一种基于Kolmogorov方程与ICMIC的图像加密方案  

An Image Encryption Scheme Based on the Kolmogorov Equation and the ICMIC

作　　者：关至轩 胡金涛 田红炯 GUAN Zhixuan;HU Jintao;TIAN Hongjiong(Department of Mathematics,School of Mathematics and Science,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院数学系,上海200234

出　　处：《重庆师范大学学报（自然科学版）》2024年第1期109-117,共9页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.12271368)。

摘　　要：针对图像传输的安全性问题,利用Kolmogorov方程解的Markov性以及无限折叠的迭代混沌映射(iterative chaotic map with infinite collapses,ICMIC)的混沌性,提出了一种可以抵御选择明文攻击的对称加密方案。首先通过设置Kolmogorov方程的系数矩阵与初始状态作为密钥参数产生转移概率矩阵,其次将转移概率矩阵输入ICMIC并由得到的结果确定密钥序列,最后由密钥序列与明文图像做模2加法运算生成密文图像。通过Matlab程序对加密方案进行实验仿真,密文图像信息熵为7.99以上,NPCR值超过99%,UACI值超过33%。实验结果表明该加密方案具有较高安全性,可以有效抵御统计攻击与差分攻击等。For the security problem of image transmission,using the Markov property of the solution of Kolmogorov equation and the chaos of infinite folding of Iterative Chaotic Map with Infinite Collapses(ICMIC),a symmetrical encryption scheme is proposed to resist encoding attack.First,the transfer probability matrix is generated by setting the coefficient matrix of the Kolmogorov equation and the initial state as the key parameter.Second,the transfer probability matrix is input into ICMIC,and the key sequence is determined by the obtained results.Finally,the ciphertext images are generated by adding the key sequence and the plaintext images.The encryption scheme was entally simulated by the MATLAB program,with ciphertext image information entropy above 7.99,NPCR over 99%,and UACI over 33%.The experimental results show that the encryption scheme has high security and can effectively resist statistical attacks and differential attacks.

关 键 词：图像加密 MARKOV过程 Kolmogorov方程 ICMIC 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]