Constructing genus 2 curves with applications
to cryptography -- Kristin Lauter

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Using standard complex
multiplication techniques to construct genus 2 curves for use in cryptography
leads immediately to questions about the primes of bad reduction for such
curves.  In joint work with Eyal Goren, we explicitly bound the primes of bad
reduction in terms of the discriminant of the quartic CM field.  Our results
also leads to a proof that the DeShalit-Goren construction gives S-units for an
explicit set S, relevant to Stark's conjectures for quartic CM fields and
generalizing the elliptic units construction.