A Pseudo-Random Permutation (PRP) is a function that cannot be distinguished (with practical effort) from a permutation selected at random with uniform probability from the family of all permutations on the function's domain.

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Pseudorandom Function Proof

Given a set of pseudorandom functions $F=\{f_s^i\}_i$ for each $s\leftarrow\{0,1\}^n$ generated at random; moreover each $f_s^i$ uses a specific PRG $G^i:\{0,1\}^n\to\{0,1\}^{2n}$, where: ...
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CPA-security of a pseudorandom permutation encryption scheme

Let $F$ be a pseudorandom permutation, and define a fixed-length encryption scheme $(Gen, Enc, Dec)$ as follows: on input $m \in$ $\{0,1\}^{n/2}$ and key $k \in \{0,1\}^n$, algorithm Enc ...