Paper 2020/1310 Original: eprint.iacr.org/2020/1310 ↗
A note on the low order assumption in class groups of imaginary quadratic number fields
Abstract
In this short note we analyze the low order assumption in the imaginary quadratic number fields. We show how this assumption is broken for Mersenne primes. We also provide a description on how to possible attack this assumption for other class of prime numbers leveraging some new mathematical tool coming from higher (cubic) number fields.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2024-09-16: last updated
- 2020-10-20: published
- Short URL
- https://ia.cr/2020/1310
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2020/1310,
author = {Karim Belabas and Thorsten Kleinjung and Antonio Sanso and Benjamin Wesolowski},
title = {A note on the low order assumption in class groups of imaginary quadratic number fields},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/1310},
year = {2020},
url = {https://eprint.iacr.org/2020/1310}
}