A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

• URL: http://arxiv.org/abs/2209.02814v5
• Date: Fri, 7 Jun 2024 12:39:10 GMT
• Title: A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem
• Authors: Christopher Battarbee, Delaram Kahrobaei, Ludovic Perret, Siamak F. Shahandashti,
• Abstract summary: Group-based cryptography is a relatively unexplored family in post-quantum cryptography. The so-called Semidirect Discrete Logarithm Problem (SDLP) is one of its most central problems. We give the first dedicated security analysis of SDLP.
• Score: 0.8947831206263182
• License: http://creativecommons.org/licenses/by/4.0/
• 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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