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

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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