source 2008 Hisil--Wong--Carter--Dawson, http://eprint.iacr.org/2008/522, Section 3.1, plus assumption Z1=1, plus standard simplification
unified
appliesto extended-1
assume Z1 = 1
assume Z2 = 1
parameter k
assume k = 2*d
compute A = (Y1-X1)(Y2-X2)
compute B = (Y1+X1)(Y2+X2)
compute C = T1 k T2
compute E = B - A
compute F = 2 - C
compute G = 2 + C
compute H = B + A
compute X3 = E F
compute Y3 = G H
compute T3 = E H
compute Z3 = 4 - C^2
