Distortion maps for elliptic curves over finite fields
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912824997969920 |
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| author | Andrusov, Nikita Büyüksimkeşyan, Sevag Noulas, Dimitrios Pazuki, Fabien Kazancıoğlu, Mustafa Umut Vilà-Casadevall, Jordi |
| author_facet | Andrusov, Nikita Büyüksimkeşyan, Sevag Noulas, Dimitrios Pazuki, Fabien Kazancıoğlu, Mustafa Umut Vilà-Casadevall, Jordi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09904 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distortion maps for elliptic curves over finite fields Andrusov, Nikita Büyüksimkeşyan, Sevag Noulas, Dimitrios Pazuki, Fabien Kazancıoğlu, Mustafa Umut Vilà-Casadevall, Jordi Number Theory Cryptography and Security 11G20, 11T71, 14G15, 14G50, 14H52, 94A60 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. |
| title | Distortion maps for elliptic curves over finite fields |
| topic | Number Theory Cryptography and Security 11G20, 11T71, 14G15, 14G50, 14H52, 94A60 |
| url | https://arxiv.org/abs/2601.09904 |