A Generalized Stability Theorem for Continuous Chaos Systems and Design of Pseudorandom Number Generator

This study first proposes a concept of generalized stability (GST) for continuous chaos system, which is the generalization of chaos generalized synchronization (CGS). Then this study sets up a constructive theorem of GST for continuous chaos system, which provides a general representation of GST in continuous chaos system. Using the theorem designs an 8- dimensional GST system consisting of a driving chaotic system and a driven chaotic system. Numerical simulation verifies the chaotic dynamic behaviors of such GST system, which is used to design a chaotic pseudorandom number generator (CPRNG). Using FIPS 140-2 test suite and G FIPS 140-2 test suite test the randomness of four 1,000-key streams consisting of 20,000 bits generated respectively by the CPRNG, the RC4 algorithm, the ZUC algorithm and a 6-dimensional CGS-based CPRNG. The results show that the randomness performances of the CPRNG is promising, and suggest that the statistical properties of the randomness of the sequences generated via the two CPRNGs and the two algorithms do not have significant differences. In addition, the key space of the CPRNG is larger than 21195.