Construction of nonlinear component of block cipher using coset graph

Adil Waheed; Fazli Subhan; Mazliham Mohd Suud; Muhammad Yasir Hayat Malik; Alina Mirza; Farkhanda Afzal; Adil Waheed; Fazli Subhan; Mazliham Mohd Suud; Muhammad Yasir Hayat Malik; Alina Mirza; Farkhanda Afzal

doi:10.3934/math.20231104

AIMS Mathematics

2023, Volume 8, Issue 9: 21644-21667. doi: 10.3934/math.20231104

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Construction of nonlinear component of block cipher using coset graph

1.
Faculty of Engineering and Computer Sciences, National University of Modern Languages, Islamabad, Pakistan
2.
Faculty of Computer and Information, Multimedia University, Cyberjaya, Malaysia
3.
Department of Mathematics, Division of Science and Technology, University of Education Lahore, Lahore, Pakistan
4.
MCS, National University of Sciences and Technology, Islamabad, Pakistan

Received: 24 February 2023 Revised: 26 May 2023 Accepted: 06 June 2023 Published: 07 July 2023
MSC : 05C10, 08A72

In recent times, the research community has shown interest in information security due to the increasing usage of internet-based mobile and web applications. This research presents a novel approach to constructing the nonlinear component or Substitution Box (S-box) of block ciphers by employing coset graphs over the Galois field. Cryptographic techniques are employed to enhance data security and address current security concerns and obstacles with ease. Nonlinear component is a keystone of cryptography that hides the association between plaintext and cipher-text. Cryptographic strength of nonlinear component is directly proportional to the data security provided by the cipher. This research aims to develop a novel approach for construction of dynamic S-boxes or nonlinear components by employing special linear group $ PSL(2, \mathbb{Z}) $ over the Galois Field $ GF\left({2}^{10}\right) $. The vertices of coset diagram belong to $ GF\left({2}^{10}\right) $ and can be expressed as powers of α, where α represents the root of an irreducible polynomial $ p\left(x\right) = {x}^{10}+{x}^{3}+1 $. We constructed several nonlinear components by using $ {GF}^{*}\left({2}^{10}\right) $. Furthermore, we have introduced an exceptionally effective algorithm for optimizing nonlinearity, which significantly enhances the cryptographic properties of the nonlinear component. This algorithm leverages advanced techniques to systematically search for and select optimal S-box designs that exhibit improved resistance against various cryptographic attacks.
- S-box,
- nonlinear component,
- coset diagram,
- nonlinearity,
- security,
- block cipher
Citation: Adil Waheed, Fazli Subhan, Mazliham Mohd Suud, Muhammad Yasir Hayat Malik, Alina Mirza, Farkhanda Afzal. Construction of nonlinear component of block cipher using coset graph[J]. AIMS Mathematics, 2023, 8(9): 21644-21667. doi: 10.3934/math.20231104

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Abstract

In recent times, the research community has shown interest in information security due to the increasing usage of internet-based mobile and web applications. This research presents a novel approach to constructing the nonlinear component or Substitution Box (S-box) of block ciphers by employing coset graphs over the Galois field. Cryptographic techniques are employed to enhance data security and address current security concerns and obstacles with ease. Nonlinear component is a keystone of cryptography that hides the association between plaintext and cipher-text. Cryptographic strength of nonlinear component is directly proportional to the data security provided by the cipher. This research aims to develop a novel approach for construction of dynamic S-boxes or nonlinear components by employing special linear group $ PSL(2, \mathbb{Z}) $ over the Galois Field $ GF\left({2}^{10}\right) $. The vertices of coset diagram belong to $ GF\left({2}^{10}\right) $ and can be expressed as powers of α, where α represents the root of an irreducible polynomial $ p\left(x\right) = {x}^{10}+{x}^{3}+1 $. We constructed several nonlinear components by using $ {GF}^{*}\left({2}^{10}\right) $. Furthermore, we have introduced an exceptionally effective algorithm for optimizing nonlinearity, which significantly enhances the cryptographic properties of the nonlinear component. This algorithm leverages advanced techniques to systematically search for and select optimal S-box designs that exhibit improved resistance against various cryptographic attacks.

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