If The NSA's Not Complaining About Encryption, It's Likely Because It Has Already Found A Way In
from the we-left-ourselves-a-key-to-the-back-door-under-the-mat dept
The NSA hasn't said much (well... compared to the FBI) over the past several months about the default phone encryption offered by Google and Apple. This lack of public outcry has to do with the NSA's capabilities, rather than a sudden interest in ensuring people around the world have access to secure communications. If it truly felt the world would be a better place with safer computing, it wouldn't have invested so much in hardware implants, software exploits and -- its biggest black budget line -- defeating encryption.
Where there's no smoke, there's a great deal of fire which can neither be confirmed nor denied. The NSA has very likely punched holes in encryption in existing encryption. But how does it do it? A brute force attack on encryption would be largely futile, even with the computing power the agency possesses. Alex Halderman and Nadia Heninger at Freedom to Tinker have a theory, and it involves a "flaw" in a highly-recommended encryption algorithm.
The key is, somewhat ironically, Diffie-Hellman key exchange, an algorithm that we and many others have advocated as a defense against mass surveillance. Diffie-Hellman is a cornerstone of modern cryptography used for VPNs, HTTPS websites, email, and many other protocols. Our paper shows that, through a confluence of number theory and bad implementation choices, many real-world users of Diffie-Hellman are likely vulnerable to state-level attackers.The belief that these common primes (or at least some of them) wouldn't be cracked relied on the assumption that no one entity would have the money to assemble the computing force needed to break the code. The problem is that the NSA likely has the time, money and power to tackle this enormous project. Here's why it first seemed unlikely:
For the nerds in the audience, here’s what’s wrong: If a client and server are speaking Diffie-Hellman, they first need to agree on a large prime number with a particular form. There seemed to be no reason why everyone couldn’t just use the same prime, and, in fact, many applications tend to use standardized or hard-coded primes. But there was a very important detail that got lost in translation between the mathematicians and the practitioners: an adversary can perform a single enormous computation to “crack” a particular prime, then easily break any individual connection that uses that prime.
For the most common strength of Diffie-Hellman (1024 bits), it would cost a few hundred million dollars to build a machine, based on special purpose hardware, that would be able to crack one Diffie-Hellman prime every year.And here's the reality of the situation, as exposed by documents leaked by Snowden.
The 2013 “black budget” request, leaked as part of the Snowden cache, states that NSA has prioritized “investing in groundbreaking cryptanalytic capabilities to defeat adversarial cryptography and exploit internet traffic.” It shows that the agency’s budget is on the order of $10 billion a year, with over $1 billion dedicated to computer network exploitation, and several subprograms in the hundreds of millions a year.What was once considered to be beyond the capabilities of even the biggest intelligence agency is obviously well within its reach. As the authors point out, this would explain the other information seen in leaked documents, like the NSA's ability to decrypt some secured connections "on command" or eavesdrop on VPN traffic.
This is still just a theory, but it does seem to explain much of what's been uncovered in leaked documents. It also shows the NSA is still doing what the NSA does best: leaving lots of stuff poorly-secured, despite directives otherwise.
Our findings illuminate the tension between NSA’s two missions, gathering intelligence and defending U.S. computer security. If our hypothesis is correct, the agency has been vigorously exploiting weak Diffie-Hellman, while taking only small steps to help fix the problem.As the authors point out, the NSA has recommended better encryption methods, but no one's in any hurry to adopt them because no one trusts the NSA to recommend a method it hasn't already weakened, if not completely compromised. If there's any truth to what's covered here, the NSA has sat quietly by and allowed researchers to recommend yet another encryption method that it's already made large strides towards defeating. And, once again, we can see that when the word "security" is combined with the word "national," it means something completely different than when it stands on its own.
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Filed Under: alex halderman, backdoors, diffie hellman, diffie hellman key exchange, encryption, hacking, https, nadia heninger, nsa, surveillance, vpns
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That's a lot of money.
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Re: That's a lot of money.
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Can you explain what it means to 'crack' a prime?
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Like using rainbow tables for md5, one could (with enough computer power) generate all the possible derivations.
Since its designed for insecure channels (ie, in order to share a secret over an untrusted/unencrypted connection), intercepting the intermediate keys (prime + secretA and prime + secretB), and checking them against the factored table gives you the secrets. do for both. then you can derive the "secret key" that allows you to decrypt subsequent chatter.
So to answer your question, its not so much as "crack" but rather "factor" all of the potential prime+randomPrime combinations ahead of time.
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https://en.wikipedia.org/wiki/RSA_(cryptosystem)
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(One of the prime numbers is very very large, the other one is 7.)
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Given C, find A and B where A^B = C. A is the "shared prime" so you have to solve log C / log A. Discrete logs are computationally expensive to calculate, even more so than factoring. (which is just brute force multiplication)
This is why DH keys can be much smaller than RSA and still be relatively secure.
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Re: 'crack' a prime
Here is a link that explains how these prime factors are used to in Public Key Encryption methods.
http://www.livinginternet.com/i/is_crypt_pkc_work.htm
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Re: Re: 'crack' a prime
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Re: Re: Re: 'crack' a prime
Since doing a search within that table will be significantly fast than computing factors, it serves as a shortcut if someone used 83 as one of their key primes.
That way, determining a private key from a public key that used 83 (or any of their cracked primes) would take hours or days instead of months or years.
Again, I'm guessing. IANAM
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Re: Re: Re: Re: 'crack' a prime
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Rainbow table
But also, even if they have rainbow tables doesn't mean that's their only inroad to cryptanalysis of public keys. Or of other standard cryptography algos.
It's probably better for us to assume The NSA is one step ahead until the its benefactors are actively complaining about how useless it is.
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Passing Keys?
The next question is along the lines of why use prime numbers. It seems to me that there are more limited quantities of those verses any large number and that might make finding them easier. I am relatively certain there is some mathematical explanation for this that is beyond my ken.
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Re: Passing Keys?
DH was designed for the very reason of passing that block cipher key over an unencrypted channel, it packs secrets in a hard to reverse format that can be combined on the other end so that both sides come to the same conclusion, without every transmitting their own secret. Otherwise you have to establish an encrypted channel to exchange the key...
You can do this with RSA, but in that case, the key for every key exchange session is the same. Break one session, break them all. DH allows a different key exchange each time, so if you crack one key, you crack only that session.
Primes are important for mathematical reasons. They have certain properties that make verifying results provable.
For example (4^3)^2) => 4^3*2 (4^6) but, so would 2^6^2 (2^6*2 => 2^2^6 => 4^6), so it breaks the "provableness" (not a mathematician pardon the bad language) because multiple inputs can yield the same result. (That's a problem when it comes to signature verification when you need to prove knowledge of a specific secret)
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Re: Passing Keys?
If one or both of the factors isn't prime, then you can't be sure if you are both using the same key. For example, when you factor 36 you can get 6x6 or 3x12 or 4x9 or 2x18.
The numbers used in cryptography are much, much bigger though and so the factoring problem is very difficult.
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Re: Re: Passing Keys?
Bigger than the national debt.
So big they are getting up there near the amount of money that the RIAA is losing due to piracy.
US $ 10 ^ 500
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Re: Passing Keys?
gpg (GnuPG) 1.4.16
Copyright (C) 2013 Free Software Foundation, Inc.
License GPLv3+: GNU GPL version 3 or later
This is free software: you are free to change and redistribute it.
There is NO WARRANTY, to the extent permitted by law.
Home: ~/.gnupg
Supported algorithms:
Pubkey: RSA, RSA-E, RSA-S, ELG-E, DSA
Cipher: IDEA, 3DES, CAST5, BLOWFISH, AES, AES192, AES256, TWOFISH,
CAMELLIA128, CAMELLIA192, CAMELLIA256
Hash: MD5, SHA1, RIPEMD160, SHA256, SHA384, SHA512, SHA224
Compression: Uncompressed, ZIP, ZLIB, BZIP2
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The NSA has very likely punched holes in encryption in existing encryption.
rewrite? edit?
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For example, the amount of effort required to take advantage of this weakness ensures that it won't be used for blanket surveillance. You'd have to be of special interest to the NSA. Whether or not you are comfortable relying on being sufficiently uninteresting is a personal call. Only you can answer that question.
If you aren't comfortable, then there are other encryption scheme you can use that don't have this weakness (although they may be a bit less convenient). This isn't a weakness of encryption as a whole, just this particular type of scheme.
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win10
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If you're of that mindset, then you also need to avoid using the telephone (cell or landline) and third party service providers such as payment processors, etc.
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What's the point of encryption?
Your communication may be safe from prying eyes of citizens, but the government is already watching you take a leak.
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We don't know what encryption the NSA can crack.
It could be that they're confident that true quantum computing devices are imminent and they'll soon be able to derive private keys from public ones thanks to fast large-number-factoring that such technology would allow. There have been some recent developments of quantum computing tech, though the news I heard was of a prototype logic gate. I don't know how fast that will turn into a mainframe at the Big Utah Intelligence Center.
Generally, it's a good idea to not depend on one layer of protection to obfuscate your communication from the NSA or from law enforcement (or from competitors). When you have active enemies, you probably want redundant layers of data security. That way, even if they can crack your communications, it may be too expensive to do so consistently.
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Re: We don't know what encryption the NSA can crack.
YES.
This is security 101. If you only have one line of defense, no matter what that defense mechanism is, then your security is woefully inadequate. Even if the attacker you're worried about isn't a government agency.
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Re: What's the point of encryption?
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They can only bug so many rooms
My guess is they'll probably have to triage data retention to the more interesting candidates. So like any other camouflage you just need to blend into the background noise.
And that is what you have when you're sucking in all the communications in the US: noise.
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Re: They can only bug so many rooms
For all we know, Microsoft may have an arraignment with the NSA for "storage" (wink wink).
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Too easy?
Security through mediocrity?
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One advantage is that most of us ARE mediocre
They can't round up every single dissident. It's only when you catch the attention of some official who wants what you got.
So yeah, having some prime real estate or a pretty spouse or a company that is doing well in a given market is more likely to get you in trouble than your bomb hobby or your radical politics and fanatical faith to Islam.
Those last things will just be the justification to disappear you so that said official can take your stuff.
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Re: Too easy?
I use double ROT-13.
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Tension? What tension?
At this point I'd say it's pretty clear there is no tension between the two goals, because they only care about one of them, and it's not the 'defending US computer security' one.
They could not care less if every non-NSA system was breached, so long as they were able to continue grabbing as much data as they can.
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They could've just asked...
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Re: They could've just asked...
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What's needed
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Why crack when you can hack?
If your device already contains pre-hacked electronic components or software then their job is already done and all your communique belong to NSA.
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pre-factored primes
If you've already cracked the first 142 digit prime, *any* encryption using that same prime is now tremendously easy to crack (if you've got the gear, and the NSA apparently does).
My assumption is they've got a bank of unique-task machines chewing their way through 512, 1024, 2048, etc bit primes to build comparison tables.
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What the fu..
Thanks for all the posts TD readers!
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There has never been a recorded instance of anyone "breaking" encryption standards. Nothing in this article has sources or even credible evidence. Please stop.
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