… elliptic curve E over a field of positive characteristic p, we consider how to efficiently determine
whether E is ordinary or supersingular… ordinary and supersingular isogeny graphs. This …

… to efficiently construct a supersingular elliptic curve over Fq … t ∈ Sq, a supersingular elliptic
curve over Fq with trace of … elliptic curves of prime order of prescribed size. The resulting …

… 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 …

… 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 …

… 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, supersingular curves always have small k. Of course, there are lots of non-…
supersingular elliptic curve. In this section we show that the use of other supersingular curves …

… An elliptic curve E over an algebraically closed field in characteristic p is supersingular if and
… that Jac(C) up to isogeny over F4 splits as a product of three supersingular elliptic curves. …

… We present new candidates for quantum-resistant public-key cryptosystems based on the
conjectured difficulty of finding isogenies between supersingular elliptic curves. The main …

… Hence, at supersingular primes, in spite of … for elliptic curves at good supersingular primes
in a way similar with Mazur’s at good ordinary primes. More precisely, let E be an elliptic curve …

… 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 …