## Order of the point

Multiplication over elliptic curve is like this:

$Q = kP$

where $Q$ and $P$ are points on an elliptic curve and $k$ is an integer. The equation above means that $P$ is added to itself $k$ times.

What I don’t understand (yet) is, why the integer $k$ need not be larger than the “order” of the point $P$ ? Understand that reducing $k$ will save a great deal of processing. But what’s the relation between the “order” of the point with this statement:

The points in elliptic curve, forms a cyclic group (a field)