Key agreement and transport protocol

0001The present invention relates to key agreement protocols for transfer and authentication of encryption keys.

0002To retain privacy during the exchange of information it is well known to encrypt data using a key. The key must be chosen so that the correspondents are able to encrypt and decrypt messages but such that an interceptor cannot determine the contents of the message.

0003In a secret key cryptographic protocol, the correspondents share a common key that is secret to them. This requires the key to be agreed upon between the correspondents and for provision to be made to maintain the secrecy of the key and provide for change of the key should the underlying security be compromised.

0004Public key cryptographic protocols were first proposed in 1976 by Diffie-Hellman and utilized a public key made available to all potential correspondents and a private key known only to the intended recipient. The public and private keys are related such that a message encrypted with the public key of a recipient can be readily decrypted with the private key but the private key cannot be derived from the knowledge of the plaintext, ciphertext and public key.

0005Key establishment is the process by which two (or more) parties establish a shared secret key, called the session key. The session key is subsequently used to achieve some cryptographic goal, such as privacy. There are two kinds of key agreement protocol; key transport protocols in which a key is created by one party and securely transmitted to the second party; and key agreement protocols, in which both parties contribute information which jointly establish the shared secret key. The number of message exchanges required between the parties is called the number of passes. A key establishment protocol is said to provide implicit key authentication (or simply key authentication) if one party is assured that no other party aside from a specially identified second party may learn the value of the session key. The property of implicit key authentication does not necessarily mean that the second party actually possesses the session key. A key establishment protocol is said to provide key confirmation if one party is assured that a specially identified second party actually has possession of a particular session key. If the authentication is provided to both parties involved in the protocol, then the key authentication is said to be mutual if provided to only one party, the authentication is said to be unilateral.

0006There are various prior proposals which claim to provide implicit key authentication.

0007Examples include the Nyberg-Rueppel one-pass protocol and the Matsumoto-Takashima-Imai (MTI) and the Goss and Yacobi two-pass protocols for key agreement.

0008The prior proposals ensure that transmissions between correspondents to establish a common key are secure and that an interloper cannot retrieve the session key and decrypt the ciphertext. In this way security for sensitive transactions such as transfer of funds is provided.

0009For example, the MTI/A0 key agreement protocol establishes a shared secret K, known to the two correspondents, in the following manner: <ol id="ol0001" compact="compact"><li>1. During initial, one-time setup, key generation and publication is undertaken by selecting and publishing an appropriate system prime p and generator α ∈ <maths id="math0001"><math display="inline"><msubsup><mi>Z</mi><mi>p</mi><mo>*</mo></msubsup></math><img file="EP1642437B1_D0001.tif" /></maths> in a manner guaranteeing authenticity. Correspondent A selects as a long-term private key a random integer "a",1≤a≤p-2, and computes a long-term public key Z_A = α^a mod p. B generates analogous keys b, Z_B. A and B have access to authenticated copies of each other's long-term public key.</li><li>2. The protocol requires the exchange of the following messages. <maths id="math0002" num="(1)"><math display="block"><mi mathvariant="normal">A</mi><mo mathvariant="normal">→</mo><mi mathvariant="normal">B</mi><mo mathvariant="normal">:</mo><mspace width="1em" /><msup><mi mathvariant="normal">α</mi><mi mathvariant="normal">x</mi></msup><mspace width="1em" /><mi>mod p</mi></math><img file="EP1642437B1_D0002.tif" /></maths><maths id="math0003" num="(2)"><math display="block"><mi mathvariant="normal">A</mi><mo mathvariant="normal">←</mo><mi mathvariant="normal">B</mi><mo mathvariant="normal">:</mo><mspace width="1em" /><msup><mi mathvariant="normal">α</mi><mi mathvariant="normal">y</mi></msup><mspace width="1em" /><mi>mod p</mi></math><img file="EP1642437B1_D0003.tif" /></maths> The values of x and y remain secure during such transmissions as it is impractical to determine the exponent even when the value of α and the exponentiation is known provided of course that p is chosen sufficiently large.</li><li>3. To implement the protocol the following steps are performed each time a shared key is required. <ol id="ol0002" compact="compact"><li>(a) A chooses a random integer x,1≤x≤p-2, and sends B message (1) i.e. α^x mod p.</li><li>(b) B chooses a random integer y,1≤y≤p-2, and sends A message (2) i.e. α^y mod p.</li><li>(c) A computes the key K = (α^y)^aZ_B^x mod p.</li><li>(d) B computes the key K = (α^x)^bZ_A^y mod p.</li><li>(e) Both share the key K - α^bx+ay.</li></ol></li></ol>

0010In order to compute the key K, A must use his secret key a and the random integer x, both of which are known only to him. Similarly B must use her secret key b and random integer y to compute the session key K. Provided the secret keys a,b remain uncompromised, an interloper cannot generate a session key identical to the other correspondent. Accordingly, any ciphertext will not be decipherable by both correspondents.

0011As such this and related protocols have been considered satisfactory for key establishment and resistant to conventional eavesdropping or man-in-the-middle attacks.

0012In some circumstances it may be advantageous for an adversary to mislead one correspondent as to the true identity of the other correspondent.

0013In such an attack an active adversary or interloper E modifies messages exchanged between A and B, with the result that B believes that he shares a key K with E while A believes that she shares the same key K with B. Even though E does not learn the value of K the misinformation as to the identity of the correspondents may be useful.

0014A practical scenario where such an attack may be launched successfully is the following. Suppose that B is a bank branch and A is an account holder. Certificates are issued by the bank headquarters and within the certificate is the account information of the holder. Suppose that the protocol for electronic deposit of funds is to exchange a key with a bank branch via a mutually authenticated key agreement. Once B has authenticated the transmitting entity, encrypted funds are deposited to the account number in the certificate. If no further authentication is done in the encrypted deposit message (which might be the case to save bandwidth) then the deposit will be made to E's account.

0015Another example is <patcit id="pcit0001" dnum="EP739106A1"><text>EP 739 106 A1</text></patcit> that discloses a key establishment protocol including the generation of a value of cryptographic function, typically a hash, a session key and public information. This value is transferred between correspondents together with the information necessary to generate the session key. Provided the session key has not been compromised, the value of the cryptographic function will be the same at each of the correspondents.

0016It is therefore an object of the present invention to provide a protocol in which the above disadvantages are obviated or mitigated.

0017In one aspect there is provided in the following a method of symmetric key agreement between a first correspondent and a second correspondent in a data communication system, each of said first correspondent and said second correspondent having a master key K, said method comprising the steps of: <ul id="ul0001" list-style="none" compact="compact"><li>said first correspondent generating a first value X and providing said first value X to said second correspondent;</li><li>said second correspondent generating a second value Y and computing a shared key k by operating a keyed cryptographic function on a combination of said first value X and said second value Y, said second correspondent using said master key K as an input to said keyed cryptographic function;</li><li>said second correspondent providing said second value Y to said first correspondent; and</li><li>said first correspondent computing said shared key <i>k</i> by operating said keyed cryptographic function on said combination of said first value X and said second value Y, said first correspondent using said master key K as an input to said keyed cryptographic function.</li></ul>

0018There is also provided a system comprising a first correspondent and a second correspondent, both configured to perform the method described above.

0019In another aspect there is provided a method of symmetric key agreement between a first correspondent and a second correspondent in a data communication system, each of said first correspondent and said second correspondent having a master key K, said method comprising the steps of: <ul id="ul0002" list-style="none" compact="compact"><li>said first correspondent generating a first value X and providing said first value X to said second correspondent;</li><li>said first correspondent obtaining a second value Y that was generated by said second correspondent; and</li><li>said first correspondent computing a shared key <i>k</i> by operating a keyed cryptographic function on a combination of said first value X and said second value Y, said first correspondent using said master key K as an input to said keyed cryptographic function; said shared key <i>k</i> also computable by said second correspondent by said second correspondent operating said keyed cryptographic function on said combination of said first value X and said second value Y using said master key K as an input to said keyed cryptographic function.</li></ul>

0020There is also provided a correspondent having a cryptographic unit configured to perform the method of the foregoing paragraph.

0021of said cryptographic function F[ð,K];

0022As the session key K can only be generated using information that is private to either A or B, the binding of K with ð with the cryptographic function h prevents E from extracting K or interjecting a new value function that will correspond to that obtained by A.

0023Embodiments of the invention will now be described by way of example only with reference to the accompanying drawings in which. <ul id="ul0003" list-style="none" compact="compact"><li><figref idref="f0001">Figure 1</figref> is a schematic representation of a data communication system.</li><li><figref idref="f0002 f0003 f0004 f0005 f0006 f0007 f0008">Figures 2 through 8</figref> are schematic representations of implementations of different protocols.</li></ul>

0024Referring therefore to <figref idref="f0001">Figure 1</figref>, a pair of correspondents, 10,12, denoted as correspondent A and correspondent B, exchange information over a communication channel 14. A cryptographic unit 16,18 is interposed between each of the correspondents 10,12 and the channel 14. A key 20 is associated with each of the cryptographic units 16,18 to convert plaintext carried between each unit 16,18 and its respective correspondent 10,12 into ciphertext carried on the channel 14.

0025In operation, a message generated by correspondent A, 10, is encrypted by the unit 16 with the key 20 and transmitted as ciphertext over channel 14 to the unit 18.

0026The key 20 operates upon the ciphertext in the unit 18 to generate a plaintext message for the correspondent B, 12. Provided the keys 20 correspond, the message received by the correspondent 12 will be that sent by the correspondent 10.

0027In order for the system shown in <figref idref="f0001">Figure 1</figref> to operate it is necessary for the keys 20 to be identical and therefore a key agreement protocol is established that allows the transfer of information in a public manner to establish the identical keys. Implementations are shown schematically in <figref idref="f0002 f0003 f0004 f0005 f0006 f0007">figures 2 through 7</figref>.

0028Referring to <figref idref="f0002">figure 2</figref>, a mutual public key authenticated key agreement protocol is complemented between a correspondent A shown on the left hand side of the figure and a correspondent B shown on the right hand side. Correspondent A has a public-private key pair P_A,S_A respectively and similarly correspondent B has a public private Key pair P_B,S_B.

0029As a first step, correspondent A generates a session private key as a random number RND_A and computes a corresponding public session key G_A =F_A (RND_A). The function F_A is a cryptographic one way function, typically an exponention by the group generator, such as a point multiplication in an elliptic curve cryptosystem.

0030The public session key G_A is forwarded to correspondent B who generates corresponding parameters of a session private key RND_B and a public session key G_B.

0031The correspondent B computes a session key K as a function of A's public information G_A,P_A AND B's private information RND_B,S_B. A corresponding key K' can be computed by A using the private information of A and the public information of B namely f(RND_A,G_B,S_A,P_B).

0032After correspondent B has generated the key K, he compiles a string (G_A ∥G_B ∥ IdA) where Id_A is a string that identifies A. The concatenated string is hashed with a cryptographic function h_k which is a keyed hash function that uses the key K to yield a string <i>hash_B,</i>

0033The string <i>hash_B is</i> forwarded to correspondent A together with Id_A and G_B.

0034Upon receipt of the message from B, correspondent A computes the key K' as described above. Correspondent A also computes a hash, <i>hashverify_B</i> from the string (G_B<i>∥</i>G_A<i>∥</i>Id_A) using the hash function keyed by the key K'. Correspondent A checks that the hashes verify to confirm the identity of the keys K,K'.

0035Correspondent A then computes a hash h_K, using the key K' on the string (G_A<i>∥</i>G_B<i>∥</i>Id_B) and forwards that together with Id_B of correspondent B. Correspondent B similarly computes a <i>hashverify_A</i> using the keyed hash function h_K using the key K on the same string and verifies that <i>hash_A</i> =<i>hashverify_A.</i>

0036A similar protocol is shown in <figref idref="f0003">figure 3</figref> to implement a mutual entity authentication protocol. In this protocol the correspondents share a key K obtained over a secure channel. The correspondents A.B, each generate a random integer which is used as the session public key of A and B respectively. Thereafter the exchange of information and verification proceeds as above with respect to <figref idref="f0002">figure 2</figref> with the shared secret key being utilised in the keyed hash functions.

0037A full mutual public key authenticated key exchange protocol is shown in <figref idref="f0004">figure 4</figref>. An initial exchange of the public keys P_A,P_B is performed over an authenticated channel followed by the exchange of information as shown in the protocol of <figref idref="f0004">figure 4</figref>. In this case the correspondent A sends G_A computed as described above with respect to <figref idref="f0002">figure 2</figref>, together with a string x₂ that A wants confirmation of receipt by B. Correspondent B computes the key K as in <figref idref="f0002">figure 2</figref> and also generates a pair of strings y₁,y₂ which B wants to have authenticated by A and receipt confirmed by A respectively. The strings are sent to A with the hash <i>hash_B</i> and identity Id_A. The hash <i>hash_B</i> is performed on a string including the message x₂ and the string y₁ to be authenticated.

0038Correspondent A computes the key K and verifies the hash as before. This also confirms receipt of x₂ by B.

0039Correspondent A in turn generates strings z_1, z₂ where z₁ is a string that A wants authenticated by B and z₂ is a string that may be used in a subsequent execution of the protocol described below. The strings, z₁ and y₂ together with the identifying information of B, Id_B, are included in the string that is hashed with the key K to provide the string <i>hash_A.</i> This is sent together with the identity of B and the strings z₁,z₂ to the correspondent B who can verify the hashes as before, thereby confirming receipt of y₂ and authentication of z₁ by the correspondent A.

0040Thus information is exchanged in an authenticated manner and a common key obtained that allows subsequent exchange of correspondence on a secure channel.

0041With the protocol described in <figref idref="f0004">figure 4</figref> it is possible to implement a mutual public key authenticated key agreement protocol by letting the strings x₂,y₁,y₂,z₁,z₂ all be empty strings. Alternatively, a mutual public key authenticated key agreement protocol with implicit key agreement can be implemented by using x₂ as a string that is assumed to represent E_K(k), the result of applying an encryption function E with key K on the value of k. Correspondent B can compute the value of K and hence retrieve the notional value of k from the string. He can use this as his shared session key with the correspondent A. The value of y₁ may be used to represent E_K(k₂₁) and z₁ as E_K(k₁₂) where k₂₁ and k₁₂ are different keys for communication or other secret information to be shared between the correspondents. In this case y₂ and z₂ are empty strings. In this way there is a key agreement on a shared key K_AB together with authenticated key transport of the keys k₂ and k₁₂ between the correspondents and authenticated key agreement on k. Moreover, if additional information is provided in the strings x₂ and y₂ then confirmation of proper receipt is also obtained.

0042The protocol of <figref idref="f0004">figure 4</figref> may also be used to increase efficiency in successive sessions by using the string z₂ to pass the information exchanged in the first pass of the next session. Thus as shown in <figref idref="f0005">figure 5</figref>, the string G_A,x₂ is sent as z₂ in the previous session. The protocol then proceeds from correspondent B as before. As seen in <figref idref="f0005">Figure 5</figref>, the third transmission may be optionally omitted. Correspondent B may also take advantage of this facility by including the information G_B,y₁ for the next session in the exchange as y₂.

0043The mutual public key authenticated key agreement protocol may also be adapted for entity authentication implementations as shown in <figref idref="f0006">figure 6</figref>. In this case, as in <figref idref="f0003">figure 3</figref> above, the key generation is omitted as the correspondents have a shared key obtained over a secure channel.

0044Similarly, the protocol of <figref idref="f0006">figure 6</figref> may be modified as illustrated in <figref idref="f0007">figure 7</figref> to take advantage of the exchange of information in a previous session, similar to that of <figref idref="f0005">figure 5</figref>.

0045It will be seen therefore that a number of versatile and flexible protocols can be developed from the general protocol to meet particular needs. These protocols may implement elliptic curve cryptography or operate in Z_p as preferred.

0046It can be readily seen that the message flows of the public-key authenticated key agreement protocol depicted in <figref idref="f0003">Figure 3</figref> and those of the entity authentication protocol depicted in <figref idref="f0002">Figure 2</figref> have identical structure. Moreover, the computation of the hash values hashA and hashB by correspondent A and B respectively, as well as the verification thereof, take strings with an identical structure as input. In fact, both protocols only differ in the way the key K used in the protocol is derived. Thus, a combined implementation of both protocols may take advantage of a common handling of telecommunication flows, including messaging, error handling and the-like, and may take advantage of a common handling of the key confirmation steps (i.e., generation and processing of hash values).

0047A similar reasoning holds for the message flows and processing steps of the public-key authenticated key agreement protocol depicted in <figref idref="f0004">Figure 4</figref> and the version thereof depicted in <figref idref="f0005">Figure 5</figref>. It will be appreciated that the latter consists of executing only part of the former. A similar remark holds for the entity authentication protocol depicted in <figref idref="f0006">Figure 6</figref> and the one depicted in <figref idref="f0007">Figure 7</figref>. It shouls also be noted that the augmented public-key authenticated key agreement protocol depicted in <figref idref="f0004">Figure 4</figref> can be used to implement the one depicted in <figref idref="f0003">Figure 3</figref> and that, similarly, the augmented entity authentication protocol depicted in <figref idref="f0006">Figure 6</figref> can be used to implement the one depicted in <figref idref="f0002">Figure 2</figref>. Thus, all the protocols described can be implemented with largely common routines to handle telecommunication and message flows and with a large degree of commonality of the implementation of the protocol steps of each and every one of the protocols.

0048It will be appreciated that although the invention has been described with reference public key based agreement protocols and entity authentication protocols, it may equally be utilized on symmetric key agreement protocols. In such an embodiment, the computation of the shared key K may be performed using a master key K_m as one input to a keyed hash function. A concatenation of the ephemeral keys G_A, G_B, is used as the other input and the resultant output is used as the shared key K.

0049Such an arrangement is shown in <figref idref="f0008">figure 8</figref>.