We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.

Let $K=\mathbb{Q}\left(\theta \right)$ be a pure cubic field, with ${\theta }^3=D$, where $D$ is a cube-free integer. We will determine the reduced ideals of the order $𝒪=\mathbb{Z}\left[\theta \right]$ of $K$ which coincides with the maximal order of $K$ in the case where $D$ is square-free and $\neg \equiv \pm 1(mod9)$.