一维鲁棒混沌映射及S盒的设计  

One-Dimensional Robust Chaotic Map and the Construction of S-Box

作　　者：韩丹丹[1] 闵乐泉[2] 赵耿[3] 张丽姣[2] 闫世杰[1] 

机构地区：[1]北京科技大学自动化学院,北京100083 [2]北京科技大学数理学院,北京100083 [3]北京电子科技学院,北京100070

出　　处：《电子学报》2015年第9期1770-1775,共6页Acta Electronica Sinica

基　　金：国家自然科学基金(No.61074192;No.61170037)

摘　　要：本文利用Li-York混沌判别定理,构造了一类分段线性连续混沌映射.基于此类映射,建立了一个构造一类分段非线性鲁棒混沌映射的判别定理.作为应用,构造了一个由多项式函数和三角函数映射合成的分段非线性鲁棒混沌映射.通过计算该混沌映射的分岔图,验证了映射在参数范围内的混沌性.作为鲁棒混沌的应用,设计了三个基于分段非线性鲁棒混沌映射的伪随机数发生器.在此基础上,利用混沌映射对初始参数的敏感性,提出了批量生成S盒的算法.S盒密码性能的分析结果表明,生成的S盒具有良好的密码学性能,可以较好的抵抗线性与差分攻击,为密码算法的研究发展提供基础与条件.Using the judgment theorem of Li-York chaos,this paper generates a class of piecewise linear chaotic maps.Based on the chaotic maps,a constructing theorem of piecewise nonlinear robust chaotic map is proposed.As an application,this theorem is used to construct a piecewise nonlinear robust chaotic map with a polynomial function and a trigonometric function.This study com-putes the bifurcation diagram of the map.The computed results demonstrate the chaotic robustness features of the map.Three pseu-do-random number generators are generated based on the piecewise nonlinear robust chaotic map.On this basis,the generation algo-rithm of S-boxes is proposed with the property of sensitivity to the initial parameters of the chaotic map.The cryptography perfor-mance is tested and the tested results show that generated S-boxes have good cryptographic properties,and can not only better resist the linear and differential attacks,but also provide the foundation and conditions for the research and development of cryptography.

关 键 词：Li-York 混沌 鲁棒混沌 伪随机数发生器 S 盒 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]