Finally we use local classifield theory to describe the Brauer group of local fields by cyclic algebras classified by their invariant. We explain how this is related to the classical discrete logarithm in finite fields. By the celebrated Hasse-Brauer-Noether-Sequence we can globalize and find an Index-Calculus-Algorithm to determine local invariants. We shall apply this both to the discrete logarithm in finite fields and to the computation of the Euler totient function.