A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem
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 re...
Gespeichert in:
Hauptverfasser: | , , , |
---|---|
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | 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. |
---|---|
DOI: | 10.48550/arxiv.2209.02814 |