Quantum Information Set Decoding Algorithms
Résumé
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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