Highly Regular Right-to-Left Algorithms for Scalar Multiplication

This papers introduces several binary scalar multiplication algorithms with applications to cryptography. Remarkably, the proposed algorithms regularly repeat the same pattern when evaluating a scalar multiplication in an (additively written) abelian group. Furthermore, they are generic and feature the following properties: – no dummy operation is involved; – no precomputation nor prior recoding is needed; – a small number of temporary registers / code memory is required; – the scalar is processed right-to-left. As a result, they are particularly well fitted for implementing cryptosystems in constrained devices, in an efficient yet secure way.