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Contribution à la cryptographie post-quantique basée sur les codes correcteurs d’erreurs en métrique rang : Hash Proof Systems et cryptographie à bas coût

Abstract : The design of a quantum computer would have a tremendous impact on the cryptography used nowadays, particularly in the asymetric cryptography do-main. Moreover, the increasing use of connected objects in our everyday lifeand their limitations in term of computation capabilities and available memory make them a key target. This thesis was focused on those two problematics, and is divided into three independent axis. The first one proposes the conception of a cryptographic primitive called Hash Proof System (HPS). Based on the language of RQC ciphertexts, we will show how to construct such a primitive and will present two applications of it : a witness encryption scheme in one hand and a password authenticated key exchange protocol on the other hand, yielding the use of a public key infrastructure unnecessary. The second one introduces a new cryptographic problem called Learning Rank with Errors (LRE), an adaptation of the LPN problem to the rank metric setting. We will show some of its properties and describe a first application of it, a symmetric authentication scheme nammed HBLRE, which is an adaptation of the HB protocol fitted to the LRE problem. Finally, the third axis of study is the adaptation and the implementation of several cryptographic schemes submitted to the NIST, namely RQC and ROLLO (which is a merge of LAKE, LOCKER and Ouroboros-R) on microcontrollers. We will describe the different algorithms that we used and explain how theyworks. We will present the rbc-library, a library aiming to facilitate the use and conception of rank metric based schemes which make use of the implementations work realised during this thesis. Lastly, we will show the performances obtained by those implementations on a microcontroller equipped with an ARM Cortex-M4 processors and compare those results with other post-quantum cryptographic schemes submitted in the NIST standardisation process.
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Submitted on : Monday, June 7, 2021 - 5:24:08 PM
Last modification on : Tuesday, June 8, 2021 - 3:24:44 AM
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Yann Connan. Contribution à la cryptographie post-quantique basée sur les codes correcteurs d’erreurs en métrique rang : Hash Proof Systems et cryptographie à bas coût. Cryptographie et sécurité [cs.CR]. Université de Limoges, 2021. Français. ⟨NNT : 2021LIMO0029⟩. ⟨tel-03252590⟩

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