As they are still so keen on controlling encryption we can assume with good confidence that so far they have failed. And given the stakes it's really not likely to be the possibly untested problem that this author speculates about.
After the Enigma was cracked, the government was terrified that the Axis would find out. If they knew they were cracked, they could change the cipher and set back the Allies significantly.
So they spent a ton of effort obscuring their own intelligence.
Whenever a decoded Enigma message told them where a U-boat would be, they sent a "spotter" boat whose job is was to be seen seeing the U-boat before it was attacked. That way there was a plausible source of information for the U-boat's location. (These spotters were so "effective", the Germans suspected there must be many more of them in the area then there actually were.)
One time they weren't able to get a spotter there in time and Churchill himself made the call to attack anyway. To cover for that and avoid arousing suspicion, they sent a radio dispatch to a fake spy thanking him for the intel, so that the message could be intercepted by the Germans.
I wouldn't be so confident if I were you.
edit: spelling
From that I would infer and speculate that the NSA found a pragmatic solution to factorization long ago.
Or they judge that a pragmatic solution is within the realm of possibility, and they don't want take the chance of being caught with their pants down. They probably have the resources to take on many extra operational costs to avoid theoretical risks. One of the quotes on his Wikipedia pages is: "Never underestimate the attention, risk, money and time that an opponent will put into reading traffic."
"assume with good confidence" - this is very naive.
They're not going to advertise their super secret breakthrough by acting like they no longer care about encryption. Such a secret is going to be compartmentalized in the organization etc.
The slides show the capabilities of one layer of the onion, but its surely naive to assume that's everything?
A total mathematical factoring break is a holy grail. I mean, they made a hollywood movie about this! In the 90s!
Sneakers: "There isn't a government on this planet that wouldn't kill us all for that thing." Obviously, that's a movie, not real life, but the sentiment is valid.
https://leaksource.info/2014/10/17/sentry-eagle-nsa-core-sec...
As you can see, the descriptions represent their most guarded secrets that can do the gravest damage. There could be an extra layer that basically has that one fact in it. I doubt it given how many different angles of attack & severity these docs cover. We also saw that predicted damage adding up after the releases of such leaks. It's more believable given it's the exact kinds of things I'd expect a post-9/11 agency to be doing if they couldn't break RSA, etc. They'd do it anyway for deniability but these are so secret they'd rather let targets go to preserve them. The secrecy level was already tight enough to cover preserving RSA so long as insiders on highest levels kept quiet.
Last part they didn't play so well. ;)
I think employees of the NSA will be used to the idea of compartmentalization.
> successfully recruit every academic
Why that ridiculously high bar?
Original article estimates 100 mathematicans have examined factoring in detail. Googling says NSA has 600 on staff. Maybe they just did a lot of work on the problem. Also, a large dedicated group may outperform the scattered efforts distributed throughout the research community.
> there's too many moving parts for me to think it likely.
Guess you're right, it'd be like as if they [insert implausibly complex project which the Snowden leaks showed they actually do.]
Compromised standards, TAOed equipment, global passive adversary, exploiting OPSEC fails. Even if the highest compartments of the NSA were able to instantly factor any RSA key, these alternative methods would still be useful for plausible deniability as well as general use by less-privileged compartments.
The FBI is lucky to receive any of the NSA's scraps (and if they did, it would be some vague tip to start looking in the right place), hence being left to push for criminalization to facilitate their actual investigations.
It took mathematicians 357 years to prove Fermat's Last Theorem.
It would be quite the bluff though.
I think the real issue with relating their position on legislation to their ability to break any given algorithm (Or the problem on which it is based) is this: Legislation will survive a new, more secure algorithm. Breaking one algorithm is subject to being patched out or the algorithm being entirely replaced. A broken system is a short-term investment, legislation is long-term (With the assumption that the government enforcing the legislation sticks around).
If they have succeeded wouldn't the very best thing for them to do is to appear "keen on controlling encryption"?