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Paper   IPM / M / 15384
School of Mathematics
  Title:   Injective encodings to binary ordinary elliptic curves
  Author(s):  Reza Rezaeian Farashahi (Joint with M. Fadavi and S. Sabbaghian)
  Status:   In Proceedings
  Proceeding: Proceedings of SAC 2018
  Vol.:  1349
  Year:  2019
  Pages:   434-449
  Editor:  C. Cid and M. J. Jacobson, Jr.
  Supported by:  IPM
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. In fact, 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 Tr(a)=1 as well as those with Tr(a+1)=0.

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