Generating a supersingular elliptic curve such that nobody knows its endomorphism ring is a
notoriously hard task, despite several isogeny-based protocols relying on such an object. A …

An important open problem in supersingular isogeny-based cryptography is to produce,
without a trusted authority, concrete examples of 'hard supersingular curves' that is …

Abstract The supersingular Endomorphism Ring problem is the following: given a
supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of …

We consider finite graphs whose vertexes are supersingular elliptic curves, possibly with
level structure, and edges are isogenies. They can be applied to the study of modular forms …

An important open problem in supersingular isogeny-based cryptography is to produce,
without a trusted authority, concrete examples of “hard supersingular curves” that is …

Let ℓ and p be two distinct prime numbers. We study ℓ-isogeny graphs of ordinary elliptic
curves defined over a finite field of characteristic p, together with a level structure. Firstly, we …

Let $ p> 3$ be a prime and $ E $ be a supersingular elliptic curve defined over $\mathbb {F}
_ {p^ 2} $. Let $ c $ be a prime with $ c< 3p/16$ and $ G $ be a subgroup of $ E [c] $ of order …