李玖1,
李国东2,,
1.北京科技大学数理学院 ??北京 ??100083
2.新疆财经大学应用数学学院 ??乌鲁木齐 ??830012
基金项目:国家自然科学基金(11461063)，新疆维吾尔自治区自然科学基金(2017D01A24)
详细信息
作者简介:臧鸿雁：女，1973年生，副教授，研究方向为混沌系统理论及混沌密码学
李玖：男，1995年生，硕士生，研究方向为混沌系统理论及图像加密
李国东：男，1972年生，教授，研究方向为细胞神经网络和混沌密码学
通讯作者:李国东?lgdzhy@126.com
中图分类号:O415.5; TP309.7计量
文章访问数:1446
HTML全文浏览量:427
PDF下载量:53
被引次数:0
出版历程
收稿日期:2017-12-04
修回日期:2018-05-02
网络出版日期:2018-06-07
刊出日期:2018-08-01
A One-dimensional Discrete Map Chaos Criterion Theorem with Applications in Pseudo-random Number Generator
Hongyan ZANG1,Jiu LI1,
Guodong LI2,,
1. Mathematics and Physics School, University of Science and Technology Beijing, Beijing 100083, China
2. College of Applied Mathematics, Xinjiang University of Finance and Economics, Urumchi 830012, China
Funds:The National Natural Science Foundation of China (11461063), The Xinjiang Uygur Autonomous Region Natural Science Foundation (2017D01A24)
摘要
摘要:该文研究了一类取模运算的1维离散动力系统，提出了一个这类离散映射的混沌判据，利用Marotto定理证明了其混沌的存在性。给出了几个满足该判据的特殊形式的系统，分析了其分岔图、Lyapunov指数谱等基本动力学性质，通过模拟结果验证了理论的正确性。基于新系统设计了一个伪随机数发生器(PRNG), SP800-22随机性检测结果表明了该序列具有良好的伪随机性。进一步给出了一个图像加密方案，其密钥空间可以达到2747。该文提出的新系统的系统参数可以无穷多，所以理论上该加密方案的密钥空间可以无穷大。
关键词:混沌判据/
Marotto定理/
返回扩张不动点/
伪随机数发生器/
图像加密
Abstract:A novel one-dimensional discrete chaotic criterion is firstly constructed by studying the modular operation of the discrete dynamical systems. The judgement of the Marotto theorem is used to prove that the suggested dynamical systems are chaotic. Secondly, several special chaotic systems satisfied with the conditions of this paper are given, and the bifurcation diagram and Lyapunov exponential spectrum are also analyzed. Numerical simulations show that the proposed chaotic systems have the positive Lyapunov exponent, which indicates the accuracy of the proposed theory. Additionally, a Pseudo-Random Number Generator (PRNG) is also designed based on the given new chaotic system. Using SP800-22 test suit, the results show that the output sequence of PRNG has good pseudorandom. Finally, as an application of the PRNG, an image encryption algorithm is given. The proposed encryption scheme is highly secure Key space of 2747 and can resist against the statistical and exhaustive attacks based on the experimental results.
Key words:Chaotic criterion/
Marotto theorem/
Snap-back repeller/
Pseudo-Random Number Generator (PRNG)/
Image encryption
PDF全文下载地址:
https://jeit.ac.cn/article/exportPdf?id=a507c45b-737f-421b-8ec5-66c76a4209ed
