基于改进Logistic混沌和交叉混沌扩散的强鲁棒性图像加密

郭媛; 贾德宝; 王充; 翟平

引用本文：

郭媛,贾德宝,王充,翟平.基于改进Logistic混沌和交叉混沌扩散的强鲁棒性图像加密[J].信息安全学报,2024,9(5):217-228 [点击复制]
GUO Yuan,JIA Debao,WANG Chong,ZHAI Ping.Robust Image Encryption Based on Improved Logistic Chaos and Cross-Chaos Diffusion[J].Journal of Cyber Security,2024,9(5):217-228 [点击复制]

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基于改进Logistic混沌和交叉混沌扩散的强鲁棒性图像加密
郭媛, 贾德宝, 王充, 翟平
0 字体:加大+\|默认\|缩小-
(齐齐哈尔大学计算机与工程学院齐齐哈尔中国 161006)

摘要:

针对现有部分图像加密算法鲁棒性弱的问题,本文提出了一种基于改进Logistic混沌和交叉混沌序列扩散的强鲁棒性加密算法。首先,对Logistic一维混沌进行变换,构造出一种混沌序列分布更加随机的新混沌系统;然后,利用螺旋矩阵变换进行第一次置乱,利用明文的哈希值构造混沌的初始密钥,引入明文相关的两个数值val₁和val₂结合新混沌系统构造交叉混沌序列;接着对置乱后的序列进行交叉混沌的扩散。为克服螺旋矩阵变换部分像素未发生改变的问题,再进行一次交叉混沌置乱,形成置乱-扩散-置乱的加密框架。最后对本算法进行仿真模拟,其中本文密文图像的平均相关系数为-0.0027,更加趋近于0,大大的破坏了图像内部之间的相关性,达到图像加密的效果。像素变化率NPCR为99.61%,归一化强度UACI为33.36%,都分别接近于理想值99.60%和33.34%;密文图像的信息熵为7.9975,接近于理想值8,密钥的敏感性为10^-17;能够在椒盐噪声和高斯噪声强度为0.2的情况下,仍然能够识别出解密图像。而且加密图像剪切1/2时,仍然能够恢复出明文图像;实验结果表明,本文算法具有较高的安全性,能够抵御选择明文攻击和穷举攻击,具有较强的抗噪声和抗剪切能力,对于图像传输过程中的安全性提供一定的保障,能够对于灰度图像达到安全稳定的加解密效果。

关键词: 图像加密鲁棒性混沌系统交叉混沌扩散螺旋矩阵置乱

DOI：10.19363/J.cnki.cn10-1380/tn.2024.09.13

投稿时间：2022-11-17修订日期：2023-02-11

基金项目:本课题得到国家自然科学基金(No.61872204)、黑龙江省自然科学基金(No.LH2021F056)、黑龙江省省属高等学校基本科研业务费科研项目(No.135509113)、研究生创新科研项目(No.YJSCX2022049)资助。

Robust Image Encryption Based on Improved Logistic Chaos and Cross-Chaos Diffusion

GUO Yuan, JIA Debao, WANG Chong, ZHAI Ping

(College of Computer and Engineering, Qiqihar University, Qiqihar 161006, China)

Abstract:

Aiming at the weak robustness of some existing image encryption algorithms, a robust encryption algorithm based on improved Logistic chaos and cross chaotic sequence diffusion is proposed in this paper. Firstly, the Logistic one-dimensional chaos is transformed to construct a new chaotic system with more random distribution of chaotic sequences. Then, the spiral matrix transformation is used for the first scrambling, the plaintext hash value is used to construct the initial key of chaos, and the two plaintext related values val₁ and val₂ are introduced to combine the new chaotic system to construct the crossed chaotic sequence. Then the chaotic sequence is diffused by cross chaos. In order to overcome the problem that some pixels of the helical matrix transformation did not change, the cross chaotic scrambling was carried out again to form a scrambling-diffusion-scrambling encryption framework. Finally, the algorithm is simulated, in which the average correlation coefficient of ciphertext image in this paper is -0.0027, approaching to 0, which greatly destroys the correlation between internal images and achieves the effect of image encryption. The pixel change rate (NPCR) and normalized intensity (UACI) were 99.61% and 33.36%, respectively, close to the ideal values of 99.60% and 33.34%. The entropy of ciphertext image is 7.9975, which is close to the ideal value 8, and the sensitivity of key is 10^-17. It can recognize the decrypted image when the intensity of salt and pepper noise and Gaussian noise is 0.2. In addition, the plaintext image can still be recovered when the encrypted image is cut by half. Experimental results show that the proposed algorithm has high security, can resist the selection of plaintext attack and brute force attack, has strong anti-noise and anti-shearing ability, for image transmission security to provide a certain guarantee, can achieve a safe and stable encryption and decryption effect for gray image.

Key words: image encryption robustness chaotic system cross chaotic diffusion spiral matrix scrambling