1. GSM Security Overview (Part 3)
Gregory Greenman

2. Agenda A5 Overview : Attack on A5 : Other Attacks on GSM Conclusion
LFSR (Linear Feedback Shift Registers)
A5/1 Description
Attack on A5 :
Space-Time Attacks Overview (by Babbage)
Cryptanalysis of A5/1 (by Shamir, Biryukov, Wagner)
Other Attacks on GSM
Conclusion

3. Feedback Function : XOR
LFSR structure b1 b2 b3 b4
...
bn-1 bn
output
new value
Feedback Function : XOR
Purpose - to produce pseudo random bit sequence
Consists of two parts :
shift register – bit sequence
feedback function
Tap Sequence :
bits that are input to the feedback function

4. LFSR Features
LFSR Period – the length of the output sequence before it starts repeating itself.
n-bit LFSR can be in 2n-1 internal states  the maximal period is also 2n-1
the tap sequence determines the period
the polynomial formed by a tap sequence plus 1 must be a primitive polynomial (mod 2)

5. LFSR Example : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12
x12+x6+x4+x+1 corresponds to LFSR of length 12 b1 b2 b3 b4 b5 b6 b7 b8 b9
b10
b11
b12

6. A5/1 Overview
“Cryptography is a mixture of mathematics and muddle, and without the
muddle the mathematics can be used against you.”
- Ian Cassells, a former Bletchly Park cryptanalyst.
A5/1 is a stream cipher, which is initialized all over again for every frame sent.
Consists of 3 LFSRs of 19,22,23 bits length.
The 3 registers are clocked in a stop/go fashion using the majority rule.

7. 18 17 16 1 1 1 1 R1 C1 1 1
clock
control 21 20 1 1 1 1 1 R2 C2 21 22 20 1 1 R3 C3

8. A5/1 : Operation All 3 registers are zeroed
64 cycles (without the stop/go clock) :
Each bit of K (lsb to msb) is XOR'ed in parallel into the lsb's of the registers
22 cycles (without the stop/go clock) :
Each bit of Fn (lsb to msb) is XOR'ed in parallel into the lsb's of the registers
100 cycles with the stop/go clock control, discarding the output
228 cycles with the stop/go clock control which produce the output bit sequence.

9. The Model
The internal state of A5/1 generator is the state of all 64 bits in the 3 registers, so there are states.
The operation of A5/1 can be viewed as a state transition : S0 S1 S2 St k0 k1 k2 kt
Standard attack assumes the knowledge of about 64 output bits (64 bits →264 different sequences).

10. Space/Time Trade-Off Attack I
Get keystream bits k1,k2,…,kM+n and prepare M subsequences :
k1,…,kn k2,…,kn+1 …
kM,…,kn+M
generate random state Si
generate n-bit keystream
look for it in the prepared keystream subsequences M

11. Space/Time Trade-Off Attack II
Select R random states S1,..,SR and for each state generate an n-bit keystream
S1 : k1,1 … k1,n S2 : k2,1 … k2,n …
SR : kR,1 … kR,n
Get keystream bits k1,k2,…,kM+n and prepare M subsequences
Look for a prepared state R

12. Shamir/Biryukov Attack Outline
2 disks (73 GB) and 2 first minutes of the conversation are needed. Can find the key in less than a second.
This attack based on the second variation of the space/time tradeoff.
There are n = 264 total states
A – the set of prepared states (and relevant prefixes)
B – the set of states through which the algo. proceeds
The main idea :
Find state s in A∩ B (the states are identified by prefix)
Run the algorithm in the reverse direction

13. Biased Birthday Attack
Birthday paradox : A ∩ B ≠ o if |A| ∙ |B| ≈ n
Each state is chosen for A with probability PA(s) and for B with probability PB(s). Then, the intersection will not be empty if Σs PA(s) ∙ PB(s) ≈ 1
The idea is to choose the states from A and B with 2 non-uniform distributions that have correlation between them

14. Disk Storage (I, j, k) state prefix State Transition :
But, for each state we can store only two bits : the clock bit and the output bit
(I, j, k)
At each step we only have to know which of the three indices should be incremented.
This could be implemented by a precomputed table with 3 input bits (clocks) and the increment vector as the output.
No shift operations !
c1 c2 c3
inc1 inc2 inc3
0 1 0
1 1 0
state
prefix
The prefixes can be sorted and thus serve as indices into the states array
The registers are small, we can precompute all their states and store them in 3 cyclic arrays

15. Special States Disk access is very time-consuming!
Keep on disk (set A) only those states, which produce a sequence that starts with a certain pattern α, | α| = k
Access the disk only when α is encountered
2k prefixes can start with α, so we reduce the number of total possible states (n) by 2k and the number of disk access times by 2k. The size of A, however, is unchanged, and we only insert the states that satisfy the condition there. Thus, we don't miss intersections.

16. Generation of Special States
Choose from all 264 states the needed 248 ?
It's too time-consuming and unrealistic.
The solution is to generate them :
19 bits C1
241 chosen bits
11 bits C2
11 bits
Each register moves approximately ¾ of the cycles.
11 bits C3
12 bits

17. Reversing A5/1 Forward state transition is deterministic …
In the reverse direction could be up to 4 predecessors (majority clock control).
Example : C1 1 1
What was the clock majority bit at the previous round ?
Here we see that there are no predecessors ! C2 1 1 1 C3

18. Estimations … We use 51 bit length prefixes (16 first bits are α)
We need 5 bytes per state to store on disk (73 G), so we can afford 146 ∙ 230/5 = 235 states
We use 51 bit length prefixes (16 first bits are α)
How many times will α be encountered in the data ?
there are 228 bits of data, that is, 177 (228-51) "relevant offsets"
2 minutes of operation, that is, 120 ∙ 1000/4.5 frames
2-16 is the fraction of all possible states which start with α
so, the number of occurrences is 2-16 ∙ 177 ∙ 120 ∙ 1000/4.5 ≈ 71

19. Tree Exploration
A state is red if the sequence of output bits produced from the state starts with α. There are 248 red states.
A state is green if the sequence produced from the state contains an α-occurrence between bit positions 101 – 277
There are 177 ∙ 248 green states
We can assume that the short path (of length 277 ) will contain only one occurrence of α, so the mapping is many-to-1
red : α
green : α

20. Tree Exploration II
The set of relevant states can be viewed as a collection of disjoint trees with red state as the root and the rest of nodes are green states.
We're interested in trees with green states at levels The weight of tree, W(s) is the number of green states at those levels.
sequence generation
reverse direction

21. Tree Exploration III
It is experimentally found that W(s) has highly non-uniform distribution :
85% of the trees die before reaching the level 100
15% of the trees have 1 ≤ W(s) ≤ 2600
Choose 235 states (biased probability) with particularly heavy trees (average weight 12500) from overall of 248 red states
The expected number of collisions :
235 ∙ ∙ 71
177 ∙ 248
≈ 0.61

22. Tree Exploration IV
Heavy trees → large number of green state candidates?
We know the exact location of α in the sequence, so we know the exact depth in the tree.
The trees are narrow, so the total number of states we'll have to check is less than 100 !

23. Attack Summary
Due to frequent reinitialization (for every new frame), it's possible to efficiently run the algorithm backwards (328 steps).
Poor choice of the clocking taps.
Each one of the registers is so small that it's possible to precompute all its states.

24. Attacks on Signaling Network
The transmissions are encrypted only between MS and BTS. After the BTS, the protocols between MSC and BSC (BSSAP) and inside the operator's network (MAP) are unencrypted, allowing anyone who has access to the signaling system to read or modify the data on the fly !
So, the SS7 signaling network is completely insecure. The attacker can gain the actual phone call, RAND & SRES…

25. Attacks on Signaling Network
If the attacker can access the HLR, s/he will be able to retrieve the Ki for all subscribers of that particular network.

26. Retrieving Ki over Air
The Ki key can be retrieved from SIM over the air :
MS is required to respond to every challenge made by GSM network (there is no authentication of BTS).
Attack based on differential cryptanalysis could take 8-15 hours and require that the signal from the legitimate BTS be disabled for that time, but it's still real …
The same attack could be applied to AuC
It also has to answer the requests made by the GSM network
It's much faster than SIM

27. SMS Architecture SMS is a "store and forward" message system
the message is sent from the originator to SMS Center, and then on to the recipient.
SMS messages can be up to 160 characters length
Sent in clear (but different formats).

28. SMS Attacks
Instructions
to Air Interface
Instructions
to SMSC
Instructions
to HandSet
Instructions
to SIM
Message Body
sms packet
Broken UDH (user data hdr) in an sms message caused crash in some Nokia phones. It required the user to put its SIM into a non-affected phone and delete the offending message.
Spoofing SMS Messages : Originating Address field can be arbitrarily set to anything.
The applications using sms should take care of authentication and also encrypt their messages !

29. Conclusions
Pros
It's the most secure cellular telecommunication system available today (2-2.5G)
Good framework for reasonably secure communications
The security model has minimal impact on manufacturers
SIM – keys,A3,A8,etc
SIM Toolkit – additional SIM functionality
Mobile Equipment – A5
The future - 3GPP :
the design is public
mutual authentication (EAP-SIM Authentication), key-length increased, security within and between networks, etc.

30. Conclusions (cont.) Cons Security by Obscurity
Only access security – doesn't provide end-to-end security
GSM Security is broken at many levels, vulnerable to numerous attacks
Even if security algorithms are not broken, the GSM architecture will still be vulnerable to attacks from inside or attacks targeting the operator's backbone
No mutual authentication
Confidential information requires additional encryption over GSM

31. References GSM Association, http://www.gsmworld.com
M. Rahnema, “Overview of the GSM System and Protocol Architecture”, IEEE Communication Magazine, April 1993
L. Pesonen, “GSM Interception”, November 1999
J.Rao, P. Rohatgi, H. Scherzer, S. Tinguely, “Partitioning Attack: Or How to Rapidly Clone Some GSM Cards”, IEEE Symposium on Security and Privacy, May 2002.
P.Kocher, J. Jaffe, “Introduction to Differential Power Analysis and Related Attacks”, Cryptography Research, 1998
S. Babbage, “A Space/Time Trade-off in Exhaustive Search Attacks on Stream Ciphers”, Europian Convention on Security and Detection, IEE Conference publication, No. 408, May 1999.
A. Biryukov, A. Shamir, D. Wagner, “Real Time Cryptanalysis of A5/1 on a PC”, Preproceedings of FSE ‘7, pp. 1-18, 2000
ISAAC, University of California, Berkeley, “GSM Cloning”,
S. Chan, “An Overview of Smart Card Security”,

32. Thank You !