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A secure and efficient conference key distribution system

Extended abstract
  • Mike Burmester
  • Yvo Desmedt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 950)

Abstract

We present practical conference key distribution systems based on public keys, which authenticate the users and which are ‘proven’ secure provided the Diffie-Hellman problem is intractable. A certain number of interactions is needed but the overall cost is low. There is a complexity tradeoff. Depending on the network used, we either have a constant (in the number of conference participants) number of rounds (exchanges) or a constant communication and computation overhead. Our technique for authentication can be extended and used as the basis for an authentication scheme which is ‘proven’ secure against any type of attack, provided the Discrete Logarithm problem is intractable.

References

  1. 1.
    M. Bellare, S. Goldwasser: New paradigms for digital signatures and message authentication based on non-interactive zero-knowledge proofs. In: G. Brassard, (ed.): Advances in Cryptology — Crypto '89. Lecture Notes in Computer Science 435. Berlin: Springer 1990, pp. 194–211Google Scholar
  2. 2.
    M. Bellare, S. Micali: How to sign given any trapdoor function. Journal of the ACM 39, 214–233 (1992)CrossRefMathSciNetGoogle Scholar
  3. 3.
    M. Bellare, S. Micali, R. Ostrovsky: Perfect zero-knowledge in constant rounds. In: Proceedings of the Twenty Second Annual ACM Symp. Theory of Computing. ACM Press 1990, pp. 482–493Google Scholar
  4. 4.
    S. Bengio, G. Brassard, Y.G. Desmedt, C. Goutier, J.-J. Quisquater: Secure implementations of identification systems. Journal of Cryptology 4, pp. 175–183 (1991)CrossRefGoogle Scholar
  5. 5.
    C. H. Bennett, G. Brassard: Quantum cryptography, and its application to provable secure key expansion, public-key distribution, and coin tossing. In: International Symposium on Information Theory (abstracts), IEEE Computer Society Press 1983, p. 91Google Scholar
  6. 6.
    R. Blom: Key distribution and key management. In: Proc. Eurocrypt 83, Udine, Italy, March 1983.Google Scholar
  7. 7.
    M. Blum, S. Micali: How to generate cryptographically strong sequences of pseudorandom bits. Siam J. Comput. 13, 850–864 (1984)CrossRefMathSciNetGoogle Scholar
  8. 8.
    C. Blundo, A. De Santis, A. Herzberg, S. Kutten, U. Vaccaro, M. Yung: Perfectly-secure key distribution for dynamic conferences. In: E. Brickell (ed.): Advances in Cryptology — Crypto 92. Lecture Notes in Computer Science 740. Berlin: Springer 1993, pp. 471–487Google Scholar
  9. 9.
    J. Boyar, M.W. Krentel, S.A. Kurtz: A discrete logarithm implementation of zeroknowledge blobs. Technical Report 87-002, University of Chicago, March 1987.Google Scholar
  10. 10.
    G. Brassard, D. Chaum, C. Crépeau: Minimum disclosure proofs of knowledge. Journal of Computer and System Sciences 37, 156–189 (1988)CrossRefMathSciNetGoogle Scholar
  11. 11.
    M. Burmester: On the risk of opening distributed keys. To appear in the Proceedings of Crypto '94. Berlin: Springer 1994.Google Scholar
  12. 12.
    J.L. Carter, M.N. Wegman: Universal classes of hash functions. Journal of Computer and System Sciences 18, 143–154 (1979)CrossRefMathSciNetGoogle Scholar
  13. 13.
    D. Chaum, J.-H. Evertse, J. van de Graaf: An improved protocol for demonstrating possession of discrete logarithms and some generalizations. In: D. Chaum, W.L. Price (eds.): Advances in Cryptology — Eurocrypt '87. Lecture Notes in Computer Science 304. Berlin: Springer 1988, pp. 127–141Google Scholar
  14. 14.
    D. Chaum, J.-H. Evertse, J. van de Graaf, R. Peralta: Demonstrating possession of a discrete logarithm without revealing it. In: A. Odlyzko (ed.): Advances in Cryptology — Crypto '86. Lecture Notes in Computer Science 263. Berlin: Springer 1987, pp. 200–212Google Scholar
  15. 15.
    D. Coppersmith, A. Odlyzko, R. Schroeppel: Discrete logarithms in GF(p). Algorithmica, pp. 1–15 (1986)Google Scholar
  16. 16.
    Y. Desmedt, M. Burmester: An efficient zero-knowledge scheme for the discrete logarithm based on smooth numbers. In: H. Imai, R.L. Rivest, T. Matsumoto (eds.): Advances in Cryptology — Asiacrypt '91. Lecture Notes in Computer Science 739. Berlin: Springer 1992, pp. 360–367Google Scholar
  17. 17.
    W. Diffie, M. E. Hellman: New directions in cryptography. IEEE Trans. Inform. Theory IT-22, 644–654 (1976)CrossRefMathSciNetGoogle Scholar
  18. 18.
    W. Diffie, P.C. van Oorschot, M.J. Wiener: Authentication and authenticated key exchanges. Designs, Codes and Cryptography 2, 107–125 (1992)CrossRefGoogle Scholar
  19. 19.
    M. J. Fischer, R. N. Wright: Multiparty secret key exchange using a random deal of cards. In: J. Feigenbaum (ed.): Advances in Cryptology — Crypto '91, Lecture Notes in Computer Science 576. Berlin: Springer 1992, pp. 141–155Google Scholar
  20. 20.
    Z. Galil, S. Haber, M. Yung: A private interactive test of a Boolean predicate and minimum-knowledge public key cryptosystems. In: Annual Symp. on Foundations of Computer Science. IEEE Computer Society Press 1985, pp. 360–371Google Scholar
  21. 21.
    S. Goldwasser, S. Micali, C. Rackoff: The knowledge complexity of interactive proof systems. Siam J. Comput. 18, 186–208 (1989)CrossRefMathSciNetGoogle Scholar
  22. 22.
    S. Goldwasser, S. Micali, R. Rivest: A digital signature scheme secure against adaptive chosen-message attacks. Siam J. Comput. 17, 281–308 (1988)CrossRefMathSciNetGoogle Scholar
  23. 23.
    D. Gordon: Discrete logarithm in GF(p) using the number field sieve. Submitted.Google Scholar
  24. 24.
    I. Ingemarsson, D.T. Tang, C.K. Wong: A conference key distribution system. IEEE Trans. Inform. Theory 28, 714–720 (1982)CrossRefMathSciNetGoogle Scholar
  25. 25.
    K. Koyama, K. Ohta: Identity-based conference key distribution systems. In: C. Pomerance (ed.): Advances in Cryptology — Crypto '87. Lecture Notes in Computer Science 293. Berlin: Springer 1988, pp. 175–185Google Scholar
  26. 26.
    K.S. McCurley: A key distribution system equivalent to factoring. J. Cryptology 1, 95–105 (1988)MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    A. Menezes, S. Vanstone, T. Okamoto: Reducing elliptic curve logarithms to logarithms in a finite field. In: Proceedings of the Twenty Third Annual ACM Symp. Theory of Computing. ACM Press 1991, pp. 80–89Google Scholar
  28. 28.
    M. Naor, M. Yung: Universal one-way hash functions and their cryptographic applications. In: Proceedings of the Twenty First Annual ACM Symp. Theory of Computing. ACM Press 1989, pp. 33–43Google Scholar
  29. 29.
    A.M. Odlyzko: Discrete logs in a finite field and their cryptographic significance. In: N. Cot, T. Beth, I. Ingemarsson, (eds.): Advances in Cryptology — Eurocrypt 84. Lecture Notes in Computer Science 209. Berlin: Springer 1984, pp. 224–314Google Scholar
  30. 30.
    E. Okamoto: Key distribution systems based on identification information. In: C. Pomerance (ed.): Advances in Cryptology — Crypto '87. Lecture Notes in Computer Science 293. Berlin: Springer 1988, pp. 194–202Google Scholar
  31. 31.
    E. Okamoto, K. Tanaka: Key distribution system based on identification information. IEEE J. Selected Areas in Commun. 7, 481–485 (1989)CrossRefGoogle Scholar
  32. 32.
    R.L. Rivest, A. Shamir, L. Adleman: A method for obtaining digital signatures and public key cryptosystems. Commun. ACM 21, 120–126 (1978)CrossRefMathSciNetGoogle Scholar
  33. 33.
    J. Rompel: One-way functions are necessary and sufficient for secure signatures. In: Proceedings of the Twenty Second Annual ACM Symp. Theory of Computing. ACM Press 1990, pp. 387–394Google Scholar
  34. 34.
    A. W. Schrift, A. Shamir: The discrete log is very discreet. In: Proceedings of the Twenty Second Annual ACM Symp. Theory of Computing. ACM Press 1990, pp. 405–415Google Scholar
  35. 35.
    A. Shamir: Efficient signature schemes based on birational permutations. To appear in the Proceedings of Crypto '93. Berlin: Springer.Google Scholar
  36. 36.
    S. Tsujii, T. Itoh: An ID-based cryptosystem based on the discrete logarithm. IEEE J. Selected Areas in Commun. 7, 467–473 (1989)CrossRefGoogle Scholar
  37. 37.
    M.N. Wegman, J.L. Carter: New hash functions and their use in authentication and set equality. J. Computer and System Sciences 22, 265–279 (1981)CrossRefMathSciNetGoogle Scholar
  38. 38.
    Y. Yacobi, Z. Shmuely: On key distribution systems. In: G. Brassard (ed.): Advances in Cryptology — Crypto '89. Lecture Notes in Computer Science 435. Berlin: Springer 1990, pp. 344–355Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Mike Burmester
    • 1
  • Yvo Desmedt
    • 2
  1. 1.Department of MathematicsRH - University of LondonEghamUK
  2. 2.Department of EE & CSUniversity of Wisconsin - MilwaukeeMilwaukeeUSA

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