Image encryption based on a new 2D logistic adjusted logistic map

Abstract

This paper proposes an encryption scheme based on a new 2-dimensional chaotic map. The new 2D chaotic map is derived from the idea of giving the two outputs of a 2D logistic map to two separate 1-dimensional logistic maps. The resulting 2D chaos based pseudo-random number generator is demonstrated to have significantly better randomness and unpredictability characteristics in terms of Lyapunov exponents as well as trajectory plots, in comparison to some recently proposed schemes based on other 2D chaotic maps. This new 2D chaotic map is then used to implement encryption of images. The proposed encryption scheme is demonstrated to be significantly better in terms of the required computational effort. For the proposed scheme, the commonly used measures of security, unpredictability and sensitivity to initial states are successfully established with the help of a set of standard simulation results.