> 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.

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.