On Indifferentiable Hashing into the Jacobian of Hyperelliptic Curves of Genus 2

  • Michel Seck
  • Hortense Boudjou
  • Nafissatou DiarraEmail author
  • Ahmed Youssef Ould Cheikh Khlil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10239)


Many authors have studied the problem of constructing indifferentiable and deterministic hash functions into elliptic and hyperelliptic curves with well-distributed encodings. In this work, we have designed three encodings suitable for indifferentiable hashing for the following hyperellitic curves of genus 2: \(\mathbb {H}^{1}: y^{2}=F_{1}(x)=x^{5}+ax^{4}+cx^{2}+dx, \ \mathbb {H}^{2}: y^{2}=F_{2}(x)=x^{5}+bx^{3}+dx+e; \ \mathbb {H}^{3}: y^{2}=F_{3}(x)=x^{5}+ax^{4}+e\). Since they are well-distributed, our encodings can be used to design indifferentiable and deterministic hash functions into the Jacobian of these hyperelliptic curves, using the technique developed by Farashahi et al. in 2013 (J. Math. Comput). Because of square rooting steps, these new encodings have the same asymptotic complexity as the work of Kammerer et al. at Pairing 2010, namely \(\mathcal {O}(\log ^{2+\circ (1)}q)\).


Indifferentiable deterministic hashing Injective encoding Elliptic curve-based cryptography Jacobian Elligator Random bit-string 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Michel Seck
    • 1
  • Hortense Boudjou
    • 2
  • Nafissatou Diarra
    • 1
    Email author
  • Ahmed Youssef Ould Cheikh Khlil
    • 1
  1. 1.Department of Mathematics-InformaticsCheikh Anta Diop UniversityDakarSenegal
  2. 2.Maroua UniversityMarouaCameroon

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