Abstract. The paper shows the existence of an efficient algorithm to solve the generalized discrete logarithm problem in quantum computing model by reducing it to the Abelian hidden subgroup problem. The proposed method can also efficiently solve the power conjugacy search subproblem in quantum computing model, on whose complexity in some groups the resistance of several cryptographic systems and protocols is based.

Keywords: quantum computing, quantum computing model, power conjugacy search problem, group-based cryptography.