Surely you'd mean to keep "unwanted presences" off the network?
An app wouldn't remove a list of problems, it'd add them. Least of all in maintaining the app over time. It's also a software only solution that would be forced to leverage the existing and easy to manipulate/disrupt existing technologies. There's no way it's transmitter will get out of atmos reliably enough for data xfer, without "modifications". We require a method that's difficult to disrupt, and preferably one that readily bypasses existing technologies.
You're planning on combining encryption systems with smartphones?
There's a reason the CPU in them things cache encryption keys, and it's not for speed of access. It might be the same reason none of these devices ever get MOD clearance, or even authorisation to be present in "sensitive" areas. Even rooted, you're less in control over that device than some random in an office in Langley Falls. Or Shenzhen. Etc.
Having third parties in posession of the private key you're using kinda nullifies the entire point of having enryption in the first place.
It's possible to authenticate to such a network using PKS-11 but this again would require purchasing more hardware for most users. Things like smartphones probably wouldn't be very simple to link to a reader, and again, is likely to clone off the key.
I'd suggest for now to use a system similar to what I use for authentication to my VPN - X.509 - Each machine has a certificate it generated, which then gets signed by the server without ever leaving the machine. As it's actually possible to trust my hardware, I can then be sure the only copy of that key exists on the machine it's used for, in the event of compromise, or a machine leaving my possession then the certificate is simply revoked remotely. In the event of compromise of any individual machines key, then the other traffic remains protected.
I've toyed with the idea of embedding keys into passports, along with ID - but again, most users will require additional hardware for NFC/RFID reading(I could possible produce these for less than $10/unit, I've not looked how much they can be bought for as a product).
As for satellites, it was my first thought. Requires line of sight and succeptable to atmospheric disturbances, and again, easily wavebubbled or simply drowned with "noise". Would also require most users to purchase additional hardware - which if at all possible should be avoided. If unavoidable, rendered as cheap as practical.