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

Introduction by Craig Costello
- https://eprint.iacr.org/2019/1321.pdf
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

Last updated 3 years ago

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

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