A novel chaotic system and design of pseudorandom number generator

Abstract

First this paper constructs a 3-dimensional discrete chaotic map. The dynamic behaviors of the chaotic map display chaotic attractor characteristics. Second a 6-dimensional chaotic generalized synchronic system is introduced based on the chaotic map and a chaos generalized synchronization (GS) theorem. Third using the chaotic generalized synchronic system and a transformation T form ℝ to an integer set {0, 1, ... , 255} designs a chaos-based pseudorandom number generator (CPRNG). Furthermore, some statistical tests of the CPRNG have been given. The outputs of the CPRNG are all passed the FIPS 140-2 criteria. Numerical simulation examples show that for the perturbations of the keys of the CPRNG which are larger than 10-14, the corresponding keystreams have an average 99.61% different codes which are different from the codes generated by unperturbed keys. The result suggests that the key stream of the CPRNG has sound pseudorandomness.