CA2525894C

CA2525894C - Key agreement and transport protocol

Info

Publication number: CA2525894C
Application number: CA2525894A
Authority: CA
Inventors: Marinus Struik
Original assignee: Certicom Corp
Current assignee: BlackBerry Ltd
Priority date: 2003-05-16
Filing date: 2004-05-17
Publication date: 2013-04-16
Anticipated expiration: 2024-05-17
Also published as: JP2006529064A; CA2525894A1; EP1642437A2; JP2011182454A; WO2004102918A3; EP1642437B1; JP4781269B2; US7334127B2; WO2004102918A2; JP5171991B2; US20040081321A1; ATE523017T1

Abstract

A key establishment protocol includes the generation of a value of cryptographic function, typically a hash, of 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. The value of the cryptographic function cannot be compromised or modified without access to the session key.

Description

a The present invention relates to key agreement protocols for transfer and s authentication of encryption keys.
4 To 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 6 to encrypt and decrypt messages but such that an interceptor caimot determine the ~ contents of the message.
s In a secret key cryptographic protocol, the correspondents share a common 9 key that is secret to them. This requires the key to be agreed upon between the i o correspondents and for provision to be made to maintain the secrecy of the key and 11 provide for change of the key should the underlying security be compromised.
12 Public key cryptographic protocols were first proposed in 1976 by Diffie-ls HeIIman and utilized a public key made available to aII potential correspondents and a 14 private key known only to the intended recipient. The public and private keys are is related such that a message encrypted with the public key of a recipient can be readily s s decrypted with the private key but the private key cannot be derived from the m lcnowledge of the plaintext, ciphertext and public key.
is I~ey establishment is the process by wluch two (or more) parties establish a i9 shared secret key, called the session key. The session key is subsequently used to a o achieve some cryptographic goal, such as privacy. There are two kinds of key a Z agreement protocol; Icey transport protocols in which a key is created by one party and a a securely transmitted to the second party; and key agreement protocols, in which both 23 parties contribute information which jointly establish the shared secret key. The a 4 number of message exchanges required between the parties is called the number of z s passes. A lcey establishment protocol is said to provide implicit key authentication (or a 6 simply key authentication) if one party is assured that no other party aside from a a ~ specially identified second party may learn the value of the session key.
The property a 8 of implicit key authentication does not necessarily mean that the second party actually

2 9 possesses the session key. A key establishment protocol is said to provide key 1 confirmation if one party is assured that a specially identified second party actually 2 has possession of a particular session key. If the authentication is provided to both

3 parties involved in the protocol, then the key authentication is said to be mutual if

4 provided to only one party, the authentication is said to be unilateral.
s There are various prior proposals which claim to provide implicit key 6 authentication.
~ Examples include the Nyberg-Rueppel one-pass protocol and the Matsumoto-s Takashima-Imai (MTI) and the Goss and Yacobi two-pass protocols for key 9 agreement.
to The prior proposals ensure that transmissions between correspondents to i1 establish a common key are secure and that an interloper cannot retrieve the session 12 lcey and decrypt the ciphertext. In this way security for sensitive transactions such as 13 transfer of funds is provided.
14 For example, the MTI/AO key agreement protocol establishes a shared secret 15 K, lcnown to the two correspondents, in the following manner:-16 1. During initial, one-time setup, key generation and publication is Z~ undertaken by selecting and publishing an appropriate system prime p and generator is a E Zp in a manner guaranteeing authenticity. Correspondent A selects as a long-19 term private key a random integer "a",1<_a<_p-2, and computes a long-term public key a o zA = a~ mod p. B generates analogous keys b, zB. A and B have access to a z authenticated copies of each other's long-term public key.
2 a 2. The protocol requires the exchange of the following messages.
z3 A -~ B: d' mod p (1) 24 AE-B: aa'modp (2) z 5 The values of x and y remain secure during such transmissions as it is z s impractical to determine the exponent even when the value of a and the a ~ exponentiation is known provided of course that p is chosen sufficiently large. , a 8 3. To implement the protocol the following steps are performed each time a 9 a shared key is required.

1 (a) A chooses a random integer x,1<_x<_p-2, and sends B message a (1) i.e. ax mod p.
s (b) B chooses a random integer y,l<_y_<p-2, and sends A message 4 (2) i.e. aa' mod p.
s (c) A computes the key K = (a'')azB" mod p.
6 (d) B computes the key K = (d')bzAy mod p.
(e) Both share the key K - ap"+a''.
8 In order to compute the key K, A must use his secret key a and the random 9 integer x, both of which are known only to him. Similarly B must use her secret key s o b and random integer y to compute the session key K. Provided the secret keys a,b m remain uncompromised, an interloper cannot generate a session key identical to the la other correspondent. Accordingly, any ciphertext will not be decipherable by both s3 correspondents.
14 As such this and related protocols have been considered satisfactory for key 15 establishment and resistant to conventional eavesdropping or man-in-the-middle i 6 attacks.
m In some circumstances it may be advantageous for an adversary to mislead one 18 correspondent as to the true identity of the other correspondent.
19 In such an attack an active adversary or interloper E modifies messages 2 o exchanged between A and B, with the result that B believes that he shares a key K
a z with E while A believes that she shares the same key K with B. Even though E does as not learn the value of K the misinformation as to the identity of the correspondents a 3 may be useful.
24 A practical scenario where such an attack may be launched successfully is the 2 5 following. Suppose that B is a bank branch and A is an account holder.
Certificates a s are issued by the bank headquarters and within the certificate is the account 2 ~ information of the holder. Suppose that the protocol for electronic deposit of funds is a a to exchange a key with a bank branch via a mutually authenticated key agreement.
29 Once B has authenticated the transmitting entity, encrypted funds are deposited to the s account number in the certificate. If no further authentication is done in the encrypted a deposit message (which might be the case to save bandwidth) then the deposit will be 3 made to E's account.
4 It is therefore an object of the present invention to provide a protocol in which the above disadvantages are obviated or mitigated.
6 According therefore to the present invention there is provided a method of ~ authenticating a pair of correspondents A,B to permit exchange of information 8 therebetween, each of said correspondents having a respective private key a,b and a 9 public key pA,pB derived from a generator a and respective ones of said private keys so a,b, said method including the steps of 11 1) a first of said correspondents A selecting a first random integer x and Zz exponentiating a function f(a) including said generator to a power g~"~ to provide a is first exponentiated function f(a)g~"~;
14 ii) said first correspondent A forwarding to a second correspondent B a message including said first exponentiated function f(a)g(";
i6 iii) said correspondent B selecting a second random integer y and exponentiating 17 a function f (a) including said generator to a power gty~ to provide a second i a exponentiated function f (a)g~y~;
19 lv) said second correspondent B constructing a session key K from information a o made public by said first correspondent A and information that is private to said a 1 second correspondent B, said session key also being constructible by said first a a correspondent A for information made public by B and information that is private to a 3 said first correspondent A;
24 v) said second correspondent B generating a value h of a function F[~,K]
a 5 where F[c~,K] denotes a cryptographic function applied conjointly to ~ and K and 2 s where ~ is a subset of the public information provided by B thereby to bind the values 2 ~ of ~ and K;
a s vi) said second of said correspondents B forwarding a message to said first z 9 correspondent A including said second exponential function f (a)gtY~ and said value h 1 of said cryptographic function F[6,K];
a vii) said first correspondent receiving said message and computing a session key 3 K' from information made public by said second correspondent B and private to said 4 first correspondent A;
viii) said first correspondent A computing a value h' of a cryptographic function 6 h,h' F[~,K']; and ix) comparing said values obtained from said cryptographic functions F to s confirm their correspondence.
9 As the session key K can only be generated using information that is private to 1o either A or B, the binding of K with d with the cryptographic function h prevents E
ii from extracting K or interjecting a new value function that will correspond to that 12 obtained by A.

14 Embodiments of the invention will now be described by way of example only with reference to the accompanying drawings in which.
16 Figure 1 is a schematic representation of a data communication system.
1~ Figures 2 through 8 are schematic representations of implementations of 18 different protocols.
19 Referring therefore to Figure 1, a pair of correspondents, 10,12, denoted as a o correspondent A and correspondent B, exchange information over a communication a 1 channel 14. A cryptographic unit 16,18 is interposed between each of the 2 2 correspondents 10,12 and the chaimel 14. A key 20 is associated with each of the a 3 cryptographic units 16,18 to convert plaintext carried between each unit 16,18 and its a 4 respective correspondent 10,12 into ciphertext carried on the channel 14.
z 5 In operation, a message generated by correspondent A, 10, is encrypted by the z 6 unit 16 with the key 20 and transmitted as ciphertext over channel 14 to the unit 18.
a 7 The lcey 20 operates upon the ciphertext in the unit 18 to generate a plaintext a 8 message for the correspondent B, 12. Provided the keys 20 correspond, the message a 9 received by the correspondent 12 will be that sent by the correspondent 10.

5 1 In order for the system shown in Figure 1 to operate it is necessary for the 2 lceys 20 to be identical and therefore a key agreement protocol is established that 3 allows the transfer of information in a public manner to establish the identical keys.
4 Implementations are shown schematically in figures 2 through 7.
Referring to figure 2, a mutual public key authenticated key agreement

6 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 a public-private key pair PA,SA respectively and similarly correspondent B has a public 9 private Key pair PB,SB.
11 As a first step, correspondent A generates a session private key as a random i2 number RNDA and computes a corresponding public session key GA =F~ (RNDA).
13 ~ The function FA is a cryptographic one way function, typically an exponention by the 14 group generator, such as a point multiplication in an elliptic curve cryptosystem.
1s The public session key GA is forwarded to correspondent B who generates 1~ corresponding parameters of a session private key RNDB and a public session key GB.

19 The correspondent B computes a session key K as a function of A's public 2 o information GA,PA AND B's private information RNDB,SB. A corresponding key K' 21 can be computed by A using the private information of A and the public information 22 of B namely f(RNDA,GB,SA,PB).

24 After correspondent B has generated the key K, he compiles a string (GA (~ GB ~~ IdA) where IdAis a string that identifies A. The concatenated string is 2 6 hashed with a cryptographic function hk which is a keyed hash function that uses the 2 ~ key K to yield a string hashB, 2 9 The string hashB is forwarded to correspondent A together with IdA and GB.

l 2 Upon receipt of the message from B, correspondent A computes the key K' as s described above. Correspondent A also computes a hash, hashve~ifyB from the string 4 (GB/IGAI/IdA) 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'.

Correspondent A then computes a hash hK~ using the key K' on the string a (GA//GB//IdB) and forwards that together with IdB of correspondent B.
Correspondent 9 B similarly computes a hashverifyA using the keyed hash function hK using the key K
on the same string and verifies that hashA =hashverifyA.

12 A similar protocol is shown in figure 3 to implement a mutual entity 1s authentication protocol. In this protocol the correspondents share a key K
obtained 14 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 16 information and verification proceeds as above with respect to figure 2 with the 1~ shared secret key being utilised in the keyed hash functions, 19 A full mutual public key authenticated key exchange protocol is shown in 2 o figure 4. An initial exchange of the public keys PA,PB is performed over an 21 authenticated channel followed by the exchange of information as shown in the 22 protocol of figure 4. In this case the correspondent A sends GA computed as described 2 3 above with respect to figure 2, together with a string x2 that A wants confirmation of 24 receipt by B. Correspondent B computes the key K as in figure 2 and also generates a pair of strings yl,y2 which B wants to have authenticated by A and receipt confirmed 26 by A respectively. The strings are sent to A with the hash hashB and identity IdA,.The 27 hash laashB is performed on a string including the message xz and the string yt to be 2 8 authenticated.

7

8 PCT/CA2004/000727 1 Correspondent A computes the key K and verifies the hash as before. This also 2 confirms receipt of xa by B.

4 Correspondent A in turn generates strings zt,z2 where zl is a string that A
wants authenticated by B and z2 is a string that may be used in a subsequent execution s of the protocol described below. The strings, zl and y2 together with the identifying ~ information of B, IdB, are included in the string that is hashed with the key K to 8 provide the string IZashA. This is sent together with the identity of B and the strings

9 Z1,Z2 to the correspondent B who can verify the hashes as before, thereby confirming so receipt of y2 and authentication of zl by the correspondent A.

12 Thus information is exchanged in an authenticated manner and a common key 13 obtained that allows subsequent exchange of correspondence on a secure channel.

With the protocol described in figure 4 it is possible to implement a mutual 16 public key authenticated key agreement protocol by letting the strings x2,yl,y2,zl,z2 all 17 be empty strings. Alternatively, a mutual public key authenticated key agreement 18 protocol with implicit key agreement can be implemented by using x2 as a string that 19 is assumed to represent EK(k), the result of applying an encryption function E with 2 o key K on the value of k. Correspondent B can compute the value of K and hence 21 retrieve the notional value of k from the string. He can use this as his shared session 22 key with the correspondent A. The value of yl may be used to represent EK(k21) and zl 2 3 as EK(k12) where k21 and k12 are different keys for communication or other secret 24 information to be shared between the correspondents. In this case y2 and z2 are empty 2 s strings. In this way there is a key agreement on a shared key K~ together with 26 authenticated key transport of the keys k21 and klz between the correspondents and z ~ authenticated key agreement on k. Moreover, if additional information is provided in 2 s the strings x2 and ya then confirmation of proper receipt is also obtained.
29' s The protocol of figure 4 may also be used to increase efficiency in successive 2 sessions by using the string z2 to pass the information exchanged in the first pass of 3 the next session. Thus as shown in figure 5, the string GA,x2 is sent as z2 in the 4 previous session. The protocol then proceeds from correspondent B as before.
As seen in Figure 5, the third transmission may be optionally omitted. Correspondent B
may 6 also take advantage of this facility by including the information GB,yI for the next 7 session in the exchange as y2.

9 The mutual public key authenticated key agreement protocol may also be 1 o adapted for entity authentication implementations as shown in figure 6. In this case, as 11 in figure 3 above, the key generation is omitted as the correspondents have a shared 12 key obtained over a secure channel.

14 Similarly, the protocol of figure 6 may be modified as illustrated in figure 7 to take advantage of the exchange of information in a previous session, similar to that of 16 figure 5.

1 s It will be seen therefore that a number of versatile and flexible protocols can i9 be developed from the general protocol to meet particular needs. These protocols may 2 o implement elliptic curve cryptography or operate in 7.~, as preferred.

2 2 It can be readily seen that the message flows of the public-key authenticated 2 3 key agreement protocol depicted in Figure 3 and those of the entity authentication 24 protocol depicted in Figure 2 have identical structure. Moreover, the computation of the hash values hashA and hashB by correspondent A and B respectively, as well as 2 6 the verification thereof, take strings with an identical structure as input. In fact, both 2 7 protocols only differ in the way the key K used in the protocol is derived. Thus, a 2 8 combined implementation of both protocols may take advantage of a common 2 9 handling of telecommunication flows, including messaging, error handling and the-1 like, and may take advantage of a common handling of the key confirmation steps 2 (i.e., generation and processing of hash values).

4 A similar reasoning holds for the message flows and processing steps of the public-key authenticated key agreement protocol depicted in Figure 4 and the version 6 thereof depicted in Figure 5. It will be appreciated that the latter consists of executing ~ only part of the former. A similar remark holds for the entity authentication protocol 8 depicted in Figure 6 and the one depicted in Figure 7. It shouls also be noted that the 9 augmented public-key authenticated key agreement protocol depicted in Figure 4 can 1 o be used to implement the one depicted in Figure 3 and that, similarly, the augmented 11 entity authentication protocol depicted in Figure 6 can be used to implement the one 12 depicted in Figure 2. Thus, all the protocols described can be implemented with 13 largely common routines to handle telecommunication and message flows and with a 14 large degree of commonality of the implementation of the protocol steps of each and every one of the protocols.
1s It will be appreciated that although the invention has been described with 1~ reference public key based agreement protocols and entity authentication protocols, it 18 may equally be utilized on.symmetric key agreement protocols. In such an 19 embodiment, the computation of the shared key K may be performed using a master 2 0 lcey Km as one input to a keyed hash function. A concatenation of the ephemeral keys 21 GA, GB, is used as the other input and the resultant output is used as the shared key K.
22 Such an arrangement is shown in figure ~.

Claims

WE CLAIM:

1. 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:
said first correspondent generating a first value X and providing said first value X to said second correspondent;
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;
said second correspondent providing said second value Y to said first correspondent;
and said first correspondent computing said shared key k 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.

2. The method of claim 1 further comprising the steps of:
said second correspondent applying a keyed hash function to a combination of said first value X, said second value Y, and identification information of one of said first correspondent and said second correspondent to yield a first hash value, said second correspondent using said shared key k computed by said second correspondent as an input to said keyed hash function;
said second correspondent providing said first hash value to said first correspondent;
said first correspondent applying said keyed hash function to a combination of said first value X, said second value Y, and said identification information of said one of said first correspondent and said second correspondent to yield a second hash value, said first correspondent using said shared key k computed by said first correspondent as an input to said keyed hash function; and said first correspondent verifying that said first hash value equals said second hash value.

3. The method of claim 2 further comprising the steps of :
said first correspondent applying said keyed hash function to a combination of said first value X, said second value Y, and identification information of the other of said first correspondent and said second correspondent to yield a third hash value, said first correspondent using said shared key k computed by said first correspondent as an input to said keyed hash function;
said first correspondent providing said third hash value to said second correspondent;
said second correspondent applying said keyed hash function to a combination of said first value X, said second value Y, and said identification information of said other of said first correspondent and said second correspondent to yield a fourth hash value, said second correspondent using said shared key k computed by said second correspondent as an input to said keyed hash function; and said second correspondent verifying that said third hash value equals said fourth hash value.

4. The method of claim 3 wherein said first hash value and said second hash value are each of the form h k(Y¦¦X¦¦Id A), and said third hash value and said fourth hash value are each of the form h k(X¦¦Y¦¦Id B), wherein h is said keyed hash function, Id A is said identification information of said one of said first correspondent and said second correspondent, and Id B is said identification information of said the other of said first correspondent and said second correspondent.

5. The method of any one of claims 1 to 4 wherein said first value X is a random integer generated by said first correspondent and said second value Y is a random integer generated by said second correspondent.

6. The method of any one of claims 1 to 5 wherein said keyed cryptographic function is another keyed hash function.

7. The method of any one of claims 1 to 5 wherein said keyed cryptographic function is said keyed hash function.

8. The method of claim 6 or claim 7 wherein said shared key k is of the form h k(X¦¦Y).

9. 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:
said first correspondent generating a first value X and providing said first value X to said second correspondent;
said first correspondent obtaining a second value Y that was generated by said second correspondent; and said first correspondent 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 first correspondent using said master key K as an input to said keyed cryptographic function; said shared key k 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.

10. The method of claim 9 further comprising the steps of:
said first correspondent receiving a first hash value from said second correspondent, said first hash value having been computed by said second correspondent by said second correspondent applying a keyed hash function to a combination of said first value X, said second value Y and identification information of one of said first correspondent and said second correspondent using said shared key k computed by said second correspondent;
said first correspondent applying said keyed hash function to a combination of said first value X, said second value Y and said identification information of said one of said first correspondent and said second correspondent to yield a second hash value, said first correspondent using said shared key k computed by said first correspondent as an input to said keyed hash function; and said first correspondent verifying that said first hash value equals said second hash value.

11. The method of claim 10 further comprising the steps of:
said first correspondent applying said keyed hash function to a combination of said first value X, said second value Y and identification information of the other of said first correspondent and said second correspondent to yield a third hash value, said first correspondent using said shared key k computed by said first correspondent as an input to said keyed hash function; and said first correspondent providing said third hash value to said second correspondent for verification, whereby said second correspondent is able to verify said third hash value by applying said keyed hash function to a combination of said first value X, said second value Y, and said identification information of said other of said first correspondent and said second correspondent using said shared key k computed by said second correspondent to yield a fourth hash value, and then verify said third hash value equals said fourth hash value.

12. The method of claim 11 wherein said second hash value is of the form h k(Y¦¦X¦¦Id A), and said third hash value is of the form h k(X¦¦Y¦¦d B), wherein h is said keyed hash function, Id A is said identification information of said one of said first correspondent and said second correspondent, and Id B is said identification information of said the other of said first correspondent and said second correspondent.

13. The method of any one of claims 9 to 12 wherein said first value X is a random integer generated by said first correspondent.

14. The method of any one of claims 9 to 13 wherein said keyed cryptographic function is another keyed hash function.

15. The method of any one of claims 9 to 13 wherein said keyed cryptographic function is said keyed hash function.

16. The method of claim 14 or claim 15 wherein said shared key k is of the form h K(X¦¦Y).

17. The method of any one of claims 1 to 16 wherein said keyed hash function is a cryptographic hash function.

18. A system comprising a first correspondent and a second correspondent, both configured to perform the method of any one of claims 1 to 8.

19. A correspondent having a cryptographic unit configured to perform the method of any one of claims 9 to 16.

20. A computer readable medium having stored thereon computer readable instructions for performing the method of any one of claims 9 to 16.