Abstract:
In the method for establishing a session key, a network and a mobile transfer codes between one another. The mobile and the network perform mutual authentication based on the codes. Besides performing this mutual authentication, the mobile and the network to establish the session key based on the codes. In one embodiment, the messages forming part of the intended session are sent with the codes, and form a basis upon which the codes for authentication have been derived.

Description:
RELATED APPLICATIONS 
     The following applications, filed on Jul. 31, 1998, are related to the subject application and are hereby incorporated by reference in their entirety: application Ser. No. 09/127,767 entitled METHOD FOR TWO PARTY AUTHENTICATION AND KEY AGREEMENT by the inventor of the subject application, application Ser. No. 09/127,768, now U.S. Pat. No. 6,243,811 entitled METHOD FOR UPDATING SECRET SHARED DATA IN A WIRELESS COMMUNICATION SYSTEM by the inventor of the subject application; application Ser. No. 09/127,766, now U.S. Pat. No. 6,249,867 entitled METHOD FOR TRANSFERRING SENSITIVE INFORMATION USING INTIALLY UNSECURED COMMUNICATION by the inventor of the subject application; application Ser. No. 09/127,045 entitled METHOD FOR SECURING OVER-THE-AIR COMMUNICATION IN A WIRELESS SYSTEM by the inventor of the subject application; and application Ser. No. 09/127,769, now U.S. Pat. No. 6,192,474 entitled METHOD FOR ESTABLISHING A KEY USING OVER-THE-AIR COMMUNICATION AND PASSWORD PROTOCOL AND PASSWORD PROTOCOL by the inventor of the subject application and Adam Berenzweig. 
     The following applications, filed concurrently with the subject application, are related to the subject application and are hereby incorporated by reference in their entirety: application Ser. No. 09/141,581 entitled METHOD FOR DETERMINING TEMPORARY MOBILE IDENTIFIERS AND MANAGING USE THEREOF by the inventor of the subject application and application Ser. No. 09/141,582 entitled METHOD FOR PROTECTING MOBILE ANONYMITY by the inventor of the subject application. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method for establishing a session key in a wireless system. 
     2. Description of Related Art 
     The U.S. currently utilizes three major wireless systems, with differing standards. The first system is a time division multiple access system (TDMA) and is governed by IS-136, the second system is a code division multiple access (CDMA) system governed by IS-95, and the third is the Advanced Mobile Phone System (AMPS). All three communication systems use the IS-41 standard for intersystem messaging, which defines the authentication procedure for call origination, updating the secret shared data, and etc. 
     FIG. 1 illustrates a wireless system including an authentication center (AC) and a home location register (HLR)  10 , a visiting location register (VLR)  15 , and a mobile  20 . While more than one HLR may be associated with an AC, currently a one-to-one correspondence exists. Consequently, FIG. 1 illustrates the HLR and AC as a single entity, even though they are separate. Furthermore, for simplicity, the remainder of the specification will refer to the HLR and AC jointly as the AC/HLR. Also, the VLR sends information to one of a plurality of mobile switching centers (MSCs) associated therewith, and each MSC sends the information to one of a plurality of base stations (BSs) for transmission to the mobile. For simplicity, the VLR, MSCs and BSs will be referred to and illustrated as a VLR. Collectively, the ACs, HLRs, VLRs, MSCs, and BSs operated by a network provider are referred to as a network. 
     A root key, known as the A-key, is stored only in the AC/HLR  10  and the mobile  20 . There is a secondary key, known as Shared Secret Data SSD, which is sent to the VLR  15  as the mobile roams (i.e., when the mobile is outside its home coverage area). The SSD is generated from the A-key and a random seed RANDSSD using a cryptographic algorithm or function. A cryptographic function is a function which generates an output having a predetermined number of bits based on a range of possible inputs. A keyed cryptographic function (KCF) is a type of cryptographic function that operates based on a key; for instance, a cryptographic function which operates on two or more arguments (i.e., inputs) wherein one of the arguments is the key. From the output and knowledge of the KCF in use, the inputs can not be determined unless the key is known. Encryption/decryption algorithms are types of cryptographic functions. So are one-way functions like pseudo random functions (PRFs) and message authentication codes (MACs). The expression KCF SK (R N ′) represents the KCF of the random number R N ′ using the session key SK as the key. A session key is a key that lasts for a session, and a session is a period of time such as the length of a call. 
     In the IS-41 protocol, the cryptographic function used is CAVE (Cellular Authentication and Voice Encryption). When the mobile  20  roams, the VLR  15  in that area sends an authentication request to the AC/HLR  10 . If operating in an unshared mode, the AC/HLR  10 , using the VLR  15  as a communication conduit, authenticates the mobile  20  using the SSD associated with the mobile  20 . However, in the shared mode, the AC/HLR  10  responds to the authentication request by sending the mobile&#39;s SSD to the VLR  15 . Once the VLR  15  has the SSD, it can authenticate the mobile  20  independently of the AC/HLR  10 . For security reasons, the SSD is periodically updated. 
     The SSD is 128 bits long. The first 64 bits serve as a first SSD, referred to as SSDA, and the second 64 bits serve as a second SSD, referred to as SSDB. The SSDA is used in the protocol to update the SSD, and the mobile  20  and the network generate session keys using SSDB. In updating the SSD, IS-41 provides of measure of security by performing mutual authentication (i.e., the mobile and the network authenticate one another) during the update process. However, in generating session keys, IS-41 does not provide for mutual authentication. 
     SUMMARY OF THE INVENTION 
     In the method for establishing a session key, a network and a mobile transfer codes between one another. The mobile uses these codes to authenticate the network, and the network uses these codes to authenticate the mobile. Besides performing this mutual authentication, the codes are used by the mobile and the network to establish the session key. In one embodiment, communication efficiency is improved by sending messages, forming part of the intended session, with the codes. Furthermore, the codes for performing mutual authentication are derived based on the messages. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention will become more fully understood from the detailed description given below and the accompanying drawings which are given by way of illustration only, wherein like reference numerals designate corresponding parts in the various drawings, and wherein: 
     FIG. 1 is a block diagram illustrating the basic components of a wireless system; 
     FIG. 2 illustrates the communication between the network and the mobile to establish a session key during call termination according to a first embodiment of the present invention; 
     FIG. 3 illustrates the communication between the network and the mobile to establish a session key during call origination according to the first embodiment of the present invention; 
     FIG. 4 illustrates the communication between the network and the mobile to establish a session key during call termination according to a second embodiment of the present invention; 
     FIG. 5 illustrates the communication between the network and the mobile to establish a session key during call origination according to the second embodiment of the present invention; 
     FIG. 6 illustrates the communication between the network and the mobile to establish a session key during call termination according to a third embodiment of the present invention; and 
     FIG. 7 illustrates the communication between the network and the mobile to establish a session key during call origination according to the third embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The method for establishing session keys according to the present invention will be described as employed by the wireless system shown in FIG.  1 . For the purposes of discussion only, operation in the shared manner will be described, but one skilled in the art will understand that the system may also operate in the unshared mode. Furthermore, while numerous sessions exist, for purposes of providing examples only, the method according to the present invention will be described with respect to establishing session keys during call origination and call termination. It will also be appreciated that, for clarity, the transfer of well-known information, such as the mobile&#39;s identity information (e.g., mobile identification number, electronic serial number, etc.), between the mobile  20  and the network has not been described. 
     FIG. 2 illustrates the communication between the network and the mobile  20  to establish a session key during call termination according to a first embodiment of the present invention. As shown, the VLR  15  generates a random number R N  using a random number generator, and sends the random number R N  to the mobile  20  as a challenge along with a call termination request. 
     In response, the mobile  20  generates a count value C M , and performs a KCF on the random number R N , the count value C M , Type data, and id data  0  using the SSDA as the key. This calculation is represented as KCF SSDA (Type,  0 , C M , R N ). Preferably, the KCF is a keyed message authentication code such as HMAC, but could be a PRF such as Data Encryption Standard-Cipher Block Chaining (DES-CBC) from NIST (National Institute of Standards). The mobile  20  includes a counter which generates the count value C M , and increments the count value C M  prior to generating the challenge response (i.e., KCF SSDA (Type,  0 , C M , R N )) to each challenge from the network. 
     The Type data represents the type of protocol being performed. Types of protocols include, for example, call termination, call origination, mobile registration, etc. The id data  0  indicates that the communication issued from a mobile, and id data  1  indicates that communication is from the network. 
     The mobile  20  sends count value C M  and KCF SSDA (Type,  0 , C M , R N ) to the network. Because the VLR  15  initiated the current call termination protocol including the protocol for establishing a session key according to the present invention, the VLR  15  knows the Type data. Also, because communication from mobiles includes the same id data, this value is known by the VLR  15  as well. Accordingly, based on the received count value C M , the VLR  15  calculates KCF SSDA (Type,  0 , C M , R N ) and determines whether this calculated value matches the version received from the mobile  20 . If a match is found, the VLR  15  authenticates the mobile  20 . 
     Once the mobile  20  has been authenticated, the VLR  15  calculates KCF SSDA (Type,  1 , C M ), and sends the calculated result to the mobile  20 . The mobile  20 , meanwhile, calculates KCF SSDA (Type,  1 , C M ) as well. The mobile  20  then verifies whether the calculated version of KCF SSDA (Type,  1 , C M ) matches the version received from the VLR  15 . If a match is found, the mobile  20  authenticates the network. Both the mobile  20  and the VLR  15  generate the session key SK as PRF A-Key (C M , R N ); wherein the PRF is preferably the DES-CBC algorithm. 
     The mobile  20  stores the count value C M  in semipermanent memory so that during power down, the count value C M  is not re-initialized. This way, repetition of a count value is prevented; repetition of the count value permits an attacker to prevail in his attack. In a preferred embodiment, the count value is initialized using a random number and generated using a large bit counter such as a 64 or 75 bit counter. This provides security even when the mobile  20  crashes and loses the stored count value. Even if an attacker can cause a mobile to crash at will, and assuming it takes at least a second to initiate a session, it will take, for example, a year before the attacker manages to have the mobile repeat a count value when a 75 bit counter is used. 
     As an alternative, instead of generating and sending a unique random number R N  to each mobile, the VLR  15  generates a global random number R N ; namely, the same random number for all the mobiles. In this alternative embodiment, the network sends the call termination request as a page on a control channel. 
     This alternative embodiment applies, however, when the anticipated response time for the mobile  20 , as monitored by the network, is kept relatively the same as when a unique random number R N  is sent. Stated another way, this alternative embodiment applies when the validity period of the global random number is kept relatively short. If a longer validity period for global random numbers is desired, then, preferably, for the duration of a global random number the VLR  15  stores the count value C M  and determines whether the received count value C M  exceeds the previously stored count value. If the received count value C M  does exceed the previously stored count value, then the VLR  15  goes forward with authenticating the mobile  20 . If the received count value C M  does not exceed the previously stored count value, the mobile  20  is not authenticated. When a new global random number is sent by the VLR  15 , the stored count values for each mobile are erased, and the process of storing and comparing count values begins again. 
     FIG. 3 illustrates the communication between the network and the mobile  20  to establish a session key during call origination according to the first embodiment of the present invention. As shown, the mobile  20  sends a call origination request to the VLR  15 . In return, the VLR  15  generates the random number R N  using a random number generator, and sends the random number R N  to the mobile  20 . 
     In response, the mobile  20  generates the count value C M , and performs a KCF on the random number R N , the dialed digits DD, the count value C M , Type data, and id data  0  using the SSDA as the key. This calculation is represented as KCF SSDA (Type,  0 , C M , R N , DD). The dialed digits DD are the telephone number of the party the mobile user wants to call. 
     The mobile  20  sends the dialed digits DD, the count value C M  and KCF SSDA (Type,  0 , C M , R N , DD) to the network. Because the VLR  15  received the call origination request, the VLR  15  knows the Type data. Accordingly, based on the received dialed digits and count value C M , the VLR  15  calculates KCF SSDA (Type,  0 , C M , R N , DD) and determines whether this calculated value matches the version received from the mobile  20 . If a match is found, the VLR  15  authenticates the mobile  20 . 
     Once the mobile  20  has been authenticated, the VLR  15  calculates KCF SSDA (Type,  1 , C M ), and sends the calculated result to the mobile  20 . The mobile  20 , meanwhile, calculates KCF SSDA (Type,  1 , C M  ) as well. The mobile  20  then verifies whether the calculated version of KCF SSDA (Type,  1 , C M ) matches the version received from the VLR  15 . If a match is found, the mobile  20  authenticates the network. 
     Both the mobile  20  and VLR  15  generate the session key SK as PRF A-Key (C M , R N ); wherein the PRF is preferably the DES-CBC algorithm. 
     As discussed above, mobile  20  stores the count value C M  in semi-permanent memory, and the count value is initialized using a random number and generated using a large bit counter such as a 64 or 75 bit counter. 
     As an alternative, instead of generating and sending a unique random number R N  to each mobile, the VLR  15  generates a global random number R N ; namely, the same random number for all the mobiles. 
     This alternative embodiment applies, however, when the anticipated response time for the mobile  20 , as monitored by the network, is kept relatively the same as when a unique random number R N  is sent. Stated another way, this alternative embodiment applies when the validity period of the global random number is kept relatively short. If a longer validity period for global random numbers is desired, then, preferably, for the duration of a global random number the VLR  15  stores the count value C M  and determines whether the received count value C M  exceeds the previously stored count value. If the received count value C M  does exceed the previously stored count value, then the VLR  15  goes forward with authenticating the mobile  20 . If the received count value C M  does not exceed the previously stored count value, the mobile  20  is not authenticated. When a new global random number is sent by the VLR  15 , the stored count values for each mobile are erased, and the process of storing and comparing count values begins again. 
     FIG. 4 illustrates the communication between the network and the mobile  20  to establish a session key during call termination according to a second embodiment of the present invention. As shown, the VLR  15  generates a random number R N  using a random number generator, and sends the random number R N  as a global challenge. When establishing a session key for call termination with the mobile  20 , the VLR  15  sends a call termination request as a page to the mobile  20  on a control channel. 
     In response, the mobile  20  generates, using a random number generator, a random number R M , and performs a KCF on the random number R N , the random number R M , Type data, and id data  0  using the SSDA as the key. This calculation is represented as KCF SSDA (Type,  0 , R M , R N ). Preferably, the KCF is a keyed message authentication code such as HMAC, but could be a PRF such as Data Encryption Standard-Cipher Block Chaining (DES-CBC) from NIST (National Institute of Standards). 
     The mobile  20  sends the random number R M  and KCFSSDA (Type,  0 , R M , R N ) to the network. Based on the received random number R M , the VLR  15  calculates KCF SSDA (Type,  0 , R M , R N ) and determines whether this calculated value matches the version received from the mobile  20 . If a match is found, the VLR  15  authenticates the mobile  20 . 
     Once the mobile  20  has been authenticated, the VLR  15  calculates KCF SSDA (Type,  1 , R M ), and sends the calculated result to the mobile  20 . The mobile  20 , meanwhile, calculates KCF SSDA (Type,  1 , R M ) as well. The mobile  20  then verifies whether the calculated version of KCF SSDA (Type,  1 , R M ) matches the version received from the VLR  15 . If a match is found, the mobile  20  authenticates the network. 
     Both the mobile  20  and the VLR  15  generate the session key SK as PRF A-Key (R M , R N ); wherein the PRF is preferably the DES-CBC algorithm. 
     Furthermore, the embodiment of FIG. 4 applies when the anticipated response time for the mobile  20 , as monitored by the network, is kept relatively the same as when a unique random number R N  is sent. Stated another way, this embodiment applies when the validity period of the global random number is kept relatively short. If a longer validity period for global random numbers is desired, then, preferably, the mobile  20  generates a count value CT in addition to the random number R M . 
     Specifically, when a new global random number R N  is received, the mobile  20  initializes a counter included therein. Each time the mobile  20  generates a random number R M  and a challenge response, the mobile  20  increments the counter to obtain the count value CT. Furthermore, the challenge response generated by the mobile  20  is KCF SSDA (Type,  0 , R M  , R N , CT), and the mobile  20  sends the count value CT, the random number R M  and this challenge response to the network. The VLR  15  stores received count values from each mobile for the duration of a global random number R N , and determines whether a count value CT received from a mobile exceeds the previously stored count value for that mobile. If the received count value CT does exceed the previously stored count value, then the VLR  15  goes forward with authenticating the mobile  20 . If the received count value CT does not exceed the previously stored count value, the mobile  20  is not authenticated. 
     If the VLR  15  goes forward with authenticating the mobile  20 , the VLR  15  generates and sends a challenge response of KCF SSDA (Type,  1 , R M , CT). Additionally, in generating the session key, the mobile  20  and the VLR  15  calculate the session key as PRF A-Key (R M , R N , CT). 
     FIG. 5 illustrates the communication between the network and the mobile  20  to establish a session key during call origination according to the second embodiment of the present invention. As shown, the mobile  20  sends a call origination request to the VLR  15 . In return, the VLR  15  generates the random number R N  using a random number generator, and sends the random number R N  as a global challenge. 
     When the mobile user dials digits to make a call, the mobile  20  generates a random number R M  using a random number generator and performs a KCF on the random number R N , the dialed digits DD, the random number R M , Type data, and id data  0  using the SSDA as the key. This calculation is represented as KCF SSDA (Type,  0 , R M , R N , DD). 
     The mobile  20  sends the dialed digits DD, the random number R M  and KCF SSDA (Type,  0 , R M , R N , DD) to the network. Based on the received dialed digits and random number R M , the VLR  15  calculates KCF SSDA (Type,  0 , R M , R N , DD) and determines whether this calculated value matches the version received from the mobile  20 . If a match is found, the VLR  15  authenticates the mobile  20 . 
     Once the mobile  20  has been authenticated, the VLR  15  calculates KCF SSDA (Type,  1 , R M ), and sends the calculated result to the mobile  20 . The mobile  20 , meanwhile, calculates KCF SSDA (Type,  1 , R M ) as well. The mobile  20  then verifies whether the calculated version of KCF SSDA (Type,  1 , R M ) matches the version received from the VLR  15 . If a match is found, the mobile  20  authenticates the network. 
     Both the mobile  20  and VLR  15  generate the session key SK as PRF A-Key (R M , R N ); wherein the PRF is preferably the DES-CBC algorithm. 
     Furthermore, the embodiment of FIG. 5 applies when the anticipated response time for the mobile, as monitored by the network, is kept relatively the same as when a unique random number R N  is sent. Stated another way, this embodiment applies when the validity period of the global random number is kept relatively short. If a longer validity period for global random numbers is desired, then, preferably, the mobile  20  generates a count value CT in addition to the random number R M . 
     Specifically, when a new global random number R N  is received, the mobile  20  initializes a counter included therein. Each time the mobile  20  generates a random number R M  and a challenge response, the mobile  20  increments the counter to obtain the count value CT. Furthermore, the challenge response generated by the mobile  20  is KCF SSDA (Type,  0 , R M  , R N , DD, CT), and the mobile  20  sends the call origination request, the dialed digits DD, the count value CT, the random number R M  and this challenge response to the network. The VLR  15  stores received count values from each mobile for the duration of a global random number R N , and determines whether a count value CT received from a mobile exceeds the previously stored count value for that mobile. If the received count value CT does exceed the previously stored count value, then the VLR  15  goes forward with authenticating the mobile  20 . If the received count value CT does not exceed the previously stored count value, the mobile  20  is not authenticated. 
     If the VLR  15  goes forward with authenticating the mobile  20 , the VLR  15  generates and sends a challenge response of KCF SSDA (Type,  1 , R M , CT). Accordingly, when using a global random number R N  only two rounds of communication are needed to establish the session key. Additionally, in generating the session key, the mobile  20  and the VLR  15  calculate the session key as PRF A-Key (R M , R N , CT). 
     Next, the third embodiment of the present invention will be described. In conventional wireless systems, after establishing the session key, messages are transferred between the mobile  20  and the network. The third embodiment of the present invention improves communication efficiency by incorporating the initial transfer of messages as part of the communication to establish the session key. 
     FIG. 6 illustrates the communication between the network and the mobile  20  to establish a session key during call termination according to a third embodiment of the present invention. As shown, the VLR  15  generates a random number R N  using a random number generator, and sends the random number R N  to the mobile  20  along with a call termination request. 
     In response, the mobile  20  generates a random number R M , and calculates a session key SK as PRF A-Key (R M , R N ). In the typical, well-known fashion, the mobile  20  also generates a message X M  and a mobile message count value CTM associated therewith. Because the generation of messages and the message count value are well-known in the art, these processes will not be described in detail. 
     The mobile  20  then performs a KCF on the message X M , the count value CTM, and the mobile id data of  0  using the session key SK as the key to generate an authentication tag. This calculation is represented as KCF SK ( 0 , CTM, X M ). Preferably, the KCF is a keyed message authentication code such as HMAC, but could be a PRF such as Data Encryption Standard-Cipher Block Chaining (DES-CBC) from NIST (National Institute of Standards). 
     The mobile  20  sends the message count value CTM, the random number R M , the message X M  and the authentication tag of KCF SK ( 0 , CTM, X M ) to the network. Based on the received random number R M , the VLR  15  calculates the session key SK in the same manner as did the mobile  20 . The VLR  15  also calculates KCF SK ( 0 , CTM, X M ) based on the received message X M  and the count value CTM, and determines whether this calculated value matches the version received from the mobile  20 . If a match is found, the VLR  15  authenticates the mobile  20 . 
     If the VLR  15  authenticates the mobile  20 , the VLR  15  processes the message X M  and the message count value CTM in the typical, well-known manner, and generates a network message X N  and network message count value CTN in the typical, well-known manner. Because these processes are so well-known in the art, they will not be described in detail. 
     The VLR  15  further calculates an authentication tag of KCF SK ( 1 , CTN, X N ), where  1  is the network id data, and sends this authentication tag to the mobile  20  along with the message X N  and the message count value CTN. The mobile  20  calculates KCF SK ( 1 , CTN, X N ) based on the received message X N  and the count value CTN. The mobile  20  then verifies whether the calculated version of KCF SK ( 1 , CTN, X N ) matches the version received from the VLR  15 . If a match is found, the mobile  20  authenticates the network; and thus, the session key SK. 
     As an alternative, instead of generating and sending a unique random number R N  to each mobile, the VLR  15  generates a global random number R N ; namely, the same random number for all the mobiles. In this alternative embodiment, the network sends the call termination request as a page on a control channel. 
     Furthermore, this alternative embodiment applies when the anticipated response time for the mobile, as monitored by the network, is kept relatively the same as when a unique random number R N  is sent. Stated another way, this embodiment applies when the validity period of the global random number R N  is kept relatively short. If a longer validity period for global random numbers is desired, then, preferably, the mobile  20  generates a count value CT in addition to the random number R M . 
     Specifically, when a new global random number R N  is received, the mobile  20  initializes a counter included therein. Each time the mobile  20  generates a random number R M  and an authentication tag, the mobile  20  increments the counter to obtain the count value CT. Furthermore, the mobile  20  sends the count value CT along with the message count value CTM, the random number R M , the message X M  and the authentication tag. The VLR  15  stores received count values from each mobile for the duration of a global random number R N , and determines whether a count value CT received from a mobile exceeds the previously stored count value for that mobile. If the received count value CT does exceed the previously stored count value, then the VLR  15  goes forward with authenticating the mobile  20 . If the received count value CT does not exceed the previously stored count value, the mobile  20  is not authenticated. Additionally, in generating the session key, the mobile  20  and the VLR  15  calculate the session key as PRF A-Key (R M , R N , CT). 
     FIG. 7 illustrates the communication between the network and the mobile  20  to establish a session key during call origination according to the third embodiment of the present invention. Once the dialed digits DD are received from a mobile user, the mobile  20  generates a random number R M  using a random number generator. As shown, the mobile  20  sends a call origination request, the random number R M  and the dialed digits DD to the VLR  15 . 
     In response, the VLR  15  generates a random number R M , and calculates a session key SK as PRF A-Key (R M , R N ). In the typical, well-known fashion, the VLR  15  also generates a message X N  and a mobile message count value CTN associated therewith. Because the generation of messages and the message count value are well-known in the art, these processes will not be described in detail. 
     The VLR  15  then performs a KCF on the message X N , the count value CTN, and the network id data of  1  using the session key SK as the key to generate an authentication tag. This calculation is represented as KCF SK ( 1 , CTN, X N ). The VLR  15  sends the message count value CTN, the random number R N , the message X N  and the authentication tag of KCF SK ( 1 , CTN, X N ) to the mobile  20 . Based on the received random number R N , the mobile  20  calculates the session key SK in the same manner as did the VLR  15 . The mobile  20  also calculates KCF SK ( 1 , CTN, X N ) based on the received message X N  and the count value CTN, and determines whether this calculated value matches the version received from the VLR  15 . If a match is found, the mobile  20  authenticates the VLR  15 . 
     If the mobile  20  authenticates the VLR  15 , the mobile  20  processes the message X N  and the message count value CTN in the typical, well-known manner, and generates a network message X M  and network message count value CTM in the typical, well-known manner. Because these processes are so well-known in the art, they will not be described in detail. 
     The mobile  20  further calculates an authentication tag of KCF SK ( 0 , CTM, X M ), where  0  is the mobile id data, and sends this authentication tag to the VLR  15  along with the message X M  and the message count value CTM. The VLR  15  calculates KCF SK ( 0 , CTM, X M ) based on the received message X M  and the count value CTM. The VLR  15  then verifies whether the calculated version of KCF SK ( 0 , CTM, X M ) matches the version received from the mobile  20 . If a match is found, the VLR  15  authenticates the mobile  20 ; and thus, the session key SK. 
     As an alternative, instead of generating and sending a unique random number R N  to each mobile, the VLR  15  generates a global random number R N ; namely, the same random number for all the mobiles. 
     Furthermore, this alternative embodiment applies when the anticipated response time for the mobile, as monitored by the network, is kept relatively the same as when a unique random number R N  is sent. Stated another way, this embodiment applies when the validity period of the global random number R N  is kept relatively short. If a longer validity period for global random numbers is desired, then, preferably, the mobile  20  generates a count value CT in addition to the random number R M . 
     Specifically, when a new global random number R N  is received, the mobile  20  initializes a counter included therein. Each time the mobile  20  generates a random number R M  and an authentication tag, the mobile  20  increments the counter to obtain the count value CT. Furthermore, the mobile  20  sends the count value CT along with the call origination request. The VLR  15  stores received count values from each mobile for the duration of a global random number R N , and determines whether a count value CT received from a mobile exceeds the previously stored count value for that mobile. If the received count value CT does exceed the previously stored count value, then the VLR  15  goes forward with authenticating the mobile  20 . If the received count value CT does not exceed the previously stored count value, the mobile  20  is not authenticated. Additionally, in generating the session key, the mobile  20  and the VLR  15  calculate the session key as PRF A-Key (R M , R N , CT). 
     Unlike some conventional methods for establishing the session key, the method according to the present invention provides an added measure of security by performing mutual authentication. 
     The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications are intended to be included within the scope of the following claims.