Injective Encodings to Binary Ordinary Elliptic Curves

  • Mojtaba Fadavi
  • Reza Rezaeian FarashahiEmail author
  • Soheila Sabbaghian
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11349)


Representing points of elliptic curves in a way that no pattern can be detected by sensors in the transmitted data is a crucial problem in elliptic curve cryptography. One of the methods that we can represent points of the elliptic curves in a way to be indistinguishable from random bit strings is using injective encoding function. So far, several injective encodings to elliptic curves have been presented, but the previous encoding functions have not supported the binary elliptic curves. More precisely, the only injective encoding to binary elliptic curves was given for Hessian curves, the family of elliptic curves with a point of order 3. In this paper, we propose approaches for constructing injective encoding algorithms to the ordinary binary elliptic curves \(y^2+xy=x^3+ax^2+b\) with \(\mathrm {Tr}(a)=1\) as well as those with \(\mathrm {Tr}(a+1)=0\).


Elliptic curve Cryptography Injective encoding 



The authors thank Diego Aranha and Anonymous reviewers for the useful comments of this work. This research was in part supported by a grant from IPM (No. 96050416).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mojtaba Fadavi
    • 1
  • Reza Rezaeian Farashahi
    • 1
    • 2
    Email author
  • Soheila Sabbaghian
    • 1
  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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