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Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form

  • Toru Akishita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2259)

Abstract

We propose a new method to compute x-coordinate of kP + lQ simultaneously on the elliptic curve with Montgomery form over IFp without precomputed points. To compute x-coordinate of kP +lQ is required in ECDSA signature verification. The proposed method is about 25% faster than the method using scalar multiplication and the recovery of Y-coordinate of kP and lQ on the elliptic curve with Montgomery form over \( \mathbb{F}_p \) and also slightly faster than the simultaneous scalar multiplication on the elliptic curve with Weierstrass form over \( \mathbb{F}_p \) using NAF and mixed coordinates. Furthermore, our methodis applicable to Montgomery method on elliptic curves over \( \mathbb{F}_{2^n } \).

Keywords

Computational Cost Elliptic Curve Signature Scheme Elliptic Curf Scalar Multiplication 
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 2001

Authors and Affiliations

  • Toru Akishita
    • 1
  1. 1.Sony CorporationTokyoJapan

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