I have only read Craig Gentry, 2009 [1] (the first proposed FHE scheme), but the main idea is that an untrusted agent can perform operations on the encrypted da

I have only read Craig Gentry, 2009 [1] (the first proposed FHE scheme), but the main idea is that an untrusted agent can perform operations on the encrypted data (i.e., addition and multiplication) and obtain an encrypted result. The untrusted agent cannot understand the result, but they can send it to the user, and the user can decrypt it. Since the scheme is asymmetric, the untrusted agent can also encrypt new data with the public key, meaning that they can do things like: `return encrypt(x) + encrypted_data_from_user * encrypt(y)` This alone doesn't let the untrusted agent evaluate a boolean condition or run an algorithm like the one you proposed, but they can at least run encrypted data through a neural network and send the encrypted output to the user. [1] https://www.cs.cmu.edu/~odonnell/hits09/gentry-homomorphic-encryption.pdf https://www.cs.cmu.edu/~odonnell/hits09/gentry-homomorphic-e...