# Tweaking textbook RSA to make the encryption a Pseudorandom function

Lets say I want to tweak/alter the textbook RSA encryption function to create a pseudorandom function by pre-processing the input.

Suppose I do something simple like add 2 to the input before encrypting it:

$$c = (m+2)^e \bmod N$$

How do I know if this is not a secure pseudorandom function? Does this give any information about N?

I am aware that no tweak can make it a pseudo-random function. I am just trying to understand which values this setting cannot output so as to build a distinguisher. Sorry if I wasn't clear earlier. My question originally meant to ask which ciphertexts cannot be the output of this setting in order to distinguish it from a purely random function. I know 1 thing - This setting will never output 0 & 1 as the input is bounded $$0<=m<2^n$$

-
Didn't you answer your own question with the edit? This function can never output zero or one. If not, please clarify your question. –  user4549 Dec 18 '12 at 11:38

This is not a secure pseudorandom function. No tweak is going to make this a pseudorandom function. After all, it is a public-key operation, so anyone who knows your algorithm can compute $f(m)$ given $m$. Consequently, it cannot possibly be pseudorandom: there will always be a trivial distinguisher.