2.1.2 Adding the points P and -P The line through P and -P is a vertical line which does not intersect the elliptic curve at a third pint; thus the points P an -P cannot be added as previously. It is for this reason that the elliptic curve group includes the point at infinity O. By definition, P + (-P) = O. As a result of this equation, P + O = -P in the elliptic curve group . O is called the additive identity of the elliptic curve group; all groups have an additive identity.
Any point added to the point of infinity yields the original point.
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