But remember that before we build our Dyson sphere, we may get quantum computers, which makes our bruteforcing polynomial rather than exponential. Cryptsystems based on discrete log, EC discrete log or prime factorization (pretty much all existing crypto-infrastructure) are vulnerable.
More on this http://en.wikipedia.org/wiki/Post-quantum_cryptography
I think that's wrong. Grover's algorithm let's us speed up any algorithm, but not exponentially. You just take the sqrt of the run time.
Shor's algorithm lets us factor numbers in polynomial time. This would break RSA, but not every algorithm in general. I think, but I'm not 100% sure, that elliptic curve methods have no known polynomial time quantum algorithms, for example.
So are quantum computers not from matter and not in space? :)
Does quantum computing somehow get around the fundamental energy requirements?
For asymmetric systems, search is reduced to polynomial (if using the discrete log, EC discrete log or prime factorization).