An Elliptic Curve scalar multiplication product involving a scalar and a base point is determined in a manner that acts as a countermeasure to side channel attacks. A key splitting strategy called Additive Splitting Using Division involves selecting a random integer and determining an integer quotient and a remainder by dividing the scalar by the random integer. The product may then be expressed as a sum of scalar multiplications, which may be evaluated using a combination of a fixed-sequence window method with the known Interleaving method. When the integer quotient and remainder are odd, major collisions may be avoided when determining the product. Accordingly, the random integer that determines whether the integer quotient and remainder are odd may be subject to some control.