一维鲁棒混沌映射及S盒的设计

doi:10.3969/j.issn.0372-2112.2015.09.014

电子学报 ›› 2015, Vol. 43 ›› Issue (9): 1770-1775.DOI: 10.3969/j.issn.0372-2112.2015.09.014

一维鲁棒混沌映射及S盒的设计

韩丹丹¹, 闵乐泉², 赵耿³, 张丽姣², 闫世杰¹

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

收稿日期:2014-06-26 修回日期:2015-04-30 出版日期:2015-09-25
- 作者简介:
- 韩丹丹 女,1989年出生于山东省济宁市兖州市,北京科技大学自动化学院博士.主要研究方向为复杂混沌动力学系统和通信安全,合作发表期刊论文和会议论文8篇.E-mail:hxu1204@163.com;闵乐泉 男,1951年出生于北京,现为北京科技大学教授,博士生导师.主要科研方向:混沌系统的广义的同步与安全通信;复杂系统建模;细胞神经网络模板的鲁棒性设计.合作发表期刊论文和会议论文200余篇,其中被SCIE收录60余篇,EI收录100余篇.E-mail:minlequan@sina.com
- 基金资助:
- 国家自然科学基金 (No.61074192,No.61170037)

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

HAN Dan-dan¹, MIN Le-quan², ZHAO Geng³, ZHANG Li-jiao², YAN Shi-jie¹

1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
2. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
3. Beijing Electronic Science and Technology Institute, Beijing 100070, China

Received:2014-06-26 Revised:2015-04-30 Online:2015-09-25 Published:2015-09-25
- Supported by:
- National Natural Science Foundation of China (No.61074192, No.61170037)

摘要/Abstract

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.

关键词: Li-York混沌, 鲁棒混沌, 伪随机数发生器, S盒

Abstract:

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 computes the bifurcation diagram of the map.The computed results demonstrate the chaotic robustness features of the map.Three pseudo-random number generators are generated based on the piecewise nonlinear robust chaotic map.On this basis,the generation algorithm of S-boxes is proposed with the property of sensitivity to the initial parameters of the chaotic map.The cryptography performance 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.

Key words: Li-York chaos, robust chaos, pseudo-random number generator, S-box

中图分类号:

TP393

韩丹丹, 闵乐泉, 赵耿, 等. 一维鲁棒混沌映射及S盒的设计[J]. 电子学报, 2015, 43(9): 1770-1775.

HAN Dan-dan, MIN Le-quan, ZHAO Geng, et al. One-Dimensional Robust Chaotic Map and the Construction of S-Box[J]. Acta Electronica Sinica, 2015, 43(9): 1770-1775.

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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

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