Elliptic Curve Addition Operation + Special Cases + Curves Not to Use

Addition Operation

First draw a line going through P and Q (infinite) that hits another point. Then trace a vertical line through that point, which will hit the curve at point P + Q

P + P special case (adding a point to itself)

Draw a tangent line on that point, where it will hit another point. Then draw a vertical line through that point, where it will hit the curve at point P + P

Point at infinity case

Just make up a point, which we call O. P + P = O and R + Q = O. O behaves like 0, as it is an idenity element, therefore P + O = P and Q + O = Q

The Weierstrass equation simplification is not possible for the

“binary curves” and “curves of characteristic 3”.