Cryptography Reading Group - Dinesh Valluri

Title: Faster Algorithms for Isogeny Problems using Torsion Point Images. 

Abstract:

In this talk, we will discuss cryptanalysis of some SIDH-type protocols due to Christophe Petit: https://eprint.iacr.org/2017/571.pdf. While finding isogenies between supersingular elliptic curves remains computationally hard to solve, knowledge of images of specific torsion points by the unknown isogeny helps build faster attacks.We will discuss the complexities involved under some restrictions of parameters (degrees of Alice and Bob's isogenies). The content of this talk serves as a technical precursor to further work on torsion point attacks on SIDH-type cryptosystems, for instance as in https://eprint.iacr.org/2020/633.pdf.