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Fast addition on non-hyperelliptic genus $3$ curves

Authors:
St?phane Flon
Roger Oyono
Christophe Ritzenthaler
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URL: http://eprint.iacr.org/2004/118
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Abstract: We present a fast addition algorithm in the Jacobian of a genus $3$ non-hyperelliptic curve over a field of any characteristic. When the curve has a rational flex and $\textrm{char}(k) > 5$, the computational cost for addition is $148M+15SQ+2I$ and $165M+20SQ+2I$ for doubling. An appendix focuses on the computation of flexes in all characteristics. For large odd $q$, we also show that the set of rational points of a non-hyperelliptic curve of genus $3$ can not be an arc.
BibTeX
@misc{eprint-2004-12090,
  title={Fast addition on non-hyperelliptic genus $3$ curves},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Jacobians, non-hyperelliptic curves, algebraic curves cryptography, discrete logarithm problem},
  url={http://eprint.iacr.org/2004/118},
  note={ oyono@exp-math.uni-essen.de 12556 received 18 May 2004},
  author={St?phane Flon and Roger Oyono and Christophe Ritzenthaler},
  year=2004
}