# Differential addition on Montgomery curve

Point multiplication using Montgomery ladder technique over Montgomery curves only require x coordinate, which in many situation leads to faster implementation as compared to point multiplication over standard curves. However, to compute point multiplication over Montgomery curves, a differential point addition operation is required https://www.hyperelliptic.org/EFD/g1p/auto-montgom-xz.html instead of typical point addition operation on standard curves.

What does this differential point addition means and how it can be computed?

Differential point addition means that to compute $x_{P+Q}$ you need not only $x_P$ and $x_Q$, but also $x_{P-Q}$.

There are a lot of possible formulas, you can find most of them here: https://www.hyperelliptic.org/EFD/g1p/auto-montgom-xz.html