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Cryptographie fondée sur les codes : nouvelles approches pour constructions et preuves ; contribution en cryptanalyse

Abstract : In this thesis we study code-based cryptography. By this term we mean the crypto-systems whose security relies on the generic decoding problem. The first of those systems is a public key encryption scheme proposed by McEliece in 1978. Four decades later, no attack is known to present a serious threat on the system, even on a quantum computer. This makes code-based cryptography a credible candidate for post-quantum cryptography. First we give attacks against the code-based signature scheme RankSign, which was proposed to the post-quantum standardization of the NIST, and against the first code-based Identity-Based-Encryption scheme. On the other hand we propose a new code-based signature scheme: Wave. For this design we introduced a new trapdoor, the family of generalized (U,U+V)-codes. We show how to decode them for weights such that the generic decoding problem is hard. Then we show how to follow the Gentry-Peikert and Vaikuntanathan strategy which has proved to be fruitful in lattice-based cryptography. This was done by avoiding any information leakage of signatures thanks to an efficient rejection sampling. Furthermore, for the first time we propose a crypto-system whose security relies on the generic decoding problem for high distances. We give in this thesis the best known algorithm to solve this problem. At last, we study one of the few alternatives to information set decoding: the statistical decoding. First we improve algorithms to compute parity-check equations of small or moderate weight and we make the first asymptotic study of its complexity. We show that statistical decoding is not competitive with information set decoding contrary to what was claimed. This study relies on new results about Krawtchouk polynomials.
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  • HAL Id : tel-02424234, version 2

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Thomas Debris-Alazard. Cryptographie fondée sur les codes : nouvelles approches pour constructions et preuves ; contribution en cryptanalyse. Cryptographie et sécurité [cs.CR]. Sorbonne Université, 2019. Français. ⟨NNT : 2019SORUS482⟩. ⟨tel-02424234v2⟩

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