Paper 2004/129 Original: eprint.iacr.org/2004/129 ↗
Generalizing Kedlaya's order counting based on Miura Theory
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- Category
- Foundations
- Publication info
- Preprint.
- History
- 2004-06-03: last updated
- 2004-06-03: published
- Short URL
- https://ia.cr/2004/129
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}