[JacobEdelman]

The problem is that there needs to be an agreed upon key that each of the parties knows before-hand. But yes, there are definitely viable ways to generate new ones or implement new, safer, standards. Alternatively, a much larger prime can be used. Also, the Diffie-Hellman protocol is a well known one that many many security researchers, programmers, and students have looked at. The flaws are not obvious, as it's initially unclear how "cracking" a large prime would work.

[too_late]

If they have special-purpose hardware specially designed for cracking primes, maybe bigger isn't better, right?

What can end-users be doing about this?