Say you just define your total hash to be the sum of hashes for some constituent data. You change a constituent datum, so you subtract the old hash, add the new

Say you just define your total hash to be the sum of hashes for some constituent data. You change a constituent datum, so you subtract the old hash, add the new hash. What will you get when you decrypt the total hash? Probably some gibberish data. If your hashing had the homomorphic property, then when you do the add/subtract song and dance with some datum’s new hash, the resulting total hash has the property that it decrypts to be the sum of the (updated) data. A practical example might be keeping track of the average salary of a group of people without ever learning the salary of any one of them. As they get raises, you learn only about their new encrypted salaries, but you can update the encryption of the average salary directly, knowing that it will decrypt to the correctly updated new average inclusive of raises you never explicitly saw. (Here I am using the term “hash” loosely to refer to the cipher text of whatever data item is encrypted.)