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
$K$
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.