Chaotical PRNG based on composition of logistic and tent maps using deep-zoom

Abstract

We propose the deep-zoom analysis of the composition of the logistic map and the tent map, which are well-known discrete one-dimensional chaotic maps. The deep-zoom technique transforms each point of a given chaotic orbit by removing the first k-digits after decimal separator. We found that the pseudo-random qualities of the composition map as a pseudo-random number generator (PRNG) improve as the k parameter increases. This was evidenced by the fact that it successfully passed the randomness tests and even outperformed the k-logistic map and the k-tent map PRNG. These dynamic properties show that the application of deep-zoom to the composition of chaotic maps, at least to these two well-known maps, is suitable for better randomization for PRNG purposes as well as for cryptographic systems.