Given an elliptic curve E over a field of positive characteristic p, we consider how to
efficiently determine whether E is ordinary or supersingular. We analyze the complexity of …

Abstract Let p> 3 p> 3 be a prime and let EE, E'E′ be supersingular elliptic curves over F _p
F p. We want to construct an isogeny ϕ: E → E'ϕ: E→ E′. The currently fastest algorithm for …

We give a new algorithm for finding an isogeny from a given supersingular elliptic curve E/F
p 2 to a subfield elliptic curve E′/F p, which is the bottleneck step of the Delfs–Galbraith …

Finding isogenies between supersingular elliptic curves is a natural algorithmic problem
which is known to be equivalent to computing the curves' endomorphism rings. When the …

Computing endomorphism rings of supersingular elliptic curves is an important problem in
computational number theory, and it is also closely connected to the security of some of the …

Let O be a maximal order in the quaternion algebra Bp over Q ramified at p and∞. The
paper is about the computational problem: construct a supersingular elliptic curve E over Fp …

We introduce a special class of supersingular curves over 𝔽 p 2, characterized by the
existence of noninteger endomorphisms of small degree. We prove a number of properties …

In this paper, we study several related computational problems for supersingular elliptic
curves, their isogeny graphs, and their endomorphism rings. We prove reductions between …

We consider the problem of sampling random supersingular elliptic curves over finite fields
of cryptographic size (SRS problem). The currently best-known method combines the …

An oriented 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 is …