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

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

Information security in a random network coding network

We consider a communication network with random network coding which can be attacked by adversaries of two types. One of them can wiretap original packets outgoing from source to destination. The other can insert its own packets into information flow, which are wrong messages for the receiver. To provide secure communication, we use a scheme based on combining the GPT (Gabidulin-Paramonov-Tretjakov) public key cryptosystem and SKK (Silva-Kschischang-Koetter) codes. Encrypted packets are transmitted to the destination through wired channels. Performance of this system is investigated. The main result is that the proposed scheme is secure against wiretapping and insertion attacks under some conditions which depend on rank code parameters