Supersingular Hyperelliptic Curve of Genus 2 over Finite Fields

Y.  Choie; E.  Jeong; E.  Lee

Paper 2002/032

Supersingular Hyperelliptic Curve of Genus 2 over Finite Fields

Y. Choie, E. Jeong, and E. Lee

Abstract

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 any 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.

Metadata

Available format(s): PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: hyperelliptic curves supersingular discrete logarithm problem
Contact author(s): ejlee @ postech ac kr
History: 2002-03-13: revised; 2002-03-12: received; See all versions
Short URL: https://ia.cr/2002/032
License: CC BY

BibTeX

@misc{cryptoeprint:2002/032,
      author = {Y.  Choie and E.  Jeong and E.  Lee},
      title = {Supersingular Hyperelliptic Curve of Genus 2 over Finite Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2002/032},
      year = {2002},
      url = {https://eprint.iacr.org/2002/032}
}