Information-set decoding for convolutional codes

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2025-05-20 DOI:10.1007/s10623-025-01649-1

Niklas Gassner, Julia Lieb, Abhinaba Mazumder, Michael Schaller

引用次数: 0

Abstract

In this paper, we present a framework for generic decoding of convolutional codes, which allows us to do cryptanalysis of code-based systems that use convolutional codes as public keys. We then apply this framework to information set decoding, study success probabilities and give tools to choose variables. Finally, we use this to attack two cryptosystems based on convolutional codes. In the case of Bolkema et al. (Variations of the McEliece cryptosystem. In: Algebraic geometry for coding theory and cryptography: IPAM, Los Angeles, CA, Feb 2016. Springer, Cham, pp 129-150, 2017. https://doi.org/10.1007/978-3-319-63931-4_5), our code recovered about 74% of errors in less than 10 h each, and in the case of Almeida et al. (Smaller keys for code-based cryptography: McEliece cryptosystems with convolutional encoders. CoRR abs/2104.06809, 2021. arXiv: https://arxiv.org/abs/2104.06809v1), we give experimental evidence that 80% of the errors can be recovered in times corresponding to about 70 bits of operational security, with some instances being significantly lower.

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卷积码的信息集解码

在本文中，我们提出了一个卷积码的通用解码框架，它允许我们对使用卷积码作为公钥的基于代码的系统进行密码分析。然后，我们将该框架应用于信息集解码，研究成功概率并给出选择变量的工具。最后，我们用它来攻击两个基于卷积码的密码系统。在Bolkema等人的案例中（McEliece密码系统的变体）。见：编码理论和密码学的代数几何：IPAM，洛杉矶，CA， 2016年2月。[j]，《中国科学》，2017年第129-150页。https://doi.org/10.1007/978-3-319-63931-4_5)，我们的代码在不到10小时的时间内恢复了大约74%的错误，并且在Almeida等人的情况下（基于代码的加密的较小密钥：带有卷积编码器的McEliece密码系统）。CoRR abs/2104.06809, 2021。arXiv: https://arxiv.org/abs/2104.06809v1)，我们给出的实验证据表明，80%的错误可以在大约70位操作安全的时间内恢复，其中一些实例明显更低。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

期刊介绍： Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.