source 1998 Cohen--Miyaji--Ono "Efficient elliptic curve exponentiation using mixed coordinates", formula (9), plus common-subexpression elimination compute ZZ1 = Z1^2 compute ZZ2 = Z2^2 compute U1 = X1 ZZ2 compute U2 = X2 ZZ1 compute S1 = Y1 Z2 ZZ2 compute S2 = Y2 Z1 ZZ1 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 compute ZZ3 = Z3^2 compute T3 = a ZZ3^2