Second-Order Chaotic Maps With Random Coefficients to Generate Complex Chaotic Sequences for High-Security Image Encryption

Abstract

Chaotic maps have been widely applied on image encryption for their complexity and sensitivity to key variation. In this work, we propose second-order chaotic maps with optimized random coefficients to generate chaotic sequences for image encryption. Two screening conditions are proposed to identify 300 candidate chaotic maps in terms of complexity indices $K$ and spectral entropy (SE). A particle swarm optimization algorithm is developed to search for the optimal chaotic maps under eight different weighting schemes. The optimal chaotic maps can achieve $N_{p} = 2$ , $D_{KY} = 2$ , CD $= 2$ , $K > 0.9$ , SE $> 0.9$ and PE $> 0.7$ . Key sensitivity analysis on all the system parameters and initial values confirms high security of the optimal chaotic maps. A hybrid sequence generation (HSG) scheme is also proposed to further reduce the image encryption time.

Keywords

• Image encryption
• chaotic map
• chaotic sequence
• key sensitivity