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Paper 2019/870

The Eleventh Power Residue Symbol

Marc Joye and Oleksandra Lapiha and 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.

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
Creative Commons Attribution
CC BY
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