Hash function based on block cipher (and proof of security in the PRP model) Do there exist proofs of security for primitives like hash functions (based on a block cipher) in the PRP model. 

I often see proofs in the random oracle model (for hash function based on compression function) and proofs in the ideal cipher model (for hash function based on block cipher).

Are there proofs of such primitive in a real world model?
A PRP is a keyed primitive, so proving properties of a keyed hash on top of it is often possible. Reducing the security of an unkeyed hash to a keyed primitive on the other hand is rarely possible.

For example keyed Skein (a hash) is provably a PRF if Threefish (a block-cipher) is a PRP:


  PRF, MAC, and KDF. We prove that if Threefish is a tweakable PRP (pseudorandom permutation) then Skein is a PRF. It is important to understand that we are referring, in this context,
  to the keyed version of Skein. The PRF property is that the input-output behavior of keyed Skein
  should look like that of a random function to an attacker who is not given the key. This proof
  supports the usage of keyed Skein for key derivation (KDF). It also supports the use of keyed Skein
  as a MAC. This is true because any PRF is a secure MAC