Hash function based on pseudorandom functions and security Are there hash functions that make use of pseudorandom functions. Precisely, I'm looking for a specification of a hash function based on PRF (and based on the security of such a primitive).
Note that a PRP is a PRF for a large enough block size. Hash functions based on block ciphers will probably be of interest to you.

There are some general schemes for using block ciphers to build hash functions. You may want to investigate them and what requirements they have for the underlying block cipher. Unfortunately, the PRP model is a weak requirement for a block cipher, schemes that use block ciphers often use stronger assumptions (like the MDC-2 hash is built on block ciphers by using the Ideal Cipher model).

For a modern example, the popular SHA-3 hash contestant Skein is based on the block cipher Threefish. You could investigate if/what PRF or PRP models are used in the analysis of Skein and Threefish.