Genus 2 point counting over prime fields

Authors:
Pierrick Gaudry;Éric Schost
Affiliations:
LORIA, CNRS/INRIA/Nancy Université, Nancy, France;Computer Science Department, The University of Western Ontario, London ON, Canada
Venue:
Journal of Symbolic Computation
Year:
2012

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Abstract

For counting points of Jacobians 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 2^1^2^8 and desirable speed properties. This curve and its quadratic twist have a Jacobian group whose order is 16 times a prime.