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 over can be embedded to that over the extension field , with This implies that supersingular hyperelliptic curves are cryptographically weaker than the general case due to the Frey-Rck attack. A family of the hyperelliptic curve of the type and 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}
}