Cube-root-subgroups of SL_2 over imaginary quadratic integers

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v29n2pp227240.pdf(142.84 KB)
Date
2021-09-01
Authors
Kureš, Miroslav
ORCID
0000-0001-6222-389X
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Referee
Mark
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Volume Title
Publisher
Vladimir Andrunakievich Institute of Mathematics and Computer Science
Abstract
All cube roots of the identity in the special linear group of $2\times 2$-matrices with entries in the ring of integers in $\mathbb Q[\sqrt{d}]$ are described. These matrices generate subgroups of the third order; it is shown that such subgroups may contain non-elementary matrices in the sense of P. M. Cohn. All this is viewed with respect to possible applications in lattice cryptography.
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Keywords
imaginary quadratic field, ring of integers, non-elementary matrices, special linear group, public key cryptography, lattice based cryptosystems
Citation
Computer Science Journal of Moldova. 2021, vol. 29, issue 2, p. 227-240.
http://www.math.md/publications/csjm/issues/v29-n2/13338/
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Peer-reviewed
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Published version
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en
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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International
http://creativecommons.org/licenses/by-nc-sa/4.0/
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http://hdl.handle.net/11012/201633
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