混沌系统的鲁棒性研究及在图像加密中的应用

发布时间：2018-07-24 07:45

【摘要】：科学技术与信息化进程的蓬勃兴起,给全球带来了信息技术飞速发展的契机。人们在享受信息网络所带来的巨大利益的同时,也面临着信息安全的巨大挑战。图像作为信息的重要载体及传输媒介,其安全性受到了越来越多的关注。信息安全的核心工具是加密。随着通信环境的日趋复杂和破译能力的不断提升,一些传统密码算法被攻破或安全性受到威胁,需要更先进的密码设计理论和创新技术。混沌的发现堪称20世纪物理学界的第三次革命。混沌动力学的一些特征与密码学的要求相吻合,混沌密码学成为密码学领域的热门课题之一1975年,Li-Yorke首次用数学语言定义了混沌术语,提出了周期三蕴含混沌的著名定理。2009年,周海玲和宋恩彬利用Li-Yorke定理提出并证明了一个有关2次多项式的混沌鲁棒定理。2015年,杨秀萍等人提出并证明了一个有关3次多项式的混沌鲁棒性定理。1999年,Banerjee等人提出了二维分段光滑映射标准型的混沌鲁棒定理。2001年,Andrecut等人提出了S单峰映射的混沌鲁棒定理。2013年,闵乐泉和陈关荣提出一个基于d比特密钥流的图像加密方案SESAE,该方案具有密钥雪崩效应,增加了破译者的难度。本文基于前人的工作,对离散混沌系统的鲁棒性、伪随机数发生器、雪崩图像加密方案进行了研究。本文主要研究成果和创新点如下：(1)关于几类离散混沌系统的鲁棒性研究本文基于Li-Yorke混沌判别定理和S单峰映射的混沌判别定理,提出了构造一维分段非线性映射的鲁棒混沌定理和3次多项式映射的鲁棒混沌定理。通过改进二维分段光滑映射标准型的混沌鲁棒定理,本文提出了二维分段光滑映射标准型的等价混沌判别定理,给出构造四维离散混沌映射的必要条件,为构造混沌系统提供了理论证明,为混沌应用提供了新的工具。(2)关于伪随机数发生器的设计与性能检测本文基于新提出的离散系统鲁棒混沌定理、三角函数和混沌广义同步定理,构造了6个新的离散混沌广义同步系统。利用这6个离散混沌广义同步系统,本文优化设计了6个具有大密钥空间的混沌伪随机数发生器(CPRNGs).利用改进的美国国家标准与技术研究院(NIST)公布的FIPS 140-2和SP800-22检测标准对CPRNGs和RC4算法、ZUC算法的伪随机性能进行检测。检测结果显示CPRNGs的随机性能与RC4算法和ZUC算法相当,其中2个CPRNGs的SP 800-22检测的14-15项检测结果优于RC4算法和ZUC算法。(3)雪崩图像加密方案的研究本文提出一个具有密钥雪崩与明文雪崩的流加密方案和一个块加密雪崩方案,推广了有关具有雪崩效应的图像加密方案SESAE 的勺研究工作。
[Abstract]:The vigorous rise of science and technology and information technology has brought the opportunity of the rapid development of information technology to the whole world. While enjoying the enormous benefits brought by the information network, people are also faced with the enormous challenge of information security. As an important carrier and transmission medium of information, the security of image has been paid more and more attention. The core tool of information security is encryption. With the increasing complexity of communication environment and the improvement of decoding ability, some traditional cryptographic algorithms are compromised or their security is threatened, which requires more advanced cryptographic design theory and innovative technology. The discovery of chaos is the third revolution in physics in the 20 th century. Some characteristics of chaotic dynamics coincide with the requirements of cryptography. Chaotic cryptography has become one of the hot topics in cryptography. In 1975, Li-Yorke first defined the term of chaos in mathematical language, and put forward a famous theorem of chaos in three cycles. Zhou Hailing and Song Enbin put forward and proved a chaotic robust theorem about quadratic polynomials by using Li-Yorke theorem. Yang Xiuping and others proposed and proved a chaotic robustness theorem for cubic polynomials. In 1999, Banerjee et al proposed a chaotic robust theorem for standard forms of two-dimensional piecewise smooth mappings. In 2001, Andrecut et al proposed a chaotic robust theorem for S unimodal mappings. Min Lequan and Chen Guanrong proposed an image encryption scheme SESAE based on d bit key stream which has the effect of key avalanche and increases the difficulty of deciphers. Based on the previous work, the robustness, pseudo random number generator and avalanche image encryption scheme of discrete chaotic systems are studied in this paper. The main achievements and innovations of this paper are as follows: (1) the robustness of some discrete chaotic systems is studied in this paper based on Li-Yorke chaos discrimination theorem and chaotic discriminant theorem of S unimodal mapping. A robust chaos theorem for constructing one-dimensional piecewise nonlinear mappings and a robust chaos theorem for cubic polynomial mappings are presented. By improving the chaos robust theorem of the standard form of two-dimensional piecewise smooth mapping, this paper presents the equivalent chaos discrimination theorem for the standard form of two-dimensional piecewise smooth mapping, and gives the necessary conditions for constructing four-dimensional discrete chaotic mapping. This paper provides a theoretical proof for constructing chaotic system and a new tool for chaotic application. (2) the design and performance detection of pseudorandom number generator is based on the new robust chaos theorem of discrete system. Six new discrete chaotic generalized synchronization systems are constructed by trigonometric functions and chaotic generalized synchronization theorems. Using these six discrete chaotic generalized synchronization systems, this paper optimizes the design of six chaotic pseudorandom number generators (CPRNGs).) with large key space. The pseudorandom performance of CPRNGs and RC4 algorithm is tested by using the improved FIPS 140-2 and SP800-22 detection standards published by (NIST) of the National Institute of Standards and Technology. The results show that the random performance of CPRNGs is comparable to that of RC4 algorithm and ZUC algorithm. The 14-15 items detected by SP800-22 of two CPRNGs are superior to those of RC4 and ZUC. (3) A stream encryption scheme with key avalanche and clear text avalanche and a block encryption avalanche scheme are proposed in this paper. The research work of image encryption scheme SESAE with avalanche effect is generalized.
【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP309.7

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