Constructing new high-order polynomial chaotic maps and application in pseudorandom number generator

Abstract

The chaotic map have been widely applied in fields such as pseudorandom number generation(PRNG) and image encryption due to its excellent chaotic performance. In this paper, two classes of high-order polynomial chaotic maps of special form are proposed based on the Li-Yorke theorem. The dynamic behavior of the proposed maps is numerically analyzed, including bifurcation and Lyapunov exponent, and the analysis results prove the validity of the proposed conclusions. The proposed polynomial chaotic maps have a larger parameters and chaotic range, as well as a more stable Lyapunov exponent. Furthermore, based on the coupling chaotic systems, we design a pseudorandom number generator(PRNG), and the number of chaos parameters are expanded through the coupling control parameters in a PRNG. Then the performance of the pseudorandom sequence generated by the PRNG is tested and analysed. The test and analysis results show that the pseudorandom sequence has favorabble security, structural complexity, and randomness. Especially, the information entropy of 7.9998 and the key space size of 2208 exceed the recently reported pseudorandom number generators(PRNGs). In comparison with other PRNGs based on chaotic maps in the recent literature, this paper provides comprehensive performance test and analysis of the proposed PRNG and demonstrates its potential for cryptographic applications.