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Quantum Information Set Decoding Algorithms

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Abstract

The security of code-based cryptosystems such as the Mc\-Eliece cryptosystem relies primarily on the difficulty of decoding random linear codes. The best decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of information set decoding techniques. It is also important to assess the security of such cryptosystems against a quantum computer. This research thread started in \cite{OS09} and the best algorithm to date has been Bernstein's quantising \cite{B10} of the simplest information set decoding algorithm, namely Prange's algorithm. It consists in applying Grover's quantum search to obtain a quadratic speed-up of Prange's algorithm. In this paper, we quantise other information set decoding algorithms by using quantum walk techniques which were devised for the subset-sum problem in \cite{BJLM13}. This results in improving the worst-case complexity of $2^{0.06035n}$ of Bernstein's algorithm to $2^{0.05869n}$ with the best algorithm presented here (where $n$ is the codelength).
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Dates and versions

hal-01661905 , version 1 (12-12-2017)

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Ghazal Kachigar, Jean-Pierre Tillich. Quantum Information Set Decoding Algorithms. PQCrypto 2017 - The Eighth International Conference on Post-Quantum Cryptography, Jun 2017, Utrecht, Netherlands. pp.69-89, ⟨10.1007/978-3-319-59879-6_5⟩. ⟨hal-01661905⟩

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