Could you use a similar idea to go after bitcoin keys? If so, you may not be able to crack any particular key, but you could steal the bitcoins from the ones you did crack.
As sowbug and tptacek mention, there are no common-factor attacks against Bitcoin keys. However, that doesn't mean that the PRNGs used in cryptocurrency implementations aren't a concern. The most famous incident was probably this
With a tiny number of exceptions, Bitcoin private keys are just random sequences of 256 bits. They don't involve primality. So unless a shared CRNG is truly awful, there shouldn't be any reason why keys would cluster around certain values.
Which is basically the thesis of the underlying "Ron Was Wrong Whit Was Right" paper --- that discrete log systems are safer than RSA. Since then, there's been more work done on the pitfalls of prime generation, perhaps most notably the "Prime And Prejudice" paper, which is really excellent and more interesting technically than this article:
Isn't the point of "Prime and Prejudice" that primality tests that are perfectly adequate for RSA key generation are inadequate to verify the primality of adversarial inputs, in protocols like negotiated DHE or whatnot?
