Type-preserving matrices and security of block ciphers
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| Title: | Type-preserving matrices and security of block ciphers |
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| Authors: | Aragona, Riccardo, Meneghetti, Alessio |
| Source: | Advances in Mathematics of Communications. 13:235-251 |
| Publication Status: | Preprint |
| Publisher Information: | American Institute of Mathematical Sciences (AIMS), 2019. |
| Publication Year: | 2019 |
| Subject Terms: | FOS: Computer and information sciences, Computer Science - Cryptography and Security, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, 20B15, 20B35, 94A60, Group Theory (math.GR), 0102 computer and information sciences, 02 engineering and technology, Cryptosystems, Group generated by the round functions, Mixing layer, Primitive groups, Algebra and Number Theory, Computer Networks and Communications, Discrete Mathematics and Combinatorics, Applied Mathematics, Mathematics - Group Theory, Cryptography and Security (cs.CR), 01 natural sciences |
| Description: | We provide a new property, called Non-Type-Preserving, for a mixing layer which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by the round functions. Our main result is to present necessary and sufficient conditions on the structure of the binary matrix associated to the mixing layer, so that it has this property. Then we show how several families of linear maps are Non-Type-Preserving, including the mixing layers of AES, GOST and PRESENT. Finally we prove that the group generated by the round functions of an SPN cipher with addition modulo a power of 2 as key mixing function is primitive if its mixing layer satisfies this property. Moreover we generalise the definition of a GOST-like cipher using a Non-Type-Preserving matrix as mixing layer and we show, under the only assumption of invertibility of the S-Boxes, that the corresponding group is primitive. |
| Document Type: | Article |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 1930-5338 |
| DOI: | 10.3934/amc.2019016 |
| DOI: | 10.48550/arxiv.1803.00965 |
| Access URL: | https://www.aimsciences.org/article/exportPdf?id=b4f5a145-2c3a-41ab-a01d-b3e126878053 http://arxiv.org/abs/1803.00965 https://aimsciences.org/article/doi/10.3934/amc.2019016 https://ui.adsabs.harvard.edu/abs/2018arXiv180300965A/abstract https://dblp.uni-trier.de/db/journals/corr/corr1803.html#abs-1803-00965 http://dblp.uni-trier.de/db/journals/corr/corr1803.html#abs-1803-00965 https://www.aimsciences.org/article/exportPdf?id=b4f5a145-2c3a-41ab-a01d-b3e126878053 https://hdl.handle.net/11572/277643 https://doi.org/10.3934/amc.2019016 https://www.aimsciences.org/article/doi/10.3934/amc.2019016 |
| Rights: | CC BY arXiv Non-Exclusive Distribution CC 0 |
| Accession Number: | edsair.doi.dedup.....616a8fb65d0823b1b6f12f41e91ce84c |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | We provide a new property, called Non-Type-Preserving, for a mixing layer which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by the round functions. Our main result is to present necessary and sufficient conditions on the structure of the binary matrix associated to the mixing layer, so that it has this property. Then we show how several families of linear maps are Non-Type-Preserving, including the mixing layers of AES, GOST and PRESENT. Finally we prove that the group generated by the round functions of an SPN cipher with addition modulo a power of 2 as key mixing function is primitive if its mixing layer satisfies this property. Moreover we generalise the definition of a GOST-like cipher using a Non-Type-Preserving matrix as mixing layer and we show, under the only assumption of invertibility of the S-Boxes, that the corresponding group is primitive. |
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| ISSN: | 19305338 |
| DOI: | 10.3934/amc.2019016 |