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Proceedings of the Seventh International Conference on Mathematics and Computing pp 725–736Cite as

On the Construction of \(4 \times 4\) Lightweight Involutory MDS Matrices Over \(\mathbb {F}_{2^{8}}\)

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1412))

Abstract

In this paper, we consider the problem of building lightweight maximum distance separable (MDS) linear layers for substitution permutation networks (SPNs) ciphers. We focus on the construction of \(4 \times 4\) involutory MDS matrices which can be implemented by the lightest (to the best of our knowledge) exclusive OR (XOR) count over \(\mathbb {F}_{2^{8}}\). We handle local optimization techniques as well as global optimization techniques, then we give \(4 \times 4\) involutory MDS matrices which require the best implementation cost of 155 XOR gates, in terms of local optimization over \(\mathbb {F}_{2^{8}}\). Moreover, we generate a new \(4 \times 4\) involutory MDS matrix over \(\mathbb {F}_{2^{8}}\) that can be implemented by only 90 XOR gates by using a global optimization technique.

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Acknowledgements

Meltem Kurt Pehlivanoğlu is partially supported by the Scientific Research Project Department of Kocaeli University under the Project No: 2017/078.

Author information

Authors and Affiliations

  1. Kocaeli University, 41001, Kocaeli, Turkey

    Meltem Kurt Pehlivanoğlu

  2. Trakya University, 22030, Edirne, Turkey

    Fatma Büyüksaraçoğlu Sakalli & Muharrem Tolga Sakalli

  3. Ondokuz Mayis University, 55200, Samsun, Turkey

    Sedat Akleylek

Authors
  1. Meltem Kurt Pehlivanoğlu
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  2. Fatma Büyüksaraçoğlu Sakalli
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  3. Sedat Akleylek
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  4. Muharrem Tolga Sakalli
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Corresponding author

Correspondence to Meltem Kurt Pehlivanoğlu .

Editor information

Editors and Affiliations

  1. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, India

    Debasis Giri

  2. The University of Texas at San Antonio, San Antonio, TX, USA

    Kim-Kwang Raymond Choo

  3. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

    Saminathan Ponnusamy

  4. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  5. Department of Computer Engineering, Ondokuz Mayis University, Atakum, Turkey

    Sedat Akleylek

  6. Department of Information Technology, Indian Institute of Engineering Science and Technology, West Bengal, India

    Santi Prasad Maity

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Cite this paper

Kurt Pehlivanoğlu, M., Büyüksaraçoğlu Sakalli, F., Akleylek, S., Tolga Sakalli, M. (2022). On the Construction of \(4 \times 4\) Lightweight Involutory MDS Matrices Over \(\mathbb {F}_{2^{8}}\). In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_53

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