基于动态复合混沌系统的S盒设计

A novel method of designing S-box based on dynamic compound chaotic system

S盒是分组密码中重要的非线性部件之一.基于多混沌系统及复合思想,并引入Arnold映射置乱算法,提出了一种混沌S盒的产生方法.首先,提出了几种混沌方程,并对方程的自相关性和互相关性进行了分析,证明它们具有很好的伪随机性.接着,引入了动态复合混沌系统,形成了一种新的混沌系统.运用线性同余发生器可以延长混沌周期的思想,结合动态复合混沌系统,形成了一种新的伪随机序列的产生方法.将所形成的伪随机序列构造成临时的S盒,再利用Arnold映射将临时S盒置乱形成新的S盒.最后,对所产生的S盒做了严格的性能测试,并将本文S盒特性与前人提出的S盒进行了对比,对比分析显示本文所提出的算法产生的S盒具有良好的密码学性能,在空间网络安全及轻量级密码中具有很好的应用前景.

Substitution box（S-box）is one of the important non-linear components in the block cipher.In recent years,many scholars have proposed relevant methods based on chaotic S-box.However,these methods mostly exploit the randomness of chaotic maps which is relatively simple.To address this problem,we propose a method of combining multi-chaotic system and linear congruence generators（LCGs）based on chaotic maps.Firstly,several chaotic equations are introduced to form a new compound chaotic system.Autocorrelation and cross-correlation of these equations are studied to prove that they are adequate to generate pseudorandom sequences.This system makes it possible to generate chaotic sequences dynamically.When the iteration value is below 0,we choose f0,or we choose f1.Then,linear congruence generator is used to exclusive-OR with chaotic sequences to make them much more chaotic and nonlinear.We also import the Lewis-Goosman-Miller minimal standard which is a kind of method to get longest LCGs cycle length.Thus,new pseudo-random sequences are developed.Subsequently,the continuous sequences are discretized to integer sequences which are formed into a temporary S-box.Finally,the S-box is scrambled to a new one by using Arnold map.The elements in the sequence change from an old position to a newposition.In the experimental part,the S-box is compared with the algorithm proposed by the predecessors.By validating nonlinearity and Output Bits Independence Criterion-Strict Avalanche Criterion（BIC-SAC）,we can know that the S-box proposed in this paper has strong cryptography characteristics.It shows that it could be a good resistance to linear attacks and differential attacks.The design of S-box takes advantage of multi-chaotic system and the pseudo-randomness of linear congruence generator.In a word,this S-box has a good application prospects in the space network security and lightweight cipher.