Publication detail

Cube-root-subgroups of SL_2 over imaginary quadratic integers

KUREŠ, M.

English title

Cube-root-subgroups of SL_2 over imaginary quadratic integers

Type

journal article in Web of Science

Language

en

Original 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.

English 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.

Keywords in English

imaginary quadratic field, ring of integers, non-elementary matrices, special linear group, public key cryptography, lattice based cryptosystems

Released

01.09.2021

Publisher

Vladimir Andrunakievich Institute of Mathematics and Computer Science

Location

Chisinau

ISSN

1561-4042

Volume

29

Number

2

Pages from–to

227–240

Pages count

14

BIBTEX


@article{BUT172038,
  author="Miroslav {Kureš},
  title="Cube-root-subgroups of SL_2 over imaginary quadratic integers",
  year="2021",
  volume="29",
  number="2",
  month="September",
  pages="227--240",
  publisher="Vladimir Andrunakievich Institute of Mathematics and Computer Science",
  address="Chisinau",
  issn="1561-4042"
}