Maybe it’s the fact it can be done with multiple operators and strong encryption that is hard to grok, but at least here is a very simple example of a limited partially homomorphic encryption:
You have a 7-bit character representation (e.g. ASCII) and your encryption is to add 1 mod 128. E.g. 0 -> 1, 1 -> 2, ... 126 -> 127, 127 -> 0.
As it turns out, all your operations can be represented as adding or subtracting constants. You can now encrypt your data (+1), send it to a remote server, send all the adding and subtracting operations, pull back the processed data, decrypt the data (-1).
Of course, this example is neither useful encryption nor generally useful operation, but can be useful for grokking why it might be possible.
You have a 7-bit character representation (e.g. ASCII) and your encryption is to add 1 mod 128. E.g. 0 -> 1, 1 -> 2, ... 126 -> 127, 127 -> 0.
As it turns out, all your operations can be represented as adding or subtracting constants. You can now encrypt your data (+1), send it to a remote server, send all the adding and subtracting operations, pull back the processed data, decrypt the data (-1).
Of course, this example is neither useful encryption nor generally useful operation, but can be useful for grokking why it might be possible.