Abstract: A nonlinear image encryption algorithm based on random Fractional Mellin Fransform (FrMT) was proposed to get rid of the potential insecurity problem of the linear encryption system. The random FrMT was constructed by combining log-polar transformation with random Fractional Fourier Fransform (FrFT), and a real-valued symmetrical random matrix was generated by Linear Congruential Generator (LCG) in randomizing process. The real value input image was encrypted by random FrMT which made the encryption be nonlinear, and the output ciphertext of the FrMT was also real-valued, which was convenient for storage and transmission. The encryption algorithm had three keys that were the parameters of LCG. Compared with FrMT, the fractional order key of random FrMT was more sensitive. The numerical simulation results demonstrate that the encryption algorithm is against common attacks, and sensitive to keys with good security.

Key words: image encryption, Fractional Mellin Transform (FrMT), Fractional Fourier Transform (FrFT), linear congruence, nonlinear encryption

摘要： 为了消除线性加密系统的安全隐患，提出了一种基于随机分数梅林变换的非线性图像加密算法。结合对数—极坐标变换和随机分数傅里叶变换构造了随机分数梅林变换，随机化过程用到的实对称随机矩阵由线性同余函数生成。输入的实值图像经随机分数梅林变换非线性加密，得到便于存储和传输的实值密文。该算法增加了线性同余函数的3个参数作为密钥，与分数梅林变换相比，随机分数梅林变换的分数阶密钥的敏感性更强。数值模拟表明该算法有较强的抗攻击能力，密钥灵敏度高，具有良好的安全性

关键词: 图像加密, 分数梅林变换, 分数傅里叶变换, 线性同余, 非线性加密