Volume 4, Issue 4
Special volume AJAX in honor of René Schoof
Abstract:
The Weil pairing on elliptic curves has deep links with discrete logarithm problems, as can be seen, for instance, in [Schoof, 2016; Menezes, Okamoto & Vanstone, 1993]. 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: Elliptic curves, Weil pairings, distortion maps.
Citation:
Nikita Andrusov, Sevag Büyüksimkeşyan, Dimitrios Noulas, Fabien Pazuki, Mustafa Umut Kazancioğlu, and Jordi Vilà-Casadevall. Distortion maps for elliptic curves over finite fields. Polynesian Journal of Mathematics, Volume 4, Issue 4, Pages 1–26. (Sept. 2026) DOI: 10.69763/polyjmath.4.4
Milestones:
Received 14 Jan 2026
Revised 8 Apr 2026
Accepted 19 Apr 2026
Published 28 Sep 2026
Communicated by Elisa Lorenzo García
The above content is published under the terms of the Creative Commons Attribution 4.0 International license.