The Montgomery ladder on binary elliptic curves
In this survey paper, we present a careful analysis of the Montgomery ladder procedure applied to the computation of the constant-time point multiplication operation on elliptic curves defined over binary extension fields. We give a general view of the main improvements and formula derivations that several researchers have contributed across the years, since the publication of Peter Lawrence Montgomery seminal work in 1987. We also report a fast software implementation of the Montgomery ladder applied on a Galbraith–Lin–Scott (GLS) binary elliptic curve that offers a security level close to 128 bits. Using our software, we can execute the ephemeral Diffie–Hellman protocol in just 95,702 clock cycles when implemented on an Intel Skylake machine running at 4 GHz.