source 2002 Billet--Joye "The Jacobi model of an elliptic curve and side-channel analysis", formula (11), plus specialization to affine assume Z1 = 1 assume Z2 = 1 compute r = 1-(X1 X2)^2 compute X3 = (X1 Y2+Y1 X2)/r compute Y3 = ((1+(X1 X2)^2) (Y1 Y2+2 a X1 X2)+2 X1 X2 (X1^2+X2^2))/r^2 compute Z3 = 1