CS97.
    J. Camenisch and M. Stadler. Efficient group signature schemes for large groups. In Advances in Cryptology — CRYPTO’ 97, vol. 1296 of LNCS, pp. 410–424, Springer-Verlag, 1997.CrossRefGoogle Scholar
  11. Cam98.
    J. Camenisch. Group signature schemes and payment systems based on the discrete logarithm problem. PhD thesis, vol. 2 of ETH Series in Information Security an Cryptography, Hartung-Gorre Verlag, Konstanz, 1998. ISBN 3-89649-286-1.Google Scholar
  12. Cop96.
    D. Coppersmith. Finding a small root of a bivariatre interger equation; factoring with high bits known. In Advances in Cryptology — EUROCRYPT’ 96, volume 1070 of LNCS, pages 178–189. Springer Verlag, 1996.Google Scholar
  13. CvH91.
    D. Chaum and E. van Heyst. Group signatures. In Advances in Cryptology — EUROCRYPT’ 91, vol. 547 of LNCS, pp. 257–265, Springer-Verlag, 1991.Google Scholar
  14. DH76.
    W. Diffie and M. E. Hellman. New directions in cryptography. IEEE Transactions on Information Theory, IT-22(6): 644–654, 1976.CrossRefMathSciNetGoogle Scholar
  15. FO97.
    E. Fujisaki and T. Okamoto. Statistical zero knowledge protocols to prove modular polynomial relations. In Advances in Cryptology — CRYPTO’ 97, vol. 1297 of LNCS, pp. 16–30, Springer-Verlag, 1997.CrossRefGoogle Scholar
  16. FO98.
    -. A practical and provably secure scheme for publicly verifiable secret] sharing and its applications. In Advances in Cryptology — EUROCRYPT’ 98, vol. 1403 of LNCS, pp. 32–46, Springer-Verlag, 1998.CrossRefGoogle Scholar
  17. FS87.
    A. Fiat and A. Shamir. How to prove yourself: practical solutions to identification and signature problems. In Advances in Cryptology — CRYPTO’ 86, vol. 263 of LNCS, pp. 186–194, Springer-Verlag, 1987.CrossRefGoogle Scholar
  18. GMR88.
    S. Goldwasser, S. Micali, and R. Rivest. A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal on Computing, 17(2):281–308, 1988.MATHCrossRefMathSciNetGoogle Scholar
  19. KP98.
    J. Kilian and E. Petrank. Identity escrow. In Advances in Cryptology — CRYPTO’ 98, vol. 1642 of LNCS, pp. 169–185, Springer-Verlag, 1998.CrossRefGoogle Scholar
  20. LR98.
    A. Lysyanskaya and Z. Ramzan. Group blind digital signatures: A scalable solution to electronic cash. In Financial Cryptography (FC’ 98), vol. 1465 of LNCS, pp. 184–197, Springer-Verlag, 1998.CrossRefGoogle Scholar
  21. Sch91.
    C. P. Schnorr. Efficient signature generation by smart cards. Journal of Cryptology, 4(3):161–174, 1991.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Giuseppe Ateniese
    • 1
  • Jan Camenisch
    • 2
  • Marc Joye
    • 3
  • Gene Tsudik
    • 4
  1. 1.Department of Computer ScienceThe Johns Hopkins UniversityBaltimoreUSA
  2. 2.IBM Research, Zurich Research LaboratoryRüschlikonSwitzerland
  3. 3.Card Security GroupGemplus Card InternationalGémenosFrance
  4. 4.Department of Information and Computer ScienceUniversity of CaliforniaIrvine, IrvineUSA

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