Generalized Stability Theorem for Non-autonomous Differential Equation with Application

This paper proposes a definition of generalized stability (GST) for non-autonomous differential equation (NDE), which is an extension of generalized synchronization for NDE. Then, a constructive theorem for NDE is introduced. Based on the GST for NDE, this article constructs a novel 8-dimensional GST system. Numerical simulations show that the dynamic behaviors of the GST system have significant chaotic attractor characteristics. As an application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST for NDE. Using the FIPS 140-2 test suite and Generalized FIPS140-2 test suite, we test the randomness of three 1,000 key streams consisting of 20,000 bits generated by the CPRNG, the RC4 algorithm and the ZUC algorithm, respectively. The numerical simulations show that 100% key streams have passed the FIPS 140-2 test suite via the CPRNG, while 98.7% key streams have passed the Generalized FIPS 140-2 test suite. Also, the SP800-22 test suite is used to test the randomness of four 100 key streams consisting of 106 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm and the KECCAK Hash Function algorithm PRNG, respectively. The results show that the randomness performances of the CPRNGis promising. Besides, the key space of the CPRNG is larger than 2 1195, which is large enough to do against brute-force attacks.