# Genus 2 Curves with Complex Multiplication

International Mathematics Research Notices, 2010.

EI

Keywords:

number theorycomplex multiplicationdeformation theory

Abstract:

Genus 2 curves are useful in cryptography for both discrete-log based and
pairing-based systems, but a method is required to compute genus 2 curves such
that the Jacobian has a given number of points. Currently, all known methods
involve constructing genus 2 curves with complex multiplication via computing
their three Igusa class polynomi...More

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