# Unkeyed, fast, one-way PRP

Are there any fast, secure, one-way, unkeyed almost-pseudorandom permutations? I am looking for something that can hide a MAC, without requiring a secret key and while being much faster than public key crypto. It is important that it is a almost-PRP, not a PRF.

By "almost-PRP", I mean "a one-to-one function that is also preimage resistant"

• What exactly do you mean with "hide a MAC"? A MAC is normally indistinguishable from random if the key is secret. If you want to make the same input generate a different MAC then you need to include (and probably save) some kind of random value. Feb 15 '16 at 0:53
• Many MACs give away the secret key if the MAC is known and the key is reused, unless a cipher is used to hide its value.
– Demi
Feb 15 '16 at 0:58
• As pg1989 explains, unkeyed PRPs can only exist for domains with at most 1 element. ​ ​
– user991
Feb 15 '16 at 1:02
• – user991
Feb 15 '16 at 1:16
• You may be looking for one-way permutations. Feb 15 '16 at 4:55

Well, no. For something to be a pseudorandom permutation on some domain $\mathcal{D}$, it must be the case that a p.p.t. adversary can't distinguish it from a randomly-chosen permutation on $\mathcal{D}$. If there is no key or if the key is public, the adversary can just make a bunch of encryption queries and check whether they have the same ciphertext as the public permutation's.