Codes additifs et matrices MDS pour la cryptographie

Abstract : This PhD focuses on the links between error correcting codes and diffusion matrices used in cryptography symmetric. The goal is to study the possible construction of additives MDS codes defined over the group (Fm2, +) of binary m-tuples and minimize cost of hardware or software implementation of these diffusion matrices. This thesis begins with the study of codes defined over the polynomial ring F[x]/f(x), these codes are a generalization of quasi-cyclic codes, and continues with the study of additive systematic codes over (Fm2, +) and there relation with linear diffusion on symmetric cryptography. An important point of this thesis is the introduction of codes with coefficients in the ring of endomorphisms of Fm2. The link between codes which are a left-submodules and additive codes have been identified. The last part focuses on the study and construction of efficient diffusion MDS matrices for the cryptographic applications, namely the circulantes matrices, dyadic matrices, and matrices with hollow representation, in ordre to minimize their implementations.
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Nora El Amrani. Codes additifs et matrices MDS pour la cryptographie. Cryptographie et sécurité [cs.CR]. Université de Limoges, 2016. Français. ⟨NNT : 2016LIMO0034⟩. ⟨tel-01716884⟩

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