Security properties of an encryption scheme built from a PRP and a PRG Note: This was my in-class problem last week and potentially will be on the exam tomorrow. Thus, I want to reconfirm my thoughts so that I'll be ready to face this type of question (if appear) tomorrow.
Question:

Assume I have an encryption where the key is computed using a PRP $P$ and the message is computed using a PRG $G$ so that
$$E(k,m) = ( P(k,r) , G(r) \oplus m )$$
(also given) $k \in K = X = Y = \{0,1\}^n$ and $m \in M = \{0,1\}^{2n}$
$P$ is the PRP, $G$ is the PRG, and $k$ and $m$ are the key and the message belonging to the keyspace $K$ and message space $M$ respectively, and $r$ is a random bitstring.

My thoughts:
First, I say that $E(k,m)$ is not perfectly secure because $|M| &gt; |K|$.
Second, I can argue that $E(k,m)$ is indistinguishable because the message is generated by a PRG (assuming that the seed is independent &amp; uniformly distributed).
Third, I claim that $E(k,m)$ is CPA-Secure too because the PRG makes the message non-deterministic.
Fourth, I think $E(k,m)$ is CCA-Secure too, right?
Please feel free to correct me, I don't mind criticism. I think some of my thoughts are still wrong. I just want to feel ready for the exam.
Fourth, I think $E(k,m)$ is CCA-Secure too, right?


Consider this: what if an attacker takes a valid ciphertext $E(k,m) = ( P(k,r) , G(r) \oplus m )$ and flips a bit, so that it is $P(k, r), G(r) \oplus m \oplus 1$.  What would happen if you gave this altered ciphertext to the decryptor?