This is an eye-opening look at the potential danger of SSL and SSH keys not being as unbreakable as once thought. At least, when not implemented correctly. Stuff like this gets me excited again about math.
If X and Y were components of public keys in the RSA cryptosystem, their shared factor would create a huge hole in the security fence. And the problem is particularly insidious in that each of the two keys, when examined in isolation, looks perfectly sound; the weakness only becomes apparent when you have both members of the pair.This potential vulnerability of factoring-based encryption methods has been known for decades, but it seemed there was no reason to worry because coincidentally shared factors are so utterly unlikely. A couple of weeks ago I heard an eye-opening talk by Nadia Heninger, a member of a group that has searched for such unlikely coincidences in the wild. They found 64,000 of them. Reason to worry.