[Resource Topic] 2002/032: Supersingular Hyperelliptic Curve of Genus 2 over Finite Fields

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Supersingular Hyperelliptic Curve of Genus 2 over Finite Fields

Authors: Y. Choie, E. Jeong, E. Lee


In this paper we describe an elementary criterion to determine
supersingular hyperelliptic curve of genus 2, using
only the given Weierstrass equation.
Furthermore, we show that the discrete logarithm problem defined on
supersingular abelian variety of dimension 2 over
{\mathbb F}_p, p>16, can be embedded to that over the extension field
{\mathbb F}_{p^{k}}, with k \leq 6.
This implies that
supersingular hyperelliptic curves are cryptographically
weaker than the general case due to
the Frey-R$\ddot{u}$ck attack.
A family of the hyperelliptic
curve H/{\mathbb F}_p of the type v^2=u^5+a and v^2 = u^5 + au have been studied and further examples are listed.

ePrint: https://eprint.iacr.org/2002/032

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