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Information about gsm encryption,
by David Margrave, George Mason University
1.0 Introduction
The motivations for security in cellular telecommunications systems are to
secure conversations and signaling data from interception as well as to
prevent cellular telephone fraud. With the older analog-based cellular
telephone systems such as the Advanced Mobile Phone System (AMPS) and the
Total Access Communication System (TACS), it is a relatively simple matter
for the radio hobbyist to intercept cellular telephone conversations with a
police scanner. A well-publicized case involved a potentially embarrassing
cellular telephone conversation with a member of the British royal family
being recorded and released to the media. Another security consideration
with cellular telecommunications systems involves identification credentials
such as the Electronic Serial Number (ESN), which are transmitted "in the
clear" in analog systems. With more complicated equipment, it is possible to
receive the ESN and use it to commit cellular telephone fraud by "cloning"
another cellular phone and placing calls with it. Estimates for cellular
fraud in the U.S. in 1993 are as high as $500 million. The procedure wherein
the Mobile Station (MS) registers its location with the system is also
vulnerable to interception and permits the subscriber’s location to be
monitored even when a call is not in progress, as evidenced by the recent
highly-publicized police pursuit of a famous U.S. athlete.
The security and authentication mechanisms incorporated in GSM make it the
most secure mobile communication standard currently available, particularly
in comparison to the analog systems described above. Part of the enhanced
security of GSM is due to the fact that it is a digital system utilizing a
speech coding algorithm, Gaussian Minimum Shift Keying (GMSK) digital
modulation, slow frequency hopping, and Time Division Multiple Access (TDMA)
time slot architecture. To intercept and reconstruct this signal would
require more highly specialized and expensive equipment than a police
scanner to perform the reception, synchronization, and decoding of the
signal. In addition, the authentication and encryption capabilities
discussed in this paper ensure the security of GSM cellular telephone
conversations and subscriber identification credentials against even the
determined eavesdropper.
2.0 Overview of GSM
GSM (group special mobile or general system for mobile communications) is
the Pan-European standard for digital cellular communications. The Group
Special Mobile was established in 1982 within the European Conference of
Post and Telecommunication Administrations (CEPT). A Further important step
in the history of GSM as a standard for a digital mobile cellular
communications was the signing of a GSM Memorandum of Understanding (MoU) in
1987 in which 18 nations committed themselves to implement cellular networks
based on the GSM specifications. In 1991 the first GSM based networks
commenced operations. GSM provides enhanced features over older analog-based
systems, which are summarized below:
Total Mobility: The subscriber has the advantage of a Pan-European system
allowing him to communicate from everywhere and to be called in any area
served by a GSM cellular network using the same assigned telephone number,
even outside his home location. The calling party does not need to be
informed about the called person's location because the GSM networks are
responsible for the location tasks. With his personal chipcard he can use a
telephone in a rental car, for example, even outside his home location. This
mobility feature is preferred by many business people who constantly need to
be in touch with their headquarters.
High Capacity and Optimal Spectrum Allocation: The former analog-based
cellular networks had to combat capacity problems, particularly in
metropolitan areas. Through a more efficient utilization of the assigned
frequency bandwidth and smaller cell sizes, the GSM System is capable of
serving a greater number of subscribers. The optimal use of the available
spectrum is achieved through the application Frequency Division Multiple
Access (FDMA), Time Division Multiple Access (TDMA), efficient half-rate and
full-rate speech coding, and the Gaussian Minimum Shift Keying (GMSK)
modulation scheme.
Security: The security methods standardized for the GSM System make it the
most secure cellular telecommunications standard currently available.
Although the confidentiality of a call and anonymity of the GSM subscriber
is only guaranteed on the radio channel, this is a major step in achieving
end-to- end security. The subscriber’s anonymity is ensured through the use
of temporary identification numbers. The confidentiality of the
communication itself on the radio link is performed by the application of
encryption algorithms and frequency hopping which could only be realized
using digital systems and signaling.
Services: The list of services available to GSM subscribers typically
includes the following: voice communication, facsimile, voice mail, short
message transmission, data transmission and supplemental services such as
call forwarding.
2.1 GSM Radio Channel
The GSM standard specifies the frequency bands of 890 to 915 MHz for the
uplink band, and 935 to 960 MHz for the downlink band, with each band
divided up into 200 kHz channels. Other features of the radio channel
interface include adaptive time alignment, GMSK modulation, discontinuous
transmission and reception, and slow frequency hopping. Adaptive time
alignment enables the MS to correct its transmit timeslot for propagation
delay. GMSK modulation provides the spectral efficiency and low out-of-band
interference required in the GSM system. Discontinuous transmission and
reception refers to the MS powering down during idle periods and serves the
dual purpose of reducing co-channel interference and extending the portable
unit's battery life. Slow frequency hopping is an additional feature of the
GSM radio channel interface which helps to counter the effects of Rayleigh
fading and co-channel interference.
2.2 TDMA Frame Structures, Channel Types, and Burst Types
The 200 kHz channels in each band are further subdivided into 577 ms
timeslots, with 8 timeslots comprising a TDMA frame of 4.6 ms. Either 26 or
51 TDMA frames are grouped into multiframes (120 or 235 ms), depending on
whether the channel is for traffic or control data. Either 51 or 26 of the
multiframes (again depending on the channel type) make up one superframe
(6.12 s). A hyperframe is composed of 2048 superframes, for a total duration
of 3 hours, 28 minutes, 53 seconds, and 760 ms. The TDMA frame structure has
an associated 22-bit sequence number which uniquely identifies a TDMA frame
within a given hyperframe. Figure 1 illustrates the various TDMA frame
structures.
Figure 1 TDMA Frame Structures
The various logical channels which are mapped onto the TDMA frame structure
may be grouped into traffic channels (TCHs) used to carry voice or user
data, and control channels (CCHs) used to carry signaling and
synchronization data. Control channels are further divided into broadcast
control channels, common control channels, and dedicated control channels.
Each timeslot within a TDMA frame contains modulated data referred to as a
"burst". There are five burst types (normal, frequency correction,
synchronization, dummy, and access bursts), with the normal burst being
discussed in detail here. The bit rate of the radio channel is 270.833
kbit/sec, which corresponds to a timeslot duration of 156.25 bits. The
normal burst is composed of a 3-bit start sequence, 116 bits of payload, a
26-bit training sequence used to help counter the effects of multipath
interference, a 3-bit stop sequence required by the channel coder, and a
guard period (8.25 bit durations) which is a "cushion" to allow for
different arrival times of bursts in adjacent timeslots from geographically
disperse MSs. Two bits from the 116-bit payload are used by the Fast
Associated Control Channel (FACCH) to signal that a given burst has been
borrowed, leaving a total of 114 bits of payload. Figure 2 illustrates the
structure of the normal burst.
Figure 2 Normal Burst Structure
2.3 Speech Coding, Channel Coding, and Interleaving
The speech coding algorithm used in GSM is based on a rectangular pulse
excited linear predictive coder with long-term prediction (RPE-LTP). The
speech coder produces samples at 20 ms intervals at a 13 kbps bit rate,
producing 260 bits per sample or frame. These 260 bits are divided into 182
class 1 and 78 class 2 bits based on a subjective evaluation of their
sensitivity to bit errors, with the class 1 bits being the most sensitive.
Channel coding involves the addition of parity check bits and half-rate
convolutional coding of the 260-bit output of the speech coder. The output
of the channel coder is a 456-bit frame, which is divided into eight 57-bit
components and interleaved over eight consecutive 114-bit TDMA frames. Each
TDMA frame correspondingly consists of two sets of 57 bits from two separate
456-bit channel coder frames. The result of channel coding and interleaving
is to counter the effects of fading channel interference and other sources
of bit errors.
3.0 Overview of Cryptography
This section provides a brief overview of cryptography, with an emphasis on
the features that appear in the GSM system.
3.1 Symmetric Algorithms
Symmetric algorithms are algorithms in which the encryption and decryption
use the same key. For example, if the plaintext is denoted by the variable
P, the ciphertext by C, the encryption with key x by the function Ex( ), and
the decryption with key x by Dx( ), then the symmetric algorithms are
functionally described as follows:
C=Ex(P)
P=Dx(C)
P=Dx(Ex(P))
For a good encryption algorithm, the security of the data rests with the
security of the key, which introduces the problem of key management for
symmetric algorithms. The most widely-known example of a symmetric algorithm
is the Data Encryption Standard (DES). Symmetric encryption algorithms may
be further divided into block ciphers and stream ciphers.
3.1.1 Block Ciphers
As the name suggests, block ciphers encrypt or decrypt data in blocks or
groups of bits. DES uses a 56-bit key and processes data in 64- bit blocks,
producing 64-bits of encrypted data for 64-bits of input, and vice-versa.
Block algorithms are further characterized by their mode of operation, such
as electronic code book (ECB), cipher block chaining (CBC) and cipher
feedback (CFB). CBC and CFB are examples of modes of operation where the
encryption of successive blocks is dependent on the output of one or more
previous encryptions. These modes are desirable because they break up the
one-to-one correspondence between ciphertext blocks and plaintext blocks (as
in ECB mode). Block ciphers may even be implemented as a component of a
stream cipher.
3.1.2 Stream Ciphers
Stream ciphers operate on a bit-by-bit basis, producing a single encrypted
bit for a single plaintext bit. Stream ciphers are commonly implemented as
the exclusive-or (XOR) of the data stream with the keystream. The security
of a stream cipher is determined by the properties of the keystream. A
completely random keystream would effectively implement an unbreakable
one-time pad encryption, and a deterministic keystream with a short period
would provide very little security.
Linear Feedback Shift Registers (LFSRs) are a key component of many stream
ciphers. LFSRs are implemented as a shift register where the vacant bit
created by the shifting is a function of the previous states. With the
correct choice of feedback taps, LFSRs can function as pseudo-random number
generators. The statistical properties of LFSRs, such as the autocorrelation
function and power spectral density, make them useful for other applications
such as pseudo-noise (PN) sequence generators in direct sequence spread
spectrum communications, and for distance measurement in systems such as the
Global Positioning System (GPS). LFSRs have the additional advantage of
being easily implemented in hardware.
The maximal length sequence (or m-sequence) is equal to 2n-1 where n is the
degree of the shift register. An example of a maximal length LFSR is shown
below in Figure 3. This LFSR will generate the periodic m-sequence
consisting of the following states (1111, 0111, 1011, 0101, 1010, 1101,
0110, 0011, 1001, 0100, 0010, 0001, 1000, 1100, 1110).
Figure 3 Four-Stage Linear Feedback Shift Register
In order to form an m-sequence, the feedback taps of an LFSR must correspond
to a primitive polynomial modulo 2 of degree n. A number of stream cipher
designs consist of multiple LFSRs with various interconnections and clocking
schemes. The GSM A5 algorithm, used to encrypt voice and signaling data in
GSM is a stream cipher based on three clock-controlled LFSRs.
3.2 Public Key Algorithms
Public key algorithms are characterized by two keys, a public and private
key, which perform complementary functions. Public and private keys exist in
pairs and ideally have the property that the private key may not be deduced
from the public key, which allows the public key to be openly distributed.
Data encrypted with a given public key may only be decrypted with the
corresponding private key, and vice versa. This is functionally expressed as
follows:
C=Epub(P), P=Dpriv(C)
C=Epriv(P), P=Dpub(C)
Public key cryptography simplifies the problem of key management in that two
parties may exchange encrypted data without having exchanged any sensitive
key information. Digital Signatures also make use of public key
cryptography, and commonly consist of the output of a one-way hash function
for a message (discussed in Section 3.3) with a private key. This enables
security features such as authentication and non- repudiation. The most
common example of a public key algorithm is RSA, named after its inventors
Rivest, Shamir, and Adleman. The security features of GSM, however, do not
make use of any type of public key cryptography.
3.3 One-Way Hash Functions
Generally, one-way hash functions produce a fixed-length output given an
arbitrary input. Secure one-way hash functions are designed such that it is
computationally unfeasible to determine the input given the hash value, or
to determine two unique inputs that hash to the same value. Examples of
one-way hash functions include MD5 developed by Ron Rivest, which produces a
128-bit hash value, and the Secure Hash Algorithm (SHA) developed by the
National Institutes of Standards and Technology (NIST), which produces a
160-bit output.
A typical application of a one-way hash function is to compute a "message
digest" which enables the receiver to verify the authenticity of the data by
duplicating the computation and comparing the results. A hash function
output encrypted with a public key algorithm forms the basis for digital
signatures, such as NIST's Digital Signature Algorithm (DSA).
A key-dependent one-way hash function requires a key to compute and verify
the hash value. This is useful for authentication purposes, where a sender
and receiver may use a key-dependent hash function in a challenge-response
scheme. A key-dependent one-way hash function may be implemented by simply
appending the key to the message and computing the hash value. Another
approach is to use a block cipher in cipher feedback (CFB) mode, with the
output being the last encrypted block (recall that in CFB mode a given
block's output is dependent on the output of previous blocks). The A3 and A8
algorithms of GSM are key- dependent one-way hash functions. The GSM A3 and
A8 algorithms are similar in functionality and are commonly implemented as a
single algorithm called COMP128.
4.0 Description of GSM Security Features
The security aspects of GSM are detailed in GSM Recommendations 02.09,
"Security Aspects," 02.17, "Subscriber Identity Modules," 03.20, "Security
Related Network Functions," and 03.21, "Security Related Algorithms".
Security in GSM consists of the following aspects: subscriber identity
authentication, subscriber identity confidentiality, signaling data
confidentiality, and user data confidentiality. The subscriber is uniquely
identified by the International Mobile Subscriber Identity (IMSI). This
information, along with the individual subscriber authentication key (Ki),
constitutes sensitive identification credentials analogous to the Electronic
Serial Number (ESN) in analog systems such as AMPS and TACS. The design of
the GSM authentication and encryption schemes is such that this sensitive
information is never transmitted over the radio channel. Rather, a
challenge-response mechanism is used to perform authentication. The actual
conversations are encrypted using a temporary, randomly generated ciphering
key (Kc). The MS identifies itself by means of the Temporary Mobile
Subscriber Identity (TMSI), which is issued by the network and may be
changed periodically (i.e. during hand-offs) for additional security.
The security mechanisms of GSM are implemented in three different system
elements; the Subscriber Identity Module (SIM), the GSM handset or MS, and
the GSM network. The SIM contains the IMSI, the individual subscriber
authentication key (Ki), the ciphering key generating algorithm (A8), the
authentication algorithm (A3), as well as a Personal Identification Number
(PIN). The GSM handset contains the ciphering algorithm (A5). The encryption
algorithms (A3, A5, A8) are present in the GSM network as well. The
Authentication Center (AUC), part of the Operation and Maintenance Subsystem
(OMS) of the GSM network, consists of a database of identification and
authentication information for subscribers. This information consists of the
IMSI, the TMSI, the Location Area Identity (LAI), and the individual
subscriber authentication key (Ki) for each user. In order for the
authentication and security mechanisms to function, all three elements (SIM,
handset, and GSM network) are required. This distribution of security
credentials and encryption algorithms provides an additional measure of
security both in ensuring the privacy of cellular telephone conversations
and in the prevention of cellular telephone fraud.
Figure 4 demonstrates the distribution of security information among the
three system elements, the SIM, the MS, and the GSM network. Within the GSM
network, the security information is further distributed among the
authentication center (AUC), the home location register (HLR) and the
visitor location register (VLR). The AUC is responsible for generating the
sets of RAND, SRES, and Kc which are stored in the HLR and VLR for
subsequent use in the authentication and encryption processes.
Figure 4 Distribution of Security Features in the GSM Network
4.1 Authentication
The GSM network authenticates the identity of the subscriber through the use
of a challenge-response mechanism. A 128-bit random number (RAND) is sent to
the MS. The MS computes the 32-bit signed response (SRES) based on the
encryption of the random number (RAND) with the authentication algorithm
(A3) using the individual subscriber authentication key (Ki). Upon receiving
the signed response (SRES) from the subscriber, the GSM network repeats the
calculation to verify the identity of the subscriber. Note that the
individual subscriber authentication key (Ki) is never transmitted over the
radio channel. It is present in the subscriber's SIM, as well as the AUC,
HLR, and VLR databases as previously described. If the received SRES agrees
with the calculated value, the MS has been successfully authenticated and
may continue. If the values do not match, the connection is terminated and
an authentication failure indicated to the MS. Figure 5 shown below
illustrates the authentication mechanism.
Figure 5 GSM Authentication Mechanism
The calculation of the signed response is processed within the SIM. This
provides enhanced security, because the confidential subscriber information
such as the IMSI or the individual subscriber authentication key (Ki) is
never released from the SIM during the authentication process.
4.2 Signaling and Data Confidentiality
The SIM contains the ciphering key generating algorithm (A8) which is used
to produce the 64-bit ciphering key (Kc). The ciphering key is computed by
applying the same random number (RAND) used in the authentication process to
the ciphering key generating algorithm (A8) with the individual subscriber
authentication key (Ki). As will be shown in later sections, the ciphering
key (Kc) is used to encrypt and decrypt the data between the MS and BS. An
additional level of security is provided by having the means to change the
ciphering key, making the system more resistant to eavesdropping. The
ciphering key may be changed at regular intervals as required by network
design and security considerations. Figure 6 below shows the calculation of
the ciphering key (Kc).
Figure 6 Ciphering Key Generation Mechanism
In a similar manner to the authentication process, the computation of the
ciphering key (Kc) takes place internally within the SIM. Therefore
sensitive information such as the individual subscriber authentication key
(Ki) is never revealed by the SIM.
Encrypted voice and data communications between the MS and the network is
accomplished through use of the ciphering algorithm A5. Encrypted
communication is initiated by a ciphering mode request command from the GSM
network. Upon receipt of this command, the mobile station begins encryption
and decryption of data using the ciphering algorithm (A5) and the ciphering
key (Kc). Figure 7 below demonstrates the encryption mechanism.
Figure 7 Ciphering Mode Initiation Mechanism
4.3 Subscriber Identity Confidentiality
To ensure subscriber identity confidentiality, the Temporary Mobile
Subscriber Identity (TMSI) is used. The TMSI is sent to the mobile station
after the authentication and encryption procedures have taken place. The
mobile station responds by confirming reception of the TMSI. The TMSI is
valid in the location area in which it was issued. For communications
outside the location area, the Location Area Identification (LAI) is
necessary in addition to the TMSI. The TMSI allocation/reallocation process
is shown in Figure 8 below.
Figure 8 TMSK Reallocation Mechanism
5.0 Discussion
This section evaluates and expands on the information presented in previous
sections. Additional considerations such as export controls on crypography
are discussed as well.
5.1 GSM Encryption Algorithms
A partial source code implementation of the GSM A5 algorithm was leaked to
the Internet in June, 1994. More recently there have been rumors that this
implementation was an early design and bears little resemblance to the A5
algorithm currently deployed. Nevertheless, insight into the underlying
design theory can be gained by analyzing the available information. The
details of this implementation, as well as some documented facts about A5,
are summarized below:
A5 is a stream cipher consisting of three clock-controlled LFSRs of degree
19, 22, and 23.
The clock control is a threshold function of the middle bits of each of the
three shift registers.
The sum of the degrees of the three shift registers is 64. The 64-bit
session key is used to initialize the contents of the shift registers.
The 22-bit TDMA frame number is fed into the shift registers.
Two 114-bit keystreams are produced for each TDMA frame, which are XOR-ed
with the uplink and downlink traffic channels.
It is rumored that the A5 algorithm has an "effective" key length of 40
bits.
5.2 Key Length
This section focuses on key length as a figure of merit of an encryption
algorithm. Assuming a brute-force search of every possible key is the most
efficient method of cracking an encrypted message (a big assumption), Table
1 shown below summarizes how long it would take to decrypt a message with a
given key length, assuming a cracking machine capable of one million
encryptions per second.
Table 1 Brute-force key search times for various key sizes Key length in
bits 32 40 56 64 128
Time required to test all possible keys 1.19 hours 12.7 days 2,291 years
584,542 years 10.8 x 10^24 years
The time required for a 128-bit key is extremely large; as a basis for
comparison the age of the Universe is believed to be 1.6x10^10 years. An
example of an algorithm with a 128-bit key is the International Data
Encryption Algorithm (IDEA). The key length may alternately be examined by
determining the number of hypothetical cracking machines required to decrypt
a message in a given period of time.
Table 2 Number of machines required to search a key space in a given time
Key length in bits 1 day 1 week 1 year
40 13 2 -
56 836,788 119,132 2,291
64 2.14x10^8 3.04x10^6 584,542
128 3.9x10^27 5.6x10^26 10.8x10^24
A machine capable of testing one million keys per second is possible by
today’s standards. In considering the strength of an encryption algorithm,
the value of the information being protected should be taken into account.
It is generally accepted that DES with its 56-bit key will have reached the
end of its useful lifetime by the turn of the century for protecting data
such as banking transactions. Assuming that the A5 algorithm has an
effective key length of 40 bits (instead of 64), it currently provides
adequate protection for information with a short lifetime. A common
observation is that the "tactical lifetime" of cellular telephone
conversations is on the order of weeks.
5.3 Export Restrictions on Encryption Technology
The goal of the GSM recommendations is to provide a pan- European standard
for digital cellular telecommunications. A consequence of this is that
export restrictions and other legal restrictions on encryption have come
into play. This is a hotly debated, highly political issue which involves
the privacy rights of the individual, the ability of law enforcement
agencies to conduct surveillance, and the business interests of corporations
manufacturing cellular hardware for export.
The technical details of the encryption algorithms used in GSM are closely
held secrets. The algorithms were developed in Britain, and cellular
telephone manufacturers desiring to implement the encryption technology must
agree to non-disclosure and obtain special licenses from the British
government. Law enforcement and Intelligence agencies from the U.S.,
Britain, France, the Netherlands, and other nations are very concerned about
the export of encryption technology because of the potential for military
application by hostile nations. An additional concern is that the widespread
use of encryption technology for cellular telephone communications will
interfere with the ability of law enforcement agencies to conduct
surveillance on terrorists or organized criminal activity.
A disagreement between cellular telephone manufacturers and the British
government centering around export permits for the encryption technology in
GSM was settled by a compromise in 1993. Western European nations and a few
other specialized markets such as Hong Kong would be allowed to have the GSM
encryption technology, in particular the A5/1 algorithm. A weaker version of
the algorithm (A5/2) was approved for export to most other countries,
including central and eastern European nations. Under the agreement,
designated countries such as Russia would not be allowed to receive any
functional encryption technology in their GSM systems. Future developments
will likely lead to some relaxation of the export restrictions, allowing
countries who currently have no GSM cryptographic technology to receive the
A5/2 algorithm.
6.0 Conclusion
The security mechanisms specified in the GSM standard make it the most
secure cellular telecommunications system available. The use of
authentication, encryption, and temporary identification numbers ensures the
privacy and anonymity of the system's users, as well as safeguarding the
system against fraudulent use. Even GSM systems with the A5/2 encryption
algorithm, or even with no encryption are inherently more secure than analog
systems due to their use of speech coding, digital modulation, and TDMA
channel access.
7.0 Acronyms
A3
Authentication Algorithm
A5
Ciphering Algorithm
A8
Ciphering Key Generating Algorithm
AMPS
Advanced Mobile Phone System
AUC
Authentication Center
BS
Base Station
CBC
Cipher Block Chaining
CEPT
European Conference of Post and Telecommunication Administrations
CFB
Cipher Feedback
CKSN
Ciphering Key Sequence Number
DES
Data Encryption Standard
DSA
Digital Signature Algorithm
ECB
Electronic Code Book
ETSI
European Telecommunications Standards Institute
GMSK
Gaussian Minimum Shift Keying
GSM
Group Special Mobile
HLR
Home Location Register
IMSI
International Mobile Subscriber Identity
Kc
Ciphering Key
Ki
Individual Subscriber Authentication Key
LAI
Location Area Identity
LFSR
Linear Feedback Shift Register
MoU
Memorandum of Understanding
MS
Mobile Station
MSC
Mobile Switching Center
NIST
National Institute of Standards and Technology1
OMS
Operation and Maintenance Subsystem
RAND
Random Number
RSA
Rivest, Shamir, Adleman
SHA
Secure Hash Algorithm
SRES
Signed Response
TACS
Total Access Communications System
TMSI
Temporary Mobile Subscriber Identity
VLR
Visitor Location Register
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European Telecommunications Standards Institute, Recommendation GSM 02.17,
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European Telecommunications Standards Institute, Recommendation GSM 03.20,
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