Abstract: In order to solve the shortcomings of the fractional Fourier transform and the traditional chaotic encryption, this paper proposes a new algorithm, two dimensional chaotic image encryption algorithm, based on two-dimensional discrete fractional Fourier transform. In this algorithm, the chaotic sequence is obtained by the input key and the combination of the auxiliary key matrix with the help of the clear text image information, and then the generated intermediate cipher is used as the input of the two-dimensional discrete fractional Fourier transform. At last, through making the scrambling operation, so that the text information is very good hidden. The experimental simulation shows that this algorithm not only can effectively resist statistical attack, differential attack, but also can greatly improve the traditional fractional Fourier transform image histogram smoothing shortcomings, achieve good encryption effect.

Key words: two dimensional discrete fractional Fourier transform, double chaos, auxiliary key matrix, scrambling

摘要： 针对现今分数阶Fourier变换和传统混沌加密的不足，提出了一种基于二维离散分数阶Fourier变换的双混沌图像加密算法。该算法首先借助明文图像信息生成辅助密钥矩阵与输入密钥相结合得到混沌序列，再将生成的中间密文作为二维离散分数阶Fourier变换输入，最后进行置乱操作，使得明文信息得到很好的隐藏。通过实验仿真表明，该算法不仅能有效抵抗统计特征攻击、差分攻击，而且大大改善经传统分数阶Fourier变换后直方图像不平滑的缺点，达到很好的加密效果。

关键词: 二维离散分数阶Fourier变换, 双混沌, 辅助密钥矩阵, 置乱