In recent years, many image encryption approaches have been proposed on the basis of chaotic maps. The various types of chaotic maps such as one-dimensional and multi-dimensional have been used to generate the secret keys. Chaotic maps require some parameters and value assignment to these parameters is very crucial. Because, poor value assignments may make the chaotic map un-chaotic. Therefore, hyper-parameter tuning of chaotic maps is required. Recently, meta-heuristic based image encryption approaches have been designed by researchers to resolve this issue. However, the majority of the techniques suffer from poor computational speed and stuck in local optima problems. Therefore, in this study, a strength Pareto evolutionary algorithm-II based meta-heuristic approach is proposed to tune the hyper-parameters of the four-dimensional chaotic map. The proposed approach is also implemented in a parallel fashion to enhance the computational speed. The effectiveness of the proposed approach is evaluated through extensive experiments. Comparative analyses show that the proposed approach outperforms the competitive approaches in terms of entropy, NPCR, UACI, and PSNR by $0.9834$0.9834 , $ 1.0728$1.0728 , $ 0.9134$0.9134 , and $ 0.8971\%$0.8971% , respectively.

中文翻译：

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基于并行强度帕累托进化算法的图像加密

近年来，已经基于混沌映射提出了许多图像加密方法。诸如一维和多维的各种类型的混沌图已经用于生成秘密密钥。混沌映射需要一些参数，并且为这些参数分配值非常关键。因为，差的价值分配可能会使混沌图变得不混乱。因此，需要对混沌映射进行超参数调整。最近，研究人员已设计了基于元启发式的图像加密方法来解决此问题。但是，大多数技术的计算速度较差，并且陷入局部最优问题。因此，在本研究中，提出了一种基于强度帕累托进化算法-II的元启发式方法来调整二维混沌图的超参数。所提出的方法也以并行方式实现以提高计算速度。通过大量实验评估了该方法的有效性。对比分析表明，在熵，NPCR，UACI和PSNR方面，所提方法优于竞争方法。$ 0.9834 $0.9834 ， $ 1.0728 $1.0728 ， $ 0.9134 $0.9134 和 $ 0.8971 \％$0.8971％ ， 分别。