There was a decision last year by the FCC about encryption. The FCC rejected a proposal to allow encryption in amateur radio.
FCC Dismisses
Here's a snippet from the news story, which states that encryption is not allowed:
But to answer your question, here's a few examples:
Encryption = encoded and obscuring. Now it was said "if the key is provided publicly." Where is this info provided? If you tune to a random frequency and there's an encrypted conversation going on, how does one know where to look for the "publicly provided" key? A website? A particular person? Just putting it on a website doesn't make it "public", if the public doesn't know where to look.
This then means that the station would also be in violation of:
Now you may say, "Wait a minute, what about other digital modes like D-STAR?" Other digital modes are "in the clear" meaning anyone the can decode the digital signal can hear the stations using the frequency, and can also hear the call signs of the stations using the frequency. When encrypted, there's no way to hear the legal ID of the stations using the frequency unless they have the encryption key. That's where we go back to my first point, how would another ham (or the FCC) know where to look for the encryption key?
There are also other sections in Part 97 which address specific allowed emission types. You can view the entire, up to date Part 97 rules here:
eCFR — Code of Federal Regulations