Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
  • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
  • H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
  • H04L9/0841—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving Diffie-Hellman or related key agreement protocols
  • H04L9/0844—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving Diffie-Hellman or related key agreement protocols with user authentication or key authentication, e.g. ElGamal, MTI, MQV-Menezes-Qu-Vanstone protocol or Diffie-Hellman protocols using implicitly-certified keys
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
  • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
  • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
  • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
  • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
  • G06F7/724—Finite field arithmetic
  • G06F7/725—Finite field arithmetic over elliptic curves
• • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
  • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
  • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
  • Y04S40/00—Systems for electrical power generation, transmission, distribution or end-user application management characterised by the use of communication or information technologies, or communication or information technology specific aspects supporting them
  • Y04S40/20—Information technology specific aspects, e.g. CAD, simulation, modelling, system security

Definitions

• the present invention relates to key agreement protocols for transfer and authentication of encryption keys.
• the correspondents In 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.
• Public 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.
• Key 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.
• 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.
• Examples include the Nyberg-Rueppel one-pass protocol and the Matsumoto- Takashima-Imai (MTI) and the Goss and Yacobi two-pass protocols for key agreement.
• Matsumoto- Takashima-Imai Matsumoto- Takashima-Imai
• the 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.
• the MTI/AO key agreement protocol establishes a shared secret K, known to the two correspondents, in the following manner: -
• a ⁇ B ⁇ x mod p (1)
• a ⁇ — B ⁇ y mod p (2)
• the values of x and y remain secure during such transmission as it is impractical to determine the exponent even when the value of and the exponentiation is known provided of course that p is chosen sufficiently large. 3.
• To implement the protocol the following steps are performed each time a shared key is required.
• A chooses a random integer x, l ⁇ x ⁇ p-2, and sends B message (1) i.e. a mod p.
• B chooses a random integer y, l ⁇ y ⁇ p-2, and sends A message (2) i.e. y mod p.
• the protocol for electronic deposit of funds is to exchange a key with a bank branch via a mutually authenticated key agreement.
• 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.
• a method of authenticating a pair of correspondents A,B to permit exchange of information therebetween each of said correspondents having a respective private key a.b and a public key p A , p B derived from a generator and a respective ones of said private keys a,b
• said method including the steps of: i) a first of said correspondents A selecting a first random integer x and exponentiating a function f( ) including said generator to a power g (x) to provide a first exponentiated function f( ⁇ ) ⁇ ( ) ; ii) said first correspondent A generating a first signature s A from said random integer x and said first exponentiated function f( ⁇ ) ⁇ (x) ; iii) said first correspondent A forwarding to a second correspondent B a message including said first exponentiated function f( ⁇ ) e( ) and the signature s A ; iv) said correspondent B selecting a second random integer
• each of said correspondents verifying the integrity of messages received by them by computing from said signature and said exponentiated function in such a received message a value equivalent to said exponentiated function and comparing said computed value and said transmitted value; vii) each of said correspondents A and B constructing a session key K by exponentiating information made public by said other correspondent with said random integer that is private to themselves.
• Figure 1 is a schematic representation of a data communication system.
• a pair of correspondents, 10,12 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.
• 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.
• the 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.
• text A will contain A's public-key certificate, issued by a trusted center; correspondent B can use his authentic copy of the trusted center's public key to verify correspondent A's certificate, hence obtaining an authentic copy of correspondent A's public key.
• E also intercepts the message from B and uses his secret random integer e to modify its contents. A will then use that information to generate the same session key allowing A to communicate with B.
• the purpose of the protocol is for parties A and B to establish a session key K.
• the protocols exemplified are role-symmetric and non-interactive.
• the system parameters for this protocol are a prime number p and a generator of the multiplicative group Z * .
• A sends ⁇ r A ,s A ,text A ⁇ to B.
• B sends ⁇ r B ,s B ,text B ⁇ to A.
• A computes B (p B ) rB and verifies that this is equal to r B .
• B computes a A (p A ) rA ⁇ x and verifies that this is equal to r A .
• B will compute a A (p E ) rA " which will not correspond with the transmitted value of r A . B will thus be alerted to the interloper E and will proceed to initiate another session key.
• Protocol 1 One drawback of the first protocol is that it does not offer perfect forward secrecy. That is, if an adversary learns the long-term private key a of party A, then the adversary can deduce all of A's past session keys.
• the property of perfect forward secrecy can be achieved by modifying Protocol 1 in the following way.
• step 1 A also sends a 1 to B, where x, is a second random integer generated by A.
• B also sends to A, where y, is a random integer.
• This drawback is primarily theoretical in nature since a well designed implementation of the protocol will prevent the private integers from being disclosed.
• a second protocol set out below addresses these two drawbacks.
• A sends ⁇ s A . text A ⁇ to B.
• B sends ⁇ s B . text B ⁇ to A. 3.
• the second protocol improves upon the first protocol in the sense that it offers perfect forward secrecy. While it is still the case that disclosure of a private random integer x allows an adversary to learn the private key a, this will not be a problem in practice because A can destroy x as soon as she uses it in step 1 of the protocol.
• the second protocol is a three-pass protocol.
• the quantity s A serves as A's signature on the value ⁇ x .
• This signature has the novel property that it can only be verified by party B. This idea can be generalized to all ElGamal-like signatures schemes.
• the first and second protocols above can be modified to improve the bandwidth requirements and computational efficiency of the key agreement.
• the modified protocols are described below as Protocol 1 ' and Protocol 2 ' .
• a and B will share the common key a AS ⁇ .
• A sends ⁇ r A , text A ⁇ to B.
• a and B thus share the common key but it will be noted that the signatures s 'A and s B need not be transmitted.
• A sends ⁇ , text A ⁇ to B.
• B sends ⁇ text B ⁇ to A.
• a further protocol is available for parties A and B to establish a session key K.
• the system parameters for this protocol are a prime number p and a generator for the multiplicative group Z p * .
• A sends ⁇ r A , s A , text A ) to B.
• A sends ⁇ r B , s B , a ', text B ) to A.
• A computes a B (p B ) B and verifies that this is equal to (r B ) .
• (r A , s A ) can be thought of as the signature of r x with the property that only A can sign the message r x .
• the protocols described above permit the establishment and authentication of a session key K. It is also desirable to establish a protocol in which permits A to transport a session key K to party B. Such a protocol is exemplified below.
• a computes session key K (p B ) x and sends ⁇ r A , s A , text A ⁇ to B.
• B computes a A (p A ) A ⁇ and verifies that this quantity is equal to r A .
• the above protocol may be modified to reduce the bandwidth by avoiding the need to transmit the signature s A as follows:
• a computes K (p B ) SA and sends ⁇ r A , text A ) to B.
• a one-pass key transport protocol is used to transmit a session key K from A to B as well as some text encrypted with the session key K.
• E records the transmission from A to B. If E can at a later time gain access to B's decryption machine (but not the internal contents of the machine, such as B's private key), then, by replaying the transmission to the machine, E can recover the original text. (In this scenario, E does not learn the session key K).
• This replay attack can be foiled by usual methods, such as the use of timestamps.
• B has limited computational resources, in which it is more suitable at the beginning of each session, for B to transmit a random bit string k to A.
• the session key that is used to encrypt the text is then k ⁇
• K i.e. k XOR'd with K.
• Suitable choices include the multiplicative group of a finite filed (in particular the finite filed GF(2 n ), subgroups of Z * of order q, and the group of points on an elliptic curve defined over a finite field.
• an appropriate generator will be used to define the public keys.
• A sends r a to B.
• the shared secret is c * 5 - 4 mod p.
• the above protocol may also be implemented using a subgroup of Z * .
• q will be a prime divisor of (p-1) and g will be an element of order p in Z * .
• A's and B's public keys will be of the form g a , g b respectively and the short-term keys r a , r b will be of the form g x , g y .
• the signature components s A , s B are computed mod q and the session key K computed mod q as before.
• the shared secret is then g S/ ⁇ SB mod p.
• protocols may be implemented in groups other than Z * and a particularly robust group is the group of points on an elliptic curve over a finite field.
• An example of such an implementation is set out below as protocol 1'".
• E is an elliptic curve defined over Fq
• P is a point of prime order n in E(Fq)
• da (l ⁇ da ⁇ n-l) is party A's long-term private key
• d b (l ⁇ d b ⁇ n-l) is party B's long-term private key
• A sends r a to B.
• the shared secret is s a s b P.

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• Engineering & Computer Science (AREA)
• Computer Security & Cryptography (AREA)
• Computer Networks & Wireless Communication (AREA)
• Signal Processing (AREA)
• Computer And Data Communications (AREA)
• Storage Device Security (AREA)
• Data Exchanges In Wide-Area Networks (AREA)

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Cited By (13)

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• 1995
  • 1995-05-17 US US08/442,833 patent/US5761305A/en not_active Expired - Lifetime
• 1996
  • 1996-10-18 DE DE69636815T patent/DE69636815T2/de not_active Expired - Lifetime
  • 1996-10-18 EP EP96944186A patent/EP0873617B1/en not_active Expired - Lifetime
  • 1996-10-18 CA CA002237688A patent/CA2237688C/en not_active Expired - Lifetime
  • 1996-10-18 AU AU14057/97A patent/AU1405797A/en not_active Abandoned
  • 1996-10-18 WO PCT/US1996/016608 patent/WO1998018234A1/en not_active Ceased
  • 1996-10-18 JP JP51929898A patent/JP4384728B2/ja not_active Expired - Lifetime

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