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