In this paper, a novel Extended Logistic Chaotic Map (ELCM) with two control parameters is proposed. Overcoming the major drawback of the standard Logistic and other existing chaotic maps, the ELCM not only has infinite chaotic range as well as good ergodicity, but also has a simple structure just like the Logistic map, which greatly facilitates its practical implementation and becomes very suitable for today's real-time applications. Moreover, a new color image encryption scheme based on chaos concept, DNA (Deoxyribonucleic Acid) encoding and Convolutional Neural Network (CNN) is also presented. To perform a chaotic scrambling, the ELCM is however used at different stages of the encryption process. In addition, a pre-trained AlexNet CNN is used to generate a public key. After XORing with the secret key, the latter is used, on the one hand, to generate the initials values and the control parameters of the ELCM. On the other hand, it will be split into two keys in order to generate a random grayscale image, which will then be XORed with the three components (i.e., R, G and B) of the color plaintext image. Afterward, a permutation operation, DNA encoding, diffusion operation as well as bit reversion operation are then applied to the R, G and B components. The performance evaluation demonstrates that the ELCM not only has an infinite chaotic parameter range, but also exhibits a high chaotic complexity. Besides, experimental results as well as security analysis confirm that with NPCR of 99.6287%, the designed color image encryption scheme achieves an average entropy of 7.9975 and a near zero correlation (-0.0027). Furthermore, the proposed encryption scheme is in fact of higher security level in comparison to other schemes recently presented in the literature, thus making it highly suitable for today's real-time applications.

中文翻译：

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现代图像密码系统的二参数扩展逻辑混沌映射

在本文中，提出了一种具有两个控制参数的新型扩展逻辑混沌图（ELCM）。 ELCM克服了标准Logistic和其他现有混沌映射的主要缺点，不仅具有无限的混沌范围和良好的遍历性，而且与Logistic映射一样具有简单的结构，这极大地方便了其实际实现，非常适合适用于当今的实时应用程序。此外，还提出了一种基于混沌概念、DNA（脱氧核糖核酸）编码和卷积神经网络（CNN）的新型彩色图像加密方案。然而，为了执行混沌加扰，ELCM 被用在加密过程的不同阶段。此外，预训练的 AlexNet CNN 用于生成公钥。与密钥进行异或后，一方面，后者用于生成 ELCM 的初始值和控制参数。另一方面，它将被分成两个密钥以生成随机灰度图像，然后将其与彩色明文图像的三个分量（即，R、G和B）进行异或。然后，对R、G和B分量应用置换操作、DNA编码、扩散操作以及位反转操作。性能评估表明，ELCM不仅具有无限的混沌参数范围，而且表现出很高的混沌复杂度。此外，实验结果和安全性分析证实，在NPCR为99.6287%的情况下，设计的彩色图像加密方案的平均熵为7.9975，相关性接近于零（-0.0027）。此外，与文献中最近提出的其他方案相比，所提出的加密方案实际上具有更高的安全级别，从而使其非常适合当今的实时应用。