Paper 2026/1325 Original: eprint.iacr.org/2026/1325 ↗
The Generalised Tate Pairing over any field
Abstract
We generalise a pairing on elliptic curves over finite fields, called the generalised Tate pairing, which is defined in terms of an arbitrary endomorphism of the curve, with certain trace requirements. We rederive this pairing from group cohomology, which allows us to generalise the pairing to principally polarized abelian varieties over any field, endomorphisms of any trace, and prove perfectness using a general duality theorem.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2026-06-26: last updated
- 2026-06-26: published
- Short URL
- https://ia.cr/2026/1325
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2026/1325,
author = {Jonathan Komada Eriksen},
title = {The Generalised Tate Pairing over any field},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/1325},
year = {2026},
url = {https://eprint.iacr.org/2026/1325}
}