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Designs, Codes and Cryptography

, Volume 28, Issue 2, pp 187–199 | Cite as

On the Security of Digital Signature Schemes Based on Error-Correcting Codes

  • Sheng-bo Xu
  • Jeroen Doumen
  • Henk van Tilborg
Article
  • 102 Downloads

Abstract

In this paper we discuss the security of digital signature schemes based on error-correcting codes. Several attacks to the Xinmei scheme are surveyed, and some reasons given to explain why the Xinmei scheme failed, such as the linearity of the signature and the redundancy of public keys. Another weakness is found in the Alabbadi-Wicker scheme, which results in a universal forgery attack against it. This attack shows that the Alabbadi-Wicker scheme fails to implement the necessary property of a digital signature scheme: it is infeasible to find a false signature algorithm Dfrom the public verification algorithm E such that E(D (\(\underline m \))) = \(\underline m \)for all messages\(\underline m \). Further analysis shows that this new weakness also applies to the Xinmei scheme.

digital signatures error-correcting codes 

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References

  1. 1.
    M. Alabbadi and S. B. Wicker, Security of Xinmei digital signature scheme, Electronic Letters, Vol. 28, No. 9 (1992) pp. 890–891.Google Scholar
  2. 2.
    M. Alabbadi and S. B. Wicker, Cryptoanalysis of the Harn and Wang modification of the Xinmei digital signature scheme, Electronic Letters, Vol. 28, No. 18 (1992) pp. 1756–1758.Google Scholar
  3. 3.
    M. Alabbadi and S. B. Wicker, Digital signature scheme based on error-correcting codes, In Proc. of 1993 IEEE International Symposium on Information Theory, San Antonio, USA (1993) p. 199.Google Scholar
  4. 4.
    M. Alabbadi and S. B. Wicker, Susceptibility of digital signature scheme based on error-correcting codes to universal forgery, In Proc. of 1994 IEEE International Symposium on Information Theory, Trondheim, Norway (1994) p. 494.Google Scholar
  5. 5.
    M. Alabbadi and S. B. Wicker, A digital signature scheme based on linear error-correcting block codes, Advance in Cryptology, ASIACRYPT '94, pp. 238–248.Google Scholar
  6. 6.
    T. A. Berson, Failure of the McEliece Public-key Cryptosystem under message-resent and related message attack, Advance in Cryptology, Crypto '97, pp. 213–220.Google Scholar
  7. 7.
    E. R. Berlekamp, R. J. McEliece and H. C. A. van Tilborg, On the inherent intractability of certain coding problems, IEEE Transactions on Information Theory, Vol. 24, No. 3 (1978) pp. 384–386.Google Scholar
  8. 8.
    F. Chabaud, On the security of some cryptosystems based on error-correcting codes, Advance in Cryptology, Eurocrypt '94, pp. 131–139.Google Scholar
  9. 9.
    A. Canteaut and N. Sendrier, Cryptanalysis of the original McEliece cryptosystem, Advance in Cryptology, Aisacrypt '98, pp. 187–199.Google Scholar
  10. 10.
    W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Transactions on Information Theory, Vol. 22, No. 6 (1976) pp. 644–654.Google Scholar
  11. 11.
    T. ElGamal, A public-key cryptosystem and a signature scheme based on discrete logarithms, Advances in Cryptography, Crypto '84, (1985) pp. 10–18.Google Scholar
  12. 12.
    L. Harn and D. C. Wang, Cryptoanalysis and modification of digital signature scheme based on errorcorrecting codes, Electronic Letters, Vol. 28, No. 2 (1992) pp. 157–159.Google Scholar
  13. 13.
    G. Kabatianskii, E. Krouk and B. Smeets, A digital signature scheme based on random error-correcting codes, The 6th IMA International Conference Cirencester, UK, December (1997) pp. 161–177.Google Scholar
  14. 14.
    R. J. McEliece, A Public-Key Cryptosystem Based on Algebraic Coding Theory, DSN progress report 42- 44 (1978) pp. 114–116.Google Scholar
  15. 15.
    J. Macwilliams and N. J. Sloane, The Theory of Error-Correcting Codes, New York: North-Holland Publishing Company (1978).Google Scholar
  16. 16.
    T. R. N. Rao and K. H. Nam, Private-key algebraic-code encryptions, IEEE Transactions on Information Theory, Vol. 35, No. 4 (1989) pp. 445–457.Google Scholar
  17. 17.
    R. L. Rivest, A. Shamir and L. M. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM, Vol. 21, No. 2 (1978) pp. 120–126.Google Scholar
  18. 18.
    J. Stern, A new identification scheme based on syndrome decoding, Advances in Cryptology: CRYPTO '93, Springer-Verlag, Berlin (1994) pp. 13–21.Google Scholar
  19. 19.
    J. van Tilburg, Cryptanalysis of Xinmei digital signature scheme, Electronic Letters, Vol. 28, No. 20 (1992) pp. 1935–1936.Google Scholar
  20. 20.
    J. van Tilburg, Cryptanalysis of the Alabbadi-Wicker digital signature scheme, In Proc. of Fourteenth Symposium on Information Theory in the Benelux, Veldhoven, Netherlands, May (1993) pp. 114–119.Google Scholar
  21. 21.
    J. van Tilburg, Security-analysis of a class of cryptosystems based on linear error-correcting codes, Ph.D Thesis, Eindhoven University of Technology (1994).Google Scholar
  22. 22.
    H. C. A. van Tilborg, An Interactive Introduction to Cryptology, Eindhoven University of Technology (1999).Google Scholar
  23. 23.
    E. Verheul, J. M. Doumen and H. C. A. van Tilborg, Sloppy Alice Attacks! Adaptive Chosen Ciphertext Attacks on the McEliece cryptosystem, in Information Coding and Mathematics, pp. 99–119, Kluwer 2002.Google Scholar
  24. 24.
    S. B. Xu and J. M. Doumen, An Attack against the Alabbadi-Wicker Scheme, The 20th symposium on information theory in the Benelux, Haasrode, Belgium 27- 28 May (1999).Google Scholar
  25. 25.
    X. M. Wang, Digital signature scheme based on error-correcting codes, Electronics Letters, Vol. 26, No. 13, 21 June (1990) pp. 898–899.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Sheng-bo Xu
    • 1
  • Jeroen Doumen
    • 2
  • Henk van Tilborg
    • 2
  1. 1.SafeNet B. V.NE VughtThe Netherlands
  2. 2.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhoventhe Netherlands

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