GSM Security and 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:

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:


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:

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

Authentication Algorithm
Ciphering Algorithm
Ciphering Key Generating Algorithm
Advanced Mobile Phone System
Authentication Center
Base Station
Cipher Block Chaining
European Conference of Post and Telecommunication Administrations
Cipher Feedback
Ciphering Key Sequence Number
Data Encryption Standard
Digital Signature Algorithm
Electronic Code Book
European Telecommunications Standards Institute
Gaussian Minimum Shift Keying
Group Special Mobile
Home Location Register
International Mobile Subscriber Identity
Ciphering Key
Individual Subscriber Authentication Key
Location Area Identity
Linear Feedback Shift Register
Memorandum of Understanding
Mobile Station
Mobile Switching Center
National Institute of Standards and Technology1
Operation and Maintenance Subsystem
Random Number
Rivest, Shamir, Adleman
Secure Hash Algorithm
Signed Response
Total Access Communications System
Temporary Mobile Subscriber Identity
Visitor Location Register


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