$\newcommand{\G}{{\mathcal{G}}}$ Diffie--Hellman key exchange is a fundamental primitive in public-key cryptography. If \(\G\) is an abelian group (written additively), then the Diffie--Hellman protocol in \(\G\) is composed of four computations in the form \[ P \longmapsto [m]P = \underbrace{P + \cdots + P}_{m \text{ times}} \] for various points \(P\) and integers \(m\); optimising this *scalar multiplication* operation is therefore crucial.