International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Paper: Fast arithmetic on Jacobians of Picard curves

Authors:
St?phane Flon
Roger Oyono
Download:
URL: http://eprint.iacr.org/2003/079
Search ePrint
Search Google
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.
BibTeX
@misc{eprint-2003-11795,
  title={Fast arithmetic on Jacobians of Picard curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Jacobians, Picard curves, algebraic curves cryptography, discrete logarithm problem},
  url={http://eprint.iacr.org/2003/079},
  note={ flon@math.uni-bonn.de, oyono@exp-math.uni-essen.de 12285 received 25 Apr 2003, last revised 21 Aug 2003},
  author={St?phane Flon and Roger Oyono},
  year=2003
}