Impact of Optimized Field Operations AB,AC and AB + CD in Scalar Multiplication over Binary Elliptic Curve

  • Christophe Negre
  • Jean-Marc Robert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7918)


A scalar multiplication over a binary elliptic curve consists in a sequence of hundreds of multiplications, squarings and additions. This sequence of field operations often involves a large amount of operations of type AB,AC and AB + CD. In this paper, we modify classical polynomial multiplication algorithms to obtain optimized algorithms which perform these particular operations AB,AC and AB + CD. We then present software implementation results of scalar multiplication over binary elliptic curve over two platforms: Intel Core 2 and Intel Core i5. These experimental results show some significant improvements in the timing of scalar multiplication due to the proposed optimizations.


Optimized field operations AB,AC and AB + CD doubleand- add halve-and-add parallel scalar multiplication software implementation carry-less multiplication 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christophe Negre
    • 1
    • 2
  • Jean-Marc Robert
    • 1
    • 2
  1. 1.Team DALIUniversité de PerpignanFrance
  2. 2.LIRMM, UMR 5506Université Montpellier 2 and CNRSFrance

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