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Unified Formulas for Some Deterministic Almost-Injective Encodings into Hyperelliptic Curves

  • Michel Seck
  • Nafissatou Diarra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10831)

Abstract

Recently, efficient deterministic and invertible encodings on some hyperelliptic curves in genus 1 and 2 using the technique in Elligator 2 (ACM CCS 2013) have been proposed. We have successfully generalized their encodings for hyperelliptic curves of genus 3, 4 and 5. We have found unified formulas (using Mersenne numbers) for the encodings into the hyperelliptic curves of genus \(g\le 5\): \( \mathbb {H}_g : y^2=f_{g}(x)=x^{(2g+1)}+a_{(2g-1)}x^{(2g-1)} + a_{(2g-3)}x^{(2g-3)}+\ldots +a_1x+a_0\). We have conjectured that our method works on arbitrary genus.

Keywords

Deterministic encoding Injective encoding Elliptic curves-based cryptography Hyperelliptic curves Elligator Random bit-string 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceCheikh Anta Diop UniversityDakarSenegal

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