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Quantum Information Set Decoding Algorithms

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10346)

Abstract

The security of code-based cryptosystems such as the McEliece 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 [23] and the best algorithm to date has been Bernstein’s quantising [5] 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 [6]. 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).

Keywords

Random Walk Linear Code Quantum Algorithm Decode Algorithm Quantum Walk 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut de Mathématiques de BordeauxUniversité de BordeauxTalence CedexFrance
  2. 2.Inria, EPI SECRETParisFrance

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