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
JacobiansPicard curvesalgebraic curves cryptographydiscrete 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2003/079}},
      url = {https://eprint.iacr.org/2003/079}
}
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