Let p be a prime number and let E be an elliptic curve defined over ℚ of conductor N. Let K
be an imaginary quadratic field with discriminant prime to pN such that all prime factors of N …

… ; i = 2;3;4;5 on elliptic curves over the finite field GF(2n). In this … 2 (with only one field inverse)
on elliptic curves defined over … review of non-supersingular elliptic curves defined over the …

… We consider supersingular elliptic curves over \(\mathbb {F}_{p^2}\) and write \(N_p\) for
the number of isomorphism classes of such curves over the algebraic closure of \(\mathbb {F}_p\)…

… supersingular isogeny graph: a graph whose vertices represent supersingular elliptic curves
(… then: given two supersingular elliptic curves, find a path in the supersingular isogeny graph …

… to the supersingular case the … elliptic curves that was originally developed by Bertolini in
the ordinary setting. In particular, given an elliptic curve E over \(\mathbb {Q}\) with supersingular …

… some complications that arise from working with supersingular primes. We begin by …
supersingular setting. After translating many results into the setting of supersingular elliptic curves, …

… elliptic curve cryptosystems which is completed in subexponential time for supersingular
elliptic curves… , in applying the MOV reduction to general elliptic curves: the problem of explicitly …

… supersingular elliptic curves. In Section 5, we determine the periods of EC-sequences constructed
from supersingular elliptic curves. … a class of supersingular elliptic curves with order 2n …

… In this paper, we will describe the use of nonsupersingular elliptic curve group over Fzm
to implement ElGamal encryption scheme and a VLSI implementation of an ElGamal ECC …

… based on supersingular isogenies, … supersingular elliptic curves were first given in [CGL09]
which constructed a hash function from the l-isogeny graph of supersingular elliptic curves. In …