An analysis of the infrastructure in real function fields

We construct a map injecting the set of infrastructure ideals in a real function field into the class group of the correspoding hyperelliptic curve. This map respects the ‘group-like’ structure of the infrastructure, as a consequence of this construction we show that calculating distances in the set of infrastructure ideals is equivalent to the DLP in the underlying hyperelliptic curve. We also give a precise description of the elements missing in the infrastructure to be a group.