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.
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| AMS Subject Classification |
11G20,11Y16, 11T23.
|
| Received |
2014-06-06
|
| Accepted |
2014-06-06
|