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New Parallel Approaches for Scalar Multiplication in Elliptic Curve over Fields of Small Characteristic | IEEE Journals & Magazine | IEEE Xplore

New Parallel Approaches for Scalar Multiplication in Elliptic Curve over Fields of Small Characteristic


Abstract:

We present two new strategies for parallel implementation of scalar multiplication over elliptic curves. We first introduce a Montgomery-halving algorithm which is a vari...Show More

Abstract:

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)-and-add 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 percent on an Intel Core i7 processor and a speed-up of 8-19 percent on a Qualcomm Snapdragon processor compared to non-parallelized approaches.
Published in: IEEE Transactions on Computers ( Volume: 64, Issue: 10, 01 October 2015)
Page(s): 2875 - 2890
Date of Publication: 09 January 2015

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