Q:

Expanding/Inverse Hash function

First off, before I ask my question, let me explain what I am NOT asking. I am NOT asking for a way/method to reverse a hash output; by definition, a hashing function is one-way.
Is there such a thing as an inverse hashing function? I am likely calling it the wrong name. What I mean is a function where, for example, if the input is 100 characters long the output will be 150 characters long. So, a one-way hash where the output is always larger than the input. However, traditional hashes usually make the output smaller than the input (if the input is of a reasonable size).
I am no security expert, so I am open to the possibility that I am mistaken. However, it seems to me that this kind of hash with a longer output would be harder to crack with a rainbow table, etc. Of course, it would be less useful than a traditional hash for things like assigning an image an ID, but for security applications, might it be superior? And of course, the ratio of input size to output size needs not be fixed, making it that much harder to predict the input.

A:

Hashing is an algorithmic manipulation of data. A cryptographic hashing function is one-way function with a fixed output size regardless of the input size.
You seem to be talking about increasing security by using a different type of hash function, so no... no cryptographic hash matches properties that I didn't describe above. For other types of hashing (particular in regards to data structures), see http://en.wikipedia.org/wiki/Hash_function.
Otherwise, the answer is no and variable lengthening of input wouldn't be an improvement as it is impossible to generate more entropy by without adding more input. You can't add more input as one-way hash function must be repeatable to be useful.

