The finite field $\mathbb F_{p^p}$, for a prime $p$, can be described as $\mathbb F_p[x]/(x^p−x−1)$. Let $G=\mathbb F_{p^p}^\times/\mathbb F_{p}^\times$. Estimate the cost of obtaining the discrete log base $x$ of an arbitrary element of G using the elements of $G$ with a representative of the form $x − a$, $a ∈ \mathbb F_p$ as factor base.
Can some one please explain this in detail to me?
So far i have found the elements in Fp*, (all the elements from 1,2,,,,p-1, for some value of p)
However i dont understand what to do next in terms of trying to find the cost of obtaining the discrete log base x? Also what is it meaning by representative of the form x − a, a ∈ Fp as factor base?