To give one small example: Clifford Cocks invented RSA about 3 years before RSA did. But he did it by himself, and he did it in his head. Cocks' version was revealed 25 years after he created it; 22 years after RSA was revealed.
They're only just released some of the stuff that Turing did.
They keep things secret, and they use things hard. There's not really anyway to know what they know about your system, which is why cryptography likes systems that seem secure even when you know everything about that system.
The point is that even though PKI had been independently developed, and made public, 3 years after Cocks did it they still kept it secret for 22 years.
So imagine what they do with the secrets that are still secret - the secrets not independently developed and made public.
I think of all the public crypto that we know duplicated intelligence-agency crypto, the public was only behind by a handful of years. We haven't heard of anything that was like "Oh yeah, the NSA had this twenty years ago." (Differential cryptanalysis is probably the biggest of these gaps, and its timeframe is something of an outlier.)
So either the public is doing a decent job of keeping up with the spooks, there's a massive misinformation campaign where intelligence agencies only admit to having discovered things that the public discovered soon afterwards, or there's a strange bimodal property where the public replicates private results either five years later or fifty.
Also, the NSA is not _fundamentally smarter_ than the rest of the world; they're just possibly more focused on it. So exactly how a clever idea would occur to them in the 1970s and 1980 and have occurred to nobody in academia since then needs some explanation.
They're only just released some of the stuff that Turing did.
They keep things secret, and they use things hard. There's not really anyway to know what they know about your system, which is why cryptography likes systems that seem secure even when you know everything about that system.
(http://www.youtube.com/watch?v=a-xEiOvXux4)