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EUROCRYPT
2004
Springer
15 years 3 months ago
Construction of Secure Random Curves of Genus 2 over Prime Fields
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...
Pierrick Gaudry, Éric Schost
ASIACRYPT
2006
Springer
15 years 1 months ago
The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
Abstract. The complex multiplication (CM) method for genus 2 is currently the most efficient way of generating genus 2 hyperelliptic curves defined over large prime fields and suit...
Pierrick Gaudry, T. Houtmann, D. Kohel, Christophe...
PAIRING
2007
Springer
108views Cryptology» more  PAIRING 2007»
15 years 3 months ago
Constructing Pairing-Friendly Genus 2 Curves with Ordinary Jacobians
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. ...
David Freeman
CHES
2004
Springer
148views Cryptology» more  CHES 2004»
15 years 3 months 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
ITNG
2007
IEEE
15 years 4 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