elliptic curve multiplication with negative factor
If you know the order of the curve (we'll call it $q$), then it's easy.

In that case, we have the identity $xP = (x + q)P$ for any $x$.  Using that identity, we can express $(-n)P$ as $(q - n)P$; by the above identity, these are the same.  If $q &gt; n$, this gives you your answer.  

The more general answer (which works for any $n$) is $(-n \bmod q)P$, using the convention that $a \bmod b$ is that integer which is between 0 and $b-1$, and which is congruent to $a$ modulo $b$.

This is exactly analogous to the $\mathbb{G}^*$ case; in that case, the size of the group is $\phi(q)$; in this Elliptic curve case, the size of the group is $q$.