Modified Niederreiter type of GPT cryptosystem based on reducible rank codes
- 387 Downloads
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.
KeywordsGPT cryptosystem Rank codes Reducible rank codes Column scrambler
Mathematics Subject Classification (2010)11T71 14G50 94A15
Unable to display preview. Download preview PDF.
- 1.McEliece R.J.: A public key cryptosystem based on algebraic coding theory. JPL DSN Prog. Rep. 42–44, 114–116 (1978)Google Scholar
- 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.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
- 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.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
- 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.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