关键词: 量子映射, 图像加密, 分数阶Fourier变换, 混沌序列

Abstract: An image encryption algorithm based on quantum chaos and fractional Fourier transform is proposed for the traditional security problem of natural chaotic system. By introducing the quantum chaotic map, the periodic window, pseudo-random and aperiodic problems of Logistic map are solved, and the problem of floating-point arithmetic loss is improved. At the same time, the chaotic system and the fractional Fourier transform are combined to realize the scrambling of the fractional domain between the spatial domain and the frequency domain, it overcomes the shortcomings of the traditional methods only in a single domain transformation and the simple use of a program, such as the small number of parameters, the simple structure of the system, the uneven histogram and so on. The experimental results and the simulation results show that the proposed algorithm has a large key space, low computational complexity and strong sensitivity, and can effectively resist the statistics.

Key words: quantum mapping, image encryption, fractional Fourier transform, chaotic sequence