Scalar Multiplication in Elliptic Curve over Fields
We present two new strategies for parallel implementation of scalar multiplication over elliptic curves. We first introduce a Montgomery-halving algorithm which is a variation of the original Montgomery-ladder for point multiplication. This Montgomery-halving can be run in parallel with the original Montgomery-ladder in order to concurrently compute part of the scalar multiplication.
We also present two point thirding formulas in some subfamilies of curves E(F3m). We use these thirding formulas to implement scalar multiplication through (Third, Double)-andadd and (Third, Triple)-and-add parallel approaches. We also provide some implementation results of the presented parallel strategies which show a speed-up of 5%-14% on an Intel Core i7 processor and a speed-up of 8%-19% on a Qualcomm Snapdragon processor compared to non-parallelized approaches.
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