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 $$0<=m<2^n$$