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