提出一种基于Fourier变换对称性和随机多分辨率奇异值分解(R-MRSVD)的彩色图像加密算法。首先计算归一化明文图像的平均值作为logistic-exponent-sine映射的初值,并生成随机矩阵和位置索引;然后对每个颜色通道分别进行二维离散Fourier变换,根据共轭对称性仅保留一半的频谱系数,并提取实部分量和虚部分量构建实数矩阵;最后对实数矩阵进行R-MRSVD和Josephus置乱操作,得到密文图像。将明文图像的像素特征作为混沌序列的初值,保证算法具有高敏感性和高安全性,同时实值的密文便于存储和传输。对算法的解密图像质量、统计特性、密钥敏感性、抗选择明文攻击、鲁棒性等性能进行测试,仿真结果表明,所提加密算法具有可行性和安全性。

In this study, a color image encryption algorithm is proposed based on the symmetry of Fourier transform and random multiresolution singular value decomposition (R-MRSVD). First, the average value of normalized plaintext images is considered to be the initial value of logistic-exponent-sine mapping. Thus, a random matrix and position index are generated. Then, a two-dimensional discrete Fourier transform is applied to each color channel. Because of the conjugate symmetry property of Fourier transforms, only half of the Fourier transform spectrum coefficients are preserved. Further, a real matrix is constructed by extracting the real and imaginary parts. Finally, R-MRSVD is performed, and the ciphertext image is obtained using Josephus scrambling operation. The pixel characteristic of the plaintext image is considered to be the initial value of the chaotic sequence; thus, the high sensitivity and security of the algorithm can be ensured. The real-valued ciphertext image is convenient for storage and transmission. The quality of the decrypted image, statistical characteristic, key sensitivity, chosen-plaintext attack, and robustness of the algorithms are verified. The simulation results demonstrate the feasibility and security of the proposed color image encryption algorithm.