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, ...

• Type: Journal
• Year: 2008
• Where: JUCS
• Authors: Omran Ahmadi, Darrel Hankerson, Francisco Rodríguez-Henríquez
• Keywords: Algorithm, Hardware Implementation, JUCS 2008, Scalar Multiplication Algorithm