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Fast arithmetic on Jacobians of Picard curves
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| 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
}