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|Title:||Software Implementation Of Koblitz Curves Over Quadratic Fields|
|Abstract:||In this work, we retake an old idea presented by Koblitz in his landmark paper , where he suggested the possibility of defining anomalous elliptic curves over the base field F-4. We present a careful implementation of the base and quadratic field arithmetic required for computing the scalar multiplication operation in such curves. In order to achieve a fast reduction procedure, we adopted a redundant trinomial strategy that embeds elements of the field F-4(m), with m a prime number, into a ring of higher order defined by an almost irreducible trinomial. We also report a number of techniques that allow us to take full advantage of the native vector instructions of high-end microprocessors. Our software library achieves the fastest timings reported for the computation of the timing-protected scalar multiplication on Koblitz curves, and competitive timings with respect to the speed records established recently in the computation of the scalar multiplication over prime fields.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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