Chaotical PRNG based on composition of logistic and tent maps using deep-zoom
This work addresses the need for better randomization in PRNGs and cryptographic systems, though it appears incremental as it builds on known chaotic maps with a specific technique.
The researchers tackled the problem of improving pseudo-random number generation by analyzing a composition of logistic and tent maps with a deep-zoom technique, finding that increasing the zoom parameter k enhanced randomness and outperformed existing chaotic map-based PRNGs in tests.
We proposed the deep zoom analysis of the composition of the logistic map and the tent map, which are well-known discrete unimodal chaotic maps. The deep zoom technique transforms each point of a given chaotic orbit by removing its first k-digits after the fractional part. We found that the pseudo-random qualities of the composition map as a pseudo-random number generator (PRNG) improves as the k parameter increases. This was proven by the fact that it successfully passed the randomness tests and even outperformed the k-logistic map and k-tent map PRNG. These dynamical properties show that using the deep-zoom on the composition of chaotic maps, at least on these two known maps, is suitable for better randomization for PRNG purposes as well as for cryptographic systems.