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 …

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 …

We give an algorithm that constructs, on input of a prime power q and an integer t, a
supersingular elliptic curve over Fq with trace of Frobenius t in case such a curve exists. If …

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

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 …

Abstract Let ℰ∕ 𝔽 q be an elliptic curve, and P a point in ℰ (𝔽 q) of prime order ℓ. Vélu's
formulæ let us compute a quotient curve ℰ′= ℰ∕⟨ P⟩ and rational maps defining a …

In this paper, we introduce a polynomial-time algorithm to compute a connecting O O-ideal
between two supersingular elliptic curves over F _p F p with common F _p F p …

We consider the endomorphism ring computation problem for supersingular elliptic curves,
constructive versions of Deuring's correspondence, and the security of Charles-Goren …