Exploration of topologies of coupled nonlinear maps (Chaos theory)

Published In 21th International Conference on Soft Computing MENDEL 2015, Brnö, Czech Republic, June 23-25, 2015, R. Matoušek (ed.), 223-236International audienceWe explore several topologies of network of 1-D coupled chaotic mapping (mainly tent map and logistic map) in order to obtain good Chaotic Pseudo Random Number Generators (CPRNG). We focus first on two-dimensional networks. Two coupled maps are studied: TTL(RC) non-alternative, and TTL(SC) alternative. In this case, those networks are equivalent to 2-D maps which achieve excellent random properties and uniform density in the phase plane, thus guaranteeing maximum security when used for chaos based cryptography.Moreover an extra new nonlinear CPRNG: MTTL(SC,2) is proposed. In addition, we explore higher dimension and the proposed ring coupling with injection mechanism enables us to achieve the strongest security requirement