  Elliptic curve multiplications can be improved by replacing the standard
ladder algorithm's base 2 representation of the scalar multiplicand, with
mixed-base representations with power-of-2 bases, processing the n bits of the
current digit in one optimized step. For this purpose, we also present a new
methodology to compute, for Weierstrass form elliptic curves in the affine
plane, operations of the type mP+nQ where m and n are small integers. This
provides implementations with the lower cost than previous algorithms, using
only one inversion. In particular, the proposed techniques enable more
opportunities for optimizing computations, leading to an important speed-up for
applications based on elliptic curves, including the post-quantum cryptosystem
Super Singular Isogeny Diffie Hellman (SIDH).
