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Contribution de l'arithmétique des ordinateurs aux implémentations résistantes aux attaques par canaux auxiliaires

Abstract : This thesis focuses on two currently unavoidable elements of public key cryptography, namely modular arithmetic over large integers and elliptic curve scalar multiplication (ECSM). For the first one, we are interested in the Adapted Modular Number System (AMNS), which was introduced by Bajard et al. in 2004. In this system of representation, the elements are polynomials. We show that this system allows to perform modular arithmetic efficiently. We also explain how AMNS can be used to randomize modular arithmetic, in order to protect cryptographic protocols implementations against some side channel attacks. For the ECSM, we discuss the use of Euclidean Addition Chains (EAC) in order to take advantage of the efficient point addition formula proposed by Meloni in 2007. The goal is to first generalize to any base point the use of EAC for ECSM; this is achieved through curves with one efficient endomorphism. Secondly, we propose an algorithm for scalar multiplication using EAC, which allows error detection that would be done by an attacker we detail.
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https://theses.hal.science/tel-03228322
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Submitted on : Tuesday, May 18, 2021 - 9:32:50 AM
Last modification on : Thursday, December 16, 2021 - 9:42:02 PM
Long-term archiving on: : Thursday, August 19, 2021 - 6:23:19 PM

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DOSSO_2020TOUL0007.pdf
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  • HAL Id : tel-03228322, version 1

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Fangan Yssouf Dosso. Contribution de l'arithmétique des ordinateurs aux implémentations résistantes aux attaques par canaux auxiliaires. Arithmétique des ordinateurs. Université de Toulon, 2020. Français. ⟨NNT : 2020TOUL0007⟩. ⟨tel-03228322⟩

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