Supersingular Isogeny Graphs in Cryptography

PCMI 2021 Graduate Summer school

Please click here for the page for 2022!

Lecturer: Kristin Lauter, TA: Jana Sotáková

• These are the materials for the 2021 version fo the course.
  Please click here for the materials for 2022.
• You can find the lectures by Kristin Lauter here and the slides here.
• First exercise sheet. Topics: elliptic curves, isogenies, supersingular isogeny graph.
• Second exercise sheet. Topics: Supersingular isogeny graphs and the Ramanujan property, SIDH key exchange.
• Third exercise sheet. Topics: quaternion algebras, maximal orders, Deuring correspondence.


Sage code for visualizing supersingular isogeny graphs (txt).

Magma code:

Solutions for exercises ex1-1.m, ex1-2.m (fixed generation of basis of the 16-torsion), ex1-3.m.
Solutions for ex3-1.m, ex3-2.m, ex3-3.m.
You can also check the interactive output of Magma as txt file. 1-1.txt, 1-2.txt, 1-3.txt; 3-1.txt, 3-2.txt, 3-3.txt.
Incomplete code to generate supersingular isogeny graphs in Magma is here ssig.m. Need to fix the multiplicity of the neighbor function.

To load this code in Magma line by line, use
iload "ex1-X.m";
This is also a great way to debug your code.