I read a question a while ago (File containing its own checksum) and I have a follow-up question.
The question was something like:
Would it be possible to add a MD5-hash as the last 128 bits of a file and have that hash be the MD5-hash of the file itself?
The answer was that it was, in theory, possible using brute force.
My question is now:
Can this be done symbolically? Call the 128 added bits [a_0, ..., a_127] and perform the last iteration of the hashing algorithm symbolically. Then the hash [h_0, ..., h_127] would depend on the a:s. Then let a_0 = h_0, a_1 = h_1 etc. If there is no solution, add some padding and try at another position.
I know that the point of a check sum is to verify a file. This is just theoretical reasoning.