Analysis of Fractional ωmbNAF for Scalar Multiplication

  • Weixuan LiEmail author
  • Wei Yu
  • Kunpeng Wang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9065)


In the current work we analyze the average Hamming weight of recoded sequence obtained by fractional ωmbNAF algorithm using Markov theory. Cost comparison between fractional ωmbNAF and different scalar recoding methods is given. Regardless of memory restraint, it is shown that \(\{2,3,5\}\mbox{NAF}_{3+\frac{3}{4}}\) improves tree-based double base chain by a factor of 6.8% and 13.2% is Jacobian curves(with efficiency-orient selected parameter a = 3) and inverted Edwards curves respectively.


Elliptic curve cryptosystem scalar multiplication Hamming weight multi-base non-adjacent form fractional window 


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.State Key Laboratory of Information Security, Institute of Information EngineeringChinese Academy of SciencesBeijingChina
  2. 2.Data Assurance and Communication Security Research CenterChinese Academy of SciencesBeijingChina
  3. 3.University of Chinese Academy of SciencesBeijingChina

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