A two-parameter modified logistic map and its application to random bit generation

Abstract

This work proposes a modified logistic map based on the system previously proposed by Han in 2019. The constructed map exhibits interesting chaos related phenomena like antimonotonicity, crisis, and coexisting attractors. In addition, the Lyapunov exponent of the map can achieve higher values, so the behavior of the proposed map is overall more complex compared to the original. The map is then successfully applied to the problem of random bit generation using techniques like the comparison between maps, XOR, and bit reversal. The proposed algorithm passes all the NIST tests, shows good correlation characteristics, and has a high key space.