二维反三角超混沌系统及其在图像加密上的应用

为了进一步提高混沌系统的混沌特性,为图像加密算法提供更可靠的混沌系统,增强图像加密算法的安全性,提出了一种基于二维反三角超混沌系统的新型图像加密算法。首先,在一维三角混沌函数的基础上构建了一个二维反三角超混沌系统,通过分岔图和Lyapunov指数等仿真实验,验证了该系统具有更广的混沌区间和更强随机性的迭代序列,遍历性更加优秀;然后,基于此混沌系统,采用"置乱-扩散"策略,根据不同密钥生成的不同超混沌序列,对图像矩阵进行无重复置乱和循环移位扩散,循环三次得到密文,完成加密过程;最后,对图像加密方案进行了直方图分析、密钥空间分析、相邻像素相关性分析、明文敏感性分析和信息熵分析等性能测试。其中密文图像的相关指标参数像素变化率(NPCR)和统一平均变化强度(UACI)的测试值非常接近于它们的理想期望值,信息熵的测试结果约为7. 997,也非常接近于理想期望值8。实验结果表明,此图像加密系统具有更可靠的安全性,抵抗攻击能力强,在图像安全领域具有较好的应用前景。

Two-dimensional inverse-trigonometric hyperchaotic system and its application in image encryption

In order to improve chaos complexity and provide more reliable chaotic system for image encryption, and enhance the security of image encryption algorithm, a new image encryption algorithm based on two-dimensional inverse-trigonometric hyperchaotic system was proposed. Firstly, based on one-dimensional triangular function, a two-dimensional inverse-trigonometric hyperchaotic system was constructed. Compared with some two-dimensional chaotic systems, this system had wider chaotic range, more random iteration sequences and better ergodicity by simulation experiments about bifurcation diagram and Lyapunov exponent. Then based on the proposed chaotic system, the "scrambling-diffusion" strategy was designed and different keys were given, which were used to generate different hyperchaotic sequences. The image matrix was scrambled without repetition by hyperchaotic sequences, then the scrambled sequence were shifted and diffused. So the ciphertext was obtained by looping thrice. Finally, histogram analysis, key space analysis, correlation analysis of adjacent pixels, plaintext sensitivity analysis and information entropy analysis were carried out. The test values of Number of Pixels Change Rate (NPCR) and Unified Average Changing Intersity (UACI) of ciphertext images were very close to their ideal expected values. The test results of information entropy were about 7.997, which was also very close to the expected value of 8. The experimental results show that the image encryption system has more reliable security, stronger ability to resist attacks, and had a good application prospect in the field of image security.