On the Complexity of Generalized Discrete Logarithm Problem

12/23/2022

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by   Cem M. Unsal, et al.

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Generalized Discrete Logarithm Problem (GDLP) is an extension of the Discrete Logarithm Problem where the goal is to find x∈ℤ_s such g^x s=y for a given g,y∈ℤ_s. Generalized discrete logarithm is similar but instead of a single base element, uses a number of base elements which does not necessarily commute with each other. In this paper, we prove that GDLP is NP-hard for symmetric groups. Furthermore, we prove that GDLP remains NP-hard even when the base elements are permutations of at most 3 elements. Lastly, we discuss the implications and possible implications of our proofs in classical and quantum complexity theory.