It seems that the minimal size of Pseudorandom permutation (PRP) output is $128$ bits. In general, I'd like to see if there's any minimal size of the output of pseudorandom function (PRF) as well? for instance can we set the output size of PRF to 32 or 40 bits.
Below, I'm trying to explain the question with an example.
Let $k_i$ be secure random key. I've a message $m$ of 32-bit. I want to encrypt it in two different ways:
Using output of a pseudorandom function (PRF) as a one time pad: I do the following:
b) $c_1=a \cdot m$.
Using a Pseudorandom permutation (PRP):
Question 1: What is the minimal size of $c_1$? Can we set the output size of PRF to 32 bits, so the size of $c_1$ would be the same?
Question 2: what is the minimal size of $c_2$? Am I right it is at least 128 bits?
Question 3: If the answer to both questions is positive, then how can we compare the security and efficiency of the above two schemes with each other?
Please kindly let me know if my question is not clear, etc instead of down voting it; and I'll address your comments.