Fast addition on non-hyperelliptic genus $3$ curves

Stéphane Flon; Roger Oyono; Christophe Ritzenthaler

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: Jacobians non-hyperelliptic curves algebraic curves cryptography discrete logarithm problem
Contact author(s): oyono @ exp-math uni-essen de
History: 2004-05-19: received
Short URL: https://ia.cr/2004/118
License: 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},
      url = {https://eprint.iacr.org/2004/118}
}