# Introduction to Isogeny Cryptography

Making this section as a motivation to make sure this is part of the book. Something to work towards.

## Page Plan

* Describe that there is a drive towards post-quantum algorithms
* The incredible fact that paths within isogeny graphs commute (with the help of torsion points)
* Supersingular $$\ell$$ isogeny graphs are $$(\ell + 1)$$regular Ramanujan graphs
* Using paths through these graphs has spawned a whole bunch of protocols
  * SIKE / BIKE / ...
  * Hashes
  * ...
* First we will look at the fundementals that allow these protocols to be expected as good candidates for post-quantum
* Then we look at these protocols in more detail. Hopefully with SageMath implementations for each

## References I plan to use

* Introduction by Craig Costello 
  * <https://eprint.iacr.org/2019/1321.pdf>&#x20;
* Mathematics of Isogeny Based Cryptography by Luca De Feo
  * <https://arxiv.org/pdf/1711.04062.pdf>-
* The Arithmetic of Elliptic Curves by Joseph H. Silverman
  * <https://www.springer.com/gp/book/9780387094939><br>