I am trying to better understand homomorphic encryption, but I feel like I keep getting inconsistent information in the papers that I am reading.
One of the papers I am reading says the following:
Earlier, homomoprhic encryption was defined as a form of encryption where a specific algebraic operation performed on plaintext is equivalent to another algebraic operation performed on its ciphertext
Meanwhile, another paper says the following:
For now, a homomorphic cryptosystem can be thought of as an oracle, or black box, that, when given two ciphertexts and an operation, returns an encryption of the result of that operation on the two corresponding plaintexts.
The wording of the first one makes it seem as though the operation does not have to be the same (it says "another"), but the wording of the second one makes it seem as though the operation IS the same.
Can somebody clear up which one is correct?