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If a 2048-bit RSA key and a 256-bit AES key are considered to be unbreakable within the foreseeable future by any kind of computer, why do the NSA and other intelligence agencies invest in supercomputers, supposedly to break encryption? Don't their endeavours essentially prove that they don't consider this hopeless?

Is it so that the supercomputers are only useful in the case that they can narrow down the brute force attack by exploiting human errors? That's the only purpose I can imagine, if we are to believe that RSA and AES with decent key length are truly unbreakable when properly implemented.

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    There could be any number of reasons, not all of them cryptanalysis. Theoretically only the one-time pad is unbreakable. What is considered strong today, may turn out to have a vulnerability in the future. – S.L. Barth - Reinstate Monica Apr 21 '15 at 13:49
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    Key words there are "properly implemented". – RoraΖ Apr 21 '15 at 14:41
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    Not everything is encrypted with 256 bit AES or 2048 bit RSA. – Bob Brown Apr 21 '15 at 15:52
  • No, but I assumed that 256 bit AES and 2048 bit RSA would be representative for the minimum encryption strength that the NSA would have to break in order to obtain useful information. I see that a lot of community members took my examples very literally. My question may be poorly phrased. I also might or might not have misunderstood something about the relative strength of ciphers. – Magnus Apr 22 '15 at 9:19
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You are making two assumptions here, that would need justification:

  1. NSA / "other agencies" invest in supercomputers. They do ? How exactly would you know that ? Did you read it on the Source of All Truths, i.e. "the Internet" ?

  2. NSA's unique goal in life is to break TLS sessions. Considering that the NSA has been created in 1952, while SSL was first released in 1995, one has to wonder what the heck NSA was doing with its budget between 1952 and 1995.

More plausibly, spy agencies are accumulating a lot of data, and must sift through it and sort it and find correlations in order to unravel connections between individuals. This is called traffic analysis, it has been done since before the invention of computers, and it is known to require a lot of computing muscle when done on a large scale. Therefore, even without any notion of encryption or breaking thereof, large spy agencies would be perfectly justified in, as you say, "investing in supercomputers". If they did not, one could then ask some questions about their budget usage.

(Interestingly, TLS has, by itself very little impact on the feasibility of traffic analysis.)

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    Yep. Definitely this - one of my previous teams bought 3 Cray Supercomputers. We used a bit of them for number crunching/rainbow tables/crypt stuff, but really they were used for virtualising entire environments for whole companies, and simulating all traffic and activity that occurred - for various reasons. – Rory Alsop Apr 21 '15 at 14:30
  • I thought it would be uncontroversial to say that they do invest in supercomputers, so I didn't cite any sources. NSA: ubm.io/1yM7NpG Norwegian Intelligence Service: bit.ly/1nhn3PY I didn't mean TLS specifically, but I said TLS because it's a very widespread, very secure encryption protocol available for the layman. I thought it would be representative with regard to the minimum level of encryption that the NSA has to break in order to obtain protected information. I know the wep page about the NIS's supercomputer is in Norwegian, but they explicitly say it's for encryption. – Magnus Apr 21 '15 at 15:07
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There are many likely reasons.

  1. 99% of popular web sites support TLS 1.0, but only 58% support TLS 1.2 (SSL Pulse, 4/5/15)
  2. The existence of strong encryption does not imply the use of strong encryption
  3. The use of strong encryption does not imply the correct use of strong encryption
  4. The NSA is arguably interested in many, many things aside from TLS web traffic
  5. On May 17, 2019, the NSA will reveal that it broke TLS 1.2 about four years prior
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Super computers have a lot more use than just 'breaking' Cryptography. the NSA could be using super computers for anything from Big Data Analysis to Breaking a specific Encryption.

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