How Far Ahead of Academia Are Government Agencies? This is a soft question regarding comparisons between government security services (eg, NSA or GCHQ) and open-source research (e.g., academia). Hopefully it's on-topic for this site!

In essence, my question is the following.


  How far ahead (if at all) of of open source (specifically academic) research are governmental agencies?


There are some various thoughts I've had on this matter.


NSA is the largest employer of mathematicians worldwide, and their primary focus is on security. So not only do they have an incredibly large number of people, but they're also very focused. On the other hand, cryptography departments at universities (that I'm aware of) don't seem to be particularly large.
We now get onto the actual people who do the work. For example, to start at the base level at GCHQ you need a 2:1 in a three-year maths degree. (I'm from the UK, and don't really know any comparison with American GPA.) In comparison with university faculties, these will all have doctorates as a minimum, and university researcher places (at least in UK universities I'm aware of) are very competitive.
At a first glance, this suggests that the standard of researchers in general is much higher in academia. Of course, one has to be careful: not everyone wants to do a PhD for starters; moreover, a lot of people may not want the job-insecurity of post-docs, and prefer to move into a more secure (likely higher-paying) job outside of academia. Furthermore, continuing from the first point, these people then spend all their time working on this stuff, with large amounts of resources (including many other people around).
As an example, when DES was replaced with AES, instead of developing AES themselves, the NIST set a challenge to other researchers. The NIST then chose the best of these (supposedly, anyway; many people have apparently legitimate claims that the most secure wasn't chosen, but instead the one the the NIST 'liked' the best).
I have heard that RSA was discovered some 8 (or maybe 3?) years before it was public, but that this was at a time when there was comparatively little open source research into such topics.
Finally, a lot of what secret agencies do is, well, secret!


Basically, there seem to be arguments for many points, and I was wondering if anyone has more insight than I do!

Very related (but not the same) is this question: How can we reason about the cryptographic capabilities of code-breaking agencies like the NSA or GCHQ?; that question is more about some specific things (eg symmetric ciphers).



To be clear, I know this question isn't definitively answerable without high-up knowledge of governmental affairs, but I feel some approximations should be possible.

Of course, none of this addresses private companies (eg, Google). These employ a lot of people, likely(?) with higher entry requirements than NSA/GCHQ (see above on why that doesn't give a clear cut implication) and also have lots of money; moreover, there's likely(?) less bureaucracy.



If any of my above claims are wrong, please do point them out! I'm not very knowledgeable in the world of cryptography. I'm a maths PhD (discrete probability), but have interest in this stuff.
Disclaimer: This post is possibly opinion based.

How far ahead (if at all) are governmental agencies of open source (specifically academic) research?

This question is impossible to answer. By definition, this require a knowledge of the state of research in such agencies which is definitively something they want to be kept as secret...
thx to @fkraiem:

However one can get a feeling of it by considering the followings:

Academic research is usually founded by companies or government agencies.
e.g. for the Gimli paper:

This work was supported in part by the Commission of the European Communities through the Horizon 2020 program under project number 645622 (PQCRYPTO) and project number 645421 (ECRYPT-CSA); the Austrian Science Fund (FWF) under grant P26494-N15; the ARC project NANOSEC; the Belgian Fund for Scientific Research (FNRS-F.R.S.); the Technology Foundation STW (project 13499 TYPHOON), from the Dutch government; the Netherlands Organisation for Scientific Research (NWO) under grant 639.073.005; and the U.S. National Science Foundation under grant 1314919. “Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


In the case of important projects, academic research is paired with companies with huge computing power (Google, Microsoft Research...) e.g. SHAttered:

This result is the product of a long term collaboration between the Cryptology Group at Centrum Wiskunde &amp; Informatica (CWI) - the national research institute for mathematics and computer science in the Netherlands - and the Google Research Security, Privacy and Anti-abuse Group. Two years ago Marc Stevens and Elie Bursztein, who leads the Google's anti-abuse research team, began collaborating on making Marc's cryptanalytic attacks against SHA-1 practical by leveraging Google expertise and infrastructure.

Sure such companies may? still not have the computing power of NSA, but the minds in there are definitively on par with such agencies.


I would also advise this to have a look at this: The Moral Character of Cryptographic Work by Phillip Rogaway [paper] [Usenix Talk], specially at the founding part (p. 36). We see a increase in the number of project founded by military agencies.
WARNING: this is a personal assumption, you may chose to disagree with it.
Knowing their missions (cf quote bellow) we can somewhat deduce that their level of research is most likely on par with academic work (why would you heavily fund something that would be bellow your current level of comprehension?)
e.g. for Defense Advanced Research Projects Agency (DARPA) :

The genesis of that mission and of DARPA itself dates to the launch of Sputnik in 1957, and a commitment by the United States that, from that time forward, it would be the initiator and not the victim of strategic technological surprises.
source.

Their goal are the following:

fund academic research
but most importantly know what you are currently researching on! $\Leftarrow$ This is information they want!


TL;DR:  I believe they are on par with current academic research.