Designs, Codes and Cryptography

, Volume 35, Issue 1, pp 63–79 | Cite as

How to Mask the Structure of Codes for a Cryptographic Use

Article

Abstract

In this paper we show how to strengthen public-key cryptosystems against known attacks, together with the reduction of the public-key. We use properties of subcodes to mask the structure of the codes used by the conceiver of the system. We propose new parameters for the cryptosystems and even a modified Niederreiter cryptosystem in the case of Gabidulin codes, with a public-key size of less than 4000 bits.

Keywords

Niederreiter cryptosystem GPT cryptosystem Reed-solomon codes Gabidulin codes Subcodes 

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References

  1. Canteaut, A., Chabaud, F. 1998A new algorithm for finding minimum-weight words in a linear code: Application to McEliece’s cryptosystem and to narrow-sense BCH codes of length 511IEEE Trans. Inform. Theory44367378Google Scholar
  2. A. Canteaut and N. Sendrier, Cryptanalysis of the original McEliece cryptosystem, In (K. Ohta and D. Pei eds.), Advances in Cryptology–-ASIACRYPT’98, number 1514 in LNCS (1998) pp. 187–199.Google Scholar
  3. F. Chabaud and J. Stern, The cryptographic security of the syndrome decoding problem for rank distance codes, In (K. Kim and T. Matsumoto eds.), Advances in Cryptology–-ASIACRYPT ‘96, volume 1163 of LNCS. Verlag (1996).Google Scholar
  4. Dür, A. 1987The automorphism group of Reed–Solomon codesJ. Comb. Theory, series A446982Google Scholar
  5. A. Ourivski, E. Gabidulin and V. Pavlouchkov, On the modified Niederreiter cryptosystem, in the Proceedings of the Information Theory and Networking Workshop, ITW(1999) p.50.Google Scholar
  6. E. M. Gabidulin, Theory of codes with maximal rank distance, Problems Inform. Transm., vol. 21 (1985).Google Scholar
  7. E. M. Gabidulin and A. V. Ourivski, Improved GPT public-key cryptosystems, In (P. Farrell, M. Darnell and B. Honary eds.), Coding Communications and Broadcasting (2000) pp. 73–102.Google Scholar
  8. Gabidulin, E. M., Paramonov, A. V., Tretjakov, O. V. 1991Ideals over a non-commutative ring and their application in cryptologyLNCS573482489Google Scholar
  9. Gibson, J. K. 1995Severely denting the Gabidulin version of the McEliece public-key cryptosystemDesigns, Codes and Cryptography63745Google Scholar
  10. J. K. Gibson, The security of the Gabidulin public-key cryptosystem, In (U. Maurer ed.), EUROCRYPT’96 (1996) pp. 212–223.Google Scholar
  11. P. J. Lee and E. F. Brickell, An observation on the security of McEliece’s public-key cryptosystem, In (C. G. Günter ed.), Advances in Cryptology–-EUROCRYPT’88, volume 330 of LNCS, Verlag (1988) pp. 275–280.Google Scholar
  12. Loidreau, P., Sendrier, N. 2001Weak keys in McEliece public-key cryptosystemIEEE Trans. Inform. Theory471207211Google Scholar
  13. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error–Correcting Codes. North Holland (1977).Google Scholar
  14. R. J. McEliece, A public-key cryptosystem based on algebraic coding theory, Technical report, Jet Propulsion Lab. DSN Progress Report (1978).Google Scholar
  15. Niederreiter, H. 1986Knapsack-type cryptosystems and algebraic coding theoryProblems of Control Inform. Theory15159166Google Scholar
  16. Roth, R. M., Seroussi, G. 1985On generator matrices of MDS codesIEEE Trans. Inform. Theory31826830Google Scholar
  17. Sidel’nikov, V. M., Shestakov, S. O. 1992On cryptosystems based on generalized Reed-Solomon codesDiscrete Mathematics45763Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.LACO, Département de MathématiquesUniversité de LimogesFrance
  2. 2.Unite de Mathématiques, AppliquéesNational Institute of Advanced Technologies (ENSTA)France

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