… the algebraic theory of elliptic curves over fields of characteristic p … for elliptic curves in
characteristic p is whether or not a curve … the following definition of supersingular for elliptic curves. …

… elliptic curves over "nite "elds and describe some general results on C(E). Let us recall some
basic facts on elliptic curves over … case of a supersingular (ss) elliptic curves is much easier …

… groups are used in a way similar to multiplicative groups of finite fields A la … elliptic curves
over finite fields with respect to application for such cryptosystems. The supersingular curves E …

… applications using supersingular curves. … supersingular curves for the identitybased
cryptosystem, since there should exist non-supersingular elliptic curves E over certain finite fields Fq …

… , named OSIDH (Oriented Supersingular Isogeny Diffie-… field, and E is a supersingular elliptic
curve over a finite field. … equivalence classes of supersingular elliptic curves which have the …

… In this paper, we study the supersingular isogeny graph G ℓ ( F p 2 ) whose vertices are (representatives
of) the F p 2 -isomorphism classes of supersingular elliptic curves defined over F p 2 , and …

… There are yet further characterizations of supersingular elliptic curves which are quite
important in various applications. See [Har IV §4] for a description in terms of sheaf cohomology, …

… general theory of elliptic curves over arbitrary fields, such as … In Section 4, we study elliptic
curves over finite fields. We … , supersingular curves, and applications to elliptic curves over Q. …

… Supersingular curves differ from ordinary curves in many ways, and this has practical implications
for algorithms that work with elliptic curves over finite fields… Given an elliptic curve, one …

… Given an elliptic curve over Fq having m points defined over Fq , we have … SUPERSINGULAR
CASE First we consider the case of supersingular elliptic curves defined over prime fields…