Distortion maps for elliptic curves over finite fields
Number Theory
2026-01-16 v1 Cryptography and Security
Abstract
The Weil pairing on elliptic curves has deep links with discrete logarithm problems. In practice, to better suit the functionalities of cryptosystems, one often needs to modify the original Weil pairing via what is called a distortion map. We propose a study on the question of the existence of distortion maps for elliptic curves over finite fields. We revisit results from the literature and provide detailed proofs. We also propose new perspectives at times.
Keywords
Cite
@article{arxiv.2601.09904,
title = {Distortion maps for elliptic curves over finite fields},
author = {Nikita Andrusov and Sevag Büyüksimkeşyan and Dimitrios Noulas and Fabien Pazuki and Mustafa Umut Kazancıoğlu and Jordi Vilà-Casadevall},
journal= {arXiv preprint arXiv:2601.09904},
year = {2026}
}