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

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