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Delaying and Merging Operations in Scalar Multiplication: Applications to Curve-Based Cryptosystems

  • Roberto Maria Avanzi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4356)

Abstract

In this paper we introduce scalar multiplication algorithms for several classes of elliptic and hyperelliptic curves. The methods are variations on Yao’s scalar multiplication algorithm where independent group operations are shown in an explicit way. We can thus merge several group operations and reduce the number of field operations by means of Montgomery’s trick. The results are that scalar multiplication on elliptic curves in even characteristic based on point halving can be improved by at least 10% and the performance of Koblitz curves by 25% to 32%.

Keywords

Elliptic Curf Scalar Multiplication Hyperelliptic Curve Accumulation Step Operation Count 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Roberto Maria Avanzi
    • 1
  1. 1.Faculty of Mathematics and Horst Görtz Institute for IT Security, Ruhr-University BochumGermany

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