Flaw found in online encryption method

interesting that they were able to identify that there was bug without being able to say what it was or how it happened.

It's mentioned all over the place in the paper: http://eprint.iacr.org/2012/064.pdf

They do, but they abbreviate it (R.S.A.)

To clarify, is this a flaw only in RSA, or RSA and DSA?

As far as I can tell, the researchers are describing features of particular Key Pairs that have been generated by Users of the RSA algorithm. The 'garbage-in, garbage-out' rule applies. If your RNG sucks, you're going to get weak keys out of it.

Is it harder to generate weak Diffie Hellman parameters using a bad RNG?

Update: Yes, apparently. From the paper: "Cryptosystems such as RSA that require, during key-setup, multiple secrets are more affected by the apparent difficulty to generate proper random values than systems such as Diffie- Hellman (cf. [8]), ElGamal, and (EC)DSA that require a single secret."

That's (mercifully) pretty intuitive.

So out of 6.4M RSA keys they found 12K where for the modulus n = pq, p or q (or both) were used for creating modulus for other key.

So when I give them my public key, they can just scan their database and with chance 0.2% find a key with a modulo that is divisible by mine p or q? Is that how it works?

edit: The K9 business looks very dodgy. When analysing the keys they found "9 primes each of whose 36 pairwise products appears as n". So next time you're factoring an RSA key your best bet is to start with primes from this K9...