Paper 2019/870
The Eleventh Power Residue Symbol
Marc Joye, Oleksandra Lapiha, Ky Nguyen, and David Naccache
Abstract
This paper presents an efficient algorithm for computing $11^{\mathrm{th}}$-power residue symbols in the cyclotomic field $\mathbb{Q}(\zeta_{11})$, where $\zeta_{11}$ is a primitive $11^{\mathrm{th}}$ root of unity. It extends an earlier algorithm due to Caranay and Scheidler (Int. J. Number Theory, 2010) for the $7^{\mathrm{th}}$-power residue symbol. The new algorithm finds applications in the implementation of certain cryptographic schemes.
Note: Fixed typo in the proof of proposition 3
Metadata
- Available format(s)
-
PDF
- Category
- Implementation
- Publication info
- Preprint.
- Keywords
- Power residue symbolcyclotomic fieldreciprocity lawcryptography.
- Contact author(s)
- marc joye @ onespan com
- History
- 2019-11-05: last of 2 revisions
- 2019-07-30: received
- See all versions
- Short URL
- https://ia.cr/2019/870
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2019/870,
author = {Marc Joye and Oleksandra Lapiha and Ky Nguyen and David Naccache},
title = {The Eleventh Power Residue Symbol},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/870},
year = {2019},
url = {https://eprint.iacr.org/2019/870}
}
