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)


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 \( \mathbb{F}_{2^n } \).


Computational Cost Elliptic Curve Signature Scheme Elliptic Curf Scalar Multiplication 
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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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