source 1998 Cohen--Miyaji--Ono "Efficient elliptic curve exponentiation using mixed coordinates", plus Z1=1, plus Z2=1, plus common-subexpression elimination assume Z1 = 1 assume Z2 = 1 compute u = Y2-Y1 compute uu = u^2 compute v = X2-X1 compute vv = v^2 compute vvv = v vv compute R = vv X1 compute A = uu-vvv-2 R compute X3 = v A compute Y3 = u(R-A)-vvv Y1 compute Z3 = vvv