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1

There are several known attack techniques on homomorphic computation. Google's first paper describes an attack involving a modified secret key. In this paper we present an attack on this fully homomorphic encryption scheme. In fact, our attack only aims at its “somewhat homomorphic encryption algorithm”. We construct a modified secret key, a modified ...


11

Even though all the operations you described can be performed homomorphically, the result remains encrypted, i.e., the attacker cannot "see" it. So homomorphic computation is not useful (on its own) as an attack, because the results remain unknown to the attacker. For example, given two ciphertexts $c, c'$, an attacker can homomorphically compute whether ...


2

Yes, standard GC are not re-usable, thus by means of GC you may outsource the computation of a single function on a single input (i.e. you delegate a function described by a Boolean circuit and later you may ask the evaluation of the function on a single input not fixed in advance). Indeed this is the approach to Verifiable Computation proposed in a paper ...


2

No, what you want to do is not possible, because encryption is randomized: if you were to encrypt the same message many times, you'd get many different ciphertexts. Therefore, Alice can't just compare two ciphertexts to see if they are the same; the two ciphertexts will be different even if they decrypt to the same thing.


0

Since Alice encrypts the message $m$ she knows the plaintext. Now Bob computes F with the public key of Alice.Alice knows the secret key of the underlying homomorphic scheme and decrypts $C'$ and obtains the underlying values. This is how homomorphic schemes operate



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