Designing S-boxes triplet over a finite chain ring and its application in RGB image encryption
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Designing S-boxes triplet over a finite chain ring and its application in RGB image encryption Saria Jahangir 1 & Tariq Shah 1 Received: 6 May 2019 / Revised: 6 March 2020 / Accepted: 23 April 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
In this article, we have developed an encryption technique to encrypt any kind of digital information. The main work is to construct the component of the block ciphers namely the substitution boxes (S-boxes) over an algebraic structure of finite chain ring; and then use these S-boxes in image encryption applications. The present formation is based on the finite commutative chain ring R9 = ℤ2 + uℤ2 + … + uk − 1ℤ2 (module over itself) which is exactly twice of 256. The multiplicative group of unit elements of R9 precisely has 256 elements and the set of all nonunit elements in R9 forms a submodule of module R9 consisting of 256 elements. By using this point we initiate a new 8 × 8 S-box triplet generation technique which addresses the group of units of R9 and the submodule of R9. This new construction technique of S-boxes ensures random values in the area of the initial domain of transformation. The proposed S-boxes have been examined by algebraic, statistical and texture analyses. A comparison of the expected and existing S-boxes reveals that the proposed S-boxes are comparatively better and can be used in the well known ciphers. Another goal of this work is to suggest an encryption technique for colored (RGB) images based on permutation keys and triplet of newly generated S-boxes. The outcomes of the security, statistical and the differential analyses have proved that our scheme is better for the image encryption. Keywords S-box . Finite chain ring . Submodule . Group of units . Nonlinearity and RGB image encryption
1 Introduction For last three decades, digital data has been exchanged enormously from one place to another due to development and advances in computer networking. The main concern in this exchange is to * Saria Jahangir [email protected] Tariq Shah [email protected]
1
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
Multimedia Tools and Applications
avoid any kind of manipulation, unauthenticated form, repudiation and the disintegration. Images are extensively used in the numerous progressions. Hence, the fortification of the image data from an unlicensed entree is compulsory. Image encryption and steganography play a substantial part in the field of information hiding. Swift development of network multimedia systems has been seen in recent years. The data duplication has been made easy by such developments. The ease with which flawless duplicates can be made may lead to large-scale unlicensed copying, which is a great alarm to the original images, music, films, and the books. Due to the copywrite concern, a number of technologies are being developed to guard against illegitimate replication. Keeping in view the rising demands of digital security mechanisms, we have devised a novel technique of im
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