  In this paper we address the problem of protecting elliptic curve scalar
multiplication implementations against side-channel analysis by using the
atomicity principle. First of all we reexamine classical assumptions made by
scalar multiplication designers and we point out that some of them are not
relevant in the context of embedded devices. We then describe the
state-of-the-art of atomic scalar multiplication and propose an atomic pattern
improvement method. Compared to the most efficient atomic scalar multiplication
published so far, our technique shows an average improvement of up to 10.6%.
