Apologies for being extremely clueless, I don't even understand advanced math, not to mention encryption, not to mention "quantum stuff" - that's why I ask here: is it theoretically possible (or could it be in the future) to use quantum computers for encryption, too? If so, would that reduce options for breaking it to "brute force on the quantum level"? Does this question even make sense?
I don't know of any research into this area, but it's conceivable that you could have an encryption algorithm that is polynomial time (given the key!) on a quantum computer but exponential time classically, and that has some better security guarantees given certain common assumptions. However, quantum algorithms of any sort are difficult enough to invent that we'll likely end up using classical algorithms that 'look' hard to break with quantum computers, i.e. ones where prime factoring doesn't help.
The real quantum defence appears to be something rather different. Quantum cryptography (https://en.wikipedia.org/wiki/Quantum_cryptography) uses polarised photons to create very strong guarantees that your communication is secure. We can say that if you do the engineering correctly, the laws of physics would have to be violated to intercept your messages.
