I am looking for a hashing algorithm that works like this. I start with a text file, and compute its hash. Now I know that I will remove one character at, say, position 67 and this character is a "m", and I would like to compute the new hash without reapplying the hash function to the full text, but instead using the hash of the full text and the knowledge that I removed 'm' from position 67. If I readd the "m" in the same place, I will again recompute with the same methodology and get the same initial hash.
What is the technical name for such hash functions, so that I can search some pointers around? a CRC is not what I need I guess, because (afaik) a CRC works on a stream addition, not on arbitrary changes throughout the initial data.