source 2007 Hisil--Carter--Dawson
assume Z1 = 1
compute A = X1^2
compute B = Y1^2
compute D = A+B
compute G = (X1+Y1)^2-D
compute X3 = (2 Y1-G)(X1+A+1)
compute Y3 = (G-2 X1)(Y1+B+1)
compute Z3 = (X1-Y1)(G+2 D)