The Generalised Tate Pairing over any field

Jonathan Komada Eriksen

Paper 2026/1325

The Generalised Tate Pairing over any field

Jonathan Komada Eriksen

, COSIC, KU LEuven

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.
Keywords: abelian varieties pairings
Contact author(s): jeriksen @ esat kuleuven be
History: 2026-06-29: approved; 2026-06-26: received; See all versions
Short URL: https://ia.cr/2026/1325
License: CC BY

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}
}