分组密码随机序列的不变量研究

Research on Invariant of Random Sequences in Block Ciphers

摘要: 对于分组密码而言，密码的安全性来自混淆、扩散性，而两者主要来自分组密码的轮函数操作。为满足加密算法标准化、加密算法本土化及各方的需求，本文使用图论的相关知识，利用最新向量逻辑——变值体系来对分组密码安全性进行研究。文章通过获取分组密码的中间随机序列，分析随机序列的特征，得到随机序列的不变量，进一步对不变量进行统计分析研究，研究方向为通过控制变量法，观察对比不变量统计可视化结果，探索不变量特征；对于同一分组密码而言，改变不变量数据量，得出同一密码不变量具有饱和态的特性的结论，为分组密码的安全性提供进一步的理论依据。

Abstract: For block cipher, the security of cipher comes from confusion and diffusion, and the two mainly come from round function operation of block cipher. In order to meet the standardization of encryption algorithms, localization of encryption algorithms and the needs of all parties, this paper uses the relevant knowledge of graph theory and the latest vector logic variable system to study the security of block ciphers. This paper obtains the intermediate random sequence of block cipher, analyzes the characteristics of the random sequence, obtains the invariant of the random sequence, and further conducts statistical analysis and research on the invariant. The research direction is to observe and compare the statistical visualization results of the invariant through the control variable method, and explore the characteristics of the invariant; For the same block cipher, by changing the amount of invariant data, it is concluded that the same cipher invariant has the characteristics of saturation state, which provides a further theoretical basis for the security of block cipher.