Is there a Pseudo Random Permutation Generator that can output all values of the length of N Is there a pseudo random permutation generator that produces all permutation of any bit length of the plaintext (this may not be clear, please let me know and I will explain).  It must be fast, and does not hold numbers in memory.
This is a permutation of (1)
(1)
This is a permutation of (1,2)
(2,1)
This is a permutation of (1,2,3)
(1,3,2) (2,3,1) (2,1,3) (3,1,2) (3,2,1) n!
Note* the above is not in a pseudo random order and not a complete set that I am looking for.
This is a pseudo random permutation with replacements that I am looking to duplicate with a generator of any size.
PRP of (1,2,3) with replacements
(1,1,1)(3,3,3)(2,3,3)(1,1,3)(3,3,2)(2,3,1)(2,2,2)(1,3,3)(3,2,3)(2,1,2)(1,2,2)(3,1,3)(1,1,2)(3,3,1)(2,3,2)(2,2,1)(1,3,2)(3,2,1)(2,1,1)(1,2,3)(3,1,1)(2,2,3)(1,3,1)(3,2,2)(2,1,3)(1,2,1)(3,1,2) N^N
If one does exist could you please post its name, if possible.
If it does not exist could you expound as to the reason why, if it is against a known proof, or it has simply not been made, yet.
The question here is very similar but it needs to be with replacements.
https://math.stackexchange.com/questions/3521660/invertible-pseudo-random-permutation-function
What would it mean if it could be made. Meaning given the length of any plaintext if that order and length is your first permutation of group g than all permutation after that would be your subgroup permutations. Given that the key length that produces the permutation is not an issue (I would be glad to explain this as well).
Another way of writing this would be. What program would generate all permutations of a given string with replacement? The given string is the complete message source or file to encrypt of any size. It will probably be recursive. Once all permutations are calculated it should loop back to the original permutation which is the file.
Use any true random permutation generator that relies on random input. Then replace the random input with the output of a PRNG primitive.