Paper 2021/1623
On the Short Principal Ideal Problem over some real Kummer fields
Andrea Lesavourey, Thomas Plantard, and Willy Susilo
Abstract
Several cryptosystems using structured lattices have been believed to be quantum resistant. Their security can be linked to the hardness of solving the Shortest Vector Problem over module or ideal lattices. During the past few years it has been shown that the related problem of finding a short generator of a principal ideal can be solved in quantum polynomial time over cyclotomic fields, and classical polynomial time over a range of multiquadratic and multicubic fields. Hence, it is important to study as many as possible other number fields, to improve our knowledge of the aformentioned problems. In this paper we generalise the work done over multiquadratic and multicubic fields to a larger range of real Kummer extensions of prime exponent p. Moreover, we extend the analysis by studying the Log-unit lattice over these number fields, in comparison to already studied fields.
Note: Code in support of the article can be found at https://github.com/AndLesav/spip-on-kummer
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Post-quantum cryptographyIdeal latticesShort Principal Ideal ProblemKummer fieldsLog-units
- Contact author(s)
- andrea lesavourey @ irisa fr
- History
- 2021-12-14: received
- Short URL
- https://ia.cr/2021/1623
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2021/1623,
author = {Andrea Lesavourey and Thomas Plantard and Willy Susilo},
title = {On the Short Principal Ideal Problem over some real Kummer fields},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1623},
year = {2021},
url = {https://eprint.iacr.org/2021/1623}
}
