Cryptanalysis of a system using matrices over group rings

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.