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arXiv · 2601.09904

Distortion maps for elliptic curves over finite fields

Nikita Andrusov·Sevag Büyüksimkeşyan·Dimitrios Noulas·Fabien Pazuki·Mustafa Umut Kazancıoğlu·Jordi Vilà-Casadevall
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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.

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Nikita Andrusov, Sevag Büyüksimkeşyan, Dimitrios Noulas, Fabien Pazuki, Mustafa Umut Kazancıoğlu, Jordi Vilà-Casadevall. 2026-01-14. Distortion maps for elliptic curves over finite fields. https://arxiv.org/abs/2601.09904

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