will intersect the curve at a third point called the inverse of R or -R. And, if we take a point symmetric to -R about the x-axis, we will get R, which is also a point on the curve. Here, 0 is a point on the curve called the point of infinity.

Please note that for any three points P, Q, and R :

• P + Q is a point on the curve
• (P + Q) + R = P + (Q + R) = 0
• P + 0 = P
• And, for any point P on the curve, we will always get another point on the curve called the inverse of P or -P, which is symmetric of P about the x-axis. And,P + (-P) = 0

Hence, the points on the elliptic curve satisfy the properties of a group.

A subgroup H of a group G is defined as :

• H is a group
• members of H is a subset of G
• H and G share the same binary operation

Scalar multiplication of a point P on the curve has the property that, after a certain point the result will repeat itself.