Designs, Codes and Cryptography

, Volume 70, Issue 1–2, pp 231–239 | Cite as

Modified Niederreiter type of GPT cryptosystem based on reducible rank codes

  • Eraj Khan
  • Ernst Gabidulin
  • Bahram Honary
  • Hassan Ahmed


GPT public key cryptosystem was proposed by Gabidulin, Paramonov and Tretjakov in 1991. This cryptosystem is based on rank error correcting codes. The main advantage of using rank codes in cryptography is that, it has smaller key size as compared to other code based public key cryptosystems. Several attacks against this system were published and some modifications were also proposed withstanding these attacks. In this paper, we have proposed a modified Niederreiter type GPT cryptosystem based on reducible rank codes by properly choosing the column scrambler matrix to withstand these attacks. Although, the idea of choosing column scrambler matrix from extension field is not new but the approach proposed in this paper, provides more elements of column scrambler matrix from extension field as compared to any previous modifications which makes system more secure against attacks.


GPT cryptosystem Rank codes Reducible rank codes Column scrambler 

Mathematics Subject Classification (2010)

11T71 14G50 94A15 


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  1. 1.
    McEliece R.J.: A public key cryptosystem based on algebraic coding theory. JPL DSN Prog. Rep. 42–44, 114–116 (1978)Google Scholar
  2. 2.
    Niederreiter H.: Knapsack-type cryptosystem and algebraic coding theory. Probl. Control Inf. Theory, 15, 19–34 (1986)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Gabidulin E.M.: Theory of codes with maximum rank distance. Probl. Inf. Transm. 21, 1–12 (1985)zbMATHGoogle Scholar
  4. 4.
    Gabidulin E.M., Paramonov A.V., Tretjakov O.V.: Ideals over a non-commutative ring and their application in cryptology. In: Davies D.W. (ed.) Advances in Cryptology—Eurocrypt ’91 Lecture Notes in Computer Science, No. 547, pp. 482–489. Springer, Berlin (1991).Google Scholar
  5. 5.
    Gabidulin E.M.: Public-key cryptosystems based on linear codes over large alphabets: efficiency and weakness. In: Farrell P.G.(ed.) Codes and Ciphers, pp. 17–32. Formara Limited, Essex (1995).Google Scholar
  6. 6.
    Gabidulin E.M., Ourivski A.V., Honary B., Ammar B.: Reducible rank codes and their applications to cryptography. IEEE Trans. Inf. Theory. 49, 3289–3293 (2003)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Gibson J.K.: Severely denting the Gabidulin version of the McEliece public key cryptosystem. Des. Codes Cryptogr. 6, 37–45 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gibson J.K.: The security of the Gabidulin public-key cryptosystem. In: Maurer U.M. (ed.) Advances in Cryptology—EUROCRYPT’96, LNCS vol. 1070, pp. 212–223. Springer, Berlin (1996).Google Scholar
  9. 9.
    Overbeck R.: A new brute-force attack for GPT and variants. In: Dawson, Ed., Vaudenay, S. (eds) Proceedings of Mycrypt 2005, vol. 3715 of LNCS, pp. 50–63. Springer Berlin/Heidelberg (2005).Google Scholar
  10. 10.
    Overbeck R.: Brute-force attacks public key cryptosystem based on Gabidulin codes. J. Cryptol. 21(2), 280–301 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Gabidulin E.M: Attacks and counter-attacks on the GPT public key cryptosystem. Des. Codes Cryptogr. 48, 171–177 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Gabidulin E.M., Rashwan H., Honary B.: On improving security of GPT cryptosystems. In: IEEE International Symposium Information Theory (ISIT 2009), pp. 1110–1114 (2009).Google Scholar
  13. 13.
    Rashwan H., Gabidulin E., Honary B.: A smart approach for GPT cryptosystem based on rank codes. In: IEEE International Symposium Information Theory (ISIT 2010), pp. 2463–2467 (2010).Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Eraj Khan
    • 1
  • Ernst Gabidulin
    • 2
  • Bahram Honary
    • 1
  • Hassan Ahmed
    • 1
  1. 1.School of Computing and CommunicationsLancaster UniversityLancasterUK
  2. 2.Department of Radio EngineeringMoscow Institute of Physics and TechnologyMoscowRussia

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