… inputs, for each prime p we constructed a supersingular curve over Fp using a variant of the
… an Fp-rational root j0, which is necessarily the j-invariant of a supersingular elliptic curve. In …

… In this note, we shall work on the supersingular elliptic curves with j -invariants … elliptic curve
defined over F p 2 . Consequently, we may and will assume the supersingular elliptic curve …

… One of the goals of this paper is to show that, as in the case of elliptic curves, supersingular
curves … for which the Frey-Rück attack applies (eg, elliptic curves over Fp with p − 1 points). …

… Remark 2 For reasons of efficiency, elliptic curve cryptosystems are usually implemented
over prime fields Fp or fields F2m of characteristic two. Supersingular curves over fields F3m of …

… component of all the j-invariants of supersingular curves over Fp [13]. Therefore, other …
one hundred supersingular elliptic curves over Fp2 . These supersingular elliptic curves were …

… (>:) Fp for the supersingular locus (cf. Section 2), and we write S' c M3' (>:) Fp for the set of
good supersingular curves of … over F4 splits as a product of three supersingular elliptic curves. …

… computational problem: construct a supersingular elliptic curve E over Fp such that End(E) …
j-invariant j(E), of the elliptic curve with End(E) ∼= O, lies in Fp. We can then prove that our …

… discussion to non-supersingular elliptic curves. However, supersingular curves may also be
… Koblitz [69] gives conjectural asymptotic formulas for the probability that #E(Fp) is prime as …

… to efficiently construct a supersingular elliptic curve over Fq with … t ∈ Sq, a supersingular
elliptic curve over Fq with trace of … We compute a supersingular elliptic curve E/Fp using Al…

… However, all the methods considered in this paper can be easily adapted to sample
supersingular elliptic curves defined over Fp (in fact, most of them can be made more efficient in this …