Subtracting a point in elliptic curve cryptography? I've had lots of practice adding points for my crypto class. However I've run into a situation where I need to subtract two points for decryption:

Pm + kPb - nb(kG) = Pm


Where Pm is the plaintext, Pb is participant b's public key, nb is participant b's private key, G is a base point in the elliptic group Ep(a,b), and k is a random positive integer chosen by participant a. 

I am able to compute nb(kG) and kPb, but I'm unsure how to subtract the two. How is this done?
The inverse of a point $P = (x_P,y_P)$ is its reflexion across the $x$-axis : $P' = (x_P,-y_P)$.

If you want to compute $Q-P$, just replace $y_P$ by $-y_P$ in the usual formula for point addition.