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A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem

Authors :
Battarbee, Christopher
Kahrobaei, Delaram
Perret, Ludovic
Shahandashti, Siamak F.
Publication Year :
2022

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.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2209.02814
Document Type :
Working Paper