Chaotic Map Optimization for Image Encryption Using Triple Objective Differential Evolution Algorithm

Abstract

Chaotic maps used to shuffle and manipulate the image pixels are important for image encryption (IE). In this study, a novel 2D optimized chaotic map (OPMAP) using a triple-objective differential evolution (TODE) algorithm is presented for IE. A model for OPMAP with eight decision variables is empirically designed, and then its variables are determined utilizing TODE through minimizing a triple-objective function that involving Lyapunov exponent (LE), entropy and 0–1 test. OPMAP is assessed with respect to credible measurements like bifurcation, 3D phase space, LE, 0–1 test, permutation entropy (PE) and sample entropy (SE). The capability of OPMAP is then verified through an IE scheme including permutation and diffusion through various cryptanalyses: key space 2298, mean entropy 7.9995, mean correlation 13.61E-5, number of pixels changing rate (NPCR) 99.6093, unified average changing intensity (UACI) 33.4630 and encryption processing time (EPT) 0.2919 (s). A detailed review of IE schemes reported elsewhere is presented and IE performance of OPMAP is also validated by comparison with those IE schemes with and without optimization used. The 2D-OPMAP-based IE is faster and has low computational complexity. Moreover, the proposed it shows better cryptanalysis results for the most of the comparisons.

Keywords

• Chaotic map
• cryptography
• differential evolution
• image encryption