A One-dimensional Discrete Map Chaos Criterion Theorem with Applications in Pseudo-random Number Generator
ZANG Hongyan① LI Jiu① LI Guodong②
①(Mathematics and Physics School, University of Science and Technology Beijing, Beijing 100083, China) ②(College of Applied Mathematics, Xinjiang University of Finance and Economics, Urumchi 830012, China)
Abstract：A novel one-dimensional discrete chaotic criterion is firstly constructed by studying the modular operation of the discrete dynamical systems. The judgement of the Marotto theorem is used to prove that the suggested dynamical systems are chaotic. Secondly, several special chaotic systems satisfied with the conditions
of this paper are given, and the bifurcation diagram and Lyapunov exponential spectrum are also analyzed. Numerical simulations show that the proposed chaotic systems have the positive Lyapunov exponent, which indicates the accuracy of the proposed theory. Additionally, a Pseudo-Random Number Generator (PRNG) is
also designed based on the given new chaotic system. Using SP800-22 test suit, the results show that the output sequence of PRNG has good pseudorandom. Finally, as an application of the PRNG, an image encryption algorithm is given. The proposed encryption scheme is highly secure Key space of 2747 and can resist against the statistical and exhaustive attacks based on the experimental results.
