Unités arithmétiques et cryptoprocesseurs matériels pour la cryptographie sur courbe hyperelliptique

Abstract : Many digital systems require primitives for asymmetric cryptography that are more and more efficient but also robust to attacks and inexpensive for embedded applications. In this perspective, and thanks to smaller finite fields, hyperelliptic curve cryptography (HECC) has been proposed as an interesting alternative to current techniques. We have studied efficient and flexible hardware HECC cryptoprocessors that are also robust against certain physical attacks. First, we proposed a new operator architecture able to compute, in parallel, several modular multiplications (A × B) mod P, where P is a generic prime of a few hundred bits and configurable at run time. It allows the computation of the vast majority of operations required for HECC. We have developed an operator generator, distributed in free software, for the exploration of many variants of our architecture. Our best operators are up to 2 times smaller and twice as fast as the best state-of-the-art solutions. They are also flexible in the choice of P and reach the maximum frequencies of the FPGA. In a second step, we developed modeling and simulation tools to explore, evaluate and validate different hardware architectures for scalar multiplication in HECC on Kummer surfaces. We have implemented, validated and evaluated the best architectures on various FPGA. They reach speeds similar to the best comparable solutions of the state of the art, but for halved surfaces. The flexibility obtained makes it possible to modify the parameters of the curves used during execution.
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Gabriel Gallin. Unités arithmétiques et cryptoprocesseurs matériels pour la cryptographie sur courbe hyperelliptique. Cryptographie et sécurité [cs.CR]. Université Rennes 1, 2018. Français. ⟨NNT : 2018REN1S071⟩. ⟨tel-01989822v2⟩

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