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» Isomorphism Classes of Picard Curves over Finite Fields
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AAECC
2005
Springer
104views Algorithms» more  AAECC 2005»
14 years 9 months ago
Isomorphism Classes of Picard Curves over Finite Fields
In this paper we determine the number of isomorphism classes of Picard curves, i.e., superelliptic curves y3 = f(x) of genus three, over finite fields of characteristic different f...
Jong Won Lee
PKC
2010
Springer
210views Cryptology» more  PKC 2010»
14 years 11 months ago
Efficient Arithmetic on Hessian Curves
This paper considers a generalized form for Hessian curves. The family of generalized Hessian curves covers more isomorphism classes of elliptic curves. Over a finite filed Fq, it ...
Reza Rezaeian Farashahi, Marc Joye
ANTS
2008
Springer
106views Algorithms» more  ANTS 2008»
14 years 11 months ago
Computing in Component Groups of Elliptic Curves
Let K be a p-adic local field and E an elliptic curve defined over K. The component group of E is the group E(K)/E0(K), where E0(K) denotes the subgroup of points of good reduction...
J. E. Cremona
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...