RO  EN

## Cube-root-subgroups of SL2 over imaginary quadratic integers

Authors: Miroslav Kureš
Keywords: Imaginary quadratic field, ring of integers, non-elementary matrices, special linear group, public-key cryptography, lattice-based cryptosystems.

### 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.

Brno University of Technology
Technická 2, 61669 Brno, Czechia
Phone: +420 541142714
E-mail:

0.14 Mb