In article <
637756e68148fcbc...@hoi-polloi.org>
Anonymous <
anon...@hoi-polloi.org> wrote:
>
> Via SlashDot.org
> There have been rumors for years that the NSA can decrypt a
> significant fraction of encrypted Internet traffic. In 2012, James
> Bamford published an article quoting anonymous former NSA officials
> stating that the agency had achieved a "computing breakthrough" that
> gave them "the ability to crack current public encryption." The
> Snowden documents also hint at some extraordinary capabilities: they
> show that NSA has built extensive infrastructure to intercept and
> decrypt VPN traffic and suggest that the agency can decrypt at least
> some HTTPS and SSH connections on demand.
>
> However, the documents do not explain how these breakthroughs work,
> and speculation about possible backdoors or broken algorithms has been
> rampant in the technical community. Yesterday at ACM CCS, one of the
> leading security research venues, we and twelve coauthors presented a
> paper that we think solves this technical mystery.
>
> If a client and server are speaking Diffie-Hellman, they first need to
> agree on a large prime number with a particular form. There seemed to
> be no reason why everyone couldn't just use the same prime, and, in
> fact, many applications tend to use standardized or hard-coded primes.
> But there was a very important detail that got lost in translation
> between the mathematicians and the practitioners: an adversary can
> perform a single enormous computation to "crack" a particular prime,
> then easily break any individual connection that uses that prime.
>
>
https://weakdh.org/imperfect-forward-secrecy-ccs15.pdf
This is not a new problem.
http://instantlogic.net/publications/DiffieHellman.pdf
4 x 8 node 6600 based VAXClusters combined with a Cray were
routinely cracking this years ago.
To be fair, most of the exploits were the result of lazy, stupid
or incompetent programmers.