最优解与二维离散分数阶Fourier的双混沌加密算法  

The optimal solution and two-dimensional discrete fractional Fourier double chaotic encryption algorithm

作　　者：汪乐乐 李国东[1] WANG Lele;LI Guodong(School of Applied Mathematics, Xinjiang University of Finance and Economics, Urumqi 830012, China)

机构地区：[1]新疆财经大学应用数学学院,乌鲁木齐830012

出　　处：《中国科技论文》2018年第17期2024-2031,共8页China Sciencepaper

基　　金：国家自然科学基金资助项目(11461063);国家社会科学基金资助项目(14BTJ021);新疆维吾尔自治区普通高等学校人文社会科学重点研究基地基金资助项目(050315B03);新疆维吾尔自治区自然科学基金资助项目(2017D01A24)

摘　　要：针对传统的自然混沌在加密系统上的不足和安全系数较低的问题,提出了二维离散分数阶Fourier变换的双混沌图像加密算法,该算法首先借助Henon映射与分数阶Fourier变换改进得到优化算法,再将经过优化算法得到的密文图像作为输入,按照最优解序列的排序,综合Logistic混沌,得到最终的密文图像;将混沌系统和Fourier变换结合起来,使得明文信息得到很好的隐藏,实现了空间域和频域的置乱。仿真实验结果表明,改进的算法达到了比较好的加密效果,不仅敏感性强,密钥空间大,而且能够有效地抵御攻击,在图像信息安全方面有一定的应用价值。To solve the shortcomings of the traditional chaotic encryption and problems of low security,the double-chaotic image encryption algorithm based on fractional Fourier transform is proposed. In this algorithm, the optimization algorithm is derived by Henon mapping and fractional Fourier transforms, then the ciphertext image obtained by the optimization algorithm is taken as input. According to the sequence of the optimal solution, the Logistic chaos is synthesized to obtain the final ciphertext image. Combining chaotic systems and Fourier transforms, this algorithm allows the plaintext to be well hidden, spatial and frequency domain scrambling is achieved. Experiment results show that the improved encryption algorithm achieves better encryption effect. It not only has strong sensitivity and large key space, but also can resist attacks effectively.It has certain application value in image information security.

关 键 词：离散余弦变换 二维离散分数阶Fourier变换 图像加密 混沌加密 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]