中文摘要：

该文基于离散分数随机变换和线性同余理论,提出一种单通道双彩色图像加密算法。输入的两幅RGB图像转换成相应的索引图像格式,其中一幅2维索引图像被编码为振幅部分,另一幅则被编码为空域相位掩模。分数域相位掩模由线性同余发生器（LCG）生成,并将彩色映射矩阵嵌入其中。引入光学幅相调制技术,在不增加光学元件的基础上实现了双彩色图像加密。离散分数随机变换的分数阶和线性同余函数的4个参数作为密钥提高了算法的安全性,对应所有密钥计算了输入图像和解密图像的均方误差。针对唯密文攻击,噪声叠加和抗裁剪性能分别进行了数值模拟,验证了该算法的可行性和有效性。

英文摘要：

A new single-channel double-color image encryption algorithm is proposed by combining Discrete Fractional Random Transform （DFrRT） with linear congruence theory. The two input RGB images are converted into their indexed image formats, and one of the 2D indexed image is encoded in amplitude part and the other is encoded into the spatial domain phase mask. The two color map matrixes are embedded in the fractional domain phase mask which is generated by Linear Congruential Generator （LCG）. The amplitude-phase encoding is introduced into the optical encryption system to implement the double-color image encryption algorithm without increasing other optical elements. The fractional order of DFrRT and the four parameters of the linear function are the keys to enhance the security of the proposed algorithm, and the Mean Square Error （MSE） between the decrypted images and the input ones for all keys are calculated. The performance of the proposed scheme is analyzed against ciphertext-only attack, noise addition and occlusion of the encrypted image, respectively. Numerical simulation results demonstrate the feasibility and effectiveness of the proposed method.