The Tate Profile

2026
OriginalPaper
Chapter

Published in:

Author: Krijn Reijnders
Published in: Progress in Cryptology – LATINCRYPT 2025
Publisher: Springer Nature Switzerland

Read first chapter Log in

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The chapter delves into the significance of the Tate pairing in curve-based cryptography, highlighting its ubiquitous role in both elliptic and hyperelliptic curves. It explores how the Tate profile can transform knowledge of rational torsion into insights about the Sylow subgroups, which is pivotal for enhancing cryptographic schemes. The text provides a detailed analysis of the Tate profile's applications, including smart torsion basis sampling, entangled basis generation, and subgroup membership testing. Additionally, it offers optimizations for computing the 2-Tate profile on Kummer surfaces, demonstrating significant improvements in efficiency. The chapter concludes with a practical example of subgroup membership testing on the Gaudry–Schost Kummer surface, showcasing the effectiveness of the optimized cubical arithmetic approach. This comprehensive exploration not only advances theoretical understanding but also provides actionable insights for practical cryptographic implementations.

AI Generated

This summary of the content was generated with the help of AI.

Notes

This work was supported in part by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement ISOCRYPT - No. 101020788), by the Research Council KU Leuven grant C14/24/099 and by CyberSecurity Research Flanders with reference number VR20192203.

Date of this document: 2025-08-25.

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Business + Economics & Engineering + Technology"

Online-Abonnement

Springer Professional "Business + Economics & Engineering + Technology" gives you access to:

more than 102.000 books
more than 537 journals

from the following subject areas:

Automotive
Construction + Real Estate
Business IT + Informatics
Electrical Engineering + Electronics
Energy + Sustainability
Finance + Banking
Management + Leadership
Marketing + Sales
Mechanical Engineering + Materials
Insurance + Risk

Secure your knowledge advantage now!

inform now

Springer Professional "Engineering + Technology"

Online-Abonnement

Springer Professional "Engineering + Technology" gives you access to:

more than 67.000 books
more than 390 journals

from the following specialised fileds:

Automotive
Business IT + Informatics
Construction + Real Estate
Electrical Engineering + Electronics
Energy + Sustainability
Mechanical Engineering + Materials

Secure your knowledge advantage now!

inform now

Springer Professional "Business + Economics"

Online-Abonnement

Springer Professional "Business + Economics" gives you access to:

more than 67.000 books
more than 340 journals

from the following specialised fileds:

Construction + Real Estate
Business IT + Informatics
Finance + Banking
Management + Leadership
Marketing + Sales
Insurance + Risk

Secure your knowledge advantage now!

inform now

previous chapter Improved Algorithms for Ascending Isogeny Volcanoes, and Applications

next chapter Extending Regev’s Quantum Algorithm to Elliptic Curves

Metadata
Footnotes
Literature

Title: The Tate Profile
Author: Krijn Reijnders
Publisher: Springer Nature Switzerland
Book: Progress in Cryptology – LATINCRYPT 2025
Print ISBN: 978-3-032-06753-1

Electronic ISBN: 978-3-032-06754-8

Copyright Year: 2026
DOI: https://doi.org/10.1007/978-3-032-06754-8_8

This content is only visible if you are logged in and have the appropriate permissions.