分数阶Duffing系统在图像加密中的应用  

Fractional Duffing System Using in Image Encryption

作　　者：张海英[1] 张卫[1,2] 刘金梅[1,2] Nigmatullin R R 

机构地区：[1]暨南大学信息科学技术学院,广东广州510632 [2]暨南大学-喀山联邦大学信息技术分形信号处理联合实验室,广东广州510632 [3]俄罗斯喀山联邦大学物理系

出　　处：《计算机工程与科学》2012年第6期18-22,共5页Computer Engineering & Science

基　　金：广东省科技计划国际合作基金资助项目(1011420800004);暨南大学创新计划国际合作基金资助项目(21609606)

摘　　要：混沌图像加密技术是近年来发展起来的一种新的图像加密技术,但目前采用的混沌系统大都是整数阶的一维、二维或三维混沌系统,很少使用分数阶的混沌系统。以Duffing系统为例,对分数阶Duffing系统和整数阶Duffing系统进行分析,当两个系统取相同参数并都达到混沌状态时,对混沌序列的伪随机性进行分析比较,可得到分数阶的混沌系统的伪随机性更强,并且分数导数的阶数也可以作为密钥,理论上比整数阶系统的密钥空间大得多,分数阶Duffing系统更适用于图像加密,并具有很好的加密效果。In recent years, the chaos-based image encryption technique is developed as a new ap proach. But one-dimensional, two-d or three-d integral chaos systems are usually used, few people apply a fractional order chaotic system. We compare the fractional Dulling system with the integral Dulling sys- tem in key spaces and pseudo random sequences. Theoretical analyses and computer simulations both confirm that the chaotic sequences of the fractional system is more random. The order number of the fractional system also can be applied as key. So, in theory, the key space of a fractional Du{fing system is bigger than that of an integral Dulling system. In conclusion, the fractional Dulling system is more suitable for image encryption,and the encryption results is good.

关 键 词：混沌 分数算子Duffing 伪随机性 图像加密 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]