Method of Searching Birationally Equivalent Edwards Curves Over Binary Fields

  • Zhengbing Hu
  • Sergiy Gnatyuk
  • Maria Kovtun
  • Nurgul Seilova
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 754)


This paper is devoted to increasing of performance of digital signature algorithms based on elliptic curves over binary fields. Group operations complexity on Edwards curves are less than on Weierstrass curves and have immunity to some side channel attacks. Hence, it is interesting to search birationally equivalent curves in Edwards form for curves in Weierstrass form presented in NIST recommended curves list. It allows using operations over points on Edwards curve in intermediate computations in scalar multiplications over curves in Weierstrass form. This approach improves the performance and security of digital signature.


Cryptography Random binary elliptic curves Weierstrass curves Edwards curves Digital signature Cube root 



This scientific work was financially supported by self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (CCNU16A02015).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Zhengbing Hu
    • 1
  • Sergiy Gnatyuk
    • 2
  • Maria Kovtun
    • 2
  • Nurgul Seilova
    • 3
  1. 1.Central China Normal UniversityWuhanChina
  2. 2.National Aviation UniversityKyivUkraine
  3. 3.Satbayev UniversityAlmatyRepublic of Kazakhstan

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