Elliptic Curves: Point Counting
Schoof-Elkies-Atkin
Free implementation
(Mike Scott)
Satoh Algorithm
[
]
The Canonical Lift of an Ordinary Elliptic Curve over a Finite Field and its Point Counting
(Takakazu Satoh)
Point counting of an elliptic curve over GF(5
569
)
(Takakazu Satoh)
Counting points on elliptic curves
(Mireille Fouquet)
On Satoh's algorithm and its implementation
(Fouquet, Gaudry, Harley, 2000)
Satoh Point Counting in Characteristic 2
(Berit Skjernaa)
Canonical Lifting of Elliptic Curves and p-Adic Point Counting -- Theoretical Background
(Takakazu Satoh, slides)
Fast Computation of Canonical Lifts of Elliptic curves and its Application to Point Counting
(Takakazu Satoh, Berit Skjernaa and Yuichiro Taguchi, 2001 (preprint))
Kedlaya's algorithm
[
]
Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology
(Kiran S. Kedlaya, math.AG/0105031)
An extension of Kedlaya's point counting algorithm to superelliptic curves
(P Gaudry, N Gurel, Asiacrypt 2001)
An extension of Kedlaya's algorithm to Artin-Schreier curves in characteristic 2
(J Denef, F Vercauteren, ANTS 5)
Counting points in medium characteristic using Kedlaya's algorithm
(P Gaudry, N Gurel, Experiment. Math, 2003)
An extension of Kedlaya.s algorithm to hyperelliptic curves in characteristic 2
(J Denef, F Vercauteren, JOC 2004)
Cryptology Pointers
by
Helger Lipmaa
Got any suggestions or additional links? Mail to
<helger.lipmaa>
gmail.com
NB! If you find any broken links, please be kind and report them to me together with their current location!
(C) Helger Lipmaa 1997-2009.