source 1998 Cohen--Miyaji--Ono "Efficient elliptic curve exponentiation using mixed coordinates", formula (5), plus common-subexpression elimination compute Z1Z1 = Z1^2 compute Z2Z2 = Z2^2 compute U1 = X1 Z2Z2 compute U2 = X2 Z1Z1 compute S1 = Y1 Z2 Z2Z2 compute S2 = Y2 Z1 Z1Z1 compute H = U2-U1 compute HH = H^2 compute HHH = H HH compute r = S2-S1 compute V = U1 HH compute X3 = r^2-HHH-2 V compute Y3 = r (V-X3)-S1 HHH compute Z3 = Z1 Z2 H