Latest encrypted devices proposal, what & how

I’m trying to better understand how integrity of the data is maintained on untrusted devices, especially if untrusted devices are used to seed trusted devices. I’m thinking of a worst case scenario where the only copy I’m left with is that on a untrusted device. Based on this copy (and knowing the key) I’d like to be able to verify I have a complete, unmodified version of the original (unencrypted) data.

As far as I understand, the untrusted device would have an encrypted copy of the database. That database only makes sense on the trusted device though since file/block hashes only match when data is unencrypted. Is that correct?

IMHO the question is how we can verify an untrusted device’s data integrity. If the untrusted device was able to verify integrity itself this would save us from having to download all the encrypted files to check their unencrypted version against (local) trusted hashes. I could imagine having an additional set of hashes per encryption key would be the most elegant solution. Would that have too much of an impact performance-wise?