[Resource Topic] 2025/477: A Note on the Advanced Use of the Tate Pairing

Welcome to the resource topic for 2025/477

Title:
A Note on the Advanced Use of the Tate Pairing

Authors: Krijn Reijnders

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.

ePrint: https://eprint.iacr.org/2025/477

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