[too_late]

Wouldn't this be easy to subvert, though?

I mean, say we put through a few patches and started generating primes more often. Then there big-ass special purpose prime machine becomes an order of magnitude less-effective, right?

I think the best way to defend against these one-to-many attacks is to spread out the cost of decrypting large quantities of data. If we all had our own keys, even if they weren't as strong as one single key that everyone used, that much more work has to be done to decrypt data for a group of users.

I know nothing about crypto, but a layman can hear about these implementation architectures and immediately realize what's wrong with it all.

[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?