Generalized logistic map and its application in chaos based cryptography

Abstract

The logistic map is commonly used in, for example, chaos based cryptography. However, its properties do not render a safe construction of encryption algorithms. Thus, the scope of the paper is a proposal of generalization of the logistic map by means of a wellrecognized family of chaotic maps. In the next step, an analysis of Lyapunov exponent and the distribution of the iterative variable are studied. The obtained results confirm that the analyzed model can safely and effectively replace a classic logistic map for applications involving chaotic cryptography.