Would'nt NSA attempts at cracking encryption systems basically be free audits on those encryption systems. (providing the public some how figures out how it was broken.)
Assuming they bothered to share the results of those attempts sure. The problem of course is that the NSA is both attempting, and in some cases succeeding in cracking encryption systems but keeping it all locked away behind security clearances. In the past we've learned quite a bit about the weaknesses of various crypto systems via post-mortems of NSA exploits, but it always comes well after the fact that the encryption is weak and broken has already become if not common knowledge than at least largely assumed. E.G. it's probably a safe bet that 1024 bit encryption is either broken by the NSA currently, or is likely to be broken soon, but it will probably be many years (barring another Snowden like event) before the public knows anything about exactly HOW the NSA has/will break it.
An extreme example for this kind of approach might be found in the history of the Enigma cipher and the British/Allied successful attempts in decryping German communications during the war. If it would have been obvious that information about an impeding attack could only have been gathered from intercepted and decrypted communications, the British would rather let boats be sunken and people die than give away the fact that the code had been broken.
Because if the fact would be known, the adversary will immediately cease to use this method of encryption, rendering the advantage of breaking the cipher void.
As a small aside, for anyone interested in this, The Imitation game was in my opinion fantastic, though I assume anyone here would already have seen it, or have plans to.
