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Structred MDS Matrices, Additive Codes Over \(\textit{GF}(2)^m\) and Symmetric Cryptography

  • Nora El AmraniEmail author
  • Thierry P. Berger
Conference paper
Part of the Lecture Notes in Intelligent Transportation and Infrastructure book series (LNITI)

Abstract

In this paper, we study the construction of diffusion matrices with suitable symmetric properties for cryptographic applications. The most famous example of diffusion matrices with symmetries are the circulant ones. In this paper, we focus on the less known dyadic family. Considering the link between optimal diffusion matrices and MDS codes, we use a coding theory approach based on additive codes over \(\textit{GF}(2)^m\). With this method, we could build diffusion matrices not only derived from a finite field but derived from the whole linear group \(\textit{GL}(m,2)\). We present some theoretical and experimental results, particularly efficient in the context of hardware implementation.

Keywords

Additive codes over \(\textit{GF}(2)^m\) Dyadic matrices Branch number MDS matrices Symmetric cryptography 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.XLIM-MATHIS, UMR CNRS 6172University of LimogesLimoges CedexFrance
  2. 2.Laboratory of Mathematics, Computing and Applications - Information Security (LabMiA-SI), Department of Mathematical, Faculty of SciencesMohammed-V University in RabatRabatMorocco

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