Building the index independently on each client means if you login from a new device you need to wait for the index to be built. That said, maybe the index can itself be encrypted and uploaded to the server to be downloaded by new clients. Also building index is potentially expensive on a mobile phone and I don't want to wait for my phone to be plugged in to be able to search recent emails. The alternative would be to have an always on computer at home that decrypts, indexes your emails and then your mobile client updates its database from there. This whole system feel so fragile though.
I'm no expert in cryptography or syncing databases but imagine there are a lot of technical and usability issues.
But how often do you log in from a new phone? And yes it could be.
> Also building index is potentially expensive on a mobile phone and I don't want to wait for my phone to be plugged in to be able to search recent emails.
As I said in more detail before, I don't think it is.
> I'm no expert in cryptography or syncing databases but imagine there are a lot of technical and usability issues.
There's a few. But making an app is already a process of dealing with dozens of technical and usability issues. None of these new ones sound like dealbreakers.
The index doesn't need the attachments, does it? At a couple kilobytes per message you can fit a whole lot of text into a reasonable amount of phone storage. And there's no reason it should be slow.
> Also if you have multiple clients, which one is going to update the index and how do they sync up?
Each client can either independently index new emails as they come in or upload something like a compressed csv of new entries for the index database. A hundred new emails should only take milliseconds to process.
> if it needs to index pdfs and images.
How do you index images? Indexing pdfs is much more of a nicety than a necessity, and it could be a setting on whether you want to spend the data. It shouldn't take long though, as far as I know. You don't need to render it or anything.
> If multiple mobile clients build their own indices syncing them and merge conflicts might arise.
If they build their own then you don't need to sync.
If they share and do sync, I still don't see how you'd get merge conflicts. Emails don't change, and index updates are just adding and removing entire emails.