Advertisement

Efficient Non-malleable Commitment Schemes

  • Marc Fischlin
  • Roger Fischlin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1880)

Abstract

We present efficient non-malleable commitment schemes based on standard assumptions such as RSA and Discrete-Log, and under the condition that the network provides publicly available RSA or Discrete-Log parameters generated by a trusted party. Our protocols require only three rounds and a few modular exponentiations. We also discuss the difference between the notion of non-malleable commitment schemes used by Dolev, Dwork and Naor [DDN00] and the one given by Di Crescenzo, Ishai and Ostrovsky [DIO98].

Keywords

Discrete Logarithm Commitment Scheme Chinese Remainder Theorem Public Parameter Noticeable Probability 
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.

References

  1. BG92.
    M. Bellare AND O. Goldreich: On Defining Proofs of Knowledge, Advances in Cryptology — Proceedings Crypto’ 92, Lecture Notes in Computer Science, vol. 740, pp. 390–420, Springer Verlag, 1993.Google Scholar
  2. BR94.
    M. Bellare AND P. Rogaway: Optimal Asymmetric Encryption, Advances in Cryptology — Proceedings Eurocrypt’ 94, Lecture Notes in Computer Science, vol. 950, pp. 92–111, Springer Verlag, 1993.CrossRefGoogle Scholar
  3. BR93.
    M. Bellare AND P. Rogaway: Random Oracles are Practical: a Paradigm for Designing Efficient Protocols, First ACM Conference on Computer and Communication Security, ACM Press, pp. 62–73, 1993.Google Scholar
  4. B00.
    D. Boneh: Finding Smooth Integers Using CRT Decoding, to appear in Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC), ACM Press, 2000.Google Scholar
  5. BCC88.
    G. Brassard, D. Chaum AND C. Crépeau: Minimum Disclosure Proofs of Knowledge, Journal of Computer and Systems Science, vol. 37(2), pp. 156–189, 1988.zbMATHCrossRefGoogle Scholar
  6. CS98.
    R. Cramer AND V. Houp: A Practical Public Key Cryptosystem Provable Secure Against Adaptive Chosen Ciphertext Attack, Advances in Cryptology — Proceedings Crypto’ 98, Lecture Notes in Computer Science, vol. 1492, pp. 13–25, Springer Verlag, 1998.CrossRefGoogle Scholar
  7. CS99.
    R. Cramer AND V. Shoup: Signature Schemes Based on the Strong RSA Assumption, ACM Conference on Computer and Communication Security, ACM Press, 1999.Google Scholar
  8. DIO98.
    G. Di Crescenzo, Y. Ishai AND R. Ostrovsky: Non-interactive and Non-Malleable Commitment, Proceedings of the 30th Annual ACM Symposium on Theory of Computing (STOC), pp. 141–150, ACM Press, 1998.Google Scholar
  9. DDN00.
    D. Dolev, C. Dwork AND M. Naor: Non-Malleable Cryptography, manuscript, to appear in SIAM Jornal on Computing, January 2000. Preliminary version in Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC), pp. 542–552, ACM Press, 1991.Google Scholar
  10. FFS88.
    U. Feige, A. Fiat AND A. Shamir: Zero-Knowledge Proofs of Identity, Journal of Cryptology, vol. 1(2), pp. 77–94, Springer-Verlag, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  11. FS90.
    A. Fiat AND A. Shamir: Witness Indistinguishable and Witness Hiding Protocols Proceedings of the 22nd Annual ACM Symposium on the Theory of Computing (STOC), pp. 416–426, ACM Press, 1990.Google Scholar
  12. G98.
    O. Goldreich: Foundations of Cryptography, Fragments of a Book, Version 2.03, 1998.Google Scholar
  13. GRS99.
    O. Goldreich, D. Ron AND M. Sudan: Chinese Remainder With Errors, Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC), pp. 225–234, ACM Press, 1999.Google Scholar
  14. K98.
    D.E. Knuth: Seminumerical Algorithms, The Art of Computer Programming, vol. 2, 3rd edition, Addison Wesley, 1998.Google Scholar
  15. L00.
    Y. Lindell: Personal communication, based on work on authenticated key-exchange with Oded Goldreich. May 2000.Google Scholar
  16. M95.
    U. Maurer: Fast Generation of Prime Numbers and Secure Public-Key Cryptographic Parameters, Journal of Cryptology, vol. 8, pp. 123–155, Springer-Verlag, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  17. O92.
    T. Okamoto: Provable Secure and Practical Identification Schemes and Corresponding Signature Schemes, Advances in Cryptology — Proceedings Crypto’ 92, Lecture Notes in Computer Science, vol. 740, pp. 31–53, Springer Verlag, 1993.Google Scholar
  18. P91.
    T.P. Pedersen: Non-Interactive and Information-Theoretical Secure Verifiable Secret Sharing, Crypto’ 91, Lecture Notes in Computer Science, Vol. 576, Springer-Verlag, pp. 129–140, 1991.Google Scholar
  19. RSA78.
    R. Rivest, A. Shamir AND L. Adleman: A Method for Obtaining Digital Signatures and Public-Key Cryptoystems, Communication of the ACM, vol. 21(2), pp. 120–126, 1978.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Marc Fischlin
    • 1
  • Roger Fischlin
    • 1
  1. 1.Fachbereich Mathematik (AG 7.2)Johann Wolfgang Goethe-Universität Frankfurt am MainFrankfurt/MainGermany

Personalised recommendations