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In this paper, we present a background on elliptic curve cryptosystems (ECCs) along with the different methods used to compute the scalar multiplication (ECSM), which is the core operation of ECCs, and the various costs associated with them. We have also provided a brief background on Simple (SPA) and Differential (DPA) power and electromagnetic analysis attacks on the classical ECSM algorithms. We study on minor collisions and to provide an analytic result for their probability of occurrence as well as effect of the fixed sequence window method.

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