Quantum algorithm for the discrete logarithm problem for matrices over finite group rings.
Alex D. Myasnikov, Alexander Ushakov · 2012
Abstract. We propose a polynomial time quantum algorithm for solving the discrete logarithm problem 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 [4]. Our result implies that the Kahrobaei et al. protocol does not belong to the realm of post-quantum cryptography. Keywords and phrases: Group-based cryptography, semidirect product, matrix monoids, group-rings, Diffie-Hellman, key-exchange, discrete logarithm problem, quantum algorithms, post-quantum cryptography.