Paper 2023/177 Original: eprint.iacr.org/2023/177 ↗
The geometric interpretation of the Tate pairing and its applications
Abstract
While the Weil pairing is geometric, the Tate pairing is arithmetic: its value depends on the base field considered. Nevertheless, the étale topology allows to interpret the Galois action in a geometric manner. In this paper, we discuss this point of view for the Tate pairing: its natural geometric interpretation is that it gives étale $\mu_n$-torsors. While well known to experts, this interpretation is perhaps less known in the cryptographic community. As an application, we explain how to use the Tate pairing to study the fibers of an isogeny, and we prove a conjecture by Castryck and Decru on multiradical isogenies.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2026-03-16: last updated
- 2023-02-12: published
- Short URL
- https://ia.cr/2023/177
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2023/177,
author = {Damien Robert},
title = {The geometric interpretation of the Tate pairing and its applications},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/177},
year = {2023},
url = {https://eprint.iacr.org/2023/177}
}