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# Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Dehornoy, Patrick / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura

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Volume 9, Issue 1

# Public-key cryptosystem based on invariants of diagonalizable groups

František Marko
/ Alexandr N. Zubkov
• Sobolev Institute of Mathematics, Siberian Branch of Russian Academy of Science (SORAN), Omsk, Pevtzova 13, 644043, Russia
• Email
• Other articles by this author:
/ Martin Juráš
Published Online: 2017-04-19 | DOI: https://doi.org/10.1515/gcc-2017-0003

## Abstract

We develop a public-key cryptosystem based on invariants of diagonalizable groups and investigate properties of such a cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of these cryptosystem and show that it is necessary to restrict the set of parameters of the system to prevent various attacks (including linear algebra attacks and attacks based on the Euclidean algorithm).

MSC 2010: 94A60; 11T71

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Published Online: 2017-04-19

Published in Print: 2017-05-01

This publication was made possible by an NPRF award NPRP 6-1059-1-208 from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.

Citation Information: Groups Complexity Cryptology, Volume 9, Issue 1, Pages 31–54, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144,

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