PRF proof and length-preserving I'm studying for my crypto exam and got stuck on following example:
Is $F'_k(x) = F_k(0||x)||F_k(1||x)$ with $x \in \{0,1\}^{n-1}$ a PseudoRandom Function PRF, under the assumption, that $F_k$ is a PRF?
In the solution, there is a reduction proof stating, that $F_k'$ is a PRF. What gets me confused is the definition for PRF, which states, that $F:\{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}^n$ has to be an efficient, length-preserving, keyed function, in order to be a PRF. In my opinion $F'_k(x)$ is not length-preserving and can therefore not be an PRF. Can someone explain this to me?
(here || denotes concatenation)
A PRF does not have to be length-preserving. We sometimes define it that way for simplicity. In general, $F:\{0,1\}^n \times \{0,1\}^{\ell_1(n)} \rightarrow \{0,1\}^{\ell_2(n)}$ for polynomials $\ell_1,\ell_2$.