Major controversy surrounds the use of Elliptic Curves in finite fields as
Random Number Generators. There is little information however concerning the
"randomness" of different procedures on Elliptic Curves defined over fields of
characteristic $0$. The aim of this paper is to investigate the behaviour of
the sequence $\psi_m=[m]P$ and then generalize to polynomial seuences of the
form $\phi_m=[p(m)]P$. We examine the behaviour of this sequence in different
domains and attempt to realize for which points it is not equidistributed in
$\mathbb{C}/\Lambda$. We will first study the sequence in the space of Elliptic
Curves $E(\mathbb{C})$ defined over the complex numbers and then reconsider our
approach to tackle real valued Elliptic Curves. In the process we obtain the
measure with respect to which the sequence $\psi$ is equidistributed in
$E(\mathbb{R})$. In Section 4 we prove that every sequence of points
$P_n=(x_n,y_n,1)$ equidistributed w.r.t. that measure is not
equidistributed$\mod(1)$ with the obvious map $x_n\to\{x_n\}$. Finally we
propose a PRNG based on polynomial sequences which will be studied in future
work.