### The Thirteenth Power Residue Symbol

Eric Brier and David Naccache

##### Abstract

This paper presents an efficient deterministic algorithm for computing $13$\textsuperscript{th}-power residue symbols in the cyclotomic field $\mathbb{Q}(\zeta_{13})$, where $\zeta_{13}$ is a primitive $13$\textsuperscript{th} root of unity. The new algorithm finds applications in the implementation of certain cryptographic schemes and closes a gap in the \textsl{corpus} of algorithms for computing power residue symbols.

Available format(s)
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
Power residue symbolcyclotomic fieldreciprocity law
Contact author(s)
david naccache @ ens fr
History
Short URL
https://ia.cr/2019/1176

CC BY

BibTeX

@misc{cryptoeprint:2019/1176,
author = {Eric Brier and David Naccache},
title = {The Thirteenth Power Residue Symbol},
howpublished = {Cryptology ePrint Archive, Paper 2019/1176},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/1176}},
url = {https://eprint.iacr.org/2019/1176}
}

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