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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)
- 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