source 2002 Izu--Takagi "A fast parallel elliptic curve multiplication resistant against side channel attacks", formulas (9) and (10) compute X4 = (X2^2 - a Z2^2)^2 - 8 b X2 Z2^3 compute Z4 = 4(X2 Z2(X2^2 + a Z2^2) + b Z2^4) compute R = 2(X2 Z3 + X3 Z2)(X2 X3 + a Z2 Z3) + 4 b Z2^2 Z3^2 compute S = (X2 Z3 - X3 Z2)^2 compute X5 = R Z1 - S X1 compute Z5 = S Z1