Your app picks up a bunch of feeds and composes them into a nice page for you, much like an RSS feed reader. The twist is that each feed is encrypted in a way that only you can decrypt, so the cryptography also gives strong identity guarantees, and allows for private messaging.

It's basically PGP + RSS, only mapped to a bunch of files of specific structure. Those could be RSS/ATOM feeds instead of JSON, to reuse an existing format. The reuse of the ideas is good, these ideas are time-proven.

As any PGP-lookalike, this thing has the key distribution problem, and won't scale to billions of users due to that. Key rotation and revocation is another problem. But for a small-scale network it should be fine, and can run on very tiny, very low-power devices, maybe even with intermittent connectivity.