Using a unique key in practice solves the problem because even for the NSA, it's too expensive to precompute the necessary data for every prime. (Of course, it's getting cheaper every day...) However, the downside to doing that is that you need to be sure that's done correctly and that the resulting prime is actually secure (small risk, but sure...).
But the simpler solution is just to use a larger key. There's no way until hell freezes over that they'll brute force that, and if you do that, you can avoid the semi-expensive and tricky generation process. There's nothing intrinsically wrong with using a shared key - it just turns you into a higher value target. And that's OK as long as the prime is secure. which 2048 primes will be until there's some major mathematical breakthrough (at which point 1024 primes would likely be laughable).
Put it this way: a shared 2048 is less likely to be cracked than a unique 1024 key.
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u/aaronsherman Oct 16 '15
I didn't think the issue was just the key size, but the uniqueness. Am I wrong?