Kinda late here, and unqualified to comment on math - just wanted to mention, in case ECC and the others eventually are compromised - there is something to fall back on. The "one time pad" method "has been proven to be impossible to crack if used correctly" (https://en.wikipedia.org/wiki/One-time_pad). Given a side channel that's secure for the purpose, I expect there could be a software implementation that would be usable indefinitely.
Most systems that attempt to implement one time pads are just stream ciphers built from crappy random number generators; they're crappier versions of RC4. Real one time pads aren't particularly useful (which is why they're rarely used): they require keys as long as their plaintexts.
If you are an organisation with deep pockets (nation state) and are willing to send trusted (armed, diplomatic) couriers to every end point you want to talk securely with (embassies) every month then it can be secure but it will definitely be expensive.
