CryptoBook

Search…

Fundamentals

Number Theory

Abstract algebra

Elliptic Curves

Lattices

Asymmetric Cryptography

Symmetric Cryptography

Isogeny Based Cryptography

Appendices

Powered By GitBook

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 graphsUsing 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

Mathematics of Isogeny Based Cryptography by Luca De Feo

The Arithmetic of Elliptic Curves by Joseph H. Silverman

Last modified 5mo ago

Export as PDF

Copy link