Received June 8, 2021, accepted June 22, 2021, date of publication July 1, 2021, date of current version July 13, 2021. Digital Object Identifier 10.1109/ACCESS.2021.3094129 A Technique for Securing Multiple Digital Images Based on 2D Linear Congruential Generator, Silver Ratio, and Galois Field ABDUL GAFFAR 1 , (Member, IEEE), ANAND B. JOSHI 1 , SONALI SINGH 1 , VISHNU NARAYAN MISHRA 2 , HAMURABI GAMBOA ROSALES 3 , LIANG ZHOU 4 , ARVIND DHAKA 5 , AND LAKSHMI NARAYAN MISHRA 6 1 Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh 226007, India 2 Department of Mathematics, Indira Gandhi National Tribal University, Amarkantak, Madhya Pradesh 484887, India 3 Faculty of Electrical Engineering, Autonomous University of Zacatecas, Zacatecas 98000, Mexico 4 Center for Medicine Intelligent and Development, China Hospital Development Institute, Shanghai Jiao Tong University, Shanghai 200240, China 5 Department of Computer and Communication Engineering, Manipal University Jaipur, Jaipur 303007, India 6 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore, Tamil Nadu 632014, India Corresponding authors: Arvind Dhaka (arvind.neomatrix@gmail.com) and Vishnu Narayan Mishra (vishnunarayanmishra@gmail.com) This work was supported in part by the Universidad Autonoma de Zacatecas, Mexico, in part by the Consejo Nacional de Ciencia y Tecnología (CONACYT) Mexico and the National Natural Science Foundation of China under Grant 82072228 and Grant 92048205, in part by the Foundation of National Key Research and Development Program of China under Grant 2020YFC2008700, in part by the Foundation of Shanghai Municipal Commission of Economy and Informatization under Grant 202001007, and in part by the Foundation of Shanghai Jiao Tong University under Grant CHDI-2019-C-02. ABSTRACT Security of multiple digital images over an unsecured channel is a current area of research in the field of image cryptography. Several techniques have been proposed for this purpose. However, the main drawbacks of the existing techniques are as follows: the existing techniques can be applied merely to the grayscale or the truecolor images; the size of the cipher (output) image is bigger than that of the plain (input) images; the authors have used a large number of parameters in the encryption/decryption process, besides the secret key; and the cipher/decipher rounds use the same key for encryption/decryption process. The proposed technique, which is based on a two-dimensional (2D) Linear Congruential Generator (LCG), silver ratio, and Galois field, is designed not merely to secure multiple digital images, namely, three truecolor, nine grayscale, and seventy-two binary images of different sizes, simultaneously, but also to address the above drawbacks. The designed technique achieves both confusion and diffusion properties essential for a secure cryptosystem. Also, the technique is empirically assessed via several statistical and security evaluation metrics, such as key sensitivity, histogram, chi-square, entropy, number of pixel change rate, structural similarity index measure, processing time, etc. The results of these evaluation metrics prove the efficiency and robustness of the designed technique. INDEX TERMS Digital images, multiple image encryption, 2D Linear Congruential Generator (LCG), silver ratio, Galois field. I. INTRODUCTION Secure communication of digital images (raster, vector, or both) over an unsecured channel has been a subject of major concern, cause in the modern era, these are frequently used for exchanging information at a lower (personal) level as well as at a higher (governmental) level. Nowadays, researchers are working on the techniques/methods that can The associate editor coordinating the review of this manuscript and approving it for publication was Mehdi Sookhak . secure multiple digital images, simultaneously. In this con- text, several methods have been proposed, which are designed either for the grayscale or the truecolor images. So, there is a need of a technique that encrypts/secures both types of images, simultaneously. The proposed technique, which is based on a two-dimensional (2D) Linear Congruential Gener- ator (LCG) [1], the silver ratio [2], and the Galois field [3] is designed to fill this gap. Moreover, besides multiple grayscale and truecolor images, the proposed technique is also applica- ble to the multiple binary images. VOLUME 9, 2021 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/ 96125