# Elliptic curve point addition with $Z_1 = Z_2 = 1$

Elliptic curve point addition and point doubling operations using Projective and Jacobian coordinates require fewer field multiplication operations when considering $Z$ coordinates of input points equal to one ($Z_1=Z_2=1$). Is there any drawback of this strategy?

• If you add two points with $Z_1=Z_2=1$, the resulting point will (in general) have $Z_3 \ne 1$. Given that we typically do a full addition chain, and not just add two points together, what is your stategy when it comes time to do the second addition? Sep 23 '15 at 20:25
• In other words, the drawback is that it only works when $Z_1=Z_2=1$. :) And of course you must normalize the resulting $(X_3,Y_3,Z_3)$ if you want the $(x_3,y_3)$ coordinates that point. Sep 23 '15 at 21:58

If you add two points with $$Z_1=Z_2=1$$, the resulting point will (in general) have $$Z_3\neq1$$. Given that we typically do a full addition chain, and not just add two points together, what is your stategy when it comes time to do the second addition? – poncho
In other words, the drawback is that it only works when $$Z_1=Z_2=1$$. :) And of course you must normalize the resulting $$(X_3,Y_3,Z_3)$$ if you want the $$(x_3,y_3)$$ coordinates that point. – Chris