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Erschienen in:
2017 | OriginalPaper | Buchkapitel
On Indifferentiable Hashing into the Jacobian of Hyperelliptic Curves of Genus 2
verfasst von : Michel Seck, Hortense Boudjou, Nafissatou Diarra, Ahmed Youssef Ould Cheikh Khlil
Erschienen in: Progress in Cryptology - AFRICACRYPT 2017
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Abstract
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 \(\mathcal {O}(\log ^{2+\circ (1)}q)\).