The Factoring Dead: Preparing for the Cryptopocalypse
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.