Abstract
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.
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References
McEliece R.J.: A public key cryptosystem based on algebraic coding theory. JPL DSN Prog. Rep. 42–44, 114–116 (1978)
Niederreiter H.: Knapsack-type cryptosystem and algebraic coding theory. Probl. Control Inf. Theory, 15, 19–34 (1986)
Gabidulin E.M.: Theory of codes with maximum rank distance. Probl. Inf. Transm. 21, 1–12 (1985)
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).
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).
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)
Gibson J.K.: Severely denting the Gabidulin version of the McEliece public key cryptosystem. Des. Codes Cryptogr. 6, 37–45 (1995)
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).
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).
Overbeck R.: Brute-force attacks public key cryptosystem based on Gabidulin codes. J. Cryptol. 21(2), 280–301 (2008)
Gabidulin E.M: Attacks and counter-attacks on the GPT public key cryptosystem. Des. Codes Cryptogr. 48, 171–177 (2008)
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).
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).
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding Theory and Applications”.
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Khan, E., Gabidulin, E., Honary, B. et al. Modified Niederreiter type of GPT cryptosystem based on reducible rank codes. Des. Codes Cryptogr. 70, 231–239 (2014). https://doi.org/10.1007/s10623-012-9757-4
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DOI: https://doi.org/10.1007/s10623-012-9757-4