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Theses

Cryptographie à base de codes correcteurs d’erreurs en métrique rang et application

Abstract : Code-based cryptography is one of the fields allowing to build post-quantum cryptosystems, i.e secure against a quantum computer. Contrary to factorization and discrete logarithm, which are the two most used problems in cryptography right now, no algorithm is known to solve the decoding problem for random codes in polynomial time using a quantum computer. In this thesis, we focus on rank-based cryptography, in which we study codes based on the rank metric instead of the Hamming metric. This metric has the advantage of allowing to build cryptosystems with lower key sizes, but is less mature than the Hamming metric. Firstly, we present two new decoding algorithms in the rank metric : the first one is a combinatorial algorithm solving the decoding problem for random codes, hence allowing to better estimate the complexity of the attacks. The second one is an improvement of the decoding algorithm for Low Rank Parity Check (LRPC). We then present two code-based cryptosystems : a rank-based signature scheme which is an adaptation of the Schnorr-Lyubashevsky approach in the Euclidean metric, and an improvement of the Hamming Quasi-Cyclic (HQC) encryption scheme, for which we propose a new analysis of the decryption failure rate and the use of another family of error correcting codes. We then study two adaptations of the Schnorr-Lyubashevsky approach : one in the Hamming metric and the other one in the rank metric, for which we propose cryptanalysis allowing to recover secret keys using information leakage from the signatures. Finally we present the choices used to implement rank-based cryptosystems in the Rank-Based Cryptography (RBC) library.
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Nicolas Aragon. Cryptographie à base de codes correcteurs d’erreurs en métrique rang et application. Cryptographie et sécurité [cs.CR]. Université de Limoges, 2020. Français. ⟨NNT : 2020LIMO0061⟩. ⟨tel-03115370⟩

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