A Note on the Advanced Use of the Tate Pairing

Krijn Reijnders

Paper 2025/477

A Note on the Advanced Use of the Tate Pairing

Krijn Reijnders

, KU Leuven

Abstract

This short note explains how the Tate pairing can be used to efficiently sample torsion points with precise requirements, and other applications. These applications are most clearly explained on Montgomery curves, using the Tate pairing of degree 2, but hold more generally for any degree or abelian variety, or even generalized Tate pairings. This note is explanatory in nature; it does not contain new results, but aims to provide a clear and concise explanation of results in the literature that are somewhat hidden, yet are extremely useful in practical isogeny-based cryptography.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Tate pairing pairings isogenies isogeny-based cryptography
Contact author(s): crypto krijn @ gmail com
History: 2025-03-14: approved; 2025-03-13: received; See all versions
Short URL: https://ia.cr/2025/477
License: CC BY

BibTeX

@misc{cryptoeprint:2025/477,
      author = {Krijn Reijnders},
      title = {A Note on the Advanced Use of the Tate Pairing},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/477},
      year = {2025},
      url = {https://eprint.iacr.org/2025/477}
}