Fonctionne avec Indico
v3.2.9
In a supersingular isogeny graph, the vertices are supersingular elliptic curves (up to isomorphism) over some finite field, and the edges are isogenies between them. Given two vertices in this graph, can one efficiently find a path connecting them? In other words, given two supersingular elliptic curves, can one find an isogeny between them?
The presumed hardness of this problems leads to cryptographic protocols that may resist even an adversary equipped with a quantum computer. We will present this problem and the underlying arithmetic theory, and discuss its difficulty. We will explain its equivalence (under the generalised Riemann hypothesis) with the endomorphism ring problem (given a supersingular elliptic curve, compute its endomorphism ring).