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)

??? [back to reading… ]

Update:

I guess now I start to grab the ideas about those previous paragraphs 🙂

I’ll check it to mathematician buddy as soon as possible 😉

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