Modified Logistic Maps for Cryptographic Application

In this paper, definition and properties of logistic map along with orbit and bifurcation diagrams, Lyapunov exponent, and its histogram are considered. In order to expand chaotic region of Logistic map and make it suitable for cryptography, two modified versions of Logistic map are proposed. In the First Modification of Logistic map (FML), vertical symmetry and transformation to the right are used. In the Second Modification of Logistic (SML) map, vertical and horizontal symmetry and transformation to the right are used. Sensitivity of FML to initial condition is less and sensitivity of SML map to initial condition is more than the others. The total chaotic range of SML is more than others. Histograms of Logistic map and SML map are identical. Chaotic range of SML map is fivefold of chaotic range of Logistic map. This property gave more key space for cryptographic purposes.