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Improved Information Set Decoding Algorithms over Galois Ring in the Lee Metric

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Abstract

The security of most code-based cryptosystems relies on the hardness of the syndrome decoding (SD) problem. The best solvers of the SD problem are known as information set decoding (ISD) algorithms. Recently, Weger, et al. (2020) described Stern’s ISD algorithm, s-blocks algorithm and partial Gaussian elimination algorithms in the Lee metric over an integer residue ring \({{\boldsymbol{Z}}_{{p^m}}}\), where p is a prime number and m is a positive integer, and analyzed the time complexity. In this paper, the authors apply a binary ISD algorithm in the Hamming metric proposed by May, et al. (2011) to solve the SD problem over the Galois ring GR(pm, k) endowed with the Lee metric and provide a detailed complexity analysis. Compared with Stern’s algorithm over \({{\boldsymbol{Z}}_{{p^m}}}\) in the Lee metric, the proposed algorithm has a significant improvement in the time complexity.

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Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing, 100093, China

    Yu Li & Li-Ping Wang

  2. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yu Li & Li-Ping Wang

Authors
  1. Yu Li
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  2. Li-Ping Wang
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Correspondence to Li-Ping Wang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61872355 and the National Key Research and Development Program of China under Grant No. 2018YFA0704703.

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Li, Y., Wang, LP. Improved Information Set Decoding Algorithms over Galois Ring in the Lee Metric. J Syst Sci Complex 36, 1319–1335 (2023). https://doi.org/10.1007/s11424-023-1512-6

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  • DOI: https://doi.org/10.1007/s11424-023-1512-6

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