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
Creative Commons Attribution
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}
}
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