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Mathématiques discrètes appliquées à la cryptographie symétrique

Abstract : In this thesis, we study the security of symmetric cryptographic primitives. These systems are based on transformations relying on mathematical objects that can be represented in multiple ways. We then exploit different induced structures to highlight new vulnerabilities. By exploiting various representations, we cryptanalyzed some schemes submitted to the CAESAR competition, and also some dedicated and generic stream ciphers. We exhibited design criteria for lightweight block ciphers in view of the NIST standardization process and in the case of stream ciphers we defined new cryptographic criteria more relevant than the usual ones. More precisely, we study the security of lightweight block ciphers with respect to the recent invariant attacks, and we show how to avoid them with an appropriate choice of the linear layer and the round constants. We propose a new cryptanalysis of the filtered registers, by decomposing elements in the multiplicative subgroups of the finite field with 2^n elements. The analysis of the FLIP cipher, but also of the Goldreich pseudo-random generator, revealed weaknesses that are exploitable in ``guess and determine'' attacks. This leads to new criteria on the Boolean functions used in this context. Finally, we cryptanalyze a weaker version of the authenticated encryption scheme Ketje using several techniques, in order to refine the security evaluation of this cipher.
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Submitted on : Thursday, October 10, 2019 - 11:12:10 AM
Last modification on : Thursday, April 2, 2020 - 3:57:20 AM


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  • HAL Id : tel-01944827, version 2


Yann Rotella. Mathématiques discrètes appliquées à la cryptographie symétrique. Cryptographie et sécurité [cs.CR]. Sorbonne Université, 2018. Français. ⟨NNT : 2018SORUS092⟩. ⟨tel-01944827v2⟩



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