Does encryption using PRP mean indistinguishable encryption against an eavesdropper? I am a student studying cryptography by reading "Introduction to Modern Cryptography".
I have some confusion about encryption using PRP (e.g., AES).

Briefly speaking, a keyed deterministic permutation $F_{k}$ is a strong PRP if no efficient adversary (who is given oracle access to $F_k$ and $F_k^{-1}$) can distinguish whether it is interacting with $F_k$ (for uniform $k$) or $f$, where $f$ is chosen uniformly from the set of all permutations having the same domain and range.

I think the definition above says nothing about the relation between two ciphertexts which are generated by a PRP.

Now, I consider the following experiment $PrivK_{\mathcal{A},\Pi}^{eav}(n)$ for any encryption scheme $\Pi= (Gen,Enc,Dec)$.


The adversary $\mathcal{A}$ is given input $1^n$, and outputs a pair of messages $m_0$,$m_1$, with $|m_0| = |m_1|$.
A key $k$ is generated by running $Gen(1^n)$, and a uniform bit $b \in \{0,1\}^n$ is chosen. Ciphertext $c \gets Enc_k(m_b)$ is computed and given to $\mathcal{A}$.
$\mathcal{A}$ outputs a bit $b^{'}$.
The output of the experiment is defined to be 1 if $b^{'}=b$, and 0 otherwise.


A private-key encryption scheme has indistinguishable encryptions in the presence of an eavesdropper if for all PPT adversaries $\mathcal{A}$ there is a negligible function $negl$ such that, for all $n$,
$Pr[PrivK_{A,\Pi}^{eav}(n)] &lt;= \frac{1}{2} + negl(n)$.

Does the encryption scheme has indistinguishable encryptions in the presence of an eavesdropper if $Enc = F_k$ and $Dec = F_k^{-1}$, where $F_k$ is a strong PRP?

In other word, when I encrypt two messages by using PRP, adversaries can be able to tell whether the two messages are identical since PRP is deterministic. However, can I ensure that it is infeasible for adversaries to learn any partial infomation about the plaintext from the cipertext?
The PRP encryption scheme is secure in your security definition, but this security is very weak. It only achieves "one-time security" and is also weaker than perfect secrecy, i.e., the adversary's advantage is not exactly 1/2.

I think the security can be stronger (but still cannot be IND-CPA for instance). With PRP security, we can view $F_k$ (and hence $Enc_k,Dec_k$) as a real random permutation $f$ (except for a negligible PRP security advantage). Then, even if the adversary knows $p$ message-ciphertext pairs, it still cannot distinguish $m_0,m_1$ if they do not belong to the known $p$ messages.