source 2008 Hisil--Wong--Carter--Dawson, http://eprint.iacr.org/2008/522, Section 3.2, plus assumption Z1=1
assume Z1 = 1
assume Z2 = 1
compute A = X1 X2
compute B = Y1 Y2
compute C = T2
compute D = T1
compute E = D + C
compute F = (X1-Y1)(X2+Y2)+B-A
compute G = B + a A
compute H = D - C
compute X3 = E F
compute Y3 = G H
compute T3 = E H
compute Z3 = F G