privacy

That’s a great question to ask! The biggest weakness of any “mathematically private” communication channel is not mathematical, but simply humans (users): Alice, Bob, and also the channel itself implemented by a human coder Chris.

While we don’t need to be paranoid but as a matter of fact, even assuming Alice does everything right, Bob may be sloppy, saving decrypted plain text in a random place (even uploading his own secret key to “cloud” or something, assuming it’s good idea to have a back-up of important files). Also the channel might have a hidden backdoor, perhaps side-channel, unknown to Chris.

It seems important to be aware of these possible human factors.

Also there is this big problem of metadata (this AT&T thing seems to be also largely about metadata).

[Additionally, though less importantly, most cryptography is based on unproven mathematical conjectures, like y=f(x) is easy to compute but it’s hard to get x from y. Which may be relevant when the one-wayness is based on the difficulty of factorization as in RSA.]