Isomorphism Classes of Picard Curves over Finite Fields

Jong Won Lee

Paper 2003/060

Isomorphism Classes of Picard Curves over Finite Fields

Jong Won Lee

Abstract

In this paper we determine the number of isomorphism classes of Picard curves, i.e., superelliptic curves $y^{3} = f (x)$ of genus three, over finite fields of characteristic different from $3$ . In the process of doing this we also provide reduced forms of Picard curves together the number of such forms up to isomorphism. In addition to its own theoretical meaning it has applications to cryptography.

Metadata

Available format(s): PDF PS
Category: Foundations
Publication info: Published elsewhere. preprint
Keywords: Picard curves superelliptic curves isomorphism classes algebraic function field
Contact author(s): lee @ exp-math uni-essen de
History: 2003-04-07: received
Short URL: https://ia.cr/2003/060
License: CC BY

BibTeX

@misc{cryptoeprint:2003/060,
      author = {Jong Won Lee},
      title = {Isomorphism Classes of Picard Curves over Finite Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/060},
      year = {2003},
      url = {https://eprint.iacr.org/2003/060}
}