信息网络安全

信息网络安全 ›› 2025, Vol. 25 ›› Issue (2): 260-269.doi: 10.3969/j.issn.1671-1122.2025.02.007

• 理论研究 • 上一篇    下一篇

基于MILP的轻量级序列密码算法线性分析

帅燕1, 胡汉平1,2()   

  1. 1.华中科技大学人工智能与自动化学院，武汉 430074
    2.图像信息处理与智能控制教育部重点实验室，武汉 430074
  • 收稿日期:2024-11-19 出版日期:2025-02-10 发布日期:2025-03-07
  • 通讯作者: 胡汉平 E-mail:hphu@hust.edu.cn
  • 作者简介:帅燕（1999—），女，重庆，硕士研究生，主要研究方向为网络空间安全、密码算法分析|胡汉平（1960—），男，湖北，教授，博士，主要研究方向为网络信息安全、模式识别与智能系统
  • 基金资助:
    湖北省重点研发计划(2020BAB104)

Linear Analysis of Lightweight Stream Cipher Algorithm Based on Mixed Integer Linear Programming

SHUAI Yan1, HU Hanping1,2()   

  1. 1. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
    2. Key Laboratory of Image Information Processing and Intelligent Control, Ministry of Education, Wuhan 430074, China
  • Received:2024-11-19 Online:2025-02-10 Published:2025-03-07

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摘要：

文章针对一种基于时变互耦合双混沌系统的轻量级序列密码算法的安全性进行评估，轻量级序列密码算法的安全性对保障物联网和移动通信等资源受限环境的数据安全至关重要。文章选取了混合整数线性规划方法作为分析工具，构建算法的数学模型，并通过对模型的优化求解，得出算法在不同运行模式下的最大线性相关系数，范围在2-54~2-26之间。实验结果表明，该算法在相关性方面存在一定的脆弱性，攻击者通过穷举110位初始密钥来破解算法，复杂度远低于其128bit初始密钥的穷举复杂度。文章不仅提供了对该算法安全性的定量评估，而且验证了在密码学中进行相关性分析的重要性以及混合整数线性规划技术在密码算法安全性评估方面的有效性。文章对于推动轻量级密码算法的安全性分析和设计具有一定的理论和实践意义，为资源受限环境下的数据安全提供了有力的理论支持。

关键词: 混沌序列密码算法, 线性分析, 混合整数线性规划

Abstract:

This paper addressed the evaluation of the security of a lightweight stream cipher algorithm based on a time-varying mutually coupled dual chaotic system, which was crucial for securing data in resource-constrained environments such as the Internet of things and mobile communications. The article selected the mixed integer linear programming method as an analytical tool to construct a mathematical model of the algorithm, and revealed the maximum linear correlation coefficients of the algorithm under different modes of operation, ranging from 2-54 to 2-26, by optimally solving the model. This finding suggests that the algorithm is vulnerable in terms of correlation, and an attacker may be able to crack the algorithm by exhaustively enumerating up to 110 bits of the initial key, which is much less complex than the complexity of exhaustively enumerating its 128-bit initial key. This paper not only provides a quantitative assessment of the security of this algorithm, but also emphasizes the importance of correlation analysis in cryptographic design and the effectiveness of the mixed integer linear programming technique in the security assessment of cryptographic algorithms. Overall, the research in this paper is of great theoretical and practical significance in advancing the security analysis and design of lightweight cryptographic algorithms, and provides strong theoretical support for data security in resource-constrained environments.

Key words: chaos-based stream cipher, linear analysis, mixed integer linear programming

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