基于不可逆分数阶离散映射的图像加密算法  

An image encryption algorithm based on a fractional-order discrete noninvertible map

作　　者：刘晓君 王普 鲁晨浩 Liu Xiaojun;Wang Pu;Lu Chenhao(School of Sciences,Xi'an University of Posts and Telecommunications,Xi'an 710121,China)

机构地区：[1]西安邮电大学理学院,西安710121

出　　处：《河南师范大学学报（自然科学版）》2024年第5期117-125,I0010,I0011,共11页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11702194);陕西省自然科学基金(2023-JC-YB-075).

摘　　要：基于分数阶离散映射系统的混沌特性,提出了一种基于分数阶循环移位彩色图像加密算法.该算法首先通过利用伪随机发生器产生随机的二进制序列与原彩色图像关联,产成各层随机的初始值参数,其次利用分数阶离散映射产生混沌序列,对彩色图像的红、绿、蓝通道分别进行循环移位置乱加密和扩散运算,最后利用产生的伪随机二进制序列和混沌序列控制对各层的加密矩阵进行矩阵变换,得到加密图像.仿真结果表明,相邻像素的相关性系数近似为0,信息熵、像素变化率和归一化像素灰度值平均改变强度的平均值分别为7.9978、99.609%和33.442%.该算法具有良好的可靠性和抗攻击能力,能够有效地提高图像的安全性.Based on the chaotic characteristics of fractional-order discrete maps,a color image encryption algorithm based on the fraction-order cyclic shift is proposed.Firstly,the random initial values are generated for each layer by a random binary sequence associated with the original color image using a pseudo-randomizer.Secondly,a fractional-order discrete map is used to generate the chaotic sequences,circular shift position chaotic encryption and diffusion operations are performed on the re,green and blue components of a color image,respectively.Finally,the encrypted image is obtained by matrix transformation of the encryption matrix for each layer based on the pseudo-random binary sequence and chaotic sequence control.Simulation results show that correlation coefficients for an image by the proposed method are approximately 0,and the average values of information entropy,number of pixels change rate and unified average changing intensity are 7.9978,99.609%and 33.442%,respectively.Therefore,the algorithm has a good reliability and an anti-attack capability.Meanwhile,the algorithm can enhance the security of images.

关 键 词：分数阶离散映射 图像加密 循环移位加密 矩阵变换 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]