[schoen]

But the thing about this setting is that you don't possess the secrets, so you can't reveal the secrets by noticing how long things take.

An analogy to think about might be blind signatures. In blind signatures you sign a blinded token and then the other party can unblind it to get a valid signature from you over a message whose content you don't know. This is classical public-key cryptography. In that case there is a secret key, and a timing attack against someone who can observe the signature creation might reveal that key. The connection between the blinded and unblinded message is also meant to be secret, and a timing attack against someone performing the blinding or unblinding operations might also reveal that relationship.

However, there is no timing attack that the signer can perform against itself to reveal the relationship between the blinded and unblinded messages, and there is no timing attack that the other party can perform against itself to reveal the secret key.

I think this analogy holds up for most purposes (indeed, blind signatures can be viewed as an extremely specific, narrow kind of homomorphic encryption), but I'd be happy to hear corrections if someone can see a way that it doesn't.

[mSparks43]

so whats the "cloud-keyset " then?

the "side channel" i am referring to is in however this impliments this mixing you refer to.

if you can observe how the internal state is changing given a cloud keyset you should be able to infer the secret key. in the same way you can infer the iv used in a mesernine twister from like 27 cycles (or whatever).

downvotes and promises definately wont reduce my skeptacism.

[enigma83]

The "cloud keyset" is another name for "public key". Usually, public key enables encryption but no decryption, here, the cloud key enables computations on ciphertexts, but not decryption.

Like in public key cryptography, you can give a RSA public key to an adversary, he can use it as much as he want, he will not be able to get any information on the private key (in any practical time). Most importantly, the cloud key is not secret, nor obfuscated: the cloud already knows each bits of it (side channel attacks are not relevant).

The "cloud key" is the public part of the key given to the cloud so that he can perform his operations (circuit, bootstrapping). There are strong security proofs that show that it is impossible to recover the secret key from the cloud key.

In the case of TFHE, if there was a polynomial algorithm that would recover even a single bit of the secret key given the cloud key, this algorithm could be used to break the LWE problem, and also worst case instances of lattice problems (which are much harder than factorization or discrete log for instance).