Algorithms for Efficient Simultaneous Elliptic Scalar Multiplication with Reduced Joint Hamming Weight Representation of Scalars

  • Yasuyuki Sakai
  • Kouichi Sakurai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2433)


The computational performance of cryptographic protocols using an elliptic curve strongly depends on the efficiency of the scalar multiplication. Some elliptic curve based cryptographic protocols, such as signature verification, require computation of multi scalar multiplications of kP + lQ, where P and Q are points on an elliptic curve. An efficient way to compute kP + lQ is to compute two scalar multiplications simultaneously, rather than computing each scalar multiplication separately. We introduce new efficient algorithms for simultaneous scalar multiplication on an elliptic curve. We also give a detailed analysis of the computational efficiency of our proposed algorithms.


Elliptic Curve Cryptosystems Scalar Multiplication 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Yasuyuki Sakai
    • 1
  • Kouichi Sakurai
    • 2
  1. 1.Mitsubishi Electric CorporationKanagawaJapan
  2. 2.Kyushu UniversityFukuokaJapan

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