Paper 2004/118

Fast addition on non-hyperelliptic genus $3$ curves

Stéphane Flon, Roger Oyono, and Christophe Ritzenthaler

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.

Metadata
Available format(s)
PDF PS
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Jacobiansnon-hyperelliptic curvesalgebraic curves cryptographydiscrete logarithm problem
Contact author(s)
oyono @ exp-math uni-essen de
History
2004-05-19: received
Short URL
https://ia.cr/2004/118
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2004/118,
      author = {Stéphane Flon and Roger Oyono and Christophe Ritzenthaler},
      title = {Fast addition on non-hyperelliptic genus $3$ curves},
      howpublished = {Cryptology ePrint Archive, Paper 2004/118},
      year = {2004},
      note = {\url{https://eprint.iacr.org/2004/118}},
      url = {https://eprint.iacr.org/2004/118}
}
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