Abstract: A color image encryption method is proposed. The method uses discrete fractional random transform (DFRNT) and Arnold transform (AT) to encrypt in the luminance hue saturation color space. A color image is converted from the standard red-green-blue (RGB) space to luminance hue saturation space . The luminance component is encrypted by a method DFRNT transform, which encrypts the pixel value and the pixel position simultaneously. The hue and saturation components are encrypted using an Arnold scrambling method that scrambling pixels. Compared with the traditional double-random-phase encoding, the DFRNT encryption method can save storage space of the encryption key. At the same time, it is as safe as the traditional dual random phase coding. The fractional order of the DFRNT, the random matrix and the iteration numbers of Arnold transform are used as the encryption keys of the algorithm. The performance of the cryptographic algorithm is analyzed against the variation in fractional order, the change of Arnold transform iteration number, known-plaintext attack, noise addition and occlusion of the encrypted image. The test results show the feasibility and effectiveness of the scheme.

Key words: Color image encryption, Discrete fractional random transform, Luminance hue saturation, Arnold transform, Double-random-phase encoding

摘要： 提出一种彩色图像加密方法，该方法在亮度色调饱和度彩色空间使用离散分数随机变换（DFRNT）和Arnold变换进行加密，彩色图像从标准红、绿、蓝空间转化为亮度色调饱和度空间。其中亮度分量通过一种将像素值和像素位置同时进行加密的DFRNT进行加密；色调和饱和度分量使用一种将像素置乱的加密方法Arnold变换进行加密。与传统的双随机相位编码相比，DFRNT加密方法可以节省密钥的存储空间，同时，与传统的双随机相位编码一样安全。将DFRNT的分数阶、随机矩阵和Arnold变换的迭代次数作为该算法的加密密钥，分别使用分数阶的变化、Arnold变换迭代次数的变化、已知的明文攻击、加噪声和加密图像遮挡等攻击手段，对该加密算法进行性能测试，测试结果表明该方案的可行性和有效性。

关键词: 彩色图像加密, 离散分数随机变换, 亮度色调饱和度, Arnold变换, 双随机相位编码