Let $p$ be a prime number. Let $f$ and $g$ be irreducible polynomials over $\mathbb{F}_p$, both of degree $n$. We know that factor-rings $\mathbb{F}_p[x]/(f)$ and $\mathbb{F}_p[x]/(g)$ are isomorphic (both of them is isomorphic to $\mathbb{F}_{p^n}$).

My question is: Is it possible to make this isomorphism *efficient*? I.e. can we find a matrix that makes an isomorphism between $\mathbb{F}_p[x]/(f)$ and $\mathbb{F}_p[x]/(g)$ for poly(n) operations in $\mathbb{F}_p$?

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