GSM Security Overview (Part 3)

Gregory Greenman

Agenda

A5 Overview : 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

LFSR structure

Purpose - to produce pseudo random bit sequenceConsists of two parts : shift register – bit sequence feedback function

Tap Sequence : bits that are input to the feedback function

b1 b2 b3 b4 ...

bn-1 bn

Feedback Function : XOR

output

new value

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)

LFSR

Example : x12+x6+x4+x+1 corresponds to LFSR of length 12

b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

A5/1 Overview

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.

“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.

1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0

1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1

1 0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1

clock control

18 17 16 0

21 20 0

02122 20

C3

C2

C1

R2

R1

R3

11

0

0

10 1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0

0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1

0 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1

1 1 1 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1

1

1

0

0

1

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.

The Model

The internal state of A5/1 generator is the state of all 64 bits in the 3 registers, so there are 264-1 states.The operation of A5/1 can be viewed as a state transition :

S0 S1 S2 St

k0 k2k1kt

Standard attack assumes the knowledge of about 64 output bits (64 bits →264 different sequences).

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

M

• generate random state Si

• generate n-bit keystream

• look for it in the prepared keystream subsequences

Space/Time Trade-Off Attack IISelect 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

R

• Get keystream bits k1,k2,…,kM+n and prepare M subsequences

• Look for a prepared state

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 statesA – the set of prepared states (and relevant prefixes)B – the set of states through which the algo. proceedsThe main idea : Find state s in A∩ B (the states are identified by prefix) Run the algorithm in the reverse direction

Biased Birthday Attack

Birthday paradox : A ∩ B ≠ o if |A| ∙ |B| ≈ nEach 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

Disk Storage

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

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 Transition :

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| = kAccess the disk only when α is encountered2k 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.

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 :

C3

C2

C1

11 bits

12 bits

19 bits

11 bits

11 bits

241 chosen bits

Each register moves approximately ¾ of the cycles.

Reversing A5/1

Forward state transition is deterministic …In the reverse direction could be up to 4 predecessors (majority clock control).Example :

101

010

101C3

C2

C1

What was the clock majority bit at the previous round ?

Here we see that there are no predecessors !

Estimations …

We need 5 bytes per state to store on disk (73 G), so we can afford 146 ∙ 230/5 = 235 statesWe 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

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 statesWe can assume that the short path (of length 277 ) will contain only one occurrence of α, so the mapping is many-to-1

red : green :α α

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 101-277. The weight of tree, W(s) is the number of green states at those levels.

sequence generatio

n

reverse direction

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 statesThe expected number of collisions : 235 ∙ 12500 ∙ 71

177 ∙ 248 ≈ 0.61

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 !

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.

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…

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.

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

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).

SMS Attacks

Instructions to SIM Message BodyInstructions

to HandSetInstructions

to SMSCInstructions

to Air Interface

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 !

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,etcSIM Toolkit – additional SIM functionalityMobile Equipment – A5

The future - 3GPP : the design is publicmutual authentication (EAP-SIM Authentication), key-length increased, security within and between networks, etc.

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

ReferencesGSM Association, http://www.gsmworld.comM. Rahnema, “Overview of the GSM System and Protocol Architecture”, IEEE Communication Magazine, April 1993L. 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, 2000ISAAC, University of California, Berkeley, “GSM Cloning”, http://www.isaac.cs.berkeley.edu/iChansaac/gsm-faq.htmlS. Chan, “An Overview of Smart Card Security”, http://home.hkstar.com/~alanchan/papers/smartCardSecurity/

Thank You !