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Code-Based Cryptography

Abstract : This chapter focuses on the essentials of code-based cryptography and on coding theory and the associated hard problems useful for cryptography as well as more recent proposals for public-key cryptography, key-exchange protocols, and digital signatures. Code-based cryptography was originally proposed using the standard Hamming metric. The M. Ajtai–C. Dwork cryptosystem also inspired the Learning with Errors lattice-based cryptosystem by O. Regev which generated a huge amount of research in lattice-based cryptography. While Hamming Quasi-Cyclic has the advantage of relying only on the hardness of the (decisional) syndrome decoding problem for random quasi-cyclic codes, it still features big keys for low encryption rates. In 2003, M. Alekhnovich proposed an innovative approach based on the difficulty of decoding purely random codes. Among many broken families in the R. J. McEliece framework, it is interesting to notice that up to now there is no specific attack when considering the smaller BCH code family rather than Goppa codes.
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https://hal-enac.archives-ouvertes.fr/hal-03687358
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Soumis le : vendredi 3 juin 2022 - 11:49:55
Dernière modification le : vendredi 3 juin 2022 - 12:00:58

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Philippe Gaborit, Jean-Christophe Deneuville. Code-Based Cryptography. Chapman and Hall/CRC, 1, 2021, 9781315147901. ⟨10.1201/9781315147901⟩. ⟨hal-03687358⟩

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