CN107231230A - Cross-domain dynamic anonymity authentication group key management method and system based on illness - Google Patents

Cross-domain dynamic anonymity authentication group key management method and system based on illness Download PDF

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CN107231230A
CN107231230A CN201710397579.3A CN201710397579A CN107231230A CN 107231230 A CN107231230 A CN 107231230A CN 201710397579 A CN201710397579 A CN 201710397579A CN 107231230 A CN107231230 A CN 107231230A
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CN107231230B (en
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杨旸
张煜超
郑相涵
刘西蒙
叶少珍
董晨
邹剑
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Fuzhou University
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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
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
    • G06F21/60—Protecting data
    • G06F21/62—Protecting access to data via a platform, e.g. using keys or access control rules
    • G06F21/6218—Protecting access to data via a platform, e.g. using keys or access control rules to a system of files or objects, e.g. local or distributed file system or database
    • G06F21/6245—Protecting personal data, e.g. for financial or medical purposes
    • G06F21/6254—Protecting personal data, e.g. for financial or medical purposes by anonymising data, e.g. decorrelating personal data from the owner's identification
    • 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

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Abstract

The present invention provides a kind of cross-domain dynamic anonymity authentication group key management method and system based on illness, the patient of the present invention can be diagnosed and be treated by different medical institutions, system allows one group of patient from different medical field to generate cluster conversation key, so as to set up safe group communication.System supports the anonymity and traceability of patient, and the identity of patient is hidden in anonymous Identity (pseudonym) by it, and only Notified body can recover their true identity.Cross-domain group key agreement ensures：Come from different medical mechanism and the certification patient with identical illness, safe group key can be generated.Patient sets up the group communication of safety using the key, so as to protect the patients' privacy information in electron medical treatment social intercourse system.System also supports dynamic management and group, and when group member is changed, system can generate new cluster conversation key.

Description

Cross-domain dynamic anonymity authentication group key management method and system based on illness
Technical field
The present invention relates to the dynamic anonymity certification group key pipe based on illness in a kind of cross-domain electron medical treatment social intercourse system Manage method and system.
Background technology
Electronic medical system is handled by the medical data of electronization, is realized suitable for the new of high-quality health care General fit calculation mode.Vital sign patient and other medical datas are collected by electromedical equipment or microsensor, The state of an illness of patient can be monitored.In medical system, medical personnel need to provide the disease and Illnesses Diagnoses of specialty for patient.Separately On the one hand, these patients are also linked up with other patients with identical illness intentionally.They are wanted to set up based on illness Communication group, to exchange the relevant information of disease, share Couple herbs and expert advice.They can chat in communication set, Have a talk their real-time disease situation, and mutually encourage Fighting Disease.
In view of the sensitiveness of medical information, the privacy of patient should be by system protection.Set up the group of a safety Information Exchange System is extremely necessary.If these patients can negotiate group key by really meeting, that It is easy for that such system can be set up.But, in the known integrated circuit it is a fact that they must not be not left in hospital for treatment, have no chance existing Meet, can only be linked up by internet in reality.We should the group key management scheme (GKM) of design safety protect Cluster conversation.On the other hand, the very possible medical institutions from different cities or country variant of patient with identical illness. Some obtain the patient of orphan disease or even are difficult that the patient for suffering from similar conditions is found in same city.In order to strengthen International Medical Assistance, we should set up the safe cluster group conversational system across medical domain.
In safe group system, the anonymity and being mutually authenticated property of patient are vital.Anonymity can be protected The true identity of patient, it is to avoid unnecessary leakage of personal information and discrimination.Authenticating user identification can anti-locking system by puppet Dress attack.A kind of mode for realizing patient's certification is data signature mechanism.The public key of user is managed by PKIX (PKI) Reason.In PKI system, certification authority (CA) is responsible for distribution, storage, checking and cancellation of doucment, so as to bring higher management Cost.The another way of design verification algorithm is the public-key cryptosystem (ID-PKC) of identity-based, wherein each user There is an identity, all user keys are generated by key generation centre (KGC).Because KGC takes care of the key of all users, one Denier KGC storage servers are by assault, then identity based cryptography is by risk.Can be with without cryptographic certificate system Key escrow is solved, because KGC only knows the part of key (partial secret key) of user within the system.
In order to realize flexible case control, after patient's rehabilitation from disease, system should cancel the key of the patient. In addition, the cluster communication system based on illness should be dynamic.On the one hand, patient freely can add or leave system and The privacy of cluster conversation will not be revealed.In addition, in the certification group key agreement based on illness, illness information should be embedded into In cluster conversation key so that the patient with different syndromes can not add the group and be communicated.Meanwhile, in information exchange mistake , it is necessary to ensure that the illness of patient can not be leaked to the attacker for being not belonging to other patients of the group or being eavesdropped in journey.
In addition to functional requirement, efficiency is also to weigh the key factor of cross-domain group key management system.It is big in hospital Most of patients can not use the electronic equipment (such as notebook computer or desktop computer) for possessing powerful calculating ability to add group chat.He Often lie and chatted on one's sick bed using mobile phone or tablet personal computer with other people, the calculating of these equipment and storage capacity extremely have Limit.However, most of existing group key agreement agreements (GKA) rely on the larger Bilinear map computing and mapping of computing cost To the Hash calculation of point, these need the scheme compared with intensive to be not particularly suited for electron medical treatment social intercourse system.
Key management and other safety methods (such as encrypt, sign) are of equal importance.In group communication, group key pipe Reason (GKM) has obtained relatively broad research.2010, Srinivasa et al. proposed the safe GKM side suitable for multicast network Case, it combines logical key tree construction and Chinese remainder theorem carries out conceptual design.The artificial mobile self-grouping network such as Drira is set Group key management scheme is counted, it is based on the clustering method for trusting guiding.In scheme, trust information is treated as key pipe Manage related cluster foundation.Harn and Lin propose the broadcast GKM schemes based on privacy sharing, and proof scheme is safe. However, Liu etc. proves that Harness scheme is easily internaled attack.Chen et al. is proposed based on unidirectional proxy re-encryption Group key management scheme.Nabbel et al. constructs the group key management scheme based on attribute, and it is according to group member Attribute management group key.In their scheme, only meeting the user of certain access control policy attribute could obtain Group key.Jiang et al. proposes self-healing group key management scheme, and the self-healing side with revocation and collusion resistant ability Method.Sun et al.[17]The GKM schemes of two resistance against colluders are proposed, repetition one-way function tree and the unidirectional work(of node is based respectively on Can tree.2017, Chen et al. was devised with dynamic group key managing project, and it is based on key tree construction.
Group key agreement agreement (GKA) is the core technology for generating cluster conversation key., Cheng et al. in 2013[22] The fault-tolerant GKA agreements based on binary tree structure are proposed, it supports the dynamic operation that participant adds or left.Yang etc. is artificial Mobile ad hoc network proposes the GKA schemes of broadcast enciphering (IBBE) mechanism of identity-based.In this programme, when keeper knows group During the identity of group membership, it is not necessary to which cluster conversation key can just be generated by carrying out interacting message, but it does not provide user authentication Mechanism.Later, Cheng et al. devised the certification GKA schemes based on Bilinear map.Xu et al. proposes the body based on short signature Part asymmetric GKA schemes of Hidden Authentication.Lv et al. is proposed without certificate GKA schemes., Sun et al. in 2015[27]Carried for mobile environment The certification GKA agreements that can verify that are gone out.The GKA agreements that Ranjani et al. proposes identity-based are actively and passively attacked to resist Hit, it is based on Bilinear map construction.Tan et al. proposes the identity-based GKA schemes of no Bilinear map.
The content of the invention
For in existing group key agreement scheme, being not carried out cross-domain secure group communication, can not support to be based on illness The group of matching sets up, the low problem of efficiency, the invention provides in a kind of cross-domain electron medical treatment social intercourse system based on illness Dynamic anonymity authentication group key management scheme, it proposes cross-domain group key agreement agreement, realizes based on illness matching The checking of patient's anonymous Identity, it would be preferable to support dynamic case control and management and group, efficiency are better than intra-class correlation scheme, and Possess higher security.
To achieve the above object, the present invention is realized using following technical scheme：A kind of cross-domain dynamic anonymity based on illness Authentication group key management method, it comprises the following steps：S1：Set up a key generation centre KGC；S2：KGC first checks medical treatment Whether mechanism MI has related medical qualification, is then MI generating portion keys；S3：MI is responsible for diagnosis and treatment to patient, And generate the part of key of patient；S4：Generate cluster conversation key patient safety from different medical mechanism.
The present invention also provides a kind of cross-domain dynamic anonymity authentication group key management system based on illness, and it includes key Generation center KGC, the key generation centre KGC are responsible for generating main public/private keys pair, and by all entity trusts ,=it is note Medical institutions' generating portion public/private keys pair of volume, so as to avoid key escrow；Medical institutions MI, medical institutions MI are needed To be registered to KGC；Medical institutions select secret value and generate the public information of secret value；In order to obtain part public/private keys pair, The public information of generation is submitted to KGC by MI；MI is responsible for and diagnosed the patient in its medical field, and is patient's generation Part public/private keys pair, so as to avoid key escrow；And patient PT, patient PT are registered to medical institutions, patient's selection Secret value and the public information for generating secret value, in order to obtain part public/private keys pair, PT is by the corresponding public information of secret value Submit to MI.
The present invention has advantages below compared with prior art：
(1) cross-domain certification key management and illness matching feature：In this programme, the patient from different medical domain passes through body After part certification, system can be set up using key and be based on for patient's generation cluster conversation key with identical illness, patient The safe group of illness, illness relevant information is shared by group communication.
(2) anonymity and traceability：Because the information of medical institutions and the illness information of patient are all sensitive, this hairs Medical institutions and the true identity of patient can not be recovered from anonymous Identity by clearly protecting the external world, realize medical institutions and patient Anonymity.In order to prevent medical institutions and patient from occurring malicious act, key generation centre KGC can recover medical institutions True identity, and the true identity of patient can be recovered by the medical institutions of its registration, it is achieved thereby that medical institutions and patient Traceability.
(3) security：This programme is protected using perfect forward security (perfect forward security) The privacy of information, even if attacker can instigate rebellion within enemy camp a group member, he can not also be inferred to before session key.This programme Various active attacks can also be resisted：Spoof attack, Tampering attack and Replay Attack etc..
(4) user's revocation of time control：In order to simplify user management process, this programme provides time-based user certainly Dynamic revocation mechanism.Once having crossed the term of validity of setting, the public/private keys of patient will be to that will cease to be in force automatically.
Brief description of the drawings
Fig. 1 is the system framework schematic diagram of one embodiment of the invention.
Fig. 2 is medical institute registration flow chart in one embodiment of the invention.
Fig. 3 is patient registration's flow chart.
Fig. 4 is group key agreement flow chart.
Embodiment
Explanation is further explained to the present invention with specific embodiment below in conjunction with the accompanying drawings.
For in existing group key agreement scheme, being not carried out cross-domain secure group communication, can not support based on disease The group of disease matching sets up, the low problem of efficiency, and the present invention devises dynamic based on illness in cross-domain electron medical treatment social intercourse system State anonymous authentication group key management method.It comprises the following steps：S1：Set up a key generation centre KGC；S2：KGC is first examined Look into whether medical institutions MI has related medical qualification, be then MI generating portion keys；S3：MI be responsible for the diagnosis of patient and Treatment, and generate the part of key of patient；S4：Generate cluster conversation key patient safety from different medical mechanism.
Fig. 1 is system framework of the invention.System includes the entity of three types：Key generation centre (KGC), therapeutic machine Structure (MI) and patient (PT) wherein key generation centre (KGC)：It is responsible for the main public/private keys pair of generation, and by all entity trusts. It is medical institutions' generating portion public/private keys pair of registration, so as to avoid key escrow.Medical institutions (MI)：Need Registered to KGC.Medical institutions select secret value and generate the public information of secret value.In order to obtain part public/private keys pair, MI The public information of generation can be submitted to KGC.MI is responsible for and diagnosed the patient in its medical field, and is patient's generation Part public/private keys pair, so as to avoid key escrow.Patient (PT)：Registered to medical institutions.Patient's selection secret value is simultaneously Generate the public information of secret value.In order to obtain part public/private keys pair, PT can submit to the corresponding public information of secret value MI.Key generation centre (KGC) is responsible for medical institutions (MI) in top.KGC first checks whether MI has related medical Qualification, is then MI generating portion keys.MI is in the second level of system, is responsible for diagnosis and treatment to patient, and generate trouble The part of key of person.The bottom of system is the patient with various disease and illness.Trouble from different medical mechanism (cross-domain) Person can safely generate cluster conversation key.
The present invention realizes the patient's anonymous Identity checking matched based on illness：In order to set up safe group key, institute The patient for having participation must be by anonymous authentication；The true identity of patient can not reveal to other patients；In same group All patients must have identical illness；The cleartext information on illness can not be revealed in verification process.
The present invention can support dynamic patient and management and group：System is provided is cancelled machine by the patient of time control System.According to estimated treatment time, system is that each patient distributes the term of validity of key, and its recessiveness is embedded into patient's In part of key.Once having spent effective time, the key of user will be cancelled automatically.In addition, group key management system is permitted Perhaps patient is dynamically added or left group.When group member changes, system can generate new cluster conversation key.Electron medical treatment Social intercourse system is the approach that patients provide convenience, to share Couple herbs, exchange medical information.The patient of the system can be with Diagnosed and treated by different medical institutions, system allows one group of patient from different medical field to generate cluster conversation Key, so as to set up safe group communication.System supports the anonymity and traceability of patient, and it hides the identity of patient In anonymous Identity (pseudonym), only Notified body can recover their true identity.Cross-domain group key agreement Ensure：Come from different medical mechanism and the certification patient with identical illness, safe group key can be generated.Patient The group communication of safety is set up using the key, so as to protect the patients' privacy information in electron medical treatment social intercourse system.System Dynamic management and group is also supported, when group member is changed, system can generate new cluster conversation key.
KGC sets up and comprised the following steps in S1：
S11：With security parameter κ ∈ Z+As input, the algorithm output safety parameter and the main public/private keys pair of system；
S12：Select the prime number p of κ bits, q and elliptic curve E/Fq, the elliptic curve of generation, which has, generates member P；
S13：Selection Expression set 1,2 ..., and p-1 }, calculate Ppub=xP, main system private key MSK=x, it is main Public key MPK=(P, Ppub)；
S14：Safe symmetric cryptography/decryption is selected to SEnc/SDec, with symmetric key spaceWith the Hash of collusion resistant FunctionWith
In an embodiment of the present invention, elliptic curve is defined as follows：Q is prime number, FqIt is the finite field for being characterized as prime number, E/ FqIt is FqOn elliptic curve, and be defined as E/Fq=(x, y) | y2=x3+ax+bmodq}；From FqMiddle random selection element a, b And meet △=4a3+72b2≠0modq.Elliptic curve group G includes E/FqOn point and particular point an O, O be referred to as infinity Point：G={ (x, y):x,y∈Fq,(x,y)∈E/Fq}U{O}；Add operation on group G is defined as follows：Assuming that P, Q are two on G Individual, l is the straight line for connecting two points, l and elliptic curve E/FqThirdly R' is met at, point R is symmetric points of the R' on x-axis, Scalar multiplication operation definition on then R=P+Q, G is:
In an embodiment of the present invention, S2 medical institutions register main flow schematic diagram referring to Fig. 3, and it includes following step Suddenly：
WhenWhen applying for addition system as i-th of medical institutions, it is registered to KGC first.KGC receive registration please First checked after askingWhether it is the medical institutions with related qualification.If it is not, KGC will refuse to ask.If it is, KGC andInteraction generationPublic/private keys pair.Key generation process is no certificate, it is therefore an objective to avoid key escrow.
1. secret value is set：Medical institutions(identity is) selection random numberCalculate Will, will by safe lane as secret valueIt is sent to KGC.
2. part of key is extracted：With KGC main private key MSK,IdentityAnd common valueIt is used as input, algorithm OutputAnonymous Identity and part private key.KGC selects random numberCalculateAnonymous Identity：KGC selects random numberCalculate KGC is calculatedBy safe lane part of keyIt is sent toReceiveAfterwards, medical institutions Verify equationWhether set up.If equation is set up, keyEffectively；It is on the contrary then invalid.
3. private key is set：Medical institutions As private key, and secure store.
4. public key is set：Medical institutions Disclosed as public key, and in systems.
In order in medical institutionsRegistration, patientExist firstChecked.On the basis of diagnostic result,KnowWith illness WithInteraction generationPublic/private keys pair.Key generation process Avoid key escrow.Treatment time on the estimation, the terms of validity of the KGC to client public key/private key pairSet Put, for example " 20170501-20171201 ".Exceed when the timeThe key of patient is automatically expired.
S3：MI is responsible for diagnosis and treatment to patient, and generates the part of key of patient, specifically includes following steps：
1. secret value is set：Patient(identity) selection random numberCalculateSo Afterwards As secret value, and pass through safe lane handleIt is sent to
2. part of key is extracted：WithKeyIdentityAnd public valueAs input, Algorithm is exportedAnonymous Identity and part of key.Select random numberCalculateIdentity：
·Select random numberCalculate
·CalculateBy safe lane part of keyIt is sent to
ReceivingAfterwards, patientVerify equationWhether into It is vertical.If equation is set up, keyEffectively；It is on the contrary then invalid.
3. private key is set：Patient As private key, private key is by secure store.
4. public key is set：Patient As public key, disclose in systems.
S4 group key agreements, broad flow diagram is referring to Fig. 4, and it comprises the following steps：
Assuming that patientWithThe secure group communication based on illness is wanted to set up to ensure disease discussion The security of relevant information, they are firstly the need of generation cluster conversation key.Assuming thatIt is the trouble with stronger computing capability Person, U0The computing capability of middle patient is slightly weak.The interaction of group key agreement performs as follows.
Step 1.SendTo U0,SendGive
Receive informationAfterwards,Select random numberAnd calculate
Wherein
Then, It is sent toWherein 1≤i≤n.
Step 2. is from other patientsPlace is receivedAfterwards, patientVerify equationWhether set up, wherein
If equation is set up, ensureIdentity be certified, andWithWith identical illness. Assuming that patient's collection by checking is combined into SetThenSelect random numberAnd calculate
Wherein,
Then, It is sent to
Step 3. is receivedSendAfterwards, each patientCalculateWherein
If Authi,0=Auth0,i, then ensureIdentity be certified, andWithWith identical Illness.ThenSession key
New patient adds group, comprises the following steps:
Assuming that one group of patient's set U for possessing relatively low computing capability0'={ PTn+1,...,PTmWant to add group, group Member generates new session key according to following steps.
Step 1. patientSendTo U0',WillIt is sent toReceiveAfterwards, patientSelectionAnd calculate Send it to again
Step 2. receives patientSendAfterwards,According to the side in group key agreement Method is verifiedAssuming that these patients are certified and with identical illness,Order
Then,Select random numberCalculate
Wherein
Then, It is sent to
Step 3. receives patientSendAfterwards, each patientMeter CalculateWherein
If Auth'i,0=Auth'0,i, then ensureIdentity be certified, andWithSuffer from Identical illness.Then,Session key
Patient exits group and comprised the following steps：
Assuming that one group of patient's set U for possessing relatively low computing capability0"={ PTj+1,...,PTnWant to leave, group member New session key is generated according to following method.Order
Then,Select random numberAnd calculate
Then, It is sent to
ReceiveSendAfterwards, each patientCalculate
Wherein
If Auth "i,0=Auth "0,i, thenSession key：
Above is presently preferred embodiments of the present invention, all changes made according to technical solution of the present invention, produced function is made During with scope without departing from technical solution of the present invention, protection scope of the present invention is belonged to.

Claims (10)

1. a kind of cross-domain dynamic anonymity authentication group key management method based on illness, it is characterised in that comprise the following steps：
S1：Set up a key generation centre KGC；
S2：KGC first checks whether medical institutions MI has related medical qualification, is then MI generating portion keys；
S3：MI is responsible for diagnosis and treatment to patient, and generates the part of key of patient；
S4：Generate cluster conversation key patient safety from different medical mechanism.
2. the cross-domain dynamic anonymity authentication group key management method according to claim 1 based on illness, its feature exists In：S1 comprises the following steps：
S11：With security parameter κ ∈ Z+As input, the algorithm output safety parameter and the main public/private keys pair of system；
S12：Select the prime number p of κ bits, q and elliptic curve E/Fq, the elliptic curve of generation, which has, generates member P；
S13：Select random numberWherein,Set { 1,2 ..., p-1 } is represented, open parameter P is calculatedpub=xP, system master Private key MSK=x, Your Majesty key MPK=(P, Ppub)；
S14：Safe symmetric cryptography/decryption is selected to SEnc/SDec, with symmetric key spaceWith the hash function of collusion resistantWith
S15：KGC issue common parameters (G, SEnc, SDec, H0,H1,...,H6) and Your Majesty's key MPK, main private key MSK it is secret by KGC Password protection is deposited.
3. the cross-domain dynamic anonymity authentication group key management method according to claim 2 based on illness, its feature exists In：Elliptic curve is defined as follows in S12：Q is prime number, FqIt is the finite field for being characterized as prime number, E/FqIt is FqOn elliptic curve, And it is defined as E/Fq=(x, y) | y2=x3+ax+b mod q}；From FqIt is middle to randomly choose element a, b and meet △=4a3+ 72b2≠0mod q.Elliptic curve group G includes E/FqOn point and particular point an O, O be referred to as infinite point：G={ (x, y):x, y∈Fq,(x,y)∈E/Fq}U{O}；Add operation on group G is defined as follows：Assuming that P, Q are two points on G, l is connection two The straight line of individual point, l and elliptic curve E/FqThirdly R' is met at, point R is symmetric points of the R' on x-axis, then R=P+Q, on G Scalar multiplication operation definition is:
4. the cross-domain dynamic anonymity authentication group key management method according to claim 1 based on illness, its feature exists In：S2 includes step in detail below：
S21：IfFor i-th of medical institutions, whenWhen applying for addition system as i-th of medical institutions, registered to KGC； KGC is first checked after registration request is receivedWhether it is the medical institutions with related qualification, if it is not, KGC will refuse to ask Ask, if into step S22；
S22：Medical institutionsIts identity isSelect random numberCalculate common value Will, will by safe lane as secret valueIt is sent to KGC；P is generation member；
S23：With KGC main private key MSK,IdentityAnd common valueIt is used as input, algorithm outputAnonymous body Part and part private key, KGC selection random numbersCalculateAnonymous Identity： KGC selects random numberCalculating parameterAnd parameterKGC is calculatedBy safe lane part of keyIt is sent toReceiveAfterwards, medical institutionsChecking etc. FormulaWhether set up, if equation is set up, keyEffectively；It is on the contrary then invalid；
S24：Private key is set：Medical institutions As private key, and secure store；
S25：Public key is set：Medical institutions Disclosed as public key, and in systems.
5. the cross-domain dynamic anonymity authentication group key management method according to claim 1 based on illness, its feature exists In：In order in i-th of medical institutionsRegistration, patientExist firstChecked；On the basis of diagnostic result,KnowWith illness WithInteraction generationPublic/private keys pair；Controlling on the estimation Treatment time, the terms of validity of the KGC to client public key/private key pairIt is configured, exceeds when the timeThe key of patient is certainly It is dynamic expired；WhereinFor set of disorders.
6. the cross-domain dynamic anonymity authentication group key management method according to claim 1 based on illness, its feature exists In：S3 comprises the following steps：
S31：Secret value is set：PatientIts identity isSelect random numberCalculating parameterThen As secret value, and pass through safe lane handleIt is sent to i-th of doctor Treat mechanismP is generation member；
S32：Part of key is extracted：WithKey IdentityAnd public valueIt is used as input, algorithm OutputAnonymous Identity and part of key,Select random numberCalculateAnonymous Identity： Select random numberCalculate CalculateIt is logical Safe lane is crossed part of keyIt is sent toReceivingAfterwards, patientVerify equationWhether set up, if equation is set up, keyEffectively；It is on the contrary then not into It is vertical；S33:Private key is set：Patient As private key, private key is by secure store；
S34：Public key is set：Patient As public key, disclose in systems.
7. the cross-domain dynamic anonymity authentication group key management method according to claim 1 based on illness, its feature exists In：Assuming that patientWithAssuming thatIt is the patient with stronger computing capability, U0The calculating of middle patient Ability is slightly weak；The interaction of group key agreement performs as follows：
S41:SendTo U0,SendGiveReceive informationAfterwards,Select random numberAnd calculate
<mrow> <msub> <mi>A</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>P</mi> <mo>,</mo> </mrow>
<mrow> <msub> <mi>b</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow>
Wherein
<mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>VT</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow> 2
<mrow> <msub> <mi>&amp;gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>VT</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Then, It is sent toWherein 1≤i≤n；
S42:From other patientsPlace is receivedAfterwards, patientVerify equationWhether set up, wherein
<mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>VT</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>VT</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
If equation is set up, ensureIdentity be certified, andWithWith identical illness, it is assumed that warp The patient's collection for crossing checking is combined into Set
S43：Select random numberAnd calculate
<mrow> <msub> <msup> <mi>&amp;Gamma;</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>a</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;Gamma;</mi> <mi>U</mi> </msub> <mo>=</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> <mo>&amp;Element;</mo> <mi>U</mi> </mrow> </msub> <msub> <msup> <mi>&amp;Gamma;</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>K</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;Gamma;</mi> <mi>U</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>P</mi> <mo>,</mo> </mrow>
<mrow> <mi>G</mi> <mi>S</mi> <mi>K</mi> <mo>=</mo> <msub> <mi>H</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mi>U</mi> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>K</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>Z</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;Gamma;</mi> <mi>U</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>A</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;Lambda;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow>
<mrow> <msub> <mi>Auth</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mi>U</mi> </msub> <mo>,</mo> <msub> <mi>&amp;Lambda;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>&amp;Gamma;</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>K</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
Wherein,
<mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>VT</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Then, It is sent to
S44：ReceiveSendAfterwards, each patientCalculateWherein
<mrow> <msub> <msup> <mi>&amp;Lambda;</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Lambda;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>K</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;CenterDot;</mo> <msub> <mi>Z</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>;</mo> </mrow>
If Authi,0=Auth0,i, then ensureIdentity be certified, andWithWith identical illness,Session key
8. the cross-domain dynamic anonymity authentication group key management method according to claim 7 based on illness, its feature exists In：Assuming that one group of patient's set U for possessing relatively low computing capability0'={ PTn+1,...,PTmWant to add group, group member New session key is generated according to following steps：
S51：PatientSendTo U0',WillIt is sent toReceiveAfterwards, patientSelectionAnd calculateAgain it It is sent to
S52：Receive patientSendAfterwards,Tested according to the method in group key agreement CardAssuming that these patients are certified and with identical illness,Order
S53：Select random numberCalculate
<mrow> <msub> <msup> <mi>&amp;Gamma;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <msup> <mi>a</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;Gamma;</mi> <msup> <mi>U</mi> <mo>&amp;prime;</mo> </msup> </msub> <mo>=</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> <mo>&amp;Element;</mo> <msup> <mi>U</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <msub> <msup> <mi>&amp;Gamma;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>K</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;Gamma;</mi> <msup> <mi>U</mi> <mo>&amp;prime;</mo> </msup> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>P</mi> <mo>,</mo> </mrow>
<mrow> <msup> <mi>GSK</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <msub> <mi>H</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <msup> <mi>U</mi> <mo>&amp;prime;</mo> </msup> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>K</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>Z</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;Gamma;</mi> <msup> <mi>U</mi> <mo>&amp;prime;</mo> </msup> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <mi>A</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>&amp;Lambda;</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <msup> <mi>&amp;alpha;</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>Auth</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mn>0</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <msup> <mi>U</mi> <mo>&amp;prime;</mo> </msup> </msub> <mo>,</mo> <msub> <mi>&amp;Lambda;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>&amp;Gamma;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>K</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
Wherein
<mrow> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>VT</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
Then, It is sent to
S54：Receive patientSendAfterwards, each patientCalculateWherein
<mrow> <msub> <msup> <mi>&amp;Lambda;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <msup> <mi>&amp;Lambda;</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>K</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;CenterDot;</mo> <msub> <msup> <mi>Z</mi> <mo>&amp;prime;</mo> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> </mrow>
If Auth'i,0=Auth'0,i, then ensureIdentity be certified, andWithWith identical Illness
S55：Session key
9. the cross-domain dynamic anonymity authentication group key management method according to claim 7 based on illness, its feature exists In：Assuming that one group of patient's set U for possessing relatively low computing capability0"={ PTj+1,...,PTnWant to leave, group member according to Following method generates new session key：
S61：Order
S62：Select random numberAnd calculate：
<mrow> <msub> <msup> <mi>&amp;Gamma;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <msup> <mi>a</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <mi>&amp;Gamma;</mi> <msup> <mi>U</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </msub> <mo>=</mo> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> <mo>&amp;Element;</mo> <mi>U</mi> </mrow> </msub> <msub> <msup> <mi>&amp;Gamma;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>K</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;Gamma;</mi> <msup> <mi>U</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <mi>P</mi> <mo>,</mo> </mrow>
<mrow> <msup> <mi>GSK</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <msub> <mi>H</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <msup> <mi>U</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>K</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>Z</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;Gamma;</mi> <msup> <mi>U</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </msub> <mo>)</mo> </mrow> <mo>&amp;CenterDot;</mo> <msub> <msup> <mi>A</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>&amp;Lambda;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <msup> <mi>&amp;alpha;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mo>&amp;lsqb;</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;beta;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>P</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <msub> <mi>P</mi> <mrow> <mi>p</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>MI</mi> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>R</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>Auth</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <mn>0</mn> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <msup> <mi>U</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </msub> <mo>,</mo> <msub> <mi>&amp;Lambda;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>&amp;Gamma;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>K</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
S63： It is sent toReceiveSendAfterwards, each patientCalculate
<mrow> <msub> <msup> <mi>Auth</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <mi>i</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>H</mi> <mn>6</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <msup> <mi>U</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </msub> <mo>,</mo> <msub> <mi>&amp;Lambda;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>&amp;Lambda;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>K</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
Wherein
<mrow> <msub> <msup> <mi>&amp;Lambda;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msub> <msup> <mi>&amp;Lambda;</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> </mrow>
<mrow> <msub> <msup> <mi>K</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>&amp;alpha;</mi> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>&amp;CenterDot;</mo> <msub> <msup> <mi>Z</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> </mrow>
If Auth "i,0=Auth "0,i, thenSession key：
<mrow> <msup> <mi>GSK</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mo>=</mo> <msub> <mi>H</mi> <mn>5</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>PID</mi> <msup> <mi>U</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> </msub> <mo>,</mo> <msub> <mi>PID</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>SP</mi> <mrow> <msub> <mi>PT</mi> <mrow> <mi>&amp;rho;</mi> <mi>i</mi> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>,</mo> <msub> <msup> <mi>K</mi> <mrow> <mo>&amp;prime;</mo> <mo>&amp;prime;</mo> </mrow> </msup> <mrow> <msub> <mi>PT</mi> <mrow> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>&amp;theta;</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </msub> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
10. a kind of described cross-domain dynamic anonymity authentication group key management system based on illness, it is characterised in that：Including
Key generation centre KGC, the key generation centre KGC is responsible for generating main public/private keys pair, and is believed by all entities Appoint ,=it is the medical institutions' generating portion public/private keys pair registered, so as to avoid key escrow；
Medical institutions MI, medical institutions MI needs to register to KGC；Medical institutions select secret value and generate the open letter of secret value Breath；In order to obtain part public/private keys pair, the public information of generation is submitted to KGC by MI；MI is responsible for and diagnosed in its doctor Patient in treatment field, and be patient's generating portion public/private keys pair, so as to avoid key escrow；
And patient PT, patient PT are registered to medical institutions, patient's selection secret value and the public information for generating secret value, in order to Part public/private keys pair are obtained, the corresponding public information of secret value is submitted to MI by PT.
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