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Paper 2019/1176
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.
Metadata
- Available format(s)
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- Power residue symbolcyclotomic fieldreciprocity law
- Contact author(s)
- david naccache @ ens fr
- History
- 2019-10-10: received
- Short URL
- https://ia.cr/2019/1176
- License
-
CC BY