source 2010 Costello--Lange--Naehrig
compute A = X1^2
compute B = Y1^2
compute C = Z1^2
compute D = a C
compute X3 = (A-D)^2
compute E = 2 (A+D)^2-X3
compute F = ((A-D+Y1)^2-B-X3)
compute Y3 = E F
compute Z3 = 4 B
