Paper 2022/1165 Original: eprint.iacr.org/2022/1165 ↗
A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem
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.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2024-06-07: last updated
- 2022-09-06: published
- Short URL
- https://ia.cr/2022/1165
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2022/1165,
author = {Christopher Battarbee and Delaram Kahrobaei and Ludovic Perret and Siamak F. Shahandashti},
title = {A Subexponential Quantum Algorithm for the Semidirect Discrete Logarithm Problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1165},
year = {2022},
url = {https://eprint.iacr.org/2022/1165}
}