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Implementation attacks and more specifically Power Analysis (PA) (the dominant type of side channel attack) and fault injection (FA) attacks constitute a pragmatic hazard for scalar multiplication, the main operation behind Elliptic Curve Cryptography. There exists a wide variety of countermeasures attempting to thwart such attacks that, however, few of them explore the potential of alternative number systems like the Residue Number System (RNS). In this paper, we explore the potential of RNS as an PA-FA countermeasure and propose an PA-FA resistant scalar multiplication algorithm and provide an extensive security analysis against the most effective PA-FA techniques. We argue through a security analysis that combining traditional PA-FA countermeasures with lightweight RNS countermeasures can provide strong PA-FA resistance.