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).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).

arXiv:1703.00263Mar 1, 201711 citations

About the peculiarities of searching for Information Sets of Block-Permutation LDPC-Codes when Correcting Error Bursts

M. N. Isaeva, Andrei A. Ovchinnikov

Modern communication standards use error-correcting coding, especially LDPC codes. Various algorithms are used to decode them, including decoding by information sets. The algorithm for decoding over information sets has exponential complexity. Errors may occur on any communication channel when transmitting messages. Traditionally, independent errors are considered when researching decoding algorithms. However, in real systems, errors are grouped into bursts. This article discusses the probability of detecting information sets while correcting error bursts. Random matrices and block permutation matrices are considered. Graphs of the dependence of the probability of finding information sets on the number of positions that are considered when searching for information sets are given.Modern communication standards use error-correcting coding, especially LDPC codes. Various algorithms are used to decode them, including decoding by information sets. The algorithm for decoding over information sets has exponential complexity. Errors may occur on any communication channel when transmitting messages. Traditionally, independent errors are considered when researching decoding algorithms. However, in real systems, errors are grouped into bursts. This article discusses the probability of detecting information sets while correcting error bursts. Random matrices and block permutation matrices are considered. Graphs of the dependence of the probability of finding information sets on the number of positions that are considered when searching for information sets are given.

Wave Electronics and its Application in Information and Telecommunication Systems (WECONF)May 29, 20231 citation

2^{0.06035n}

of Bernstein's algorithm to

2^{0.05869n}

with the best algorithm presented here (where

n

is the codelength).