# meaning of Reduce f modulo the order of the base point G

I am trying to perform some math operations related to Elliptic curve cryptography, and came across this sentence: Reduce f modulo the order of the base point G. What does it mean?

• Do you know what "reduce $x$ modulo $y$" and "the order of a point" mean? – Ilmari Karonen Jun 2 '16 at 21:08

## 1 Answer

First a preliminary: a base point $G$ on an elliptic curve generates a group of points on the curve such that every point in that group can be written as $dG$ ($d$ times $G$) where $d$ is an integer. This group is also cyclic in that for a certain value $q > 1$ we have that $qG = \mathcal{O}$, where $\mathcal{O}$ is the identity element, known as the point at infinity. This value $q$ is known as the group order. Reducing $f$ modulo $q$ is equivalent to calculating the remainder of dividing $f$ by $q$.

For standardized elliptic curves you won't need to calculate the group order yourself, it's usually included with the rest of the curve parameters.