[mSparks43]

you dont need to get the key, you just need to decrypt the data.

they do not need to be one in the same, if, statistically you can infer input given output.

And i never said sure in any way shape or form. what i said is i am skeptical of the motivations driving a project like this, when we know for an absolute fact bad men are trying to steal our secrets. It seems like a lot of work and very heavy math for something that will never tip the balance that is holding the cloud back with people not trusting it to keep their secrets.

for example, if you can do something as simple as compute a hash of the unencrypted data, you can instantly decrypt all data with known hashes with a high degree of certainty, without ever knowing the keys - side channel attack.

[enigma83]

In homomorphic encryption, the cloud performs operations on encrypted data, and gets only an encrypted result. He does not have any information on the decrypted result.

That's the difference between FHE and IO or multilinear maps. The second ones are almost all broken, mostly because of the attacks you mention. FHE, on the other hand, has semantic security.