Question

On an elliptic curve, what is the negative of a point A ? What is zero on an elliptic curve? In answering both questions, consider the case where x and y vary over the real numbers

Answer 1

#1. Let P + Q = R is the additive property defined geometrically. Elliptic curve groups are additive groups I.e. their basic function is addition. The addition of two points in an elliptic curve is defined geometrically.

The negative of a point P = (X1,Y1) is its reflection in the x-axis: the point -P is (X1,-Y1).

Notice that for each point P on an elliptic curve, the point -P is also on the curve.

#2.If three points on an elliptic curve lie on a straight line, their sum is defined to be 0 . This point is known as zero point on an elliptical curve or point at infinity