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