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