Not all public key cyphers are based on the difficulty of factorizing huge primes. Quantum computing only solves a small subset of problems we have, but it doesn't solve NP.
AES-256 takes 2^256 guesses to break by brute force and by using Grover's quantum algorithm that's only improved to 2^128. It is something, but I can bet that AES-256 will at some point become insufficient due to Moore's law, not due to quantum computing - a theory that has originated in the 1980-1981 and that has yet to yield actual machines that we can use. And of course, Moore's law also works in our favour, since with more power and specialized chips, we'll be able to use bigger keys that aren't likely to be breakable by Moore's law or Quantum computing in the next century or even millennium.
As long as we cannot reduce NP problems to P, then virtually unbreakable cryptography is possible. Also, cryptography as a (mathematical) field is pretty new.
> not due to quantum computing - a theory that has originated in the 1980-1981 and that has yet to yield actual machines that we can use.
Uhm – classical computer science originated sometime in the early 19th century (possibly earlier) in the form of analytical engines and the first actually usable machines[0] were created just a bit before World War II. General relativity originated before WWI and was first used well after WW II. Quantum mechanics was invented at the beginning of the last century and the first usable LASERs were built in the 1960s.
Really, 30 years is not that long in the context of ‘hard’ science. Even in the ‘fast-moving’[1] field of software engineering, people still use SMTP (1982), TCP/IP (1975) and FTP (1971).
[0] ‘Usable’ in the same sense that QC are not usable yet because people can perfectly factor 15 without Shor’s algorithm.
[1] Because it’s young and hence easy to discover new stuff.
Given the accelerated R&D that happened since the 70-ties in computer science, the huge resources that this industry can throw at problems and the fact that quantum computing can theoretically solve many important problems for us, 30 years is a long time.
I'm not saying that it won't happen eventually. I'm only saying that Moore's law is a more imminent threat to current encryption methods and that quantum computing still doesn't solve NP and as long as NP is not P, unbreakable encryption is a reality that quantum computing won't change.
The problem here is that QC is not lagging behind in the field of computer science (all the theories are there) nor the field of hardware engineering (the engineers can build every we tell them to), but in (condensed matter) physics. And physics is something you can only speed up so much, especially given that there are many other equally exciting, high-profile projects (think LHC).
AES-256 takes 2^256 guesses to break by brute force and by using Grover's quantum algorithm that's only improved to 2^128. It is something, but I can bet that AES-256 will at some point become insufficient due to Moore's law, not due to quantum computing - a theory that has originated in the 1980-1981 and that has yet to yield actual machines that we can use. And of course, Moore's law also works in our favour, since with more power and specialized chips, we'll be able to use bigger keys that aren't likely to be breakable by Moore's law or Quantum computing in the next century or even millennium.
As long as we cannot reduce NP problems to P, then virtually unbreakable cryptography is possible. Also, cryptography as a (mathematical) field is pretty new.