Generalizing Kedlaya's order counting based on Miura Theory

Joe Suzuki

Paper 2004/129

Generalizing Kedlaya's order counting based on Miura Theory

Joe Suzuki

Abstract

K. Kedlaya proposed an method to count the number of ${\mathbb F}_q$-rational points in a hyper-elliptic curve, using the Leschetz fixed points formula in Monsky-Washinitzer Cohomology. The method has been extended to super-elliptic curves (Gaudry and Gürel) immediately, to characteristic two hyper-elliptic curves, and to $C_{ab}$ curves (J. Denef, F. Vercauteren). Based on Miura theory, which is associated with how a curve is expressed as an affine variety, this paper applies Kedlaya's method to so-called strongly telescopic curves which are no longer plane curves and contain super-elliptic curves as special cases.

Metadata

Available format(s): PDF PS
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: Kedlaya Miura order counting elliptic curves
Contact author(s): suzuki @ math sci osaka-u ac jp
History: 2004-06-03: received
Short URL: https://ia.cr/2004/129
License: CC BY

BibTeX

@misc{cryptoeprint:2004/129,
      author = {Joe Suzuki},
      title = {Generalizing Kedlaya's order counting based on Miura Theory},
      howpublished = {Cryptology {ePrint} Archive, Paper 2004/129},
      year = {2004},
      url = {https://eprint.iacr.org/2004/129}
}