Well, the lazy way to do this is for everyone to use the same prime, but to pick a safe prime so large it is out of reach of the NSA. Isn't the all promise of

Well, the lazy way to do this is for everyone to use the same prime, but to pick a safe prime so large it is out of reach of the NSA. Isn't the all promise of cryptography predicated on the idea that you can impose exponential effort by merely incurring polynomial effort?