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The discrete logarithm is an important crypto primitive for public key cryptography. The main source for suitable groups are divisor class groups of carefully chosen curves over finite fields. Because of index-calculus algorithms one has to avoid curves of genus ≥ 4 and non-hyperelliptic curves of genus 3. An important observation of Smith [S] is that for "… (More)

The main motivation for the paper is to understand which hyperelliptic curves of genus 3 defined over a field K of characteristic = 2 appear as the image of the Donagi-Livné-Smith construction. By results in [FK] this means that one has to determine the intersection W of a Hurwitz space defined by curves of genus 3 together with cover maps of degree 4 to P… (More)

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