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Short Memory Scalar Multiplication on Koblitz Curves

  • Katsuyuki Okeya
  • Tsuyoshi Takagi
  • Camille Vuillaume
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3659)

Abstract

We present a new method for computing the scalar multiplication on Koblitz curves. Our method is as fast as the fastest known technique but requires much less memory. We propose two settings for our method. In the first setting, well-suited for hardware implementations, memory requirements are reduced by 85%. In the second setting, well-suited for software implementations, our technique reduces the memory consumption by 70%. Thus, with much smaller memory usage, the proposed method yields the same efficiency as the fastest scalar multiplication schemes on Koblitz curves.

Keywords

Elliptic curve cryptosystems Koblitz curves scalar multiplication NAF polynomial basis normal basis change-of-basis smartcard 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Katsuyuki Okeya
    • 1
  • Tsuyoshi Takagi
    • 2
  • Camille Vuillaume
    • 1
  1. 1.Systems Development LaboratoryHitachi, Ltd.KawasakiJapan
  2. 2.Future UniversityHakodateJapan

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