Paper 2022/1135 Original: eprint.iacr.org/2022/1135 ↗
Full Quantum Equivalence of Group Action DLog and CDH, and More
Abstract
Cryptographic group actions are a relaxation of standard cryptographic groups that have less structure. This lack of structure allows them to be plausibly quantum resistant despite Shor's algorithm, while still having a number of applications. The most famous example of group actions are built from isogenies on elliptic curves. Our main result is that CDH for abelian group actions is quantumly *equivalent* to discrete log. Galbraith et al. (Mathematical Cryptology) previously showed *perfectly* solving CDH to be equivalent to discrete log quantumly; our result works for any non-negligible advantage. We also explore several other questions about group action and isogeny protocols.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2022-08-31: last updated
- 2022-08-31: published
- Short URL
- https://ia.cr/2022/1135
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2022/1135,
author = {Hart Montgomery and Mark Zhandry},
title = {Full Quantum Equivalence of Group Action DLog and CDH, and More},
howpublished = {Cryptology {ePrint} Archive, Paper 2022/1135},
year = {2022},
url = {https://eprint.iacr.org/2022/1135}
}