Monoidal categories, representation gap and cryptography
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913229844774912 |
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| author | Khovanov, Mikhail Sitaraman, Maithreya Tubbenhauer, Daniel |
| author_facet | Khovanov, Mikhail Sitaraman, Maithreya Tubbenhauer, Daniel |
| contents | The linear decomposition attack provides a serious obstacle to direct applications of noncommutative groups and monoids (or semigroups) in cryptography. To overcome this issue we propose to look at monoids with only big representations, in the sense made precise in the paper, and undertake a systematic study of such monoids. One of our main tools is Green's theory of cells (Green's relations).
A large supply of monoids is delivered by monoidal categories. We consider simple examples of monoidal categories of diagrammatic origin, including the Temperley-Lieb, the Brauer and partition categories, and discuss lower bounds for their representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01805 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Monoidal categories, representation gap and cryptography Khovanov, Mikhail Sitaraman, Maithreya Tubbenhauer, Daniel Representation Theory Cryptography and Security Group Theory Quantum Algebra Primary: 18M05, 20M30, Secondary: 94A60 The linear decomposition attack provides a serious obstacle to direct applications of noncommutative groups and monoids (or semigroups) in cryptography. To overcome this issue we propose to look at monoids with only big representations, in the sense made precise in the paper, and undertake a systematic study of such monoids. One of our main tools is Green's theory of cells (Green's relations). A large supply of monoids is delivered by monoidal categories. We consider simple examples of monoidal categories of diagrammatic origin, including the Temperley-Lieb, the Brauer and partition categories, and discuss lower bounds for their representations. |
| title | Monoidal categories, representation gap and cryptography |
| topic | Representation Theory Cryptography and Security Group Theory Quantum Algebra Primary: 18M05, 20M30, Secondary: 94A60 |
| url | https://arxiv.org/abs/2201.01805 |