I know very little about cryptography, so I apologize if the question does not make sense.
Let's say we design a function $F(P, X) \rightarrow K$ that takes in a pre-shared private key $P$ and a publicly available source of randomness (say a server that generates true random numbers) $X$. The output $K$ of this function is a new key that we use as a one-time-pad to encrypt and decrypt a message.
The sender pre-share the key $P$, the function $F$ and the source of randomness to the receiver before their communication. For every new message $M$, the sender collects the random information $X$, generates a one-time-pad $K$ using the function $F$ and encrypts the message with $K$. The receiver generates the same $K$ and decrypts the message.
My questions are
- This scheme is not information theoretic secure, right? because AFAIK, the one-time-pad cannot be reused in any way, but in this case, we are reusing $P$ for every message, which can be considered as part of the one-time-pad $K$
- Is this scheme viable? Is it more secure than simply encrypting/decrypting with the pre-shared key $P$?