[bdhe]

This is not about some new vulnerability.

A more accurate statement is: the thesis that "when hundreds and thousands of RSA keys are generated, the entropy of each key (given the remaining keys) is still large" is shown (in this paper) to be empirically false because people in practice use weak pseudorandom generators.

This is important because when working with the security of RSA, we assume that N=pq for random looking primes p and q. In isolation this is true, but when there are tons of other keys out there, p and q no longer are random.

I also fail to understand why you mention Lenstra being a co-author of the paper.

[tptacek]

I take him to mean, "it is understandable that the NY Times would write up a story on RSA vulnerabilities when one of the authors is Arjen Lenstra, because Arjen Lenstra is a giant in the field".

I agree with you (and not the parent) about the importance of the study.