source 2008 Hisil--Wong--Carter--Dawson, http://eprint.iacr.org/2008/522, Section 3.1, plus assumption Z1=1, plus standard simplification assume Z1 = 1 assume Z2 = 1 compute A = X1 X2 compute B = Y1 Y2 compute C = T1 d T2 compute E = (X1+Y1)(X2+Y2)-A-B compute F = 1 - C compute G = 1 + C compute H = B - a A compute X3 = E F compute Y3 = G H compute T3 = E H compute Z3 = 1 - C^2