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

Let $\Delta$ be a numerical semigroup. In this work we show that $𝒥\left(\Delta \right)=\{I\cup \{0\}:I\text{is}\text{an}\text{ideal}\text{of}\Delta \}$ is a distributive lattice, which in addition is a Frobenius restricted variety. We give an algorithm which allows us to compute the set ${𝒥}_a\left(\Delta \right)=\{S\in 𝒥\left(\Delta \right):max(\Delta \setminus S)=a\}$ for a given $a\in \Delta .$ As a consequence, we obtain another algorithm that computes all the elements of $𝒥\left(\Delta \right)$ with a fixed genus.