source 2008 Bernstein--Birkner--Joye--Lange--Peters http://eprint.iacr.org/2008/013 Section 6, plus Z2=1, plus Z1=1, plus standard simplification
assume Z1 = 1
assume Z2 = 1
compute C = X1 X2
compute D = Y1 Y2
compute E = d C D
compute X3 = (1-E) ((X1+Y1)(X2+Y2)-C-D)
compute Y3 = (1+E) (D-a C)
compute Z3 = 1-E^2