Computational Alternatives to Random Number Generators

  • David M’Raïhi
  • David Naccache
  • David Pointcheval
  • Serge Vaudenay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1556)


In this paper, we present a simple method for generating random-based signatures when random number generators are either unavailable or of suspected quality (malicious or accidental). By opposition to all past state-machine models, we assume that the signer is a memoryless automaton that starts from some internal state, receives a message, outputs its signature and returns precisely to the same initial state; therefore, the new technique formally converts randomized signatures into deterministic ones.

Finally, we show how to translate the random oracle concept required in security proofs into a realistic set of tamper-resistance assumptions.


Hash Function Signature Scheme Random Number Generator Random Oracle Discrete Logarithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    D. Bayer, S. Haber, and W. S. Stornetta. Improving the Efficiency and Reliability of Digital Time-Stamping. Sequences II, Methods in Communication, Security and Computer Science, pages 329–334, 1993.Google Scholar
  2. 2.
    M. Bellare, R. Canetti, and H. Krawczyk. Keying Hash Functions for Message Authentication. In Crypto’ 96, LNCS 1109. Springer-Verlag, 1996.Google Scholar
  3. 3.
    M. Bellare, R. Canetti, and H. Krawczyk. Message Authentication using Hash Functions: The hmac construction. RSA Laboratories’ Cryptobytes, 2(1), Spring 1996.Google Scholar
  4. 4.
    L. Blum, M. Blum, and M. Shub. A Simple Unpredictable Random Number Generator. SIAM Journal on computing, 15:364–383, 1986.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    R. Canetti, O. Goldreich, and S. Halevi. The Random Oracles Methodology, Revisited. In Proc. of the 30th STOC. ACM Press, 1998.Google Scholar
  6. 6.
    L. Carter and M. Wegman. Universal Hash Functions. Journal of Computer and System Sciences, 18:143–154, 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    F. Chabaud. Recherche de Performance dans l’Algorithmique des Corps Finis, Applications a la Cryptographie. PhD thesis, École Polytechnique, 1996.Google Scholar
  8. 8.
    D. Chaum. Blind Signatures for Untraceable Payments. In Crypto’ 82, pages 199–203. Plenum, NY, 1983.Google Scholar
  9. 9.
    T. El Gamal. A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. In IEEE Transactions on Information Theory, volume IT-31, no. 4, pages 469–472, July 1985.CrossRefMathSciNetGoogle Scholar
  10. 10.
    A. Fiat and A. Shamir. How to Prove Yourself: practical solutions of identification and signature problems. In Crypto’ 86, LNCS 263, pages 186–194. Springer-Verlag, 1987.Google Scholar
  11. 11.
    S. Goldwasser, S. Micali, and R. Rivest. A Digital Signature Scheme Secure Against Adaptative Chosen-Message Attacks. SIAM Journal of Computing, 17(2):281–308, April 1988.Google Scholar
  12. 12.
    L. C. Guillou and J.-J. Quisquater. A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory. In Eurocrypt’ 88, LNCS 330, pages 123–128. Springer-Verlag, 1988.Google Scholar
  13. 13.
    S. Haber and W. S. Stornetta. How to Timestamp a Digital Document. Journal of Cryptology, 3:99–111, 1991.CrossRefGoogle Scholar
  14. 14.
    B. Kaliski. Timing Attacks on Cryptosystems. RSA Laboratories’ Bulletin, 2, January 1996.Google Scholar
  15. 15.
    P. C. Kocher. Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems. In Crypto’ 96, LNCS 1109, pages 104–113. Springer-Verlag, 1996.Google Scholar
  16. 16.
    M. Luby and Ch. Rackoff. How to Construct Pseudorandom Permutations from Pseudorandom Functions. SIAM Journal of Computing, 17(2):373–386, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    U. M. Maurer. A Simplified and Generalized Treatment of Luby-Rackoff Pseudorandom Permutation Generators. In Eurocrypt’ 92, LNCS 658, pages 239–255. Springer-Verlag, 1993.Google Scholar
  18. 18.
    R. J. McEliece. A Public-Key Cryptosystem Based on Algebraic Coding Theory. DSN progress report, 42-44:114–116, 1978. Jet Propulsion Laboratories, CAL-TECH.Google Scholar
  19. 19.
    J. Patarin. Etude des Générateurs de Permutations Pseudo-aléatoires Basés sur le Schéma du DES. PhD thesis, Université de Paris VI, November 1991.Google Scholar
  20. 20.
    D. Pointcheval and J. Stern. Security Proofs for Signature Schemes. In Eurocrypt’ 96, LNCS 1070, pages 387–398. Springer-Verlag, 1996.Google Scholar
  21. 21.
    D. Pointcheval and J. Stern. Security Arguments for Digital Signatures and Blind Signatures. Journal of Cryptology, 1998. To appear.Google Scholar
  22. 22.
    C. P. Schnorr. Efficient Identification and Signatures for Smart Cards. In Crypto’ 89, LNCS 435, pages 235–251. Springer-Verlag, 1990.Google Scholar
  23. 23.
    D. Shanks. Class number, a theory of factorization, and genera. In Proceedings of the symposium on Pure Mathematics, volume 20, pages 415–440. AMS, 1971.MathSciNetGoogle Scholar
  24. 24.
    S. Vaudenay. Provable Security for Block Ciphers by Decorrelation. In STACS’98, LNCS 1373, pages 249–275. Springer-Verlag, 1998.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • David M’Raïhi
    • 1
  • David Naccache
    • 2
  • David Pointcheval
    • 3
  • Serge Vaudenay
    • 3
  1. 1.Gemplus CorporationRedwood CityUSA
  2. 2.Gemplus Card InternationalIssy-les-MoulineauxFrance
  3. 3.LIENS - CNRS, Ecole Normale SupérieureParisFrance

Personalised recommendations