Does a two-way fixed-length hash function exist? Just wondering if a two-way fixed-length hash function exists. I'm not talking about encryption where your output is the same size if not larger than your input. I guess the best way I can put it is "like SHA or MD5, but also reversible." (I know SHA and MD5 aren't reversible by design, but you get the point).
What I understood from your question is that you want to map your data uniquely such that the output has less bits relative to the input. You can use data compression techniques to compress your data. Then, if you need the security, use cryptography. Although hash functions are able to compress your data, but they can't be reversed by everyone. This goal is opposite of their nature and their duties.