The thing that I always want to know with FHE: the gold standard of modern encryption is IND-CCA security. FHE by definition cannot meet that standard (being able to change a ciphertext to have predictable effects on the plaintext is the definition of a chosen ciphertext attack). So how close do modern FHE schemes get? ie how much security am I sacrificing to get the FHE goodness?
Is the used scheme fully homomorphic encryption or just homomorphic wrt a specific operation? Because they only mention "homomorphic" without the "fully".
Swift Homomorphic Encryption implements the Brakerski-Fan-Vercauteren (BFV) HE scheme (https://eprint.iacr.org/2012/078, https://eprint.iacr.org/2012/144) (without bootstrapping). This is a leveled HE scheme, which supports a limited number of encrypted adds and multiplies (among other operations).
[Disclosure: I work on the team responsible for the feature]
You can't attain IND-CCA2 (adaptively choosing cyphertexts based on previous decryptions). You can attain IND-CCA1 (after a decryption oracle, you're done fiddling with the system).
Right, but IND-CCA1 is kind of a toy security goal though. A sort theoretical consolation prize if you can’t achieve the real thing. And AFAICT, no actually implemented schemes do obtain even CCA1?
Sure, but that's "how much security you're sacrificing to get the FHE goodness," and, as always in crypto systems, implementations might not be that good.
> A sort theoretical consolation prize if you can’t achieve the real thing
The real thing exists largely because it makes proofs easier. For something like FHE you can bolt on some extra user-space features to build something like IND-vCCA (your decryption oracle refuses to operate if the result was not obtained by executing the right algorithm on the right ciphertext), which may or may not make FHE suitable for this or that target application. It's not a weak property though.
> The real thing exists largely because it makes proofs easier.
I would not say that. It exists because practical padding oracle attacks (which are adaptive CCA) have been known for decades. CCA2 very much captures real-world attacks. Is there any realistic attack that is captured by CCA1? (Or vCCA).
Padding oracle attacks also generalise to any kind of parsing after decryption. Padding tends to be studied because it is independent of any particular format/application and also part of several encryption scheme definitions. The definition of CCA2 captures very realistic scenarios - almost all applications do some parsing after decryption and so are quite likely to reveal an oracle. Would vCCA also capture such attacks?
