基于Hopfield网络“伪吸引子”与交替量子随机行走的抗攻击彩色图像加密方案  

Anti-Attack Color Image Encryption Scheme Based on Hopfield Network“Pseudo Attractor”and Alternating Quantum Random Walk

作　　者：宋昭阳 王一诺 王浩文 马鸿洋 SONG Zhao-yang;WANG Yi-nuo;WANG Hao-wen;MA Hong-yang(School of Information and Control Engineering,Qingdao University of Technology,Qingdao,Shandong 266520,China;School of Science,Qingdao University of Technology,Qingdao,Shandong 266520,China)

机构地区：[1]青岛理工大学信息与控制工程学院,山东青岛266520

出　　处：《电子学报》2023年第8期2030-2042,共13页Acta Electronica Sinica

基　　金：国家自然科学基金(No.11975132);山东省自然科学基金(No.ZR2021MF049,No.ZR2019YQ01);山东省自然科学基金联合基金(No.ZR202108020011)。

摘　　要：近年来,图像信息的安全传输已成为互联网领域的重要研究课题.本文提出了一种将Hopfield网络伪吸引子特性与交替量子随机行走概率分布矩阵相结合的抗攻击彩色图像加密方案.研究发现,若控制Hopfield网络状态矩阵的精度参数,将交替量子随机行走产生的概率分布矩阵4分块中的1个子块M1作为伪随机数矩阵参与加密,Hopfield网络的训练矩阵与输入矩阵分别为矩阵M1的4分块中的2个对角子块之一时,能产生伪吸引子.该伪吸引子的矩阵形式通过张量运算、进制转换等处理后,能作为密钥矩阵对原始图像进行基于空间域上的像素值排序自适应置乱以及元素数值的混淆,生成加密图像.其中,密钥矩阵是图像加密中的关键部分,具备优异统计学属性的密钥矩阵能极大的提高图像加密的效果.本文所提加密方案在统计学特性测试中,实现了平均信息熵为7.999 4,像素数改变率的平均值为99.621 8%,统一平均变化强度的平均值为33.537 9%,平均相关性为0.003 9等.同时本文还对所提加密方案进行了各种噪声模拟测试以验证其实际应用中遇到常见噪声及攻击干扰情况下的鲁棒性.The secure transmission of image information has attracted wide attention in the field of the Internet in recent years.We propose an attack-resistant color image encryption scheme that combines the pseudo-attractor property of Hopfield network with the probability distribution matrix of alternating quantum random walk.We find that by controlling the accuracy parameters of the Hopfield network state matrix,one sub-block M1 of the 4-block probability distribution matri⁃ces generated by the alternating quantum random walk is involved in the encryption as a pseudo-random number matrix.And when the training matrix and the input matrix of Hopfield network are one of the 2 diagonal sub-blocks of the 4-block matrix M1,respectively,the pseudo-attractor can be generated.The matrix form of this pseudo-attractor,after processing by tensor calculation and binary conversion,can be used as a key matrix to generate an encrypted image based on adaptive per⁃mutation of pixel value ordering on the spatial domain and confusion of element values for the original image.The key ma⁃trix is a critical part of image encryption,and a key matrix with excellent statistical properties can obviously improve the effectiveness of image encryption.In the statistical characteristic test,the encryption scheme proposed in this paper achieves an average information entropy of 7.9994,an average value of 99.6218%of the number of pixels changed rate(NPCR),an average of 33.5379%of the uniform average change intensity(UACI),and an average correlation decreases to 0.0039.Our encryption scheme is also tested in the presence of various noise simulations to verify its robustness against common noise and attack interference in practical applications.

关 键 词：信息安全 图像加密 神经网络 HOPFIELD网络 量子随机行走 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构] TN919.81[自动化与计算机技术—计算机科学与技术]