Fast addition on non-hyperelliptic genus 3 curves

@article{Flon2004FastAO,
  title={Fast addition on non-hyperelliptic genus 3 curves},
  author={St{\'e}phane Flon and Roger Oyono and Christophe Ritzenthaler},
  journal={IACR Cryptology ePrint Archive},
  year={2004},
  volume={2004},
  pages={118}
}
We present a fast addition algorithm in the Jacobian of a genus 3 non-hyperelliptic curve over a field k of any characteristic. When the curve has a rational flex and k is a finite field of characteristic greater than 5, the computational cost for addition is 163M + 2I and 185M + 2I for doubling. We study also the rationality of intersection points of a line with a quartic and give geometric characterizations of C3,4 curves and Picard curves. To conclude, an appendix gives a formula to compute… CONTINUE READING
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