You do need to update yourself. There are standard gates, complete computation theories, and algorithms for lots of interesting problems. Those aren't even new.

Either they have made a breakthrough in number theory that allows factorisation over finite fields, or they have a quantum computer already, or they are banking on having one soon. In any case, storage is so cheap that it makes sense to just record the traffic (which is useful for sigint anyway) and refer back to it “if and when”.

Of course, much of what we consider “public-key encrypted” traffic is actually encrypted with a symmetric cipher whose encryption is impervious to Shor’s Algorithm… it is the key-exchange process that really uses the textbook public-key encryption algorithms. So much of the traffic is technically impervious to whatever advances they have made, but of course once you have captured the key-exchange “handshake” that sets up the session and exchanges the symmetric cipher keys, you’re all set to retrieve the plaintext from the intercept.

There are public-key algorithms (particularly those based on lattices) that we currently hold to be secure against attack by quantum computers. I am surprised these are not seeing more adoption amongst the “enlightened paranoid cypherpunk elite”. Here is a primer on such “post-quantum cryptography” approaches, courtesy of the good folks at Wikipedia: https://en.wikipedia.org/wiki/Post-quantum_cryptography