7 search results - page 1 / 2 » Constructing Pairing-Friendly Genus 2 Curves with Ordinary J... |
PAIRING
2007
Springer
13 years 11 months ago
2007
Springer
We provide the first explicit construction of genus 2 curves over finite fields whose Jacobians are ordinary, have large prime-order subgroups, and have small embedding degree. ...
PAIRING
2010
Springer
13 years 3 months ago
2010
Springer
Constructing pairing-friendly hyperelliptic curves with small ρ-values is one of challenges for practicability of pairing-friendly hyperelliptic curves. In this paper, we describe...
ANTS
2010
Springer
13 years 9 months ago
2010
Springer
![Visualizing Elements of Sha[3] in Genus 2 Jacobians](https://www.sciweavers.org/files/imagecache/thumbnail/default/content.jpg "Visualizing Elements of Sha[3] in Genus 2 Jacobians")
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...
EUROCRYPT
2004
Springer
13 years 10 months ago
2004
Springer
For counting points of Jacobians of genus 2 curves defined over large prime fields, the best known method is a variant of Schoof’s algorithm. We present several improvements on...
IEICET
2008
13 years 5 months ago
2008
The hyperelliptic curve cryptosystems take most of the time for computing a scalar multiplication kD of an element D in the Jacobian JC of a hyperelliptic curve C for an integer k....