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Groups from cyclic infrastructures and PohligHellman in certain infrastructures
1.  Institut für Mathematik, Universität Zürich, CH8057, Switzerland 
We recall the PohligHellman method, define the concept of a cyclic infrastructure and briefly describe how to obtain such infrastructures from certain function fields of unit rank one. Then, we describe how to obtain cyclic groups from discrete cyclic infrastructures and how to apply the PohligHellman method to compute absolute distances, which is in general a computationally hard problem for cyclic infrastructures. Moreover, we give an algorithm which allows to test whether an infrastructure satisfies certain requirements needed for applying the PohligHellman method, and discuss whether the PohligHellman method is applicable in infrastructures obtained from number fields. Finally, we discuss how this influences cryptography based on cyclic infrastructures.
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