Cube-root-subgroups of SL_2 over imaginary quadratic integers

Cube-root-subgroups of SL_2 over imaginary quadratic integers

WoS Article

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.

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.

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

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

KUREŠ, M.

2022

01.09.2021

Vladimir Andrunakievich Institute of Mathematics and Computer Science

Chisinau

1561-4042

Computer Science Journal of Moldova

29

2

Republic of Moldova

227

240

14

http://www.math.md/publications/csjm/issues/v29-n2/13338/

http://hdl.handle.net/11012/201633

v29-n2-(pp227-240)