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We propose a polynomial time quantum algorithm for solving the discrete logarithm problem (DLP) in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis and V. Shpilrain [Groups Complex. Cryptol. 5 (2013), 97–115]. Our result implies that the Kahrobaei–Koupparis–Shpilrain protocol does not belong to the realm of post-quantum cryptography.

Quantum algorithm for discrete logarithm problem for matrices over finite group rings