On the Complexity of Generalized Discrete Logarithm Problem

Cem M Unsal; Rasit Onur Topaloglu

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arXiv · 2212.12577

On the Complexity of Generalized Discrete Logarithm Problem

Cem M Unsal·Rasit Onur Topaloglu

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Abstract

Generalized Discrete Logarithm Problem (GDLP) is an extension of the Discrete Logarithm Problem where the goal is to find $x\in\mathbb{Z}_s$ such $g^x\mod s=y$ for a given $g,y\in\mathbb{Z}_s$. 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.

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BibTeX RIS

Cem M Unsal, Rasit Onur Topaloglu. 2022-12-23. On the Complexity of Generalized Discrete Logarithm Problem. https://arxiv.org/abs/2212.12577

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