A note on the low order assumption in class groups of imaginary quadratic number fields

Karim Belabas; Thorsten Kleinjung; Antonio Sanso; Benjamin Wesolowski

Paper 2020/1310

A note on the low order assumption in class groups of imaginary quadratic number fields

Karim Belabas

Thorsten Kleinjung

Antonio Sanso

Benjamin Wesolowski

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: Published elsewhere. Mathematical Cryptology
Keywords: IQC
Contact author(s): Karim Belabas @ math u-bordeaux fr
thorsten @ kleinjung ch
antonio sanso @ gmail com
benjamin wesolowski @ ens-lyon fr
History: 2024-09-16: last of 3 revisions; 2020-10-20: received; See all versions
Short URL: https://ia.cr/2020/1310
License: CC BY

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}
}