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Fast addition on non-hyperelliptic genus $3$ curves
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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 }