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 (+1)(\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