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

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 <italic>K</italic> and 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 <italic>N_p</italic> = 2, <italic>D_KY</italic> = 2, CD= 2, <italic>K</italic> > 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.