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arXiv · 2209.02814

A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Christopher Battarbee·Delaram Kahrobaei·Ludovic Perret·Siamak F. Shahandashti
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Abstract

Group-based cryptography is a relatively unexplored family in post-quantum cryptography, and the so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. However, the complexity of SDLP and its relationship to more well-known hardness problems, particularly with respect to its security against quantum adversaries, has not been well understood and was a significant open problem for researchers in this area. In this paper we give the first dedicated security analysis of SDLP. In particular, we provide a connection between SDLP and group actions, a context in which quantum subexponential algorithms are known to apply. We are therefore able to construct a subexponential quantum algorithm for solving SDLP, thereby classifying the complexity of SDLP and its relation to known computational problems.

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Christopher Battarbee, Delaram Kahrobaei, Ludovic Perret, Siamak F. Shahandashti. 2022-09-06. A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem. https://arxiv.org/abs/2209.02814

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