An image encryption scheme based on an optimal chaotic map derived by multi-objective optimization using ABC algorithm

A novel optimal chaotic map (OCM) is proposed for image encryption scheme (IES). The OCM is constructed using a multi-objective optimization strategy through artificial bee colony (ABC) algorithm. An empirical model for the OCM with four unknown variables is first constituted, and then, these variables are optimally found out using ABC for minimizing the multi-objective function composed of the information entropy and Lyapunov exponent (LE) of the OCM. The OCM shows better chaotic attributes in the evaluation analyses using metrics such as bifurcation, 3D phase space, LE, permutation entropy (PE) and sample entropy (SE). The encrypting performance of the OCM is demonstrated on a straightforward IES and verified by various cryptanalyses that compared with many reported studies, as well. The main superiority of the OCM over the studies based on optimization is that it does not require any optimization in the encrypting operation; thus, OCM works standalone in the encryption. However, those reported studies use ciphertext images obtained through encrypting process in every cycle of optimization algorithm, resulting in long processing time. Therefore, the IES with OCS is faster than the others optimization-based IES. Furthermore, the proposed IES with the OCM manifests satisfactory outcomes for the compared results with the literature.