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Attacks and counter-attacks on the GPT public key cryptosystem

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Abstract

The public key cryptosystem based on rank error correcting codes (the GPT cryptosystem) was proposed in 1991. Several attacks against this system were published, including Gibson’s attacks and recent Overbeck’s attacks. In this paper, we improve the GPT system by more careful choice of parameters to withstand these attacks.

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References

  1. McEliece, R.J.: A Public Key Cryptosystem Based on Algebraic Coding Theory. JPL DSN Progress Report 42–44, pp. 114–116. Pasadena, CA (1978).

  2. 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-Verlag, Berlin and Heidelberg (1991).

  3. Gabidulin E.M. (1995). Public-key cryptosystems based on linear codes over large alphabets: efficiency and weakness. In: Farrell P.G. (ed) Codes and Ciphers. Formara Limited, Essex, pp. 17–32

    Google Scholar 

  4. Gibson J.K. (1995). Severely denting the Gabidulin version of the McEliece public key cryptosystem. Des. Codes Cryptogr. 6(1): 37–45

    Article  MATH  MathSciNet  Google Scholar 

  5. Gibson, J.K.: The security of the Gabidulin public-key cryptosystem. In: Maurer, U.M. (ed.) Advances in Cryptology— EUROCRYPT’96, LNCS 1070, pp. 212–223 (1996).

  6. Gabidulin E.M., Ourivski A.V. (2000). Improved GPT public key cryptosystems. In: Farrell P., Darnell M., Honary B. (eds) Coding, Communications, and Broadcasting. Research Studies Press, Ciphertext, pp. 73–102

    Google Scholar 

  7. Ourivski A.V., Gabidulin E.M. (2003). Column scrambler for the GPT cryptosystem. Discrete Appl. Math. 128(1): 207–221

    Article  MATH  MathSciNet  Google Scholar 

  8. Gabidulin E.M., Ourivski A.V., Honary B., Ammar B. (2003). Reducible rank codes and their applications to cryptography. IEEE Trans. Inf. Theory 49(12): 3289–3293

    Article  MathSciNet  Google Scholar 

  9. Kshevetskiy, A.S., Gabidulin, E.M.: High-weight errors in public-key cryptosystems based on reducible rank codes. ISCTA (2005).

  10. Overbeck, R.: A new structural attack for GPT and variants. In: Proc. of Mycrypt’2005, vol. 3517 of LNCS, pp. 5–63. Springer-Verlag (2005).

  11. Gabidulin E.M. (1985). Theory of codes with maximum rank distance. Probl. Inform. Transm. 21(1): 1–12

    MATH  MathSciNet  Google Scholar 

  12. Gabidulin, E.M.: A fast matrix decoding algorithm for rank-error-correcting codes. In: Cohen, G., Litsyn, S., Lobstein, A., Zemor, G.(eds.) Algebraic Coding, pp. 126–132. Lecture Notes in Computer Science No. 573. Springer-Verlag, Berlin (1992).

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  1. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Ernst M. Gabidulin

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  1. Ernst M. Gabidulin
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Correspondence to Ernst M. Gabidulin.

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Gabidulin, E.M. Attacks and counter-attacks on the GPT public key cryptosystem. Des. Codes Cryptogr. 48, 171–177 (2008). https://doi.org/10.1007/s10623-007-9160-8

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  • DOI: https://doi.org/10.1007/s10623-007-9160-8

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