Deuring Correspondence and Public Key Cryptography
Supervised by Craig Costello (Microsoft Research, Redmond), 2023
Work done between Fall 2022 and Fall 2023 (October 17, 2022 to December 07, 2023). Requirement for UArizona’s Comprehensive Exam.
Here are the report and presentation about the connection between Deuring correspondence and isogeny-based signature schemes.
Update (December 15, 2024): Over the last year I came across the following projects that can help construct various graphs to illustrate Deuring correspondence as I did in my report.
- Isogeny Database (Dec 2, 2020) by Enric Florit
- Isogeny Database with Endomorphism Rings (Sep 21, 2023) by James Clements
- Supersingular l and L isogeny graphs, (Dec 9, 2023) by James Rickards
Update (July 16, 2025): Some useful explainations from online forums.
- Given quaternion maximal order, find the corresponding j-invariant by David Jao. (pdf)
- Find endomoprhism ring of isogenous supersingular curve by Jonathan Love (pdf)