Applications of Pizer Graphs

Supersingular Isogeny Graph has applications in both mathematics and cryptography. We list several of their applications below.

1. In mathematics Supersingular Isogeny Graph is used in the following computational problems:

1. The endomorphism ring computation problem: Given $$p$$ and a supersingular $$j$$-invariant $$j$$, compute the endomorphism ring of $$E(j)$$ [EHLMP18].
2. The Deuring correspondence problem: Given a maximal order
$$\mathcal{O} \in B_{p,\inf}$$, return a supersingular j-invariant such that the endomorphism ring $$E(j)$$ is isomorphic to $$\mathcal{O}$$ [EHLMP18].
2. In cryptography Supersingular Isogeny Graph is used in encryption scheme [MOT20], signature scheme [Unknown bib ref: SKLPW20], hash function [CGL06], verifiable delay function ((#cite LMPS19)). These schemes are secure against the attack on SIKE.