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An Encoding for the Theta Model of Elliptic Curves

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Innovations and Interdisciplinary Solutions for Underserved Areas (InterSol 2018)

Abstract

The use of elliptic curves in cryptography requires to be able to transform an information (generally a bit string) to a point of an elliptic curve. This transformation, called encoding, must be such that the encoded message can be easily and uniquely recovered from the corresponding point. In this paper we propose a new encoding that maps an element of \(\mathbb {F}_q\) to a point on the theta model for elliptic curves \(E_\lambda :\ 1+x^2+y^2+x^2y^2=\lambda ^2xy\) recently introduced in [9]. In particular, we show that this new encoding is efficiently computable (deterministic and polynomial-time). We also present a Sage software implementation to ensure the correctness of the encoding on this curve.

This work is supported by the Pole of research in Mathematics with Applications to Information Security (PRMAIS, SubSaharan Africa) sponsored by Simons Foundation and LIRIMA-MACISA Project.

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Author information

Authors and Affiliations

  1. Cheikh Anta Diop University, Dakar, Senegal

    Nafissatou Diarra

  2. The University of Bamenda, Bamenda, Cameroon

    Emmanuel Fouotsa

Authors
  1. Nafissatou Diarra
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  2. Emmanuel Fouotsa
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Corresponding author

Correspondence to Nafissatou Diarra .

Editor information

Editors and Affiliations

  1. Cheikh Anta Diop University, Dakar, Senegal

    Cheikh M.F. Kebe

  2. University System of Maryland, Bambey, Senegal

    Assane Gueye

  3. Assane University, Seck de Ziguinchor, Senegal

    Ababacar Ndiaye

  4. Carnegie Mellon University, Kigali, Rwanda

    Aminata Garba

Appendices

A An Implementation of Theta-Model-Encoding in Sage

figure c

B Example with \(q=503,u=-1,c=3\):.

figure d

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© 2018 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

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Diarra, N., Fouotsa, E. (2018). An Encoding for the Theta Model of Elliptic Curves. In: Kebe, C., Gueye, A., Ndiaye, A., Garba, A. (eds) Innovations and Interdisciplinary Solutions for Underserved Areas. InterSol 2018. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 249. Springer, Cham. https://doi.org/10.1007/978-3-319-98878-8_21

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  • DOI: https://doi.org/10.1007/978-3-319-98878-8_21

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  • Print ISBN: 978-3-319-98877-1

  • Online ISBN: 978-3-319-98878-8

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