On improving security of GPT cryptosystems

The public key cryptosystem based on rank error correcting codes (the GPT cryptosystem) was proposed in 1991. Use of rank codes in cryptographic applications is advantageous since it is practically impossible to utilize combinatoric decoding. This enabled using public keys of a smaller size. Several attacks against this system were published, including Gibson's attacks and more recently Overbeck's attacks. A few modifications were proposed withstanding Gibson's attack but at least one of them was broken by the stronger attacks by Overbeck. A tool to prevent Overbeck's attack is presented in [12]. In this paper, we apply this approach to other variants of the GPT cryptosystem.Comment: 5 pages. submitted ISIT 2009.Processed on IEEE ISIT201

A Smart Approach for GPT Cryptosystem Based on Rank Codes

The concept of Public- key cryptosystem was innovated by McEliece's cryptosystem. The public key cryptosystem based on rank codes was presented in 1991 by Gabidulin -Paramonov-Trejtakov(GPT). The use of rank codes in cryptographic applications is advantageous since it is practically impossible to utilize combinatoric decoding. This has enabled using public keys of a smaller size. Respective structural attacks against this system were proposed by Gibson and recently by Overbeck. Overbeck's attacks break many versions of the GPT cryptosystem and are turned out to be either polynomial or exponential depending on parameters of the cryptosystem. In this paper, we introduce a new approach, called the Smart approach, which is based on a proper choice of the distortion matrix X. The Smart approach allows for withstanding all known attacks even if the column scrambler matrix P over the base field Fq.Comment: 5 pages. to appear in Proceedings of IEEE ISIT201

Properties of subspace subcodes of Gabidulin codes

International audienceWe investigate properties of subspace sub codes of Gabidulin codes. They are isomorphic to Gabidulin codes with the same minimum rank distance and smaller parameters. We design systematic encoding and decoding algorithms for subspace subcodes. We show that the direct sum of subspace subcodes of Gabidulin codes is isomorphic to the direct product of Gabidulin codes with smaller parameters. Thanks to this structure there is a great deal of correctable error-patterns whose rank exceeds the error-correcting capability. Finally we show that for particular sets of parameters, subfield subcodes of Gabidulin codes can be uniquely characterised by elements of the general linear group GL(n)(GF(q)) of non-singular q-ary matrices of size n