Open Source Attempt To Crack GSM Encryption 78
Lexta writes with an interesting tidbit from IEEE Spectrum: "'Karsten Nohl, chief research scientist with H4RDW4RE, a Sunnyvale, Calif.-based security research firm, is mounting what could be the most ambitious attempt yet to compromise the GSM phone system.' The intended approach is to create an open source project to spread the computation of a giant look-up table across more than 80 machines. Interestingly, they've openly stated that nVidia's CUDA technology will be used to execute parallel elements of the problem on GPUs as well."
Oh my gosh (Score:2, Informative)
Two points.. (Score:5, Informative)
2) This has been known pretty much from the beginning, and updating has been started years ago. As said in TFA, only news of this is the plan to make it publicly available.
Re:A big book (Score:5, Informative)
TFA:
Any crypto experts want to take a stab at explaining, in lay geek terms, how this is even remotely possible? That's a ~50,000:1 compression ratio.
Trading space for time.
128 petabytes would enable instant lookup of collisions. Cutting size in half, and you'd need 2 operations to find a collision. Cut size in half again would need to double the time again. Repeat until you reach the desired space/time trade-off.
P.C. van Oorschot, M.J. Wiener. Improving meet-in-the-middle attacks by orders of magnitude, Crypto'96, Springer LNCS vol.1109, pp.229-236, 1996. ps, pdf. A more complete treatment is given in the 1999 Journal of Cryptology paper.
P.C. van Oorschot, M.J. Wiener. Parallel collision search with applications to hash functions and discrete logarithms. pp.210-218, proceedings, 2nd ACM Conference on Computer and Communications Security, Nov. 1994, Fairfax, Virginia. ps, pdf. The Crypto'96 paper builds on this, and a more complete treatment is in the 1999 Journal of Cryptology paper.
P.C. van Oorschot, M.J. Wiener. Parallel collision search with cryptanalytic applications. Journal of Cryptology, vol.12 no.1 (Jan. 1999) pp.1-28. pdf.
Re:A big book (Score:5, Informative)
The article doesn't contain enough information about A5/1 or the details of the attack for a crypto expert to explain exactly what he plan to do. However it does mention that he intend to create a rainbow table, so I can at least explain what a rainbow table is, and what the 128PB might mean. The article say it is a 64 bit encryption, but 128PB doesn't sound like the right size given a 64 bit encryption, the 128PB sounds more like a 54 bit encryption. And though it doesn't sound like a huge difference those 10 bits does mean a factor of 1024 times less work to brute force, and these days the difference between 54 and 64 bits may very well be the difference between feasible and not feasible to break. Of course in a few years 64 bits may be feasible to brute force as well.
Compressing 128PB down to 2-3TB doesn't sound realistic at first, but then consider that those 128PB are not just 128PB of random data, they are generated by a very simple algorithm. The entire code to generate those 128PB would probably fit in less than 1MB. But the time it would take to actually run the code for long enough to generate the 128PB is prohibitive. Also notice, that what is going to happen is not really a compression of the 128PB of data. The output of the algorithm is going to be a few TB of data, but that data can't actually be used to reproduce the original 128PB of data, which wouldn't be very interesting anyway. What you really want is a function that given some input can output the encryption key, and that can happen through a very simple table lookup, which would be very fast, but infeasible since very few people have the resources to store the complete 128PB lookup table. Instead you use a more complicated algorithm, which use 50.000 times less stored data, but OTOH may run 100.000 times (or even more) slower than the simple table lookup. But 100.000 table lookups would still only take a fraction of a second on a modern CPU.
Back to the rainbow tables. It is a tool to speed up the task of reversing a one way function. A one way function is a function that maps from one set of values to another set of values. The function is fast to compute in one direction, but there is no simple way to compute in the other direction. One example of a one way function is a hash function, which maps from strings of arbitrary lengths to the much smaller set of strings of one fixed length.
Let's assume our one way function is called f and maps from the set S to the set T. Then we can define a different function g, which maps from T to some interesting subset of S. For example it has been used in the past with a function that maps from 128 bit strings (outputs from MD5) to the set of passwords consisting of 7 alphanumeric characters (which is a subset of the possible inputs to MD5). If you combine g and f, you get a function mapping from T to T. If you start with a value in T and keep applying this combination, you will keep getting values in T.
Now you decide how many times in a row you will apply this combination, let's call that number n. A small n will produce very large rainbow tables, that may be faster to use. OTOH a large n will produce smaller rainbow tables that will be slower to use. This choice is the compromise mentioned in the article. He is probably going to use a value of n around 65536 or so.
Now you start producing chains (this is the large amount of work that this project will aim to distribute). You take some input in T, then you apply the combination of the two functions n times and get an output in T. You repeat that with a few hundred billion different values in T. The output will be a lot of pairs of values, from those pairs you create a lookup table.
Now assume you have a value x, which is the output of the one way function f, and you want to find out what the input may have been. Then you can apply the combination of functions n times and get n different values in T, look
Re:A big book (Score:4, Informative)
From Wikipedia [wikipedia.org]:
Way to make an already weak cipher even weaker.
Re:Sp3ll1ng (Score:2, Informative)