### Elliptic curves: double and add

Written by Dominik Joe Pantůček on 2018-05-03

Last time we have shown how to perform scalar multiplication of point on elliptic curve in simple Weierstrass form over a finite field. We have also shown that all the required properties hold for all rational points of the curve - which is a good thing. The problem we have not tackled yet is the complexity of the scalar multiplication operation. Today we are about to present a method of performing fast scalar multiplication in which the complexity of the operation grows much slower than the size of the scalar.