CN107437993A - One kind is based on without the side's authentication key agreement method of certificate two and device - Google Patents

One kind is based on without the side's authentication key agreement method of certificate two and device Download PDF

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Publication number
CN107437993A
CN107437993A CN201610362863.2A CN201610362863A CN107437993A CN 107437993 A CN107437993 A CN 107437993A CN 201610362863 A CN201610362863 A CN 201610362863A CN 107437993 A CN107437993 A CN 107437993A
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China
Prior art keywords
key
params
user
identity information
subscriber identity
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Chinese (zh)
Inventor
刘勇
张家明
陆小慧
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ZTE Corp
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ZTE Corp
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Priority to CN201610362863.2A priority Critical patent/CN107437993A/en
Priority to PCT/CN2017/081153 priority patent/WO2017202161A1/en
Publication of CN107437993A publication Critical patent/CN107437993A/en
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    • 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
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention discloses a kind of method and apparatus based on two side's authenticated key agreements without certificate, the device includes parameter module and negotiation module, by the master key for generating system public parameter collection and the key production center (KGC), part of key, secret value, private key, public key, the step of two side's key agreements, it can overcome the defect that certificate management problem complicated under conventional public-key cipher system and the intrinsic key escrow of Identity- based cryptography, and independent of Bilinear map computing, improve the efficiency of system, the wireless mobile apparatus being limited especially suitable for computing capability.

Description

One kind is based on without the side's authentication key agreement method of certificate two and device
Technical field
The present invention relates to field of information security technology, espespecially a kind of method based on two side's authenticated key agreements without certificate And device.
Background technology
At present, the key agreement cryptographic primitive important as one, it may ensure that two or more users are open Network environment in a shared session key established by interactive information, the user for participating in communication is close by shared session Key carrys out encryption and decryption communication data so as to ensure the safety of network service.Wherein, authenticated key agreement is a kind of (explicit with certification Certification or implicit authentication) function key agreement, it can provide the authentication function of the identity and key to communication user, so as to The attack of the third party can effectively be resisted.
In the prior art, authentication key agreement method is under conventional public-key cipher system mostly or ID-based cryptosystem body Itd is proposed under system, wherein, for being that Al-Riyami and Paterson et al. were carried in 2003 years based on certificateless cryptosystem A kind of new public-key cryptosystem gone out, the system have organically combined identity-based cryptosystems and conventional public-key cipher system Advantage, and effectively overcome defect present in both cipher systems.Therefore, it is a performance based on certificateless cryptosystem It is excellent, it is easy to the new public key cryptosystem applied in open network environment.
But the certificate management of complexity can be efficiently solved the problems, such as using authentication key agreement method of the prior art And key escrow, but these are all relied on based on Al-Riyami and Paterson et al. the cryptographic key negotiation method proposed Bilinear map computing, calculation cost is very big, causes peace of the limited wireless mobile apparatus of computing capability in open network environment Full application is on the hazard.
The content of the invention
In order to solve the above-mentioned technical problem, the invention provides a kind of side based on two side's authenticated key agreements without certificate Method and device, it can overcome the defect that certificate management problem complicated under conventional public-key cipher system and Identity- based cryptography institute Intrinsic key escrow, and independent of Bilinear map computing, the efficiency of system is improved, especially suitable for calculating energy The limited wireless mobile apparatus of power.
Present invention offer is a kind of based on the method without the side's authenticated key agreement of certificate two, applied to session participating user, institute The method of stating includes：
Obtain master key msk and system common parameter that key generation centre KGC is generated by systematic parameter generating algorithm Collect params；
It is public according to corresponding to subscriber identity information, the master key msk and system common parameter collection params generate session Key and private key；
Carried out according to the subscriber identity information, the public key, the private key and the system common parameter collection params Session authentication key is consulted.
Preferably, generating master key msk and system common parameter collection params by systematic parameter generating algorithm includes：
According to predetermined security parameter k ∈ Z+, select the Big prime p and q of two k bits and meet q | p-1, generate one Prime field elliptic curve E/FPUpper rank is q addition cyclic group G, and a first P of generation is determined from the cyclic group G, and in key SetIn at random determine an integer s as system master key msk；
According to formula Ppus=sP calculates the open first P of generationpus, and according to the first hash functionWith Second hash functionThe system public parameter is obtained to integrate as params={ FP,E/ FP,G,k,P,Ppub,H1,H2, wherein, H1It is { 0,1 }*ArriveCryptographic Hash function, H2It is cartesian product { 0,1 }*×{0, 1}*×G4To setCryptographic Hash function, security parameter k represent security parameter bit length, k ＞ 0, { 0,1 }*Table Show the set of the uncertain binary string of length,Represent the set for the binary string that length is k, G44 additions are represented respectively Cyclic group G cartesian product, { 0,1 }*×{0,1}*×G4Represent { 0,1 }*、{0,1}*And G4Cartesian product, q | p-1 represent p- 1 can be divided exactly by q, E/FPRepresent E：y2=x3+ ax+b is finite field FPOn elliptic curve, x is transverse axis coordinate, and y is that the longitudinal axis is sat Mark, a, b are constant.
Preferably, session pair is generated according to subscriber identity information, the master key msk and system common parameter collection params The public key and private key answered include：
According to the system common parameter collection params and subscriber identity information, the secret value of the user is generated；
According to the system common parameter collection params and subscriber identity information, the public key of the user is generated；
Obtain the user's that the KGC generates according to the system common parameter collection params and subscriber identity information Part private key；
According to the system common parameter collection params, subscriber identity information and the part private key, the user is generated Private key.
Preferably, according to the system common parameter collection params and subscriber identity information, the secret of the user is generated Value includes：
In the cipher key setsOne integer of middle selectionAs secret value.
Preferably, according to the system common parameter collection params and subscriber identity information, the public key of the user is generated Including：
According to the secret value x of generationi, according to formula Pi=xiP calculates the public key P for obtaining the useri。
Preferably, according to the system common parameter collection params and subscriber identity information, the part of the user is generated Private key includes：
In the cipher key setsOne integer of middle selectionAccording to formula Ri=riP is calculated Obtain the first parameter of public key R of the useri, according to formula si=ri+sH1(IDi,Ri,Pi) (mod q) calculating acquisition use The second parameter of public key s at familyi, by (si, Ri) it is used as part private key Di, IDiSubscriber identity information is represented, mod represents remainder.
Preferably, according to the system common parameter collection params, subscriber identity information and the part private key, institute is generated Stating the private key of user includes：
According to formula siP=Ri+H1(IDi,Ri,Pi)PpubWhether establishment determines the part private key DiIt is whether effective；
As the part private key DiWhen effective, by (xi, si, Ri) it is used as private key Si。
Preferably, according to the subscriber identity information, the public key, the private key and the system common parameter collection The params authenticated key agreements that conversate include：
Session setup side is in the cipher key setsOne integer of middle selectionAccording to formula TA=tAP calculates initiator's session key element TA, by (IDA, RA, TA) it is used as initiator's session key parameter MAIt is sent to session Responder；
Conversational response side receives initiator's session key parameter MAAfterwards, in the cipher key setsOne integer of middle selectionAccording to formula TB=tBP calculates response session key element TB, will (IDB, RB, TB) it is used as responder's session key parameter MBIt is sent to session setup side；
Session setup side receives responder's session key parameter MBAfterwards, calculate：WithWherein, WB=RB+H1(IDB,RB, PB)Ppub, according to formulaCalculate and obtain initiator's session key KAB；
Conversational response side calculates：Wherein, WA=PA+RA+H1 (IDA,RA,PA)Ppub+TA；According to formulaCalculate and obtain responder's meeting Talk about key KBA；
And verified by following equation：
KAB=KBA=K, user A and user B generate identical session key.
The present invention also provides a kind of to be included based on the device without the side's authenticated key agreement of certificate two, described device：
Acquisition module, it is arranged to obtain the master key msk that key generation centre KGC is generated by systematic parameter generating algorithm With system common parameter collection params；
Generation module, it is arranged to be given birth to according to subscriber identity information, the master key msk and system common parameter collection params Into public key and private key corresponding to session；
Negotiation module, it is arranged to according to the subscriber identity information, the public key, the private key and the public ginseng of the system Manifold params conversates authenticated key agreement.
Preferably, what the acquisition module obtained is public by systematic parameter generating algorithm generation master key msk and system Parameter set params refers to：
According to predetermined security parameter k ∈ Z+, select the Big prime p and q of two k bits and meet q | p-1, generate one Prime field elliptic curve E/FPUpper rank is q addition cyclic group G, and a first P of generation is determined from the cyclic group G, and in key SetIn at random determine an integer s as system master key msk；
According to formula Ppus=sP calculates the open first P of generationpus, and according to the first hash functionWith Second hash functionThe system public parameter is obtained to integrate as params={ FP,E/ FP,G,k,P,Ppub,H1,H2, wherein, H1It is { 0,1 }*ArriveCryptographic Hash function, H2It is cartesian product { 0,1 }*×{0, 1}*×G4To setCryptographic Hash function, security parameter k represent security parameter bit length, k ＞ 0, { 0,1 }*Table Show the set of the uncertain binary string of length,Represent the set for the binary string that length is k, G44 additions are represented respectively Cyclic group G cartesian product, { 0,1 }*×{0,1}*×G4Represent { 0,1 }*、{0,1}*And G4Cartesian product, q | p-1 represent p- 1 can be divided exactly by q, E/FPRepresent E：y2=x3+ ax+b is finite field FPOn elliptic curve, x is transverse axis coordinate, and y is that the longitudinal axis is sat Mark, a, b are constant.
Preferably, the generation module is according to subscriber identity information, the master key msk and system common parameter collection Public key and private key include corresponding to params generation sessions：
According to the system common parameter collection params and subscriber identity information, the secret value of the user is generated；
According to the system common parameter collection params and subscriber identity information, the public key of the user is generated；
Obtain the user's that the KGC generates according to the system common parameter collection params and subscriber identity information Part private key；
According to the system common parameter collection params, subscriber identity information and the part private key, the user is generated Private key.
Preferably, the generation module generates institute according to the system common parameter collection params and subscriber identity information Stating the secret value of user includes：
In the cipher key setsOne integer of middle selectionAs secret value.
Preferably, the generation module generates institute according to the system common parameter collection params and subscriber identity information Stating the public key of user includes：
According to the secret value x of generationi, according to formula Pi=xiP calculates the public key P for obtaining the useri。
Preferably, the generation module generates institute according to the system common parameter collection params and subscriber identity information Stating the part private key of user includes：
In the cipher key setsOne integer of middle selectionAccording to formula Ri=riP is calculated Obtain the first parameter of public key R of the useri, according to formula si=ri+sH1(IDi,Ri,Pi) (mod q) calculating acquisition use The second parameter of public key s at familyi, by (si, Ri) it is used as part private key Di, IDiSubscriber identity information is represented, mod represents remainder.
Preferably, the generation module is according to system common parameter collection params, subscriber identity information and the portion Divide private key, generating the private key of the user includes：
According to formula siP=Ri+H1(IDi,Ri,Pi)PpubWhether establishment determines the part private key DiIt is whether effective；
As the part private key DiWhen effective, by (xi, si, Ri) it is used as private key Si。
Preferably, the negotiation module is public according to the subscriber identity information, the public key, the private key and the system The parameter set params authenticated key agreements that conversate include altogether：
Session setup side is in the cipher key setsOne integer of middle selectionAccording to formula TA=tAP calculates initiator's session key element TA, by (IDA, RA, TA) it is used as initiator's session key parameter MAIt is sent to session Responder；
Conversational response side receives initiator's session key parameter MAAfterwards, in the cipher key setsOne integer of middle selectionAccording to formula TB=tBP calculates response session key element TB, will (IDB, RB, TB) it is used as responder's session key parameter MBIt is sent to session setup side；
Session setup side receives responder's session key parameter MBAfterwards, calculate： WithWherein, WB=RB+H1(IDB,RB,PB)Ppub, according to formulaCalculate and obtain initiator's session key KAB；
Conversational response side calculates：Wherein, WA=PA+RA+H1 (IDA,RA,PA)Ppub+TA；According to formulaCalculate and obtain responder's meeting Talk about key KBA；
And verified by following equation：
KAB=KBA=K, user A and user B generate identical session key.
Other features and advantages of the present invention will be illustrated in the following description, also, partly becomes from specification Obtain it is clear that or being understood by implementing the present invention.The purpose of the present invention and other advantages can be by specification, rights Specifically noted structure is realized and obtained in claim and accompanying drawing.
Brief description of the drawings
Accompanying drawing is used for providing further understanding technical solution of the present invention, and a part for constitution instruction, with this The embodiment of application is used to explain technical scheme together, does not form the limitation to technical solution of the present invention.
Fig. 1 is that a kind of flow of the method based on two side's authenticated key agreements without certificate provided in an embodiment of the present invention is shown It is intended to；
Fig. 2 is that a kind of structure of the device based on two side's authenticated key agreements without certificate provided in an embodiment of the present invention is shown It is intended to；
Fig. 3 is a kind of flow for method based on two side's authenticated key agreements without certificate that the embodiment of the present invention one provides Schematic diagram.
Embodiment
For the object, technical solutions and advantages of the present invention are more clearly understood, below in conjunction with accompanying drawing to the present invention Embodiment be described in detail.It should be noted that in the case where not conflicting, in the embodiment and embodiment in the application Feature can mutually be combined.
Can be in the computer system of such as one group computer executable instructions the flow of accompanying drawing illustrates the step of Perform.Also, although logical order is shown in flow charts, in some cases, can be with suitable different from herein Sequence performs shown or described step.
The present embodiments relate to method can apply to open network environment, it is necessary to carry out information safety protection Communication or internet, but be not limited thereto.
The present embodiments relate to method, it is intended to solve in the prior art based on the cryptographic key negotiation method without certificate all according to Rely in Bilinear map computing, its calculating process is complicated, causes the limited wireless mobile apparatus of computing capability in open network environment In the technical problem that is on the hazard of safety applications.
Technical scheme is described in detail with specifically embodiment below.These specific implementations below Example can be combined with each other, and may be repeated no more for same or analogous concept or process in some embodiments.
Fig. 1 is a kind of flow of the embodiment of the method one based on two side's authenticated key agreements without certificate provided by the invention Schematic diagram.The present embodiment is referred to based on without specific mistake of the certificate independent of two side's authenticated key agreements of Bilinear map computing Journey.As shown in figure 1, this method includes：
S101, obtain the master key msk (Master that key generation centre KGC is generated by systematic parameter generating algorithm Session Key) and system common parameter collection params；
S102, session correspondence is generated according to subscriber identity information, the master key msk and system common parameter collection params Public key and private key；
S103, according to the subscriber identity information, the public key, the private key and the system common parameter collection params Conversate authenticated key agreement.
Wherein, step S101 is specifically included：
According to predetermined security parameter k ∈ Z+, select the Big prime p and q of two k bits and meet q | p-1, generate one Prime field elliptic curve E/FPUpper rank is q addition cyclic group G, and a first P of generation is determined from the cyclic group G, and in key SetIn at random determine an integer s as system master key msk；
According to formula Ppus=sP calculates the open first P of generationpus, and according to the first hash functionWith Second hash functionThe system public parameter is obtained to integrate as params={ FP,E/ FP,G,k,P,Ppub,H1,H2, wherein, H1It is { 0,1 }*ArriveCryptographic Hash function, H2It is cartesian product { 0,1 }*×{0, 1}*×G4To setCryptographic Hash function, security parameter k represent security parameter bit length, k ＞ 0, { 0,1 }*Table Show the set of the uncertain binary string of length,Represent the set for the binary string that length is k, G44 additions are represented respectively Cyclic group G cartesian product, { 0,1 }*×{0,1}*×G4Represent { 0,1 }*、{0,1}*And G4Cartesian product, q | p-1 represent p- 1 can be divided exactly by q, E/FPRepresent E：y2=x3+ ax+b is finite field FPOn elliptic curve, x is transverse axis coordinate, and y is that the longitudinal axis is sat Mark, a, b are constant.
According to said process, the master key that generation KGC is preserved is msk=s, system public parameter collection params={ FP,E/ FP,G,k,P,Ppub,H1,H2}。
Step S102 is specifically included：
S1021, according to the system common parameter collection params and subscriber identity information, generate the secret of the user Value；
S1022, according to the system common parameter collection params and subscriber identity information, generate the public key of the user；
S1023, the KGC is obtained according to the system common parameter collection params and subscriber identity information generation The part private key of user；
S1024, according to the system common parameter collection params, subscriber identity information and the part private key, generate institute State the private key of user.
Step S1021 includes：
In the cipher key setsOne integer of middle selectionAs secret value.
Step S1022 includes：
According to the secret value x of generationi, according to formula Pi=xiP calculates the public key P for obtaining the useri。
Step S1023 includes：
In the cipher key setsOne integer of middle selectionAccording to formula Ri=riP is calculated Obtain the first parameter of public key R of the useri, according to formula si=ri+sH1(IDi,Ri,Pi) (mod q) calculating acquisition use The second parameter of public key s at familyi, by (si, Ri) it is used as part private key Di, IDiSubscriber identity information is represented, mod represents remainder.
Step S1024 includes：
According to formula siP=Ri+H1(IDi,Ri,Pi)PpubWhether establishment determines the part private key DiIt is whether effective；
As the part private key DiWhen effective, by (xi, si, Ri) it is used as private key Si。
Step S103 is specifically included：
Session setup side is in the cipher key setsOne integer of middle selectionAccording to formula TA=tAP calculates initiator's session key element TA, by (IDA, RA, TA) it is used as initiator's session key parameter MAIt is sent to session Responder；
Conversational response side receives initiator's session key parameter MAAfterwards, in the cipher key setsOne integer of middle selectionAccording to formula TB=tBP calculates response session key element TB, will (IDB, RB, TB) it is used as responder's session key parameter MBIt is sent to session setup side；
Session setup side receives responder's session key parameter MBAfterwards, calculate：WithWherein, WB=RB+H1(IDB,RB, PB)Ppub, according to formulaCalculate and obtain initiator's session key KAB；
Conversational response side calculates：Wherein, WA=PA+RA+H1 (IDA,RA,PA)Ppub+TA；According to formulaCalculate and obtain responder's meeting Talk about key KBA；
Verification process is as follows：
Specifically, session participating user includes session setup side A and conversational response side B,.
1) user A randomly chooses an integerCalculate TA=tAP is simultaneously MA=(IDA,RA,TA) it is sent to user B。
2) when user B receives MA=(IDA,RA,TA) after, an integer can be randomly choosedCalculate TB=tBP and handle MB=(IDB,RB,TB) it is sent to user A.
3) when user A receives MB=(IDB,RB,TB) after, user A can be calculated successively：Wherein, WB=RB+H1(IDB,RB,PB) Ppub, then user A calculate and obtain session key：
User B is calculated successively：Wherein, WA=PA+ RA+H1(IDA,RA,PA)Ppub+TA；Then user B is calculated and is obtained session key：
The correctness of this method is easy to verify by following equation：
Therefore, KAB=KBA=K, user A and user B generate identical session key.
A kind of method based on two side's authenticated key agreements without certificate provided in an embodiment of the present invention, this method pass through life Into system public parameter collection and the key production center (KGC) master key, part of key, secret value, private key, public key, two Fang Mi The step of key is consulted, can overcome the defect that certificate management problem complicated under conventional public-key cipher system and ID-ased cryptography body The intrinsic key escrow of system, and independent of Bilinear map computing, the efficiency of system is improved, especially suitable for meter Calculate the wireless mobile apparatus of limited ability.
Fig. 2 is a kind of structure of the device embodiment one based on two side's authenticated key agreements without certificate provided by the invention Schematic diagram, as shown in Fig. 2 the device includes：
Acquisition module, it is arranged to obtain the master key msk that key generation centre KGC is generated by systematic parameter generating algorithm With system common parameter collection params；
Generation module, it is arranged to be given birth to according to subscriber identity information, the master key msk and system common parameter collection params Into public key and private key corresponding to session；
Negotiation module, it is arranged to according to the subscriber identity information, the public key, the private key and the public ginseng of the system Manifold params conversates authenticated key agreement.
Wherein, what the acquisition module obtained generates master key msk and the public ginseng of system by systematic parameter generating algorithm Manifold params refers to：
According to predetermined security parameter k ∈ Z+, select the Big prime p and q of two k bits and meet q | p-1, generate one Prime field elliptic curve E/FPUpper rank is q addition cyclic group G, and a first P of generation is determined from the cyclic group G, and in key SetIn at random determine an integer s as system master key msk；
According to formula Ppus=sP calculates the open first P of generationpus, and according to the first hash functionWith Second hash functionThe system public parameter is obtained to integrate as params={ FP, E/FP,G,k,P,Ppub,H1,H2, wherein, H1It is { 0,1 }*ArriveCryptographic Hash function, H2It is cartesian product { 0,1 }*× {0,1}*×G4To setCryptographic Hash function, security parameter k represent security parameter bit length, k ＞ 0, { 0,1 }* The set of the uncertain binary string of length is represented,Represent the set for the binary string that length is k, G44 are represented respectively to add Method cyclic group G cartesian product, { 0,1 }*×{0,1}*×G4Represent { 0,1 }*、{0,1}*And G4Cartesian product, q | p-1 represent P-1 can be divided exactly by q, E/FPRepresent E：y2=x3+ ax+b is finite field FPOn elliptic curve, x is transverse axis coordinate, and y is that the longitudinal axis is sat Mark, a, b are constant.
Wherein, the generation module is according to subscriber identity information, the master key msk and system common parameter collection params Public key and private key include corresponding to generation session：
According to the system common parameter collection params and subscriber identity information, the secret value of the user is generated；
According to the system common parameter collection params and subscriber identity information, the public key of the user is generated；
Obtain the user's that the KGC generates according to the system common parameter collection params and subscriber identity information Part private key；
According to the system common parameter collection params, subscriber identity information and the part private key, the user is generated Private key.
Wherein, the generation module is according to the system common parameter collection params and subscriber identity information, described in generation The secret value of user includes：
In the cipher key setsOne integer of middle selectionAs secret value.
Wherein, the generation module is according to the system common parameter collection params and subscriber identity information, described in generation The public key of user includes：
According to the secret value x of generationi, according to formula Pi=xiP calculates the public key P for obtaining the useri。
Wherein, the generation module is according to the system common parameter collection params and subscriber identity information, described in generation The part private key of user includes：
In the cipher key setsOne integer of middle selectionAccording to formula Ri=riP is calculated Obtain the first parameter of public key R of the useri, according to formula si=ri+sH1(IDi,Ri,Pi) (mod q) calculating acquisition use The second parameter of public key s at familyi, by (si, Ri) it is used as part private key Di, IDiSubscriber identity information is represented, mod represents remainder.
Wherein, the generation module is according to system common parameter collection params, subscriber identity information and the part Private key, generating the private key of the user includes：
According to formula siP=Ri+H1(IDi,Ri,Pi)PpubWhether establishment determines the part private key DiIt is whether effective；
As the part private key DiWhen effective, by (xi, si, Ri) it is used as private key Si。
Wherein, the negotiation module is public according to the subscriber identity information, the public key, the private key and the system The parameter set params authenticated key agreements that conversate include：
Session setup side is in the cipher key setsOne integer of middle selectionAccording to formula TA=tAP calculates initiator's session key element TA, by (IDA, RA, TA) it is used as initiator's session key parameter MAIt is sent to session Responder；
Conversational response side receives initiator's session key parameter MAAfterwards, in the cipher key setsOne integer of middle selectionAccording to formula TB=tBP calculates response session key element TB, will (IDB, RB, TB) it is used as responder's session key parameter MBIt is sent to session setup side；
Session setup side receives responder's session key parameter MBAfterwards, calculate：WithWherein, WB=RB+H1(IDB,RB, PB)Ppub, according to formulaCalculate and obtain initiator's session key KAB；
Conversational response side calculates：Wherein, WA=PA+RA+H1 (IDA,RA,PA)Ppub+TA；According to formulaCalculate and obtain responder's meeting Talk about key KBA；
And verified by following equation：
KAB=KBA=K, user A and user B generate identical session key.
Device provided in an embodiment of the present invention, above method embodiment can be performed, its implementing principle and technical effect class Seemingly, will not be repeated here.
Embodiment is specifically enumerated below to be described in detail：
Embodiment one
Involved entity is as follows in the present embodiment system：
(1)KGC：It is responsible for systematic parameter generation, i.e. KGC master keys and system public parameter collection, and produces User Part private The trusted third party of key；
(2) user A：The original initiation entity of session；
(3) user B：The response entity of session；
Fig. 3 is a kind of flow of the embodiment of the method two based on two side's authenticated key agreements without certificate provided by the invention Schematic diagram, comprise the following steps that：
Step A, generate KGC master key and system public parameter collection；Comprise the following steps that：
Step 1：KGC runtimes parameter produces algorithm：KGC is according to the security parameter k ∈ Z of setting+, select two k ratios Special Big prime p and q and meet q | p-1, and generate a prime field elliptic curve E/FPUpper rank is q addition cyclic group G.
Step 2：KGC selects the first P of a generation from cyclic group G and in set Zq *One integer s of middle random selection, and count Calculate Ppub=sP, wherein：Set
Step 3：Define two hash functionsIts In：H1It is { 0,1 }*ArriveCryptographic Hash function, H2It is cartesian product { 0,1 }*×{0,1}*×G4To setPassword Hash function is learned, integer k ＞ 0, k represent the bit length of system security parameter, { 0,1 }*Represent the uncertain binary system of length The set of string,Represent the set for the binary string that length is k, G44 group G cartesian product, { 0,1 } are represented respectively*×{0, 1}*×G4Represent { 0,1 }*、{0,1}*And G4Cartesian product.
Step 4：According to step 1, the implementing result of step 2 and step 3, the secret master keys preserved of generation KGC are msk= S, system public parameter integrate as params={ FP,E/FP,G,k,P,Ppub,H1,H2}。
Step B, according to the system public parameter collection, subscriber identity information, generate the secret value of user；Detailed process For：
Step 5：IDiGatheringOne integer of middle random selectionAs the secret value of oneself.
Step C, according to the system public parameter collection, subscriber identity information, generate the public key of user；Detailed process is：
Step 6：IDiAccording to the secret value x selectediCalculate and obtain the public key P of oneselfi=xiP。
Step D, according to the system public parameter collection, subscriber identity information, generate the part of key of user；Detailed process For：
Step 7：Identity is IDiUser i identity information IDiWith public key PiSubmit to KGC.
Step 8：KGC is randomly choosedCalculate Ri=riP and si=ri+si=ri+sH1(IDi,Ri,Pi)(mod q)。
Step 9：KGC is by safe lane IDiPart private key Di=Di=(si,Ri) it is sent to user.
Step E, according to the system public parameter collection, subscriber identity information, generate the private key of user；Detailed process is：
Step 10：IDiBy judging equation siP=Ri+H1(IDi,Ri,Pi)PpubIt is whether private into Rob Roy verification portion Key Di=(si,Ri) whether effective.
Step 11：IDiThe private key of oneself is arranged to Si=(xi,si,Ri)。
Step F, according to the system public parameter collection, the identity information of session setup side and conversational response side, public key, private Key, generate the session key of two sides；Detailed process is：
Step 12：Session setup side A randomly chooses an integerCalculate TA=tAP。
Step 13：Session setup side A is MA=(IDA,RA,TA) conversational response side B is sent to, wherein, IDAIt is session setup Square A identity information, RAIt is session setup side A part private key.
Step 14：Receive MA=(IDA,RA,TA) after, conversational response side B randomly chooses an integerCalculate TB =tBP。
Step 15：Conversational response side B is MB=(IDB,RB,TB) conversational response side A is sent to, wherein, IDBIt is conversational response Square B identity information, RBIt is session setup side B part private key.
Step 16：Session setup side A receives MB=(IDB,RB,TB) after, session setup side A is calculated successively：Wherein, WB=RB+H1(IDB, RB,PB)Ppub, xAIt is session setup side A secret value, sAIt is session setup side A part private key, IDBIt is conversational response side B Identity information, RBIt is conversational response side B part private key, PBIt is conversational response side B public key；Then A is calculated and to obtain session close Key：
Step 17：Conversational response side B is calculated successively：Wherein, WA=PA+RA+H1(IDA,RA,PA)Ppub+TA, xBIt is conversational response side B secret value, sBIt is conversational response side's part B private key, IDA It is session setup side A identity information, PAIt is session setup side A public key, RAIt is session setup side A part private key；Then B Calculate and obtain session key：
The embodiment is by generating the master key of system public parameter collection and the key production center (KGC), part of key, secret The step of close value, private key, public key, two side's key agreements, it can overcome the defect that certificate management complicated under conventional public-key cipher system Problem and the intrinsic key escrow of Identity- based cryptography, and independent of Bilinear map computing, improve The efficiency of system, the wireless mobile apparatus being limited especially suitable for computing capability.
Although disclosed herein embodiment as above, described content be only readily appreciate the present invention and use Embodiment, it is not limited to the present invention.Technical staff in any art of the present invention, taken off not departing from the present invention On the premise of the spirit and scope of dew, any modification and change, but the present invention can be carried out in the form and details of implementation Scope of patent protection, still should be subject to the scope of the claims as defined in the appended claims.

Claims (16)

  1. It is 1. a kind of based on the method without the side's authenticated key agreement of certificate two, it is characterised in that described applied to session participating user Method includes：
    Obtain master key msk and system common parameter collection that key generation centre KGC is generated by systematic parameter generating algorithm params；
    According to subscriber identity information, the master key msk and system common parameter collection params generate session corresponding to public key and Private key；
    Conversated according to the subscriber identity information, the public key, the private key and the system common parameter collection params Authenticated key agreement.
  2. 2. according to the method for claim 1, it is characterised in that by systematic parameter generating algorithm generate master key msk and System common parameter collection params includes：
    According to predetermined security parameter k ∈ Z+, select the Big prime p and q of two k bits and meet q | p-1, generate a prime number Domain elliptic curve E/FPUpper rank is q addition cyclic group G, and a first P of generation is determined from the cyclic group G, and in cipher key setsIn at random determine an integer s as system master key msk；
    According to formula Ppus=sP calculates the open first P of generationpus, and according to the first hash functionWith second Hash functionThe system public parameter is obtained to integrate as params={ FP,E/FP, G,k,P,Ppub,H1,H2, wherein, H1It is { 0,1 }*ArriveCryptographic Hash function, H2It is cartesian product { 0,1 }*×{0,1}* ×G4To setCryptographic Hash function, security parameter k represent security parameter bit length, k ＞ 0, { 0,1 }*Represent The set of the uncertain binary string of length,Represent the set for the binary string that length is k, G4Represent that 4 additions follow respectively Ring group G cartesian product, { 0,1 }*×{0,1}*×G4Represent { 0,1 }*、{0,1}*And G4Cartesian product, q | p-1 represent p-1 It can be divided exactly by q, E/FPRepresent E：y2=x3+ ax+b is finite field FPOn elliptic curve, x is transverse axis coordinate, and y is ordinate of orthogonal axes, A, b is constant.
  3. 3. according to the method for claim 2, it is characterised in that according to subscriber identity information, the master key msk and system Public key and private key include corresponding to common parameter collection params generation sessions：
    According to the system common parameter collection params and subscriber identity information, the secret value of the user is generated；
    According to the system common parameter collection params and subscriber identity information, the public key of the user is generated；
    Obtain the part for the user that the KGC generates according to the system common parameter collection params and subscriber identity information Private key；
    According to the system common parameter collection params, subscriber identity information and the part private key, the private of the user is generated Key.
  4. 4. according to the method for claim 3, it is characterised in that according to the system common parameter collection params and user's body Part information, generating the secret value of the user includes：
    In the cipher key setsOne integer of middle selectionAs secret value.
  5. 5. according to the method for claim 4, it is characterised in that according to the system common parameter collection params and user's body Part information, generating the public key of the user includes：
    According to the secret value x of generationi, according to formula Pi=xiP calculates the public key P for obtaining the useri。
  6. 6. according to the method for claim 5, it is characterised in that according to the system common parameter collection params and user's body Part information, generating the part private key of the user includes：
    In the cipher key setsOne integer of middle selectionAccording to formula Ri=riP, which is calculated, to be obtained The first parameter of public key R of the useri, according to formula si=ri+sH1(IDi,Ri,Pi) (mod q) calculating acquisition user The second parameter of public key si, by (si, Ri) it is used as part private key Di, IDiSubscriber identity information is represented, mod represents remainder.
  7. 7. according to the method for claim 6, it is characterised in that according to described system common parameter collection params, Yong Hushen Part information and the part private key, generating the private key of the user includes：
    According to formula siP=Ri+H1(IDi,Ri,Pi)PpubWhether establishment determines the part private key DiIt is whether effective；
    As the part private key DiWhen effective, by (xi, si, Ri) it is used as private key Si。
  8. 8. according to the method for claim 7, it is characterised in that according to the subscriber identity information, the public key, the private Key and the system common parameter collection params authenticated key agreement that conversates include：
    Session setup side is in the cipher key setsOne integer of middle selectionAccording to formula TA= tAP calculates initiator's session key element TA, by (IDA, RA, TA) it is used as initiator's session key parameter MAIt is sent to conversational response Side；
    Conversational response side receives initiator's session key parameter MAAfterwards, in the cipher key setsIn Select an integerAccording to formula TB=tBP calculates response session key element TB, by (IDB, RB, TB) as response Square session key parameter MBIt is sent to session setup side；Session setup side receives responder's session key parameter MBAfterwards, count Calculate：WithWherein, WB=RB+H1 (IDB,RB,PB)Ppub, according to formulaCalculate and to obtain initiator's session close Key KAB；
    Conversational response side calculates：Wherein, WA=PA+RA+H1(IDA, RA,PA)Ppub+TA；According to formulaCalculate and obtain responder's session key KBA；
    And verified by following equation：
    KAB=KBA=K, user A and user B generate identical session key.
  9. It is 9. a kind of based on the device without the side's authenticated key agreement of certificate two, it is characterised in that described device includes：
    Acquisition module, it is arranged to obtain the master key msk that generate by systematic parameter generating algorithm of key generation centre KGC and is Unite common parameter collection params；
    Generation module, it is arranged to generate meeting according to subscriber identity information, the master key msk and system common parameter collection params Public key corresponding to words and private key；
    Negotiation module, it is arranged to according to the subscriber identity information, the public key, the private key and the system common parameter collection Params conversates authenticated key agreement.
  10. 10. device according to claim 9, it is characterised in that what the acquisition module obtained is generated by systematic parameter Algorithm generation master key msk and system common parameter collection params refers to：
    According to predetermined security parameter k ∈ Z+, select the Big prime p and q of two k bits and meet q | p-1, generate a prime number Domain elliptic curve E/FPUpper rank is q addition cyclic group G, and a first P of generation is determined from the cyclic group G, and in cipher key setsIn at random determine an integer s as system master key msk；
    According to formula Ppus=sP calculates the open first P of generationpus, and according to the first hash functionWith second Hash functionThe system public parameter is obtained to integrate as params={ FP,E/FP, G,k,P,Ppub,H1,H2, wherein, H1It isArriveCryptographic Hash function, H2It is cartesian product { 0,1 }*×{0,1}* ×G4To setCryptographic Hash function, security parameter k represent security parameter bit length, k ＞ 0, { 0,1 }*Represent The set of the uncertain binary string of length,Represent the set for the binary string that length is k, G4Represent that 4 additions follow respectively Ring group G cartesian product, { 0,1 }*×{0,1}*×G4Represent { 0,1 }*、{0,1}*And G4Cartesian product, q | p-1 represent p-1 It can be divided exactly by q, E/FPRepresent E：y2=x3+ ax+b is finite field FPOn elliptic curve, x is transverse axis coordinate, and y is ordinate of orthogonal axes, A, b is constant.
  11. 11. device according to claim 10, it is characterised in that the generation module is according to subscriber identity information, described Public key and private key include corresponding to master key msk and system common parameter collection params generation sessions：
    According to the system common parameter collection params and subscriber identity information, the secret value of the user is generated；
    According to the system common parameter collection params and subscriber identity information, the public key of the user is generated；
    Obtain the part for the user that the KGC generates according to the system common parameter collection params and subscriber identity information Private key；
    According to the system common parameter collection params, subscriber identity information and the part private key, the private of the user is generated Key.
  12. 12. device according to claim 11, it is characterised in that the generation module is according to the system common parameter collection Params and subscriber identity information, generating the secret value of the user includes：
    In the cipher key setsOne integer of middle selectionAs secret value.
  13. 13. device according to claim 12, it is characterised in that the generation module is according to the system common parameter collection Params and subscriber identity information, generating the public key of the user includes：
    According to the secret value x of generationi, according to formula Pi=xiP calculates the public key P for obtaining the useri。
  14. 14. device according to claim 13, it is characterised in that the generation module is according to the system common parameter collection Params and subscriber identity information, generating the part private key of the user includes：
    In the cipher key setsOne integer of middle selectionAccording to formula Ri=riP, which is calculated, to be obtained The first parameter of public key R of the useri, according to formula si=ri+sH1(IDi,Ri,Pi) (mod q) calculating acquisition user The second parameter of public key si, by (si, Ri) it is used as part private key Di, IDiSubscriber identity information is represented, mod represents remainder.
  15. 15. device according to claim 14, it is characterised in that the generation module is according to the system common parameter collection Params, subscriber identity information and the part private key, generating the private key of the user includes：
    According to formula siP=Ri+H1(IDi,Ri,Pi)PpubWhether establishment determines the part private key DiIt is whether effective；
    As the part private key DiWhen effective, by (xi, si, Ri) it is used as private key Si。
  16. 16. device according to claim 15, it is characterised in that the negotiation module according to the subscriber identity information, The public key, the private key and the system common parameter collection params authenticated key agreement that conversates include：
    Session setup side is in the cipher key setsOne integer of middle selectionAccording to formula TA= tAP calculates initiator's session key element TA, by (IDA, RA, TA) it is used as initiator's session key parameter MAIt is sent to conversational response Side；
    Conversational response side receives initiator's session key parameter MAAfterwards, in the cipher key setsIn Select an integerAccording to formula TB=tBP calculates response session key element TB, by (IDB, RB, TB) as response Square session key parameter MBIt is sent to session setup side；
    Session setup side receives responder's session key parameter MBAfterwards, calculate： WithWherein, WB=RB+H1(IDB,RB,PB)Ppub, according to formulaCalculate and obtain initiator's session key KAB；
    Conversational response side calculates：Wherein, WA=PA+RA+H1(IDA, RA,PA)Ppub+TA；According to formulaCalculate and obtain responder's session key KBA；
    And verified by following equation：
    KAB=KBA=K, user A and user B generate identical session key.
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CN114024668B (en) * 2021-10-18 2023-01-31 武汉大学 Efficient certificateless authentication key agreement method and system without bilinear pairing operation
CN114024668A (en) * 2021-10-18 2022-02-08 武汉大学 Efficient certificateless authentication key agreement method and system without bilinear pairing operation
WO2024114205A1 (en) * 2022-11-30 2024-06-06 大唐移动通信设备有限公司 Key negotiation method and apparatus
CN116599659A (en) * 2023-05-26 2023-08-15 重庆大学 Certificate-free identity authentication and key negotiation method and system
CN116599659B (en) * 2023-05-26 2024-01-26 重庆大学 Certificate-free identity authentication and key negotiation method and system

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Application publication date: 20171205