Elliptic Curve Point Addition For y^2 + xy = x^3 + a x^2 + b.

1. Compute NEWP = P + P (Double P, P ≠ O)

1. Let m = P.X + P.Y / P.X
2. Let New.X = m * m + m + a
3. Let New.Y = X * X + (m + 1) * New.X

2. Compute NEWP = P + Q (P ≠ Q, P ≠ O, Q ≠ O)

1. Let m = (P.Y + Q.Y) / (P.X + Q.X)
2. Let New.X = m * m* + m + P.X + Q.X + a
3. Let New.Y = m * (P.X + New.X) + New.X + P.Y

3. Compute NEWP = P + O

1. Let NEWP = P