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

• 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