基于抗退化混沌系统和初等元胞自动机的动态S盒设计  

Design of Dynamic S-box Based on Anti-degradation Chaotic System and Elementary CellularAutomata

作　　者：赵耿 高世蕊 马英杰 董有恒 ZHAO Geng;GAO Shirui;MA Yingjie;DONG Youheng(Department of Cyber Space Security,Beijing Electronic Science and Technology Institute,Beijing 100071,China;School of Cyberspace Security,Beijing University of Posts and Telecommunications,Beijing 100089,China)

机构地区：[1]北京电子科技学院网络空间安全系,北京100071 [2]北京邮电大学网络空间安全学院,北京100089

出　　处：《计算机科学》2023年第11期333-339,共7页Computer Science

基　　金：北京高校“高精尖”学科建设项目(3201017);国家自然科学基金(61772047)。

摘　　要：S盒是多数分组密码算法的基本非线性模块,可以满足分组密码算法的混淆、扩散要求。为了提高混沌S盒的安全性,文中利用抗退化混沌系统生成S盒元素,基于初等元胞自动机生成S盒检索表的方式来生成S盒。抗退化混沌系统可以避免发生Skew Tent系统进入不动点的情况,消除低精度下系统进入短周期的现象。因为初等元胞自动机的迭代规则为二元域上的运算,且满足时空上的离散性,所以,将初等元胞自动机运用到混沌分组密码中时,不用考虑动力学退化的问题。当初等元胞自动机的迭代规则为全局混沌规则时,只要元胞个数足够,就可以保证输出的伪随机性。利用初等元胞自动机生成S盒的检索表,在保证S盒设计的混淆原则的同时还可以简化S盒的生成步骤。最后对所设计的S盒进行安全性分析对比,实验结果表明,所提方法生成的S盒具有良好的安全性,满足分组密码的混淆、扩散原则,可用于混沌分组密码算法设计中。S-box is the basic non-linear module of most block cipher algorithms,which can meet the obfuscation and proliferation requirements of block cipher algorithms.In order to improve the safety of chaotic S-boxes,this paper uses an anti-degenerative chaotic system to generate S-box elements,and generates an S-box based on elementary cellular automata to generate S-box retrieval table.The anti-degradation chaotic system can avoid the situation that the Skew Tent system enters the fixed point and eliminate the phenomenon of the system entering a short period of time at low precision.Because the elementary cellular automata is an operation on the binary domain and satisfies the discreteness in time and space,the elementary cellular automata is applied to the chaotic block cipher without considering the problem of dynamics degradation.In the case of global chaos rules,if the number of cells is enough,the pseudorandom of the output can be guaranteed.The use of elementary cellular automata to generate a search table for the S-box can not only ensure the confusion principle of S-box design,but also simplify the steps of S-box generation.Finally,the security analysis and comparison of the designed S-box shows that the S-box generated by the proposed method has good security,satisfies the principle of confusion and diffusion of block ciphers,and can be used in the design of chaotic block cipher algorithms.

关 键 词：S盒 抗退化 混沌 初等元胞自动机 LORENZ系统 Skew Tent系统 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]