Fast arithmetic on Jacobians of Picard curves

Stéphane Flon; Roger Oyono

Paper 2003/079 Original: eprint.iacr.org/2003/079 ↗

Fast arithmetic on Jacobians of Picard curves

Stéphane Flon

Roger Oyono

Abstract

In this paper we present a fast addition algorithm in the Jacobian of a Picard curve over a finite field $\mathbb F _q$ of characteristic different from $3$. This algorithm has a nice geometric interpretation, comparable to the classic "chord and tangent" law for the elliptic curves. Computational cost for addition is $144M + 12SQ + 2I$ and $158M + 16SQ + 2I$ for doubling.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2003-08-21: last updated; 2003-04-28: published
Short URL: https://ia.cr/2003/079
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2003/079,
      author = {Stéphane Flon and Roger Oyono},
      title = {Fast arithmetic on Jacobians of Picard curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2003/079},
      year = {2003},
      url = {https://eprint.iacr.org/2003/079}
}