International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Joe Suzuki

Publications

Year
Venue
Title
2004
EPRINT
Generalizing Kedlaya's order counting based on Miura Theory
Joe Suzuki
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.
1999
ASIACRYPT
1999
EUROCRYPT
1998
ASIACRYPT