The problem seems simple at first: just assign an id and represent that in binary.

The issue arises because the user is capable of changing as many 0 bits to a 1 bit. To clarify, the hash could go from 0011 to 0111 or 1111 but never 1010. Each bit has an equal chance of being changed and is independent of other changes.

What would you have to store in order to go from hash -> user assuming a low percentage of bit tampering by the user? I also assume failure in some cases so the correct solution should have an acceptable error rate.

I would an estimate the maximum number of bits tampered with would be about 30% of the total set.

I guess the acceptable error rate would depend on the number of hashes needed and the number of bits being set per hash.

I'm worried with enough manipulation the id can not be reconstructed from the hash. The question I am asking I guess is what safe guards or unique positioning systems can I use to ensure this happens.