> Mathematically-secure cryptography ... is unbreakable
To expand on sibling comments: Cryptography essentially depends on the assumption that P=NP (well, not exactly, but...). It's possible, though unlikely, that mathematical discoveries could undermine all possible conventional cryptographic schemes.
As for brute-force, that's a tricky one as well. If you allow a strengthening of Moore's law that says that operations per second per dollar increase exponentially, then you can construct the following "polynomial time" algorithm for any cryptographic problem:
Wait n*k years, where
- n is the problem size in bits, and
- k is a scaling factor to get the exponents to align
Buy a computer
Run the brute force algorithm on your new computer
To expand on sibling comments: Cryptography essentially depends on the assumption that P=NP (well, not exactly, but...). It's possible, though unlikely, that mathematical discoveries could undermine all possible conventional cryptographic schemes.
As for brute-force, that's a tricky one as well. If you allow a strengthening of Moore's law that says that operations per second per dollar increase exponentially, then you can construct the following "polynomial time" algorithm for any cryptographic problem: