Are there circuits that operate on plaintext, analogous to how FHE works?

Question

Fully Homomorphic Encryption lets us operate over encrypted data. Is there something analogous that let us operate over plaintexts directly, without knowing the circuit?

For example, let's say that I store AES of the user's password, and I want to be able to change the user's password to password +1 at my will without interacting with him. The user would be able to send me a circuit that decrypts the AES, adds +1 to the password, and re-encrypts it. The difference from FHE here is that I would be able to see the result AES(password+1) in plaintext, where in FHE I'd have the FHE(AES(password+1))

This talks about circuits Representing a function as FHE circuit. No, you can design an FHE protocol that, you will have still the AES encrypted password+1. It is quite costly, though. With a true FHE that has semantical security, you can execute almost all circuits with some huge cotst. — kelalaka, Jan 31 '22 at 13:45
In your case, why does the user has the AES key of the password? — kelalaka, Jan 31 '22 at 13:47
And Can we proxy-re-encrypt using homomorphic encryption schemes? — kelalaka, Jan 31 '22 at 14:42
Not sure if I totally understand your answer but maybe you want to check out the malleability property, however malleable ciphers aren't semantically secure. — tur11ng, Jan 31 '22 at 18:27
Obfuscation allows someone to run an unkown circuit on a known input and get the answer in clear. You can search for indistinguishability obfuscation, for example. — Hilder Vitor Lima Pereira, Feb 01 '22 at 12:19

Are there circuits that operate on plaintext, analogous to how FHE works?

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