In this paper we propose a multiplicative blinding scheme for protecting implementations of a scalar multiplication over elliptic curves. Specifically, this blinding method applies to elliptic curves in the short Weierstra?? form over large prime fields. The described countermeasure is shown to be a generalization of the use of random curve isomorphisms to prevent side-channel analysis, and our best configuration of this countermeasure is shown to be equivalent to the use of random curve isomorphisms. Furthermore, we describe how this countermeasure, and therefore random curve isomorphisms, can be efficiently implemented using Montgomery multiplication.