A Novel Group Theoretic and Graphical Approach for Designing Cryptographically Strong Nonlinear Components of Block Ciph
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A Novel Group Theoretic and Graphical Approach for Designing Cryptographically Strong Nonlinear Components of Block Ciphers Abdul Razaq1 · Atta Ullah2 · Hanan Alolaiyan3 · Awais Yousaf4
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Substitution box is a significant and only nonlinear constituent of block cipher. S-box plays a central role in converting the intelligible message or plain text, into an enciphered format. Construction of strong S-boxes is an important area of interest for security experts. In this work, we develop a new method to evolve S-boxes with the help of coset graph for the action of PSL(2, ℤ) on projective line over the finite field GF (28), a special type of bijective map g and the symmetric group S256 The capability of the proposed S-boxes to mitigate cryptanalysis is investigated through various performance analyzing parameters. The outcomes of the comparison with the familiar S-boxes indicate that the working abilities of newly designed S-boxes are better than that of many of the well-known S-boxes. Keywords Symmetric key cryptography · S-box · Coset diagram · Nonlinearity · Bit independence criterion · SAC
* Abdul Razaq [email protected] Atta Ullah [email protected] Hanan Alolaiyan [email protected] Awais Yousaf [email protected] 1
Department of Mathematics, Division of Science and Technology, University of Education Lahore, Lahore, Pakistan
2
Department of Mathematics, National University of Technology, Islamabad, Pakistan
3
Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
4
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
13
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A. Razaq et al.
1 Introduction Recent developments in the fields of cloud computing and social networking for communication have significantly increased the amount of private user data [1, 2]. Therefore, the problem of guaranteeing privacy and security of secret data is more prominent than ever before. In the past few decades, block cryptosystems have played a decisive role in ensuring data privacy for communication and storage. The rapid growth in the modern mobile user devices has led to massive usage of network resources which results in a dramatic increase of traffic load. The massive transmission of the information through the Internet has brought about a revolution in communication and information technology in recent years, but at the same time it raised various security and privacy concerns. Therefore, the secure transmission of confidential data is a real challenge. It certainly requires a significant security level. The prime objective is to prevent unapproved access to the secret information. In order to accomplish the sufficient safety level, numerous approaches such as have been developed such as steganography, watermarking and cryptography. In this work, we are dealing with cryptography. In all cryptographic systems the block cipher is the most effective algorithm for data encryption and S-box plays a key role in
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