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?

  • 3
    $\begingroup$ Do you know what "reduce $x$ modulo $y$" and "the order of a point" mean? $\endgroup$ – Ilmari Karonen Jun 2 '16 at 21:08

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.

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.