Paper 2023/177

The geometric interpretation of the Tate pairing and its applications

Damien Robert, Inria Bordeaux - Sud-Ouest Research Centre, Institut de Mathématiques de Bordeaux
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.

Note: Gave more examples of 'pairing the volcano' situation

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint.
Keywords
pairingsisogenies
Contact author(s)
damien robert @ inria fr
History
2023-05-13: last of 4 revisions
2023-02-12: received
See all versions
Short URL
https://ia.cr/2023/177
License
Creative Commons Attribution
CC BY

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},
      note = {\url{https://eprint.iacr.org/2023/177}},
      url = {https://eprint.iacr.org/2023/177}
}
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