On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form
Maximum Distance Separable (MDS) matrices are used as the main component of diffusion layers in block ciphers. MDS matrices have the optimal diffusion properties and the maximum branch number, which is a criterion to measure diffusion rate and security against linear and differential cryptanalysis....
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10086484/ |
| _version_ | 1827963797539651584 |
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| author | Meltem Kurt Pehlivanoglu Fatma Buyuksaracoglu Sakalli Sedat Akleylek Muharrem Tolga Sakalli |
| author_facet | Meltem Kurt Pehlivanoglu Fatma Buyuksaracoglu Sakalli Sedat Akleylek Muharrem Tolga Sakalli |
| author_sort | Meltem Kurt Pehlivanoglu |
| collection | DOAJ |
| description | Maximum Distance Separable (MDS) matrices are used as the main component of diffusion layers in block ciphers. MDS matrices have the optimal diffusion properties and the maximum branch number, which is a criterion to measure diffusion rate and security against linear and differential cryptanalysis. However, it is a challenging problem to construct hardware-friendly MDS matrices with optimal or close to optimal circuits, especially for involutory ones. In this paper, we consider the generalized subfield construction method from the global optimization perspective and then give new <inline-formula> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> involutory MDS matrices over <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{2^{3}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{2^{5}}$ </tex-math></inline-formula>. After that, we present 1,176 (<inline-formula> <tex-math notation="LaTeX">$=28\times 42$ </tex-math></inline-formula>) new <inline-formula> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> involutory and MDS diffusion matrices by 33 XORs and depth 3. This new record also improves the previously best-known cost of 38 XOR gates. |
| first_indexed | 2024-04-09T17:04:46Z |
| format | Article |
| id | doaj.art-e713ab78569e45f0ac9a6730fcdc6d13 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-04-09T17:04:46Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-e713ab78569e45f0ac9a6730fcdc6d132023-04-20T23:00:17ZengIEEEIEEE Access2169-35362023-01-0111327083271510.1109/ACCESS.2023.326292410086484On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield FormMeltem Kurt Pehlivanoglu0https://orcid.org/0000-0002-7581-9390Fatma Buyuksaracoglu Sakalli1https://orcid.org/0000-0002-6100-6655Sedat Akleylek2https://orcid.org/0000-0001-7005-6489Muharrem Tolga Sakalli3https://orcid.org/0000-0002-6322-0989Department of Computer Engineering, Faculty of Engineering, Kocaeli University, Kocaeli, TurkeyDepartment of Computer Engineering, Faculty of Engineering, Trakya University, Edirne, TurkeyCyber Security and Information Technologies Research and Development Center, Ondokuz Mayis University, Samsun, TurkeyDepartment of Computer Engineering, Faculty of Engineering, Trakya University, Edirne, TurkeyMaximum Distance Separable (MDS) matrices are used as the main component of diffusion layers in block ciphers. MDS matrices have the optimal diffusion properties and the maximum branch number, which is a criterion to measure diffusion rate and security against linear and differential cryptanalysis. However, it is a challenging problem to construct hardware-friendly MDS matrices with optimal or close to optimal circuits, especially for involutory ones. In this paper, we consider the generalized subfield construction method from the global optimization perspective and then give new <inline-formula> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> involutory MDS matrices over <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{2^{3}}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\mathbb {F}_{2^{5}}$ </tex-math></inline-formula>. After that, we present 1,176 (<inline-formula> <tex-math notation="LaTeX">$=28\times 42$ </tex-math></inline-formula>) new <inline-formula> <tex-math notation="LaTeX">$4 \times 4$ </tex-math></inline-formula> involutory and MDS diffusion matrices by 33 XORs and depth 3. This new record also improves the previously best-known cost of 38 XOR gates.https://ieeexplore.ieee.org/document/10086484/Diffusion layersgeneralized subfield constructionglobal optimizationlightweight cryptographyMDS matrices |
| spellingShingle | Meltem Kurt Pehlivanoglu Fatma Buyuksaracoglu Sakalli Sedat Akleylek Muharrem Tolga Sakalli On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form IEEE Access Diffusion layers generalized subfield construction global optimization lightweight cryptography MDS matrices |
| title | On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form |
| title_full | On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form |
| title_fullStr | On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form |
| title_full_unstemmed | On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form |
| title_short | On the Construction of New Lightweight Involutory MDS Matrices in Generalized Subfield Form |
| title_sort | on the construction of new lightweight involutory mds matrices in generalized subfield form |
| topic | Diffusion layers generalized subfield construction global optimization lightweight cryptography MDS matrices |
| url | https://ieeexplore.ieee.org/document/10086484/ |
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