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Paper: Generalizing Kedlaya's order counting based on Miura Theory

Authors:
Joe Suzuki
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URL: http://eprint.iacr.org/2004/129
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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 G\"{u}rel) 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.
BibTeX
@misc{eprint-2004-12101,
  title={Generalizing Kedlaya's order counting based on Miura Theory},
  booktitle={IACR Eprint archive},
  keywords={foundations / Kedlaya, Miura, order counting, elliptic curves},
  url={http://eprint.iacr.org/2004/129},
  note={ suzuki@math.sci.osaka-u.ac.jp 12568 received 30 May 2004},
  author={Joe Suzuki},
  year=2004
}