[mtreis86]

There are a number of reversible hash algos. The point of hash is that the small changes in the input produce big changes in the output so even a 1-bit change to the input produces a completely different output. Some hash algos having trap door functionality is really more of a bonus.

[eru]

You can only reverse your hash function, if you output is at least as long as your input.

The kind of function you describe is useful, too, of course. You can build something like them out of almost any modern encryption method:

Encryption methods have to be reversible, so you can decrypt; and they are expected not to betray anything about their inputs, so there are probably some that have this avalanche property, or can be patched to have it fairly simply.

[enkid]

Sure, I guess I wasn't being specific enough. Once of the reasons to use SHA-256 is because that's hard to do.