Genus 2 point counting over prime fields
Identifieur interne : 001950 ( Hal/Checkpoint ); précédent : 001949; suivant : 001951Genus 2 point counting over prime fields
Auteurs : Pierrick Gaudry [France] ; Éric Schost [Canada]Source :
- Journal of Symbolic Computation [ 0747-7171 ] ; 2012.
Abstract
For counting points of genus 2 curves over a large prime field, the best known approach is essentially an extension of Schoof's genus 1 algorithm. We propose various practical improvements to this method and illustrate them with a large scale computation: we counted hundreds of curves, until one was found that is suitable for cryptographic use, with a state-of-the-art security level of approximately 2^128 and desirable speed properties. This curve and its quadratic twist have a Jacobian group whose order is 16 times a prime.
Url:
DOI: 10.1016/j.jsc.2011.09.003
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