关键词: Fibonacci模数列, Fibonacci矩阵, 猫映射, 最佳周期, 图像置乱

Abstract: The periodicity theorems of modular series of Fibonacci series were firstly presented, and then the periodicity property of Fibonacci _Q transform matrix was generalized. The relationship between the period of the Fibonacci _Q matrix and that of cat map was discussed, and the inherent relationship between the period of cat map and that of series generated from Fibonacci series was disclosed. The best transform period was secondly defined, and the best periodicity theorem for cat map was given. Finally, the relevant theory was verified correct by several simulation experiments of cat map in image scrambling, which provided mathematical foundation for image scrambling.

Key words: Fibonacci mode series, Fibonacci matrix, cat map, best period, image scrambling