2014 / December Volume 9 No.4
Generators of Elliptic Curves over Finite Fields
Published Date |
2014 / December
|
---|---|
Title | Generators of Elliptic Curves over Finite Fields |
Author | |
Keyword | |
Download | |
Pagination | 657-670 |
Abstract | We prove estimates on character sums on the subset of points of an
elliptic curve over $F_{q^n}$ with $x$-coordinate of the form $\alpha + t$
where $t \in F_q$ varies and fixed $\alpha$ is such that $F_{q^n} = F_q(\alpha)$.
We deduce that, for a suitable choice of
$\alpha$, this subset has a point of maximal order in $E(F_{q^n})$. This provides a
deterministic algorithm for finding a point of maximal order which for a very wide class
of finite fields is faster than other
available algorithms.
|
AMS Subject Classification |
11G20,11Y16, 11T23.
|
Received |
2014-06-06
|
Accepted |
2014-06-06
|