Generation algorithm and applications of a pseudorandom number based on fractals

A generation algorithm of the pseudorandom number is proposed based on the theory of the Hilbert-Peano curve fractals in Hilbert space. A random seed image is copied, and randomly rescaled, shifted and rotated iteratively until the whole space is occupied. The algorithm has the features of simplicity, high efficiency, better parameter controllability and cannot be inverse. It can be applied to the field of information security as a security key generation algorithm. As an example, the algorithm has been used in the XOR-based stream cipher image encryption technique. Satisfactory results have been demonstrated numerically.