Rational Isogenies from Irrational Endomorphisms

Explore a cryptographic presentation from Eurocrypt 2020 that delves into rational isogenies derived from irrational endomorphisms. Learn about the fundamentals of CSIDH, isogeny graphs, and notation specific to this topic. Discover the intricacies of square roots in cl(0), twisting endomorphisms, and the case where p ≡ 1 mod 4. Examine a practical example and gain insights into the F,-ification of the KLPT algorithm. Enhance your understanding of advanced cryptographic concepts in this 24-minute talk by Wouter Castryck, Lorenz Panny, and Frederik Vercauteren.

Intro
The upshot for non-isogenists
Overview of CSIDH
Isogeny graphs
Notation for this talk
Square roots in cl(0)
Twisting endomorphisms
The case p = 1 mod 4
An example
One last thing: F,-ifying the KLPT algorithm