source 2002 Izu--Takagi "A fast parallel elliptic curve multiplication resistant against side channel attacks", formulas (8) and (10), plus common-subexpression elimination, plus assumption Z1=1 assume Z1 = 1 parameter b4 assume b4 = 4 b compute XX = X2^2 compute ZZ = Z2^2 compute aZZ = a ZZ compute E = (X2 + Z2)^2 - XX - ZZ compute X4 = (XX - aZZ)^2 - b4 E ZZ compute Z4 = 2 E(XX + aZZ) + b4 ZZ^2 compute A = X2 X3 compute B = Z2 Z3 compute C = X2 Z3 compute D = X3 Z2 compute X5 = (A - a B)^2 - b4 B(C + D) compute Z5 = X1 (C - D)^2