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New AES Attack Documented
avxo writes "Bruce Schneier covers a new cryptanalytic related-key attack on AES that is better than brute force with a complexity of 2^119. According to an e-mail by the authors: 'We also expect that a careful analysis may reduce the complexities. As a preliminary result, we think that the complexity of the attack on AES-256 can be lowered from 2^119 to about 2^110.5 data and time. We believe that these results may shed a new light on the design of the key-schedules of block ciphers, but they pose no immediate threat for the real world applications that use AES.'"
erm only a 99.7% improvement.
The troll with karma.
Crypto is broken. It's not IF, but WHEN. That's why crypto is pointless to use. this is why I use open source, and even keep all doors unlocked. It's pointless to try and protect propery, real or intellectual/imaginary.
For those who don't have a degree in oh-shit-that's-a-big-number, can someone give a comparative analysis of what "2^119" complexity means? I mean what else is "2^119" hard to solve? And yes, the math nerds are undoubtedly either dying of laughter or yelling at the screen for my abuse of powers of two... I don't care.
#fuckbeta #iamslashdot #dicemustdie
I believe the complexity is a rough measure of how long it should take to break the code. So in this case, a reduction from 2^119 to 2^110.5 is approximately 360 times faster (that is, a 2^119 complexity attack takes 360 times as long as a 2^110.5 complexity attack).
For those who are asking "what's 2^119 complexity mean?"
2^64 is about as hard a problem as we can reasonably solve these days.
2^80 is about as hard a problem as we can unreasonably solve. I.e. we can do it, but it would take the budget of a country for several years to do.
A can of soda has about 2^83 molecules in it.
2^119 is still way beyond anything we can reasonably do, but isn't so hard that we can rule out any theoretical possibility of solving it.
A house sized computer built of solid nano-compute units, each a few hundred molecules on a side, with a cycle time of about 10 petahertz could do it in less than a lifetime.
Perhaps possible but I wouldn't worry about it.
2^256 is so hard that it may not even be theoretically possible to solve - or maybe you could if you're willing to destroy a few solar systems, and wait a few million years.
While cracking 2^256 may not be theoretically impossible, it would be easier to look everywhere the information you want might be hidden - including inside the mind of your opponent - even if he's dead.
Could somebody rephrase that in a way that people like me, who aren't cryptography specialists can understand what they're talking about?
Sure I'll rephrase it for you. "Don't worry."
What? You wanted something deeper without having to know anything? Ok...so AES was thought to require 2^128 time units to brute force. So 2^119 time complexity means essentially that the new algorithm takes 2^119 units of time to complete which is a lot better, and they think it might be able to optimize it down to 2^110 units of time.
What a 'unit of time is' is a computing science hand-wave because it doesn't really matter what it is. When comparing algorithms for large problems you are interested in how it compares relative to other algorithms, not how much absolute time it will take on a Commodore 64 or Intel i7 or whether its programmed in Smalltalk vs C. Those details while important in their own right aren't really relevant to the comparison of the algorithms themselves.
A 2^110 algorithm is significantly better than a 2^119 algorithm for 'large problems' regardless of what we set the unit of time to be, and in turn 2^119 is much better than 2^128.
In practice the unit of time is rooted in how long it takes a computer to do 'an operation'. So it might be milliseconds or nanoseconds, or whatever. And the upshot is that even 2^110 is STILL gazillion years even if its programmed in C on an i7 and every i7 on the planet is contributing to the effort...
Hence... "Don't worry."
Its mathematically very interesting, but for the moment, its nothing to "worry" about.
It means you only have to test 2^119 possible keys to break 256-bit AES - still far beyond what's ever going to be feasible (do the math - give everybody on the planet a million PCs running at 1THz and see how long it takes to do 2^119 things, then figure out where you're going to get that much electricity from)
Interesting to note is that AES-128 is immune to this attack - it's now the strongest variant of AES. Everybody (like me) who thought the 256-bit and 192-bit were a waste of time now has a reason to be smug about it.
Reason: Both AES-192 and AES-256 are just AES-128 internally but they mess around with the key data between each loop of the encryption process. The new attack only works on the "messing around" part of the process so AES-128 is unaffected.
No sig today...
Given that the new theory lowers the time to break it with about 99.7% if it before took 1 million years it now only takes 3000 years.
Remember for everý less bit it takes to decrypt - it halves the time it takes to break a cipher.
Just saying it like it are.
Security
Parent is slightly off on the Quantum computing comment. Quantum computers can break cryptographic protocols based on the difficulty of integer factorization (RSA/PGP/GPG/PKI/SSL/TLS), and discrete-logarithms (all of the above plus elgamal, elliptic curves). However, AES is a block cipher which relies on neither of these pure-math problems.
The only advantage of QCs in breaking AES is that Grover's Algorithm can be applied for random guessing of the encryption key. AES-256 has 2^256 possible encryption keys. It takes a classical computer an average of n/2 guesses to find the right key, or 2^255 operations. However a QC running Grover's Algorithm does it in an average of approx sqrt(n) "guesses." This means that it takes about 2^128 operations to get the AES-256 key using a quantum computer.
As previous posters have mentioned, 2^128 is still far out of our reach. And to subvert QCs for this type of problem, all we have to do is double our key length to get the same security. Perhaps if we find a way to combine Grover's Algorithm with this new AES vulnerability, we can get it down to 2^60 to 2^64, but that is still extremely prohibitive. Additionally, that's a big "if," since Grover's Algorithm is intended for pure-guessing problems.
The usual threat model for a cipher is either a "chosen plaintext attack" (CPA) or a "chosen ciphertext attack" (CCA). In both of those, you have a lot of plaintext-ciphertext pairs all encrypted under the same key, and your job is to use that info against the cipher. Not necessarily to actually compute the key (which would totally destroy the cipher) but even to be able to infer anything about it statistically (for example, to have a better than random chance of guessing whether a new plaintext/ciphertext pair was encrypted with the same key).
This attack is a related-key attack, which traditionally means that you get to see the same plaintext encrypted under enormous numbers (like 2^119 in this case) of different but related keys, rather than under the same key (or a "small" number of keys like a few trillion). This is a threat model that most ciphers aren't designed against and it's instead countered by designing the application to not rely on it. For example, don't use the cipher as a hash function by using the plaintext as a key and encrypting some constant. Properly designed crypto applications don't let attackers access the keys, and they generate their keys randomly rather than letting them be related. I don't think related-key attack resistance was part of the specification given to entrants of the AES contest, and IIRC the AES standard doesn't claim such resistance.
Nonetheless, the designers of Rijndael (the cipher that is the basis of AES) designed Rijndael to be "ideal", which among other things Rijndael was supposed resist related-key attacks, which was above and beyond the AES requirements.
This new discovery finds that the AES cipher in fact does not meet Rijndael's design goals. Rijndael's design goals, however, exceeded the requirements stated in the AES standardization process, and any applications using AES are supposed to only use the characteristics of AES stated in the standard. So, even if this attack were of low enough complexity to be practical, it STILL should not affect valid AES applications, unless they are relying on characteristics that AES was never promised to have.
I'm not familiar with the term "complexity" being used in this context and with these specific numbers.
Because it's not a problem that scales with n, it's an attack on one particular value of n. Ideally brute forcing an n-bit cipher has complexity O(2^n). For 256 bit AES, they've found an attack that instead of the ideal 2^256 attempts takes 2^119 attempts. But you can't say O(2^119) because that is equal to O(1), and any function with n would be false since it doesn't apply to other n. I guess you could say an attack with "complexity O(2^(n*119/256) for n=256" but you're likely to confuse a hundred times as many as are enlightened.
Live today, because you never know what tomorrow brings
Almost everyone here seems to be missing the bit in the summary that mentions that it's time and data complexity. It's not nearly as bad as 2^119 time and some tiny data.
If you want your secrets to remain secret past the end of your life expectancy, then, in order to choose a key length, you have to be a futurist. You have to anticipate how much faster computers will get during this time. You must also be a student of politics. Because if the entire world were to become a police state obsessed with recovering old secrets, then vast resources might be thrown at the problem of factoring large prime numbers.
So the length of the key that you use is, in and of itself, a code of sorts. A knowledgeable government eavesdropper, noting Randy's and Avi's use of a 4096-bit key, will conclude one of the following:
-Avi doesn't know what he's talking about. This can be ruled out with a bit of research into his past accomplishments. Or,
-Avi is clinically paranoid. This can also be ruled out with some research. Or,
-Avi is extremely optimistic about the future development of computer technology, or pessimistic about the political climate, or both. Or,
-Avi has a planning horizon that extends over a period of at least a century.
-- Neal Stephenson, Cryptonomicon
Lord Farquaad: I've tried to be fair to you creatures, now my patience has reached it's end! Tell me or I'll...
Gingerbread Man: NO! Not the buttons! Not my gumdrop buttons!
Lord Farquaad: Alright then! Who's hiding them?
Gingerbread Man: Ok. I'll tell you. Do you know... the muffin man?