This study has been COTried out in the context of COSTAciion 262, COST European Framework of Coopemtion: www.cordis.lulcostl~,~lti~t home. him

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Abstract-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.

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

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The public key cryptosystem (PKC) 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 by Gabidulin, which makes the cryptographer define a proper column scrambler matrix over the extension field without violating the standard mode of GPT cryptosystem. In this paper, we apply this tool to another variant of the GPT cryptosystem. Furthermore we increase the security of the proposed system against all known attacks and reduce the public key size to 4 Kbits instead of 10 Kbits.

It has been 20 years since the word ultrawideband has first been used in open literature. In these 20 years, ideas have been transformed into real products. Yet some might object that ultrawidebandhas not yet lived up to the promises of gigabit wireless. This review shows that despite some drawbacks, ultrawideband is not only needed because of the spectrum gridlock but it still can deliver its promises including gigabit wireless. To do so the gap between the potential, which is achievable, and the current performance must be closed. Thus, this review identifies some main issues of UWB (range, BER performance, data-rate, chip complexity and issues associated by strong narrowband interference). It shows that their reasons are well understood and addressed by erudite research which includes low complexity chip design, alternative modulation schemes, multiple antenna systems, UWB radio-over-fibre, higher band UWB and interferer detection and suppression techniques. A specific feature of this review is the cross-layer approach. The latest findings from different system layers, e.g., wave propagation, are linked to the system performance or complexity. Aims and structureThe ultrawideband wireless communication technology for civilian use has been subject to intensive scientific investigation for the last two decades. At the time of writing this article, the search for "ultrawideband" and "UWB" in IEEExplore TM gives 860 journal papers and 1560 conference papers between 1991 and 2011. This amount of scientific work has resulted in serious progress from theoretical considerations to real products in the market place. However, the intensity of research activities is not being reduced as there is still a gap between the theoretical potential and the actual performance of practical systems. The main objective of this paper is to show that this gap is well understood and how on-going research activities aim to close it.As the gap must be identified first, the paper begins with explanation of the need for ultrawideband wireless communication (Section 2.1) followed by brief summary of the history of the technology (Section 2.2) and its current situation, achievements and issues which are thought to be the reason for the existence of the gap (Section 2.3). Section 3 then introduces the current UWB regulations in the leading markets to provide more understanding for the framework of UWB systems and also to introduce some recent changes which for instance increased the need for development of efficient detect and avoid algorithms. Section 4 then identifies range, BER performance, data-rate, chip complexity and issues associated by strong narrowband interference as the most burning issues of current UWB. Section 5 then groups current research activities in six subsets, describes them and shows how these activities aim to address one or more issues listed in section 4.

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