  Regev recently introduced a quantum factoring algorithm that may be perceived
as a $d$-dimensional variation of Shor's factoring algorithm. In this work, we
extend Regev's factoring algorithm to an algorithm for computing discrete
logarithms in a natural way. Furthermore, we discuss natural extensions of
Regev's factoring algorithm to order finding, and to factoring completely via
order finding. For all of these algorithms, we discuss various practical
implementation considerations, including in particular the robustness of the
post-processing.
