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

2021/11/04 by Alvarenga, João Pedro do Valle, Machicao, Jeaneth, Bruno, Odemir
#Chaotic Dynamics (nlin.CD) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Physical sciences

paper · doi:10.48550/arxiv.2111.05101

Abstract

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.

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