Method for establishing a key using over-the-air communication and password protocol

Abstract: In the password protocol, the communicating parties exchange calculation results, which each include an exponential, to generate a key. In generating the calculation results, each party adds the password to their respective exponential. If the authorizing information previously sent by one party is acceptable to the other party, then this other party uses the key established according to the password protocol. The channel authorizing information is sent over a secure communication channel. The secure communication channel is also used in other embodiments to verify a hash on at least one calculation result sent between the parties. If the hash is verified, then a key is established using the calculation results sent between the parties

Description: Field Of The Invention The present invention relates to a password protocol and a method for establishing a key using over-the-air communication and, in one embodiment, the password protocol. Description Of Related Art In a wireless communication system, the handsets, often called mobiles, purchased by mobile users are typically taken to a network service provider, and long keys and parameters are entered into the handset to activate service. The network of the service provider also maintains and associates with the mobile, a copy of the long keys and parameters for the mobile. As is well-known, based on these long keys and parameters, information can be securely transferred between the network and the mobile over the air. Alternatively, the user receives long keys from the service provider over a secure communication channel, like a telephone/land line, and must manually enter these codes into the mobile. Because the transfer of the long keys and parameters is performed via a telephone/land line or at the network service provider as opposed to over the air, the transfer is secure against over the air attacks. However, this method of securely transferring information places certain burdens and restrictions on the mobile user. Preferably, the mobile user should be able to buy their handsets and then get service from any service provider without physically taking the handsets to the provider's location or having to manually, and error free, enter long keys into the mobile. The capability to activate and provision the mobile remotely is part of the North American wireless standards, and is referred to as over the air service provisioning" (OTASP). Currently, the North American Cellular standard IS41-C specifies an OTASP protocol using the well-known Diffie-Hellman (DH) key agreement for establishing a secret key between two parties. Fig. 1 illustrates the application of the DH key agreement to establishing a secret key between a mobile 20 and a network 10 used in IS41-C. Namely, Fig. 1 shows, in a simplified form for clarity, the communication between a network 10 and a mobile 20 according to the DH key agreement. As used herein, the term network refers to the authentication centers, home location registers, visiting location registers, mobile switching centers, and base stations operated by a network service provider. The network 10 generates a random number R N , and calculates (g^R N mod p). As shown in Fig. 1, the network 10 sends a 512-bit prime number p, the generator g of the group generated by the prime number p, and (g^R N mod p) to the mobile 20. Next, the mobile 20 generates a random number R M , calculates (g^R M mod p), and sends (g^R M mod p) to the network 10. The mobile 20 raises the received (g^R N mod p) from the network 10 to the power R M to obtain (g^R M R N mod p). The network 10 raises the received (g^R M mod p) from the mobile 20 to the power R N to also obtain (g^R M R N mod p). Both the mobile 20 and the network 10 obtain the same result, and establish the 64 least significant bits as the long-lived key called the A-key. The A-key serves as a root key for deriving other keys used in securing the communication between the mobile 20 and the network 10. One of the problems with the DH key exchange is that it is unauthenticated and susceptible to a man-in-the-middle attack. For instance, in the above mobile-network two party example, an attacker can impersonate the network 10 and then in turn impersonate the mobile 20 to the network 10. This way the attacker can select and know the A-key as it relays messages between the mobile 20 and the network 10 to satisfy the authorization requirements. The DH key exchange is also susceptible to off-line dictionary attacks. Another well-known protocol for protecting the over-the-air transfer of information, such as the A-key, is the Diffie-Hellman Encrypted Key Exchange (DH-EKE). DH-EKE is a password based protocol for exchanging information, and assumes that both the mobile user and the network service provider have established a password prior to the over-the-air transfer. Unlike the DH key exchange system discussed with respect to Fig. 1, the DH-EKE protects against man-in-the-middle attacks and off-line dictionary attacks. The DH-EKE will be described with respect to Fig. 2, which illustrates the communication between the mobile 20 and the network 10 according to the DH-EKE protocol. As shown, the mobile 20 sends a 512-bit prime number p and the generator g to the network 10 along with (g^R M mod p) encrypted according to an encryption/decryption algorithm ENC using the password P, known to the mobile user and the network 10, as the encryption key. This calculation is represented as ENC P (g^R M mod p). The network 10 decrypts (g^R M mod p) using the password P, and calculates (g^R M mod p)^ R N , which equals (g^R M R N mod p). The network 10 selects (g^R M R N mod p), a hash of this value, or some portion thereof as a session key SK. The network 10 then sends (g^R N mod p) encrypted according to ENC using the password P and a random number R N ' encrypted according to ENC using the session key SK to the mobile 20. The mobile 20 decrypts (g^R N mod p) using the password P, and calculates (g^R N mod p)^R M , which equals (g^R M R N mod p). Then, the mobile 20 selects (g^R M R N mod p), the hash thereof, or a portion thereof as did the network 10 as the session key SK. Using the session key SK, the mobile 20 then decrypts R N '. Next, the mobile 20 generates a random number R M ', encrypts the random numbers R M ' and R N ' according to ENC using the session key SK, and sends the encrypted random numbers R N ' and R M ' to the network 10. The network 10 decrypts the random numbers R N ' and R M ' using the session key SK, and determines whether the decrypted version of R N ' equals the version of R N ' originally sent to the mobile 20. The session key SK is verified by the network 10 when the decrypted version of R N ' equals the version of R N ' originally sent to the mobile 20. The network 10 then sends the random number R M ' encrypted according to ENC using the session key SK to the mobile 20. The mobile 20 decrypts the random number R M ' using the session key SK, and determines whether the calculated version of R M ' equals the version of R M ' originally sent to the network 10. The session key SK is verified by the mobile 20 when the decrypted version of R M ' equals the version of R M ' originally sent to the network 10. Once the network 10 and the mobile 20 have verified the session key SK, the session key SK is used as the A-key, and communication between the mobile 20 and the network 10 is reconfigured using the A-key. While the DH-EKE protocol eliminates man-in-the-middle and off-line dictionary attacks, information may still leak, and an attacker may recover the password P. Jablon D P: "Strong Password-Only Authenticated Key Exchange" Computer Communications Review, Association For Computing Machinery. New York, US, vol. 26, no. 5, 1 October 1996 (1996-10-01), pages 5-26, XP000641968 ISSN: 0146-4833 is directed to key exchange and in particular to two methods of strong password-only authentication which are both forms of authenticated key exchange. The first method is a simple password exponential key exchange (SPEKE) which has two stages. The first stage uses a Diffie-Hellman (DH) exchange to establish a shared key K, but instead of a commonly used fixed primitive face g, a function f converts a password S into a base for exponentiation. The remainder of the first stage is Diffie-Hellman exchange. The second stage is a verification stage to confirm knowledge of K before proceeding to use it as a session key. The Diffie-Hellman Encrypted Key Exchange (DH-EKE) is another method of authentication having two stages. The first stage uses a DH exchange to establish a shared key K, where one or both parties encrypts the exponential using a password S. With knowledge of S, they can each decrypt the other's message in a second stage using E S -1 and compute the same key K. Summary of the Invention Methods according to the invention are as set out in the independent claims. Preferred forms are set out in the dependent claims. In the password protocol, the communicating parties exchange calculation results, which each include an exponential, to generate a key. In generating the calculation results, each party adds the password to their respective exponential. If the authorizing information previously sent by one party is acceptable to the other party, then this other party uses the key established according to the password protocol. The authorizing information is sent over a secure communication channel. By adding the password to the respective exponentials, less information on the password leaks and the computation becomes more efficient. The secure communication channel is also used in other embodiments to verify a hash on at least one calculation result sent between the parties. Unlike the password protocol, however, the calculation results do not include the password. If the hash is verified, then a key is established using the calculation results sent between the parties. This verification process provides a measure of security prior to establishing the key. The present invention has various applications including the wireless industry wherein the parties are a mobile user and a network. 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 shows the communication between a network and a mobile according to the Diffie-Hellman key agreement; Fig. 2 shows the communication between a network and a mobile according to the Diffie-Hellman Encrypted Key Exchange protocol; Fig. 3 shows the communication between a network and a mobile user via a telephone/landline and a mobile according to an embodiment of the present invention; Fig. 4 shows the communication between a network and a mobile user via a telephone/landline and a mobile according to a second method; and Fig. 5 shows the communication between a network and a mobile user via a telephone/landline and a mobile according to a third method. Detailed Description Of The Preferred Embodiments The system and method according to the present invention for establishing a key using over-the-air communication will be described as applied to a wireless system. Namely, establishing a key between a mobile 20 and a network 10 using both a telephone/land line 30 and, a password protocol will be described. Fig. 3 illustrates the communication between (1) the network provider and the network 10, collectively referred to as the network 10, and (2) a mobile user via a telephone/land line 30 and the mobile 20 according to an embodiment of the present invention. As shown, via the telephone/land line 30 a mobile user provides the network 10 with authorizing information (e.g., credit card information for billing purposes). If the network 10 accepts the authorizing information, the network 10 provides the mobile user with a four (4) digit password P via the telephone/land line 30. It could be, however, that the password P may be more or less than four digits. The mobile user then enters this short password P into the mobile 20 as part of an activation program. Using a random number generator, the mobile 20 generates a random number R M , and using a pre-stored 512-bit prime number p and the generator g of the group generated by the prime number p, calculates ((g^R M + P) mod p). The mobile 20 sends the prime number p and the generator g to the network 10 along with ((g^R M + P) mod p). Because ((g^R M + P) mod p) equals (g^R M mod p) + (P mod p) and the network 10 knows the password P, the network 10 calculates (P mod p) and extracts (g^R M mod P) from ((g^R M + P) mod p). After generating a random number R N , the network 10 calculates (g^R M mod p)^R N , which equals (g^R M R N mod p). The network 10 selects (g^R M R N mod p), the hash thereof, or a portion thereof as a session key SK. For example, if incorporated in the IS41 protocol, the 64 least significant bits of (g^R M R N mod p) would be selected as a session key SK. The network 10 then calculates and sends ((g^R N + P) mod p) to the mobile 20. The mobile 20, after extracting (g^R N mod p), calculates (g^R N mod p)^R M , which equals (g^R M R N mod p). The mobile 20 selects (g^R M R N mod p), the hash thereof, or a portion thereof in the same manner as the network 10 as a session key SK. For example, if incorporated in the IS41 protocol, the 64 least significant bits of (g^R M R N mod p) would be selected as a session key SK. Once the network 10 and the mobile 20 have the session key SK, the session key SK is used as the A-key, and communication between the mobile 20 and the network 10 is reconfigured using the A-key. The over-the-air exchange according to the present invention discussed above uses a password protocol (i.e., the transfers of ((g^R M + P) mod p) and ((g^R N + P) mod p) in Fig. 3) which does not leak information to the degree that the DH-EKE protocol leaks information. Furthermore, this password protocol is secure because removing the effect of the password does not reveal anything. R M and RN are uniform random numbers. Raising them to g and then reducing by mod p also results in uniform and random numbers because of the permutation induced by exponentiation mod p. So, adding a P mod p to that number does not change the uniformity and randomness of the result. All numbers are equally likely, and removing the effects of other passwords also creates equally likely numbers, so there is no leaking of information. One skilled in the art will also appreciate that the password protocol discussed above is not limited in application to the over-the-air exchange of information. For example, this password protocol could be applied to entity authentication and session key agreement. Fig. 4 illustrates the communication between the network 10 and a mobile user via the telephone/land line 30 and the mobile 20 according to a second method. As shown, via the telephone/land line 30 a mobile user provides the network 10 with authorizing information. If the network 10 accepts the authorizing information, then when the mobile 20 issues an initialization request as part of the mobile's initialization procedure, the initialization process will continue. For example, the mobile 20 generates a random numbers R M , calculates (g^R M mod p), and sends an initialization request along with (g^R M mod p) to the network 10. The network 10 generates a random number R N and sends (g^R N mod p) to the mobile 20. Both the mobile 20 and the network 10 performs h((g^R N mod p), (g^R M mod p)), which is a collective hash on (g^R N mod p) and (g^R M mod P) using the well-known Secure Hashing Algorithm (SHA). It should be noted, however, that any hashing algorithm can be used. The mobile 20 displays the results of the hash, and the mobile user, via the telephone/land line 30, gives the digits of the hash to the network 10. If the network 10 finds a match between the digits provided by the mobile user and the hash performed by the network 10, then communication is verified and the A-key is established as (g^R M R N mod p), the hash thereof, or a portion thereof. Namely, the mobile 20 will have established the A-key as such, but the network 10 will only associate this A-key with the mobile 20 if the hash is verified. As an alternative, or third method, along with the authorizing information, the mobile user 20 supplies sufficient information (e.g., the mobile's identification number, etc.) to the network 10 such that the network 10 can contact the mobile 20 and send (g^R N mod p) as an initial communication. This third method is subject to a birthday attack; namely, half as many attempts by a man-in-the-middle need to be made to attack this protocol than one would initially assume. However, according to an alternative of the third method, if the hash is changed to h((g^R M mod p), (g^R N mod p), (g^R M R N mod p)), then the attack is significantly slowed because the attacker must do exponentiation along with the hashes. As another alternative to the third embodiment, the hash performed to verify communication between the mobile 20 and the network 10 includes the identification number of the mobile 20. According to a further modification of the third method (i.e., a fourth method), the mobile 20 does not send (g^R M mod p) to the network 10, as shown in Fig. 4, until after receiving (g^R N mod p) from the network 10. In the third embodiment, the man-in-the-middle attacker was able to see both (g^R M mod p) and (g^R N mod p), and thus exploit the birthday attack. According to this fourth embodiment, the attacker has to commit to a (g^R N mod p) before the mobile 20 responds with a (g^R M mod p). This reduces, by one, the attacker's degrees of freedom. Fig. 5 illustrates the communication between the network 10 and a mobile user via the telephone/land line 30 and the mobile 20 according to a fifth method. As shown, via the telephone/land line 30 a mobile user provides the network 10 with authorizing information. As discussed above, along with the authorizing information, the mobile 20 can supply the network 10 with sufficient information (e.g., the mobile identifier, etc.) for the network 10 to make initial contact with the mobile 20. If the network 10 accepts the authorizing information, then the initialization process will continue. The initialization process continues with one of the mobile 20 and the network 10 sending an initialization request to the other party. For example, if the mobile 20 sends the initialization request, then the network 10 generates a random number R N , calculates (g^R N mod p) and the hash of (g^R N mod p), and sends h(g^R N mod p) to the mobile 20. The mobile 20 generates a random number R M , calculates (g^R M mod p), and sends (g^R M mod p) to the network 10. The network 10 in return sends (g^R N mod p) to the mobile 20. Next, the mobile 20 calculates the hash of the received (g^R N mod p), and confirms whether this calculated version of h(g^R N mod p) equals the version initially received from the network 10. If confirmed, the initialization process continues. Namely, both the mobile 20 and the network 10 perform h((g^R M mod p), h(g^R N mod p)). The mobile 20 displays the results of the hash, and the mobile user, via the telephone/land line 30, gives the digits of the hash to the network 10. If the network 10 finds a match with the hash performed by the network 10, then communication is verified and the A-key is established as (g^R M R N mod p), the hash thereof, or a portion thereof. Namely, the mobile 20 will have established the A-key as such, but the network 10 will only associate this A-key with the mobile 20 if the hash is verified. As discussed above, instead of the mobile 20 sending the initialization request, the network 10 sends the initialization request. If the network 10 sends the initialization request, then the mobile 20 generates a random number R M , calculates (g^R M mod p), calculates the hash of (g^R M mod p), and sends h(g^R M mod p) to the network 10. The network 10 in return generates a random number R N , calculates (g^R N mod p) and sends (g^R N mod p) to the mobile 20. The mobile 20 sends (g^R M mod p) to the network 10, and the network 10 calculates the hash of (g^R M mod p). The network 10 then confirms whether the calculated version of h(g^R M mod p) equals the version initially received from the mobile 20. If equal, the initialization process continues. Namely, both the mobile 20 and the network 10 perform h((g^R N mod p), h(g^R M mod p)). The mobile 20 displays the results of the hash, and the mobile user, via the telephone/land line 30, gives the digits of the hash to the network 10. If the network 10 finds a match with the hash performed by the network 10, then communication is verified and the A-key is established as (g^R M R N mod p), the hash thereof, or a portion thereof. Namely, the mobile 20 will have established the A-key as such, but the network 10 will only associate this A-key with the mobile 20 if the hash is verified. As a further alternative, the final hash performed to verify communication between the mobile 20 and the network 10 includes the identification number of the mobile 20. A man-in-the-middle attacker cannot use a birthday type attack because when acting as the network 10 he has to commit to the exponential he is using (via the hash) before he sees the mobile users exponential. Similarly, the attacker, when acting as the mobile 20, has to commit to the exponential before the value of the network's exponential, associated with the hash, is revealed. In some of the previous methods, the prime number p and the generator g were assumed to be fixed and pre-stored in the mobile 20. However, if that is not the case, then the attacker can replace g and p with g' and p', which will allow the attacker to calculate the discrete logarithm efficiently. If g and p are also sent over the air then they should also be used as part of the hash calculation, h(g,p, (g^R M mod p), (g^R N mod p)) in order to stop the substitution of g and p by the attacker. Furthermore, although each method was described using a telephone/land line 30, other forms of secure communication could replace the telephone/land line 30. For instance, a previously activated mobile could replace the telephone/land line. Alternatively, but less secure, the telephone/land line communications could be performed over a voice channel between the mobile 20 and the network 10, and the remaining communication would occur over a control channel between the mobile 20 and the network 10. 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 scope of the invention, and all such modifications are intended to be included within the scope of the following claims.

Claims: A method of establishing a key at a first party using a password, comprising: (a) generating, at said first party, a first random number R M ; (b) producing a first calculation result by calculating (((g^R M ) + P) mod p), where P is a password, p is a prime number, and g is a generator of a group generated by said prime number p; (c) sending said prime number p, said generator g, and said first calculation result to a second party; (d) receiving a second calculation result equal to (((g^R N ) + P) mod p) from said second party, where R N is a second random number; and (e) establishing a key based on said second calculation result and said first random number. The method of claim 1, wherein said step (e) comprises: (e1) calculating (P mod p); (e2) subtracting (P mod p) from said second calculation result of (((g^R N ) + P) mod p) to obtain ((g^R N ) mod p); and (e3) establishing said key based on ((g^R N ) mod p) and said first random number. The method of claim 1, wherein said first party is a mobile in a wireless system and said second party is a network. The method of claim 1, prior to said step (b), further comprising: (f) sending authorizing information over a secure communication channel to said second party; and (g) receiving said password from said second party over said secure communication channel if said second party accepts said authorizing information. The method of claim 4, wherein said first party is a mobile user in a wireless system and said second party is a network; and said secure communication channel is a land line. A method of establishing a key at a first party using a password, comprising: (a) receiving, at a first party, a prime number p, a generator g of a group generated by said prime number p, and a first calculation result from a second party, said first calculation result being a result of calculating (((g^R M ) + P) mod p), where P is a password and R M is a first random number; (b) generating a second random number R N ; (c) producing a second calculation result by calculating (((g^R N ) +P) mod p); (d) sending said second calculation result to said second party; and (e) establishing a key based on said first calculation result and said second random number. The method of claim 6, wherein said step (e) comprises: (e1) calculating (P mod p); (e2) subtracting (P mod p) from said first calculation result of (((g^R M ) + P) mod p) to obtain ((g^R M ) mod p) and (e3) establishing said key based on ((g^R M ) mod p) and said second random number. The method of claim 6, wherein said first party is a network in a wireless system and said second party is a mobile. The method of claim 6, prior to said step (a), further comprising: (f) receiving authorizing information over a secure communication channel from said second party; and (g) sending said password to said second party over said secure communication channel if said authorizing information is acceptable. The method of claim 9, wherein said first party is a network in a wireless system and said second party is a mobile user; and said secure communication channel is a land line.

Inventors: BERENZWEIG ADAM L, PATEL SARVAR, BERENZWEIG, ADAM L., PATEL, SARVAR
Applicants: LUCENT TECHNOLOGIES INC, LUCENT TECHNOLOGIES INC.
Application year: 1999
Main classification: H04L9
IPC codes: H04L29, H04L9, H04W12