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MICS
2010
112views more  MICS 2010»
13 years 10 months ago
Traces of the Group Law on the Kummer Surface of a Curve of Genus 2 in Characteristic 2
In the early 1990s, Flynn gave an explicit description of the Jacobian of a genus 2 hyperelliptic curve to perform efficient arithmetic on these objects. In this paper, we give a ...
Sylvain Duquesne
JOC
2006
103views more  JOC 2006»
13 years 11 months ago
An Extension of Kedlaya's Algorithm to Hyperelliptic Curves in Characteristic 2
We present an algorithm to compute the zeta function of an arbitrary hyperelliptic curve over a finite field Fq of characteristic 2, thereby extending the algorithm of Kedlaya for ...
Jan Denef, Frederik Vercauteren
ANTS
2008
Springer
111views Algorithms» more  ANTS 2008»
14 years 1 months ago
Computing L-Series of Hyperelliptic Curves
We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic...
Kiran S. Kedlaya, Andrew V. Sutherland
ANTS
2008
Springer
133views Algorithms» more  ANTS 2008»
14 years 1 months ago
Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors
We discuss arithmetic in the Jacobian of a hyperelliptic curve C of genus g. The traditional approach is to fix a point P C and represent divisor classes in the form E - d(P) wher...
Steven D. Galbraith, Michael Harrison, David J. Mi...
ITNG
2007
IEEE
14 years 5 months ago
Fast explicit formulae for genus 2 hyperelliptic curves using projective coordinates
This contribution proposes a modification of method of divisors group operation in the Jacobian of hyperelliptic curve over even and odd characteristic fields in projective coordi...
Thomas Wollinger, Vladyslav Kovtun