In this paper, we combine the RNS representation and the Montgomery ladder on elliptic curves in Weierstrass form. These two techniques are relevant for implementation of elliptic curve cryptogra- phy on embedded devices since they have leak-resistance properties. We optimize formulae for addition and doubling of the Montgomery lad- der in terms of modular reductions to obtain a competitive and secure implementation. Afterwards, we explain the advantages of the RNS rep- resentation, especially in hardware and for embedded devices, and show that, contrary to other approaches, ours takes optimal advantage of a dedicated parallel architecture.