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The proof is loosely as below. Lets assume a one round Feistel network, where $2n$ bits are divided into $n$ bits each $L_0, R_0$ The encryption is defined as $L_{1} = R_{0}, \\ R_{1} = L_0 \oplus f(R_0) $ where f is any random function (PRF) and $\oplus$ is XOR operation Now the cipher text is $L_{2} = R_{1}, R_{2} = L_1 $ Decryption is same as ...


This will not be secure in general, and is not recommended. The reason is that a PRG is guaranteed to produce a pseudorandom output only if its input is uniformly random (or pseudorandom). Moreover, several PRG outputs are jointly pseudorandom only if the PRG is run on independent seeds. But here you are invoking the PRG on "structured" inputs, i.e., the ...

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