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» Factorization with genus 2 curves
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DCG
2011
13 years 2 months ago
The Expected Genus of a Random Chord Diagram
To any generic curve in an oriented surface there corresponds an oriented chord diagram, and any oriented chord diagram may be realized by a curve in some oriented surface. The gen...
Nathan Linial, Tahl Nowik
JOC
2006
103views more  JOC 2006»
13 years 7 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
AAECC
2007
Springer
88views Algorithms» more  AAECC 2007»
13 years 7 months ago
Hyperelliptic curves with reduced automorphism group A5
We study genus g hyperelliptic curves with reduced automorphism group A5 and give equations y2 = f(x) for such curves in both cases where f(x) is a decomposable polynomial in x2 or...
David Sevilla, Tanush Shaska
ACISP
2005
Springer
14 years 1 months ago
A Complete Divisor Class Halving Algorithm for Hyperelliptic Curve Cryptosystems of Genus Two
We deal with a divisor class halving algorithm on hyperelliptic curve cryptosystems (HECC), which can be used for scalar multiplication, instead of a doubling algorithm. It is not ...
Izuru Kitamura, Masanobu Katagi, Tsuyoshi Takagi
CHES
2004
Springer
148views Cryptology» more  CHES 2004»
14 years 26 days ago
Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations
We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3 over prime fields. To achieve a fair comparison between the different types of groups,...
Roberto Maria Avanzi