… of sampling random supersingular elliptic curves over finite … supersingular isogeny graph.
Unfortunately, this method is not suitable when the endomorphism ring of the generated curve …

… problem in many supersingular elliptic curves is … elliptic curve cryptosystem in disguise. We
did not yet succeed in fully generalizing them to other classes of (supersingular) elliptic curves…

… in many supersingular elliptic curves is efficiently … an elliptic curve cryptosystem in disguise.
We did not attempt to fully generalize them to other classes of (supersingular) elliptic curves, …

… introduce supersingular elliptic curves over a finite field and relevant concepts, such as
formal group of an elliptic curve, Frobenius maps, etc. The definition of a supersingular curve is …

… We will denote the elliptic curve that Vélu’s formula yields by E / S and the (Vélu) isogeny
by \(\phi _S : E \rightarrow E/S\). As noted above, \(\phi _S\) is unique up to isomorphism. Thus, …

… elliptic curve defined over II~. We show here that E has infinitely many primes of supersingular
… computations for the curve X t (11) to find its first few supersingular primes as listed at the …

… We see that the elliptic curve in question is supersingular if and only if p = Z mod 3 , and
an easy calculation … Since we are dealing with a supersingular elliptic curve E, we have 2 …

… supersingular elliptic curves. One problem is, given a maximal order O in Bp, to compute an
elliptic curve … a list of all isomorphism classes of supersingular elliptic curves E over Fp2 (or …

… conjecture for elliptic curves with su… at supersingular primes when the analytic rank is 0 or
1. The main result enables us to present a number of explicit infinite families of elliptic curves …

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