Ismail Samar M, Said Lobna A, Radwan Ahmed G, Madian Ahmed H, Abu-Elyazeed Mohamed F
Faculty of IET, German University in Cairo (GUC), Cairo 11865, Egypt.
NISC Research Center, Nile University, Cairo 12588, Egypt.
J Adv Res. 2018 Feb 3;10:85-98. doi: 10.1016/j.jare.2018.01.009. eCollection 2018 Mar.
This paper presents the design of the generalized Double Humped (DH) logistic map, used for pseudo-random number key generation (PRNG). The generalized parameter added to the map provides more control on the map chaotic range. A new special map with a zooming effect of the bifurcation diagram is obtained by manipulating the generalization parameter value. The dynamic behavior of the generalized map is analyzed, including the study of the fixed points and stability ranges, Lyapunov exponent, and the complete bifurcation diagram. The option of designing any specific map is made possible through changing the general parameter increasing the randomness and controllability of the map. An image encryption algorithm is introduced based on pseudo-random sequence generation using the proposed generalized DH map offering secure communication transfer of medical MRI and X-ray images. Security analyses are carried out to consolidate system efficiency including: key sensitivity and key-space analyses, histogram analysis, correlation coefficients, MAE, NPCR and UACI calculations. System robustness against noise attacks has been proved along with the NIST test ensuring the system efficiency. A comparison between the proposed system with respect to previous works is presented.
本文介绍了用于伪随机数密钥生成（PRNG）的广义双峰（DH）逻辑映射的设计。添加到映射中的广义参数可对映射的混沌范围进行更多控制。通过操纵广义参数值，获得了具有分岔图缩放效果的新特殊映射。分析了广义映射的动态行为，包括对不动点和稳定范围、李雅普诺夫指数以及完整分岔图的研究。通过改变通用参数，可以设计任何特定映射，从而增加映射的随机性和可控性。基于使用所提出的广义DH映射生成伪随机序列，引入了一种图像加密算法，用于医学MRI和X射线图像的安全通信传输。进行了安全性分析以巩固系统效率，包括：密钥敏感性和密钥空间分析、直方图分析、相关系数、平均绝对误差（MAE）、归一化像素变化率（NPCR）和统一平均变化强度（UACI）计算。已证明系统对噪声攻击具有鲁棒性，并通过NIST测试确保了系统效率。还给出了所提出系统与先前工作的比较。
