A fundamental domain in the special linear group $SL_2(\mathbb{f}_p[x])$ and secret sharing on its basis
Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 7-16
Voir la notice de l'article provenant de la source Math-Net.Ru
The problem of developing the mathematical foundations of modular secret sharing in the special linear group over the ring of polynomials in one variable over the finite Galois field with $p$ elements is being solved. Secret sharing schemes should meet a large number of requirements: perfectness and ideality of a scheme, possibility of verification, changing a threshold without participation of a dealer, implementation of a non-threshold access structure and some others. Every secret sharing scheme developed to date does not fully satisfy all these requirements. The development of a scheme on a new mathematical basis is intended to expand the list of these configurations, thereby creating more possibilities for a user to choose the optimal option. A fundamental domain with respect to the action of the main congruence subgroup by right shifts in the special linear group of dimension 2 over the ring of polynomials is constructed. On this basis, methods for modular threshold secret sharing and its reconstruction are proposed.
Keywords:
a special linear group, a congruence subgroup, a fundamental domain, modular secret sharing, a threshold access structure.
@article{TIMB_2024_32_2_a0,
author = {G. V. Matveev and A. A. Osinovskaya and V. I. Yanchevskiǐ},
title = {A fundamental domain in the special linear group $SL_2(\mathbb{f}_p[x])$ and secret sharing on its basis},
journal = {Trudy Instituta matematiki},
pages = {7--16},
publisher = {mathdoc},
volume = {32},
number = {2},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a0/}
}
TY - JOUR
AU - G. V. Matveev
AU - A. A. Osinovskaya
AU - V. I. Yanchevskiǐ
TI - A fundamental domain in the special linear group $SL_2(\mathbb{f}_p[x])$ and secret sharing on its basis
JO - Trudy Instituta matematiki
PY - 2024
SP - 7
EP - 16
VL - 32
IS - 2
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a0/
LA - ru
ID - TIMB_2024_32_2_a0
ER -
%0 Journal Article
%A G. V. Matveev
%A A. A. Osinovskaya
%A V. I. Yanchevskiǐ
%T A fundamental domain in the special linear group $SL_2(\mathbb{f}_p[x])$ and secret sharing on its basis
%J Trudy Instituta matematiki
%D 2024
%P 7-16
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a0/
%G ru
%F TIMB_2024_32_2_a0
G. V. Matveev; A. A. Osinovskaya; V. I. Yanchevskiǐ. A fundamental domain in the special linear group $SL_2(\mathbb{f}_p[x])$ and secret sharing on its basis. Trudy Instituta matematiki, Tome 32 (2024) no. 2, pp. 7-16. http://geodesic.mathdoc.fr/item/TIMB_2024_32_2_a0/