What is the default hash code that Mathematica uses?

The online documentation says

Hash[expr] 
  gives an integer hash code for the expression expr.
Hash[expr,"type"]
  gives an integer hash code of the specified type for expr.

It also gives "possible hash code types":

• "Adler32" Adler 32-bit cyclic redundancy check


• "CRC32" 32-bit cyclic redundancy check


• "MD2" 128-bit MD2 code


• "MD5" 128-bit MD5 code


• "SHA" 160-bit SHA-1 code


• "SHA256" 256-bit SHA code


• "SHA384" 384-bit SHA code


• "SHA512" 512-bit SHA code

Yet none of these correspond to the default returned by Hash[expr].

So my questions are:

• What method does the default Hash use?


• Are there any other hash codes built in?

Answer

The default hash algorithm is, more-or-less, a basic 32-bit hash function applied to the underlying expression representation, but the exact code is a proprietary component of the Mathematica kernel. It's subject to (and has) change between Mathematica versions, and lacks a number of desirable cryptographic properties, so I personally recommend you use MD5 or one of the SHA variants for any serious application where security matters. The built-in hash is intended for typical data structure use (e.g. in a hash table).

The named hash algorithms you list from the documentation are the only ones currently available. Are you looking for a different one in particular?