Quantum Information Set Decoding Algorithms

Ghazal Kachigar; Jean-Pierre Tillich

Paper 2017/213

Quantum Information Set Decoding Algorithms

Ghazal Kachigar and Jean-Pierre Tillich

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 Overbeck and Sendrier's 2009 survey on code-based cryptography, and the best algorithm to date has been Bernstein's quantising 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 by Bernstein, Jeffery, Lange and Meurer. 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).

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. PQCrypto 2017 (to appear)
Keywords: code-based cryptography quantum cryptanalysis decoding algorithm
Contact author(s): ghazal kachigar @ u-bordeaux fr
History: 2017-04-23: revised; 2017-03-02: received; See all versions
Short URL: https://ia.cr/2017/213
License: CC BY

BibTeX

@misc{cryptoeprint:2017/213,
      author = {Ghazal Kachigar and Jean-Pierre Tillich},
      title = {Quantum Information Set Decoding Algorithms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/213},
      year = {2017},
      url = {https://eprint.iacr.org/2017/213}
}