… on the protocols using supersingular elliptic curves due to their efficiency. … elliptic curves
is much slower than SIDH and CSIDH. The endomorphism ring of a supersingular elliptic curve …

… elliptic curves into supersingular and ordinary may look arbitrary and unmotivated, but we
will later see how different these two classes of curves … supersingular elliptic curves. First, any …

… solves this problem in the full supersingular isogeny … of supersingular elliptic curves over
\({\mathbb {F}}_p\). We give an algorithm to construct isogenies between supersingular curves …

… of sampling random supersingular elliptic curves over finite … supersingular isogeny graph.
Unfortunately, this method is not suitable when the endomorphism ring of the generated curve …

… 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, …

… In this section, we describe Sutherland’s algorithm [4] of supersingular elliptic curves. …
one hundred supersingular elliptic curves over Fp2 . These supersingular elliptic curves were …

… supersingular elliptic curve is a curve which is enhanced with the information of an
endomorphism. Computing the full endomorphism ring of a supersingular elliptic curve … elliptic …

… a supersingular elliptic curve (the Deuring correspondence in one direction). The other
direction—constructing a supersingular elliptic curve … to find a supersingular elliptic curve with a …

… In this paper we give a new algorithm for computing the endomorphism ring of a
supersingular elliptic curve E: first we compute two cycles through E in the supersingular l-isogeny …

… This includes background on supersingular elliptic curve isogenies and we review the … In
Sections 4 and 5 we present our commitment schemes based on supersingular isogeny graphs …