Fast arithmetic on Jacobians of Picard curves

Stéphane Flon; Roger Oyono

Paper 2003/079

Fast arithmetic on Jacobians of Picard curves

Stéphane Flon and 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 PS
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Jacobians Picard curves algebraic curves cryptography discrete logarithm problem
Contact author(s): flon @ math uni-bonn de
oyono @ exp-math uni-essen de
History: 2003-08-21: revised; 2003-04-28: received; See all versions
Short URL: https://ia.cr/2003/079
License: CC BY

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}
}