| |
| Li and Yorke's seminal paper published in 1975 has provided a criterion for the existence of chaos in one-dimensional difference equations. Generally speaking, it is difficult to use this criterion to verify whether a high order polynomial discrete mapping is chaotic. Because one needs to solve several high order polynomial equations on the polynomial parameters. Firstly, this paper introduces two theorems of the existence of chaos on two kinds of specific 2n order and 2n+1 order polynomial discrete mappings. These two theorems provide chaotic parameter intervals of the specific polynomials, which satisfy the Li-Yorke criterion. Secondly, four examples are presented to verify the effectiveness of the theorems. Thirdly, by using a generalized synchronization theorem and the chaos mappings given in the four examples, a new 8-dimensional chaotic generalized synchronization system (8DCGSS) is constructed. Then a chaotic PRNG (CPRNG) is designed. The keyspace of the CPRNG is larger than 2^1117. Finally, by using the FIPS 140-2 randomness test and a generalized FIPS 140-2 randomness test, the randomness of the keystreams generated via the CPRNG is measured. The results show that the CPRNG is able to generate sound pseudorandom keystreams. |
|
| Keywords:Dynamic system theory, Chaos; Li-Yorke criterion; 2n order and 2n+1 order polynomials; Chaotic criterion theorems; Peudorandom number generator; FIPS 140-2 randomness test |
|
