An Elementary Approach to the Group Law on Elliptic Curves
Number Theory
2024-06-24 v2
Abstract
We revisit the group structure on elliptic curves and give a simple and elementary proof of the associativity of the addition. We do this by providing an explicit formula for the sum of three points, only using the explicit definition of the group structure. In the process we find a nice geometric interpretation of the sum of three points on the elliptic curve.
Cite
@article{arxiv.2401.02346,
title = {An Elementary Approach to the Group Law on Elliptic Curves},
author = {Sander Zwegers},
journal= {arXiv preprint arXiv:2401.02346},
year = {2024}
}
Comments
6 pages, extended and updated