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A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions

This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all [Image: see text] involutory maximum distance separable (MDS) matrices over [Image: see text] . The proposed method reduces the search space complexity at the level of [Image: s...

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Autores principales: Tuncay, Gökhan, Büyüksaraçoğlu Sakallı, Fatma, Kurt Pehlivanoğlu, Meltem, Yılmazgüç, Gülsüm Gözde, Akleylek, Sedat, Sakallı, Muharrem Tolga
Formato: Online Artículo Texto
Lenguaje:English
Publicado: PeerJ Inc. 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10557520/
https://www.ncbi.nlm.nih.gov/pubmed/37810342
http://dx.doi.org/10.7717/peerj-cs.1577
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author Tuncay, Gökhan
Büyüksaraçoğlu Sakallı, Fatma
Kurt Pehlivanoğlu, Meltem
Yılmazgüç, Gülsüm Gözde
Akleylek, Sedat
Sakallı, Muharrem Tolga
author_facet Tuncay, Gökhan
Büyüksaraçoğlu Sakallı, Fatma
Kurt Pehlivanoğlu, Meltem
Yılmazgüç, Gülsüm Gözde
Akleylek, Sedat
Sakallı, Muharrem Tolga
author_sort Tuncay, Gökhan
collection PubMed
description This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all [Image: see text] involutory maximum distance separable (MDS) matrices over [Image: see text] . The proposed method reduces the search space complexity at the level of [Image: see text] , where n represents the number of all [Image: see text] invertible matrices over [Image: see text] to be searched for. Hence, this enables us to generate all [Image: see text] involutory MDS matrices over [Image: see text] and [Image: see text] . After applying global optimization technique that supports higher Exclusive-OR (XOR) gates (e.g., XOR3, XOR4) to the generated matrices, to the best of our knowledge, we generate the lightest involutory/non-involutory MDS matrices known over [Image: see text] , [Image: see text] and [Image: see text] in terms of XOR count. In this context, we present new [Image: see text] involutory MDS matrices over [Image: see text] , [Image: see text] and [Image: see text] , which can be implemented by 13 XOR operations with depth 5, 25 XOR operations with depth 5 and 42 XOR operations with depth 4, respectively. Finally, we denote a new property of Hadamard matrix, i.e., (involutory and MDS) Hadamard matrix form is, in fact, a representative matrix form that can be used to generate a small subset of all [Image: see text] involutory MDS matrices, where k > 1. For k = 1, Hadamard matrix form can be used to generate all involutory MDS matrices.
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spelling pubmed-105575202023-10-07 A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions Tuncay, Gökhan Büyüksaraçoğlu Sakallı, Fatma Kurt Pehlivanoğlu, Meltem Yılmazgüç, Gülsüm Gözde Akleylek, Sedat Sakallı, Muharrem Tolga PeerJ Comput Sci Cryptography This article presents a new hybrid method (combining search based methods and direct construction methods) to generate all [Image: see text] involutory maximum distance separable (MDS) matrices over [Image: see text] . The proposed method reduces the search space complexity at the level of [Image: see text] , where n represents the number of all [Image: see text] invertible matrices over [Image: see text] to be searched for. Hence, this enables us to generate all [Image: see text] involutory MDS matrices over [Image: see text] and [Image: see text] . After applying global optimization technique that supports higher Exclusive-OR (XOR) gates (e.g., XOR3, XOR4) to the generated matrices, to the best of our knowledge, we generate the lightest involutory/non-involutory MDS matrices known over [Image: see text] , [Image: see text] and [Image: see text] in terms of XOR count. In this context, we present new [Image: see text] involutory MDS matrices over [Image: see text] , [Image: see text] and [Image: see text] , which can be implemented by 13 XOR operations with depth 5, 25 XOR operations with depth 5 and 42 XOR operations with depth 4, respectively. Finally, we denote a new property of Hadamard matrix, i.e., (involutory and MDS) Hadamard matrix form is, in fact, a representative matrix form that can be used to generate a small subset of all [Image: see text] involutory MDS matrices, where k > 1. For k = 1, Hadamard matrix form can be used to generate all involutory MDS matrices. PeerJ Inc. 2023-09-19 /pmc/articles/PMC10557520/ /pubmed/37810342 http://dx.doi.org/10.7717/peerj-cs.1577 Text en © 2023 Tuncay et al. https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, reproduction and adaptation in any medium and for any purpose provided that it is properly attributed. For attribution, the original author(s), title, publication source (PeerJ Computer Science) and either DOI or URL of the article must be cited.
spellingShingle Cryptography
Tuncay, Gökhan
Büyüksaraçoğlu Sakallı, Fatma
Kurt Pehlivanoğlu, Meltem
Yılmazgüç, Gülsüm Gözde
Akleylek, Sedat
Sakallı, Muharrem Tolga
A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions
title A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions
title_full A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions
title_fullStr A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions
title_full_unstemmed A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions
title_short A new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (MDS) matrices over binary field extensions
title_sort new hybrid method combining search and direct based construction ideas to generate all 4 × 4 involutory maximum distance separable (mds) matrices over binary field extensions
topic Cryptography
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10557520/
https://www.ncbi.nlm.nih.gov/pubmed/37810342
http://dx.doi.org/10.7717/peerj-cs.1577
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