Academic Journal
Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs: Adding level structure to supersingular elliptic curve isogeny graphs
| Title: | Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs: Adding level structure to supersingular elliptic curve isogeny graphs |
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| Authors: | Arpin, Sarah |
| Source: | Journal de théorie des nombres de Bordeaux. 36:405-443 |
| Publication Status: | Preprint |
| Publisher Information: | MathDoc/Centre Mersenne, 2024. |
| Publication Year: | 2024 |
| Subject Terms: | supersingular, Curves over finite and local fields, Mathematics - Number Theory, elliptic curves, FOS: Mathematics, Algebraic coding theory, cryptography (number-theoretic aspects), Number Theory (math.NT), 0101 mathematics, level structure, 01 natural sciences, isogeny graphs |
| Description: | In this paper, we add the information of level structure to supersingular elliptic curves and study these objects with the motivation of isogeny-based cryptography. Supersingular elliptic curves with level structure map to Eichler orders in a quaternion algebra, just as supersingular elliptic curves map to maximal orders in a quaternion algebra via the classical Deuring correspondence. We study this map and the Eichler orders themselves. We also look at isogeny graphs of supersingular elliptic curves with level structure, and how they relate to graphs of Eichler orders. |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 2118-8572 |
| DOI: | 10.5802/jtnb.1283 |
| DOI: | 10.48550/arxiv.2203.03531 |
| Access URL: | http://arxiv.org/abs/2203.03531 https://zbmath.org/7948972 https://doi.org/10.5802/jtnb.1283 |
| Rights: | arXiv Non-Exclusive Distribution |
| Accession Number: | edsair.doi.dedup.....9fbb350f5867918568f441abb2df62e8 |
| Database: | OpenAIRE |
| ISSN: | 21188572 |
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| DOI: | 10.5802/jtnb.1283 |