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Conference Papers Year : 2021

Classical and Quantum Algorithms for Generic Syndrome Decoding Problems and Applications to the Lee Metric

Abstract

The security of code-based cryptography usually relies on the hardness of the syndrome decoding (SD) problem for the Hamming weight. The best generic algo-rithms are all improvements of an old algorithm by Prange, and they are known under the name of Information Set Decoding (ISD) algorithms. This work aims to extend ISD algorithms’ scope by changing the underlying weight function and alphabet size of SD. More precisely, we show how to use Wagner’s algorithm in the ISD framework to solve SD for a wide range of weight functions. We also calculate the asymptotic complexities of ISD algorithms both for the classical and quantum case. We then apply our results to the Lee metric, which currently receives a significant amount of attention. By providing the parameters of SD for which decoding in the Lee weight seems to be the hardest, our study could have several applications for designing code-based cryptosystems and their security analysis, especially against quantum adversaries.

Dates and versions

hal-03529777 , version 1 (17-01-2022)

Identifiers

Cite

André Chailloux, Thomas Debris-Alazard, Simona Etinski. Classical and Quantum Algorithms for Generic Syndrome Decoding Problems and Applications to the Lee Metric. PQCrypto 2021 - Post-Quantum Cryptography 12th International Workshop, Jul 2021, Daejeon, South Korea. pp.44-62, ⟨10.1007/978-3-030-81293-5_3⟩. ⟨hal-03529777⟩
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