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JUCS
2008

Parallel Formulations of Scalar Multiplication on Koblitz Curves

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Parallel Formulations of Scalar Multiplication on Koblitz Curves
We present an algorithm that by using the and -1 Frobenius operators concurrently allows us to obtain a parallelized version of the classical -and-add scalar multiplication algorithm for Koblitz elliptic curves. Furthermore, we report suitable irreducible polynomials that lead to efficient implementations of both and -1 , thus showing that our algorithm can be effectively applied on all the NIST-recommended curves. We also present design details of software and hardware implementations of our procedure. In a two-processor workstation software implementation, we report experimental data showing that our parallel algorithm is able to achieve a speedup factor of almost 2 when compared with the standard sequential point multiplication. In our hardware implementation, the parallel version yields a more modest acceleration of 17% when compared with the traditional point multiplication algorithm. Although the focus is on Koblitz curves, analogous strategies are discussed for other curves, ...
Omran Ahmadi, Darrel Hankerson, Francisco Rodr&iac
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where JUCS
Authors Omran Ahmadi, Darrel Hankerson, Francisco Rodríguez-Henríquez
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