Chapter 3 Supersingular isogeny graphs and Quaternion Algebras
¶These are notes for BUNTES Fall 2018, the topic is Supersingular isogeny graphs and Quaternion Algebras.
http://math.bu.edu/people/midff/buntes/fall2018.html.
Outline:
- Background, isogeny graphs, applications.
- Supersingular isogeny graph cryptography (candidate for post-quantum cryptography).
- Introduction to Quaternion algebras.
- The Deuring correspondence:\begin{equation*} \left\{ \text{maximal orders }\ints \subseteq B_{p,\infty}\right\}/\sim \leftrightarrow \left\{ j \text{ s.s. }\in \FF_{p^2}\right\}/\Gal{\FF_{p^2}}{\FF_p}\text{.} \end{equation*}