| Summary: | 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 <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">$N_{p} = 2$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$D_{KY} = 2$ </tex-math></inline-formula>, CD <inline-formula> <tex-math notation="LaTeX">$= 2$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$K > 0.9$ </tex-math></inline-formula>, SE <inline-formula> <tex-math notation="LaTeX">$> 0.9$ </tex-math></inline-formula> and PE <inline-formula> <tex-math notation="LaTeX">$> 0.7$ </tex-math></inline-formula>. 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.
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