private keys for multiple devices
A simple solotion could be that all phones need to have the same pre-shared key.
The pre-shared key could be downloaded once at first run, maybe from a password protected httpS site, or maybe from a url that delivers an encrypted and signed file with private/public key.

Then the pre-shared key is used on all phones, and it is used to encrypt by the sender, and decrypt by everyone else.

This simple solution provides only encryption, because  this is what the only requirement of the original question.

This doesn't address all security issues, for example replay attack and impersonation.
If you needed more than just encryption, then the solution will have to be a bit more complex.