Generators of Elliptic Curves over Finite Fields
by
Jose Felipe Voloch
Igor E. Shparlinski
Vol. 9 No. 4 (2014) P.657~P.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.
KEYWORDS
Elliptic curves, generators, finite fields.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 11G20,11Y16, 11T23.
MILESTONES
Received: 2013-11-25
Revised : 2014-06-06
Accepted: 2014-06-06
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