Speeding up elliptic scalar multiplication using multidoubling

Yasuyuki Sakai, Kouichi Sakurai

Research output: Contribution to journalLetterpeer-review

2 Citations (Scopus)


We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2k P directly from P without computing the intermediate points, where P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

Original languageEnglish
Pages (from-to)1075-1083
Number of pages9
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number5
Publication statusPublished - 2002

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics


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