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» Isomorphism Classes of Picard Curves over Finite Fields
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AAECC
2005
Springer
104views Algorithms» more  AAECC 2005»
13 years 4 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»
13 years 6 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»
13 years 6 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
13 years 8 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...