双超混沌系统结合压缩感知和Fibonacci变换的彩色图像加密  

Double hyperchaotic systems combine compressed sensing and Fibonacci transform for color image encryption

作　　者：贾静雯 张钊[1] 周红艳 陈雪波[2] JIA Jingwen;ZHANG Zhao;ZHOU Hongyan;CHEN Xuebo(School of Computer Science and Software Engineering,University of Science and Technology Liaoning,Anshan 114051,China;School of Electronic and Information Engineering,University of Science and Technology Liaoning,Anshan 114051,China)

机构地区：[1]辽宁科技大学计算机与软件工程学院,辽宁鞍山114051 [2]辽宁科技大学电子与信息工程学院,辽宁鞍山114051

出　　处：《光学精密工程》2025年第4期624-640,共17页Optics and Precision Engineering

基　　金：国家自然科学基金项目(No.71771112);流程工业综合自动化国家重点实验室开放课题基金资助项目(No.PAL-N201801);辽宁省高校基本科研业务费专项资金(No.LJ212410146025)。

摘　　要：为了解决现有混沌图像加密算法中低维混沌系统混沌性质弱、安全性低,高维混沌系统传输成本高、存储空间大以及压缩感知技术中传统测量矩阵占用空间大、传输成本高等问题,本文提出一种双超混沌系统结合压缩感知和Fibonacci变换的彩色图像加密算法。首先,通过Lorenz超混沌系统优化Arnold算法,提高安全性。其次,利用6D超混沌系统改进压缩感知的测量矩阵,减少空间资源和传输成本。再次,采用具有大密钥空间和高安全性的6D超混沌系统进行置乱,提高安全性。最后,利用Fibonacci Q矩阵分块扩散,增强不可预测性。此外,在图像重建中引入2D投影梯度嵌入解密算法,与传统重建算法相比,具有更高的安全性和计算效率。实验结果表明:信息熵均超过7.999,更接近理想值8,相关系数接近0,像素数变化率和统一变化率接近理想值99.6094%和33.4635%。在有效保护图像安全性和完整性的同时,具有很强的抗统计攻击和差分攻击能力以及更好的鲁棒性。In order to solve the problems in the existing chaotic image encryption algorithms,such as the weak chaotic property and low security of low-dimensional chaotic systems,the high transmission cost and large storage space of high-dimensional chaotic systems,as well as the large occupied space and high transmission cost of traditional measurement matrices in compressed sensing technology,this paper proposed a color image encryption algorithm combining dual hyperchaotic systems with compressed sensing and Fibonacci transformation.Firstly,the Arnold algorithm was optimized through the Lorenz hyperchaotic system to improve security.Secondly,the measurement matrix of compressed sensing was improved by using the 6D hyperchaotic system to reduce space resources and transmission costs.Thirdly,scrambling was performed using the 6D hyperchaotic system with a large key space and high security to enhance security.Finally,the Fibonacci Q matrix was used for block diffusion to enhance unpredictability.In addition,the 2D projection gradient embedding decryption algorithm was introduced in image reconstruction.Compared with the traditional reconstruction algorithm,it had higher security and computational efficiency.Experimental results show that the information entropy exceeds 7.999,which is closer to the ideal value of 8,the correlation coefficient is close to 0,the rate of pixel number change and the uniform change rate are close to the ideal values of 99.6094%and 33.4635%.While effectively protecting the security and integrity of the image,it has strong resistance to statistical attacks and differential attacks as well as better robustness.

关 键 词：图像加密 混沌系统 压缩感知 Fibonacci Q矩阵 

分 类 号：TP394.1[自动化与计算机技术—计算机应用技术] TH691.9[自动化与计算机技术—计算机科学与技术]