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A dynamic nonlinear transform arithmetic for improving the properties chaos-based PRNG

Chaotic systems have many excellent properties which make them attractive in designing pseudorandom number generator (PRNG). However due to the degeneration phenomenon, the property of chaos-based PRNG with finite precision is poor, e.g. short cycle-length, non-ideal distribution, etc. Therefore, a high efficiency dynamic nonlinear transform arithmetic, which is used to improving the properties of chaos-based PRNG, is designed. Using the novel arithmetic, both cycle-length and the distribution property are guaranteed. Using group theory and information theory, it is proved that processed by the DNT arithmetic, the cycle-length of the output sequence is no less than 256!. While implemented on FPGA platform, the processing speed of the dynamic nonlinear transforming arithmetic is no less than 1Gbps.