A Characterization of Semi-Involutory MDS Matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909445112463360 |
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| author | Chatterjee, Tapas Laha, Ayantika |
| author_facet | Chatterjee, Tapas Laha, Ayantika |
| contents | In symmetric cryptography, maximum distance separable (MDS) matrices with computationally simple inverses have wide applications. Many block ciphers like AES, SQUARE, SHARK, and hash functions like PHOTON use an MDS matrix in the diffusion layer. In this article, we first characterize all $3 \times 3$ irreducible semi-involutory matrices over the finite field of characteristic $2$. Using this matrix characterization, we provide a necessary and sufficient condition to construct MDS semi-involutory matrices using only their diagonal entries and the entries of an associated diagonal matrix. Finally, we count the number of $3 \times 3$ semi-involutory MDS matrices over any finite field of characteristic $2$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_12842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Characterization of Semi-Involutory MDS Matrices Chatterjee, Tapas Laha, Ayantika Cryptography and Security 05B20, 12E20, 15B99 (Primary), 94A60, 94B05 (Secondary) In symmetric cryptography, maximum distance separable (MDS) matrices with computationally simple inverses have wide applications. Many block ciphers like AES, SQUARE, SHARK, and hash functions like PHOTON use an MDS matrix in the diffusion layer. In this article, we first characterize all $3 \times 3$ irreducible semi-involutory matrices over the finite field of characteristic $2$. Using this matrix characterization, we provide a necessary and sufficient condition to construct MDS semi-involutory matrices using only their diagonal entries and the entries of an associated diagonal matrix. Finally, we count the number of $3 \times 3$ semi-involutory MDS matrices over any finite field of characteristic $2$. |
| title | A Characterization of Semi-Involutory MDS Matrices |
| topic | Cryptography and Security 05B20, 12E20, 15B99 (Primary), 94A60, 94B05 (Secondary) |
| url | https://arxiv.org/abs/2406.12842 |