Welcome to the resource topic for 2023/177
Title:
The geometric interpretation of the Tate pairing and its applications
Authors: Damien Robert
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.
ePrint: https://eprint.iacr.org/2023/177
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