… Since every isogeny has a dual isogeny [38, Theorem III.6.1], the … of elliptic curves defined
over Fq. Accordingly, we define an isogeny class to be an equivalence class of elliptic curves, …

… We present an overview of supersingular isogeny cryptography and how it fits into the broad
… elliptic curve isogenies and the computational problems relevant for supersingular isogeny …

… 19], using supersingular elliptic curves. Since the discrete logarithm problem is unimportant
… elliptic curves are used in an isogeny-based system, we propose using supersingular curves …

… We will denote the elliptic curve that Vélu’s formula yields by E / S and the (Vélu) isogeny
by \(\phi _S : E \rightarrow E/S\). As noted above, \(\phi _S\) is unique up to isomorphism. Thus, …

… supersingular isogeny graphs In this section, we consider a graph related to oriented
supersingular elliptic curves… -isogeny between K-oriented supersingular elliptic curves …

… isogeny graph. In this paper we consider the structure of the isogeny graph of supersingular
elliptic curves … We give an algorithm to construct isogenies between supersingular curves …

… supersingular elliptic curve isogenies and we review the techniques used for computing such
isogenies. … In Section 3 we introduce the mixing constant for any regular graph and analyse …

… to supersingular elliptic curves and study these objects with the motivation of isogeny-based …
We also look at isogeny graphs of supersingular elliptic curves with level structure, and how …

… function from supersingular elliptic curve isogenies by taking … based on supersingular
elliptic curve isogenies. Finally, we … based on supersingular elliptic curve isogenies, propose a …

… problems for supersingular elliptic curves, their isogeny graphs, and … \)-isogeny graph,
computing maximal orders isomorphic to the endomorphism ring of a supersingular elliptic curve, …