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Cryptanalysis of a system using matrices over group rings

Cryptanalysis of a system using matrices over group rings Abstract In several recent works of D. Kahrobaei, C. Koupparis, and V. Shpilrain, public-key protocols have been proposed which depend on the difficulty of computing discrete logarithms in matrix rings over group rings. In particular, the specific ring of 3×3 matrices over 𝔽 7 S 5 ${\mathbb {F}_7S_5}$ has been proposed for use in some of these protocols. In this paper, we show that the discrete logarithm problem in this matrix ring can be solved on a modern PC in seconds, and we give a solution to the challenge problem over 𝔽 2 S 5 ${\mathbb {F}_2S_5}$ proposed in one of the aforementioned works. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Cryptanalysis of a system using matrices over group rings

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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2015-0008
Publisher site
See Article on Publisher Site

Abstract

Abstract In several recent works of D. Kahrobaei, C. Koupparis, and V. Shpilrain, public-key protocols have been proposed which depend on the difficulty of computing discrete logarithms in matrix rings over group rings. In particular, the specific ring of 3×3 matrices over 𝔽 7 S 5 ${\mathbb {F}_7S_5}$ has been proposed for use in some of these protocols. In this paper, we show that the discrete logarithm problem in this matrix ring can be solved on a modern PC in seconds, and we give a solution to the challenge problem over 𝔽 2 S 5 ${\mathbb {F}_2S_5}$ proposed in one of the aforementioned works.

Journal

Groups Complexity Cryptologyde Gruyter

Published: Nov 1, 2015

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