CN105245331B - Two side's quantum key agreement protocols based on four particle GHZ states - Google Patents
Two side's quantum key agreement protocols based on four particle GHZ states Download PDFInfo
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Abstract
The invention discloses a kind of two side's quantum key agreement protocols based on four particle GHZ states：Step 1：Alice and Bob generates respective classic key and consults function at random；Step 2：The GHZ and sub-sequence of n four particles of Alice selections, will inveigle three sequences of photon radom insertion to be sent to Bob；Step 3：Photon is inveigled in Bob measurements；Alice calculates error rate；Step 4：The corresponding particles of three every to sequence number identical in sequence of Alice perform CNOT operation twice；Step 5：Alice performs unitary transformation and obtains new sequence, selects and inveigles photon insetion sequence to be sent to Bob；Step 6：Photon is inveigled in Bob measurements；Alice compares measurement result and calculates error rate；Error rate is low to perform step 7；Otherwise return to step 2；Step 7：Alice generates shared key；Step 8：Bob generates shared key.The present invention can resist existing participant's attack and external attack.Meanwhile quantum bit efficiency far is higher than existing protocol.
Description
Technical field
The invention belongs to quantum communications field, and in particular to a kind of quantum key consults (Quantum key
Agreement) agreement, particularly a kind of two side's quantum key agreement protocols based on four particle GHZ states.
Background technology
Quantum cryptography is the new technology of communication and network security, and its security is ensured by fundamental principles of quantum mechanics
's.It is the difference for calculating safety mostly with conventional cipher, quantum cryptography can realize unconditional security, thus attract a large amount of passes
Note.Quantum key consults the new important branch that (QKA) agreement is quantum cryptography, and it allows participant to pass through disclosed amount
Subchannel consults a classical shared secret key, and the contribution of each participant is identical, any one participant
Or the subset that forms of participant all can not be independent the determination shared key.Consult the foundation of (QKA) agreement using quantum key
The AES of shared secret key and one-time pad, communicating pair can realize the secret communication of unconditional security.
Existing most of quantum key agreement protocols are to be based on single-particle or Bell state, the key based on multiparticle Entangled State
Agreement cans be counted on one's fingers, and they or the external attacks such as special Roy's wooden horse can not be resisted, be unsafe, or quantum bit
Rate is too low.
D.S.Shen, W.P.Ma and L.L.Wang are in paper " Two-party quantum key agreement
with four-qubit cluster states”(Quantum Inf.Process.2014:Four are utilized in 2313-2324)
The Cluster State of son proposes both sides' QKA agreement, and this agreement has the sub- bit efficiency of higher amount.Agreement comprises the concrete steps that：
The Cluster State of some four particles of each self-generating of first, communicating pair A and B.Communication party A (communication party B) is by by Cluster State
The sequence insertion that three (first) particles are formed issues communication party B (communication party A), and reservation and its particle sequence after inveigling photon
Row.Second, after communicating pair receives corresponding particle sequence, eavesdropping monitoring is performed together.3rd, communicating pair just each receives
Particle sequence perform the unitary transformation of oneself.It is inserted into after trick photon and it is mutually issued into other side.4th, communicating pair is received
To after corresponding particle sequence, eavesdropping monitoring is performed together.5th, communication party A (communication party B) are to by first in Cluster State
The sequence that (the 3rd) particle is formed performs respective unitary transformation.Then both sides perform the survey of cluster base to respective Cluster State
Amount, both sides can obtain identical measurement result.Shared privacy key can be obtained according to the correspondence of coding and measurement result.Should
It is in place of agreement Shortcomings：Because the agreement is a Ping-Pong agreement, i.e., same particle is passed in quantum channel
Defeated one back and forth, therefore the agreement can not resist invisible photon eavesdropping (IPE) Trojan attack and delay photon Trojan attack.
W.Huang, Q.Su, X.Wu, Y.B.Li and Y.Sun are in paper " Quantum key agreement
against collective decoherence”(Int.J.Theor.Phys.2014:Four particles are utilized in 2891-2901)
DF states propose both sides' QKA agreements that joint noise is immunized in an energy.Agreement comprises the concrete steps that：First, communication party A are generated
Two random bit strings, a personal contribution string as shared key, the control string of an alternatively measurement base.Second,
Communication party A prepares the sequence of the DF states of four particles according to the control string of personal contribution string and selection measurement base, and inserts and lure
Communication party B is issued after deceiving photon.3rd, after communication party B receives the sequence of DF states of four particles, both sides perform eavesdropping prison jointly
Survey.If by detection, communication party B announces the personal contribution string of his shared key.4th, communication party A are according to oneself and communication
Square B personal contribution string, the shared secret key of both sides can be calculated.5th, communication party A disclose the control of his selection measurement base
System string.Using this control string, communication party B can measure all DF states, the shared close of communication party A can be obtained according to measurement result
The personal contribution string of key.Therefore, communication party B can also calculate the shared secret key of both sides.It is in place of the agreement Shortcomings：
The quantum bit efficiency of the agreement is too low, and its quantum bit efficiency is only 10%.
The content of the invention
For defect present in above-mentioned prior art or deficiency, it is an object of the present invention to provide one kind to be based on four
Two side's quantum keys of sub- GHZ states are consulted.
In order to realize above-mentioned task, the present invention, which adopts the following technical scheme that, to be solved：
A kind of two side's quantum key agreement protocols based on four particle GHZ states, specifically comprise the following steps：
Step 1：Alice and Bob generates the classic key K of respective 2n bits at randomAAnd KB：And consult with minor function：
Step 2：Alice at random from set | G1>abcd,|G2>abcd,|G3>abcd,|G4>abcdIn selection n four particles
GHZ, and the GHZ of this n four particles all particles are divided into four orderly sequence Sa,Sb,ScAnd Sd, wherein sequence Sa,Sb,
ScAnd SdIt is made up of respectively the particle a, b, c and d in each GHZ states；Alice from set | 0>,|1>,|+>,|->In select at random
Go out 3m trick photon, and photon radom insertion sequence S is inveigled by this 3mb,ScAnd Sd, and insert m in each sequence and lure
Photon is deceived, respectively obtains new sequence S 'b,S'cAnd S'd；Alice is by sequence S 'b,S'cAnd S'dBob is sent to, oneself retains sequence
Arrange Sa；N, m are the positive integer more than 1；
Step 3：When Bob receives sequence S 'b,S'cAnd S'dAfterwards, Alice is informed by classical authenticated channel；Alice passes through
Classical authenticated channel, which is announced, inveigles photon in sequence S 'b,S'cAnd S'dIn position and corresponding measurement base | 0>,|1>Or |+
>,|->}；Bob is gone to measure corresponding trick photon with correct measurement base, and measurement result is told by classical authenticated channel
Alice；Alice compares measurement result and inveigles the original state of photon, and calculates error rate；If error rate is less than setting
Gate value is limited, then performs step 4；Otherwise, return to step 2；
Step 4：Alice is to sequence Sb,ScAnd SdThe corresponding particle of middle every three of sequence number identical performs CNOT operation twice；
Then, Bob is to sequence ScAnd SdMiddle sequence number identical each two particle c, d are performedBase measures；According to measurement result, Bob
Learn sequence SaAnd SbIn corresponding particle a, which Bell state b be collapsed to；At the beginning of the n GHZ state that Alice selects according to oneself
Primary state, it may be determined that the state that particle a and b are collapsed to, and the state that particle c and d are collapsed to；
Step 5：Alice is according to classic key KATo sequence SaIn the individual particles of i-th (i=1,2 ..., n) perform unitary and become
ChangeObtain new sequenceAnd unitary transformationSubscript i1And i2It is equal to successivelyDibit
Value；Then, Alice is to sequencePerform an in-place computation Πn, obtain the sequence of a randomizationThen, Alice from
Set | 0>,|1>,|+>,|->In select at random m trick photon, and by this m trick photon radom insertion sequence
To new sequenceBy sequenceIt is sent to Bob；
Step 6：When Bob receives this sequenceAfterwards, Alice is informed by classical authenticated channel；Alice is recognized by classics
Demonstrate,prove channel and announce trick photon in sequenceIn position and corresponding measurement base | 0>,|1>Or |+>,|->}；Bob is with just
True measurement base goes to measure corresponding trick photon, and tells measurement result to Alice by classical authenticated channel；Alice ratios
Compared with measurement result and the original state of trick photon, and calculate error rate；If error rate performs less than the limit gate value of setting
Step 7；Otherwise, return to step 2；
Step 7：The sequence S that Bob will be obtained in step 4cAnd SdIn all two particle c of sequence number identical, d'sBase
Measurement result changes into 2n classical bits using following formula：
|00>→00,|01>→01,|10>→10,|11>→11；
And by this 2n classical bits and key KBXOR is carried out, computing knot is then announced by classical authenticated channel
Fruit；
Alice is according to the sequence S obtained in step 4cAnd SdIn corresponding two particle c, d'sBase measurement result
Calculate Bob key KB；And according to key KAAnd KB, the shared key of Alice calculating both sides：K=H (KA,KB)。
Step 8：Alice announces the in-place computation Π that step 5 usesn；Bob is to sequenceCorresponding inverse permutation is performed to obtain
Original seriesThen, Bob is successively to sequenceAnd SbMiddle two particles of sequence number identical perform Bell measurements；According to measurement
As a result and corresponding initial Bell state, Bob calculate KA, so as to generate shared key：K=H (KA,KB)。
Further, in the step 1,
Further, in the step 2,
Further, in the step 4, to sequence Sb,ScAnd SdThe corresponding particle of middle every three of sequence number identical performs twice
CNOT operation is specifically to be handled according to formula (5)-(8)；
Further, in the step 4
Further, in the step 5, the unitary transformation is U00,U01,U10And U11, U00=I=| 0><0|+|1><1
|, U01=X=| 0><1|+|1><0 |, U10=Z=| 0><0|-|1><1 | and U11=iY=| 0><1|-|1><0|；{|0>,|1>}
Z bases are formd, |+>,|->X bases are formd, wherein,
Further, in the step 3 and step 6, limit gate value takes 0.1~0.2.
Beneficial effects of the present invention：
Two side's quantum key agreement protocols based on four particle GHZ states of the present invention can ensure that communicating pair is liberally established
Shared classic key between them, using the AES of the classical privacy key and one-time pad, communicating pair can
To realize the secret communication of unconditional security.Obviously existing participant's attack and external attack can be resisted.Simultaneously as should
Each particle in agreement is only transmitted once, therefore attacker can not be successfully executed Trojan horse attack.By dividing
Analysis finds that the agreement is not only safe in noiseless quantum channel, and it is also safety on quantum noise channel.Separately
Outside, the quantum bit efficiency far of agreement of the invention is higher than existing protocol.
Embodiment
1st, pre-knowledge
First, four unitary transformation U are introduced00,U01,U10And U11, i.e. U00=I=| 0><0|+|1><1 |, U01=X=| 0>
<1|+|1><0 |, U10=Z=| 0><0|-|1><1 | and U11=iY=| 0><1|-|1><0|.Also, | 0>,|1>Form Z
Base, |+>,|->X bases are formd, wherein,Four Bell state definition
It is as follows：
They form one group of complete orthogonal basis in four-dimensional Hilbert spaces.When a unitary transformationPerform when on first particle of a Bell state, this Bell state is converted into another
Bell state.Relation between four Bell states and four unitary transformations is as follows：
The GHZ states of four four particles as follows use in the agreement of the present invention as quantum information source, i.e.,
When we are using particle b as control quantum bit, particle c and d is as target quantum bit, respectively to aforementioned four
After the GHZ states of four particles perform CNOT operation twice, system changes as follows respectively：
Obviously, understand after performing CNOT operation twice that the GHZ states of each above-mentioned four particle can collapse according to expression formula
It is reduced to the quantum state of two independent two particles not tangled.
2nd, two side's quantum key agreement protocols of the invention
Two side's quantum key agreement protocols based on four particle GHZ states of the present invention, specifically comprise the following steps：
Step 1：Alice and Bob generates the classic key of respective 2n bits according to following formula at random：
Wherein
And consult with minor function：
Step 2：Alice at random from set | G1>abcd,|G2>abcd,|G3>abcd, | G4>abcdIn selection n four particles
GHZ, and the GHZ of this n four particles all particles are divided into four orderly sequence Sa,Sb,ScAnd Sd, wherein sequence Sa,Sb,
ScAnd SdIt is made up of respectively the particle a, b, c and d in each GHZ states；Alice from set | 0>,|1>,|+>,|->In select at random
Go out 3m trick photon, and photon radom insertion sequence S is inveigled by this 3mb,ScAnd Sd, and ensure to insert in each sequence
M trick photon, respectively obtains new sequence S 'b,S'cAnd S'd；Alice is by sequence S 'b,S'cAnd S'dBob is sent to, from
Oneself retains sequence Sa；N, m are the positive integer more than 1；
Step 3：When Bob receives sequence S 'b,S'cAnd S'dAfterwards, Alice is informed by classical authenticated channel；Alice passes through
Classical authenticated channel, which is announced, inveigles photon in sequence S 'b,S'cAnd S'dIn position and corresponding measurement base | 0>,|1>Or |+
>,|->}；Bob is gone to measure corresponding trick photon with correct measurement base, and measurement result is told by classical authenticated channel
Alice；Alice compares measurement result and inveigles the original state of photon, and calculates error rate；If error rate is less than setting
Gate value is limited, then performs step 4；Otherwise, return to step 2；
Step 4：Alice is to sequence Sb,ScAnd SdMiddle every three particles of sequence number identical perform CNOT operation twice；Then,
Bob is to sequence ScAnd SdMiddle sequence number identical each two particle c, d are performedBase measures；According to measurement result and formula (5)-
(8), Bob learns sequence SaAnd SbIn corresponding particle a, which Bell state b be collapsed to；The n GHZ that Alice selects according to oneself
The initial state of state, it may be determined that the state that particle a and b are collapsed to, and the state that particle c and d are collapsed to；
It is above-mentioned to sequence Sb,ScAnd SdMiddle every three particles of sequence number identical perform CNOT operation twice and specifically referred to：According to
Formula (5)-(8) are handled, i.e., with SbIn particle b as control quantum bit, sequence ScAnd SdIn particle c, d conduct
Target quantum bit, perform CNOT operation twice；
It is above-mentioned
Step 5：Alice is according to classic key KATo sequence SaIn the individual particles of i-th (i=1,2 ..., n) perform unitary and become
ChangeObtain new sequenceAnd unitary transformationSubscript i1And i2It is equal to successivelyDibit
Value；Then, Alice is to sequencePerform an in-place computation Πn(in-place computation refers to that position rearrangement reaction arranges), obtain one at random
The sequence of changeThen, Alice from set | 0>,|1>,|+>,|->In select m trick photon at random, and by this m
Inveigle photon radom insertion sequenceObtain new sequenceBy sequenceIt is sent to Bob；
In the present invention, four unitary transformation U00,U01,U10And U11, i.e. U00=I=| 0><0|+|1><1 |, U01=X=| 0>
<1|+|1><0 |, U10=Z=| 0><0|-|1><1 | and U11=iY=| 0><1|-|1><0|.Also, | 0>,|1>Form Z
Base, |+>,|->X bases are formd, wherein,
Step 6：When Bob receives this sequenceAfterwards, Alice is informed by classical authenticated channel；Alice is recognized by classics
Demonstrate,prove channel and announce trick photon in sequenceIn position and corresponding measurement base | 0>,|1>Or |+>,|->}；Bob is with just
True measurement base goes to measure corresponding trick photon, and tells measurement result to Alice by classical authenticated channel；Alice ratios
Compared with measurement result and the original state of trick photon, and calculate error rate；If error rate performs less than the limit gate value of setting
Step 7；Otherwise, return to step 2；
In step 3 and step 6, limit gate value takes 0.1~0.2.
Step 7：The sequence S that Bob will be obtained in step 4cAnd SdIn all two particle c of sequence number identical, d'sBase
Measurement result changes into 2n classical bits using following formula：
|00>→00,|01>→01,|10>→10,|11>→11；
And by this 2n classical bits and key KBXOR is carried out, computing knot is then announced by classical authenticated channel
Fruit；
Alice is according to the sequence S obtained in step 4cAnd SdIn corresponding two particle c, d'sBase measurement result
Calculate Bob key KB；And according to key KAAnd KB, the shared key of Alice calculating both sides：K=H (KA,KB)。
Step 8：Alice announces the in-place computation Π that step 5 usesn；Bob is to sequenceCorresponding inverse permutation is performed to obtain
Original seriesThen, Bob is successively to sequenceAnd SbThe corresponding particle of two of middle sequence number identical performs Bell measurements；
According to measurement result and corresponding initial Bell state, Bob calculates KA, so as to generate shared key：K=H (KA,KB)。
4 securities and efficiency analysis
The QKA agreements of one safety can not only resist external attack, and can resist participant's attack.
4.1 participants attack
Below, we will illustrate that a dishonest participant can not possibly obtain this shared key alone.Since
Alice just obtains Bob key K after the message quantum bit after coding is issued Bob by herB, therefore, Alice can not root
Her privacy key K is adjusted according to the hope of oneselfA.If Alice wants to change sequence in the 7th stepCoordinate, his repaiies
The entanglement transfer of particle will be caused so that Bob measurement result is no longer controlled by Alice by changing.As a result, Alice and Bob will
Generate different shared keys.That is, Alice oneself can not control this shared key alone.On the other hand, delay is surveyed
Amount technology ensure that Bob can not know sequence before the result after he selects cloth XORActual order.Therefore Bob
Can not be according to Alice key KATo change his key KB.So Alice and Bob all can not successful execution participant attack
Hit.
4.2 external attack
Assuming that Eve is a listener-in for wanting to steal shared key, the possible way that she attacks has：Trojan Horse is attacked
Hit, measurement-multi-sending attack, intercepting and capturing-multi-sending attack and tangle-measure attack.
Trojan horse attack：In this agreement, because each photon in quantum channel is only transmitted once, therefore
Eve can not successfully perform invisible photon eavesdropping (IPE) Trojan attack and delay photon Trojan attack.
Measurement-multi-sending attack：Eve can be respectively to sequence S 'b,S'c, S'dAndIn particle perform measurement-repeating transmission
Attack.However, Eve measurement will influence sequence S 'b,S'c, S'dAndIn trick particle state.In second step and
In the eavesdropping detection of 5th step, Alice and Bob can be with 1- (3/4)m(m represents to be used for the number for the trick particle for detecting this attack
Amount) probability find Eve attack.
Intercepting and capturing-multi-sending attack：If Eve performs intercepting and capturing-multi-sending attack, she intercepts and captures sequence S ' firstb,S'c, S'dOrSo
Her forgery sequence is sent afterwards to Bob.After agreement terminates, she performs corresponding measurement to the particle in this four sequences again.
However, the sequence that Eve is forged can neither can not pass through second of safety monitoring by first time safety monitoring.When m trick
When particle be used to monitor this eavesdropping attack, the eavesdropping verification and measurement ratio of safety monitoring twice is 1- (1/2m).Therefore, Eve
Intercepting and capturing-multi-sending attack also have failed.
Tangle-measure attack：Eve can also be gone to tangle this transmission particle (sequence with oneself pre-prepd auxiliary particle
Arrange S 'b,S'c, S'dOrIn particle), then will transmission particle issue Bob again.After agreement terminates, she measures accordingly again
Auxiliary particle, so as to extract on key KAUseful information.However, Eve is not aware that trick photon before eavesdropping detects
Position, she tangle operation U certainly can also be performed to inveigle photon on.Also, state is inveigled to become following two particle
Entangled State：
U(|0>|E>)=a | 0>|e00>+b|1>|e01>,
U(|1>|E>)=c | 0>|e10>+d|1>|e11>,
Wherein | e00>, | e01>, | e10>With | e11>It is the pure state uniquely determined by unitary transformation U, and | a |2+|b|2=
1, | c |2+|d|2=1.Obviously, CNOT conversion is unitary transformation U special circumstances.If Eve wants to lead in second step or the 5th step
Eavesdropping detection is crossed, Eve unitary transformation U must is fulfilled for condition b=c=0 and a | e00>=d | e11>.As equation a | e00>=d | e11
>During establishment, Eve cannot distinguish between auxiliary photon a | e00>And d | e11>, so as to which Eve can not obtain key K by observing auxiliary photonA
Useful information.If however, a | e00>≠d|e11>, Eve attack will disturb trick state |+>With |->.Therefore, Eve
Attack will be found by Alice and Bob.Each the eavesdropping verification and measurement ratio of trick photon is：
4.3 quantum noise channels
In quantum noise channel, quantum bit error rate (QBER) τ introduced by noise span approximation exists
2%-8.9%, it depends on the situation such as distance factor of channel.If the quantum bit error rate that Eve attack introduces is small
In τ, then she can just hide her attack with noise.According to above-mentioned safety analysis, each inveigled in this agreement
The eavesdropping verification and measurement ratio of photon is at least 25%, and it is much larger than τ.Therefore, the suitable eavesdropping test limit gate value of selection can ensure that this
Agreement is also safety on quantum noise channel.
According to above-mentioned analysis, this agreement is all safe on noiseless quantum channel and quantum noise channel.
5 efficiency analysis
For a QKA agreement, Cabello quantum bit efficiency is defined as：Wherein c represents what is consulted
The quantity of classical bit, the quantity for the quantum bit used in q presentation protocols.Therefore, our the quantum bit efficiency of agreement are：The quantity of four particle GHZ states wherein in n presentation protocols, m represent to inveigle photon in each quantum sequence of transmission
Quantity.Make m=n, Wo Menyou
Claims (4)
1. a kind of two side's quantum key agreement methods based on four particle GHZ states, it is characterised in that specifically comprise the following steps：
Step 1：Alice and Bob generates the classic key K of respective 2n bits at randomAAnd KB：And consult with minor function：Wherein,
Step 2：Alice at random from set | G1>abcd,|G2>abcd,|G3>abcd,|G4>abcdIn selection n four particles GHZ,
And the GHZ of this n four particles all particles are divided into four orderly sequence Sa,Sb,ScAnd Sd, wherein sequence Sa,Sb,ScWith
SdIt is made up of respectively the particle a, b, c and d in each GHZ states；Alice from set | 0>,|1>,|+>,|->In select at random
3m trick photon, and inveigle photon radom insertion sequence S by this 3mb,ScAnd Sd, and m trick of insertion in each sequence
Photon, respectively obtain new sequence S 'b,S′cWith S 'd；Alice is by sequence S 'b,S′cWith S 'dBob is sent to, oneself retains sequence
Sa；N, m are the positive integer more than 1；
Step 3：When Bob receives sequence S 'b,S′cWith S 'dAfterwards, Alice is informed by classical authenticated channel；Alice passes through classics
Authenticated channel, which is announced, inveigles photon in sequence S 'b,S′cWith S 'dIn position and corresponding measurement base | 0>,|1>Or |+>,|-
>}；Bob is gone to measure corresponding trick photon with correct measurement base, and measurement result is told by classical authenticated channel
Alice；Alice compares measurement result and inveigles the original state of photon, and calculates error rate；If error rate is less than setting
Gate value is limited, then performs step 4；Otherwise, return to step 2；
Step 4：Alice is to sequence Sb,ScAnd SdThe corresponding particle of middle every three of sequence number identical performs CNOT twice and grasped
Make；Then, Bob is to sequence ScAnd SdMiddle sequence number identical each two particle c, d are performedBase measures,According to measurement result, Bob learns sequence SaAnd SbIn corresponding particle a, b is collapsed to
Which Bell state；The initial state for the n GHZ state that Alice selects according to oneself, it may be determined that the state that particle a and b are collapsed to,
And the state that particle c and d are collapsed to；
Step 5：Alice is according to classic key KATo sequence SaIn i-th of particle perform unitary transformationObtain new sequenceAnd unitary transformationSubscript i1And i2It is equal to successivelyTwo bit value, i=1,2 ..., n；Then, Alice is to sequencePerform an in-place computation Πn, obtain the sequence of a randomizationThen, Alice from set | 0>,|1>,|+>,|-
>In select at random m trick photon, and by this m trick photon radom insertion sequenceObtain new sequenceBy sequenceIt is sent to Bob；
Step 6：When Bob receives this sequenceAfterwards, Alice is informed by classical authenticated channel；Alice passes through classical authenticated channel
Announce and inveigle photon in sequenceIn position and corresponding measurement base | 0>,|1>Or |+>,|->}；Bob correctly surveys
Amount base goes to measure corresponding trick photon, and tells measurement result to Alice by classical authenticated channel；Alice compares measurement
As a result with the original state of inveigling photon, and error rate is calculated；If error rate performs step 7 less than the limit gate value of setting；
Otherwise, return to step 2；
Step 7：The sequence S that Bob will be obtained in step 4cAnd SdIn all two particle c of sequence number identical, d'sBase measures
As a result 2n classical bits are changed into using following formula：
|00>→00,|01>→01,|10>→10,|11>→11；
And by this 2n classical bits and key KBXOR is carried out, operation result is then announced by classical authenticated channel；
Alice is according to the sequence S obtained in step 4cAnd SdIn corresponding two particle c, d'sBase measurement result calculates
Bob key KB；And according to key KAAnd KB, the shared key of Alice calculating both sides：K=H (KA,KB)；
Step 8：Alice announces the in-place computation Π that step 5 usesn；Bob is to sequencePerform corresponding inverse permutation obtain it is original
SequenceThen, Bob is successively to sequenceAnd SbMiddle two particles of sequence number identical perform Bell measurements；According to measurement result
With corresponding initial Bell state, Bob calculates KA, so as to generate shared key：K=H (KA,KB)。
2. two side's quantum key agreement methods as claimed in claim 1 based on four particle GHZ states, it is characterised in that described
In step 4, to sequence Sb,ScAnd SdIt is specifically according to public affairs that the corresponding particle of middle every three of sequence number identical, which performs CNOT operation twice,
Formula (5)-(8) are handled；
3. two side's quantum key agreement methods as claimed in claim 1 based on four particle GHZ states, it is characterised in that described
In step 5, the unitary transformation is U00,U01,U10And U11, U00=I=| 0><0|+|1><1 |, U01=X=| 0><1|+|1><0
|, U10=Z=| 0><0|-|1><1 | and U11=iY=| 0><1|-|1><0|；{|0>,|1>Z bases are formd, |+>,|->Shape
Into X bases, wherein,
4. two side's quantum key agreement methods as claimed in claim 1 based on four particle GHZ states, it is characterised in that described
In step 3 and step 6, limit gate value takes 0.1~0.2.
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| CN106712936B (en) * | 2016-12-20 | 2019-07-16 | 中国电子科技集团公司第三十研究所 | Multi-party quantum key agreement protocol based on ring structures |
| CN106685654B (en) * | 2017-01-12 | 2020-10-27 | 成都信息工程大学 | Quantum key distribution method with bidirectional identity authentication |
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| CN108768623B (en) * | 2018-04-11 | 2020-07-28 | 西北大学 | Quantum invisible communication method for transmitting 4 particle states based on 5 particle Brown state |
| CN108809644B (en) * | 2018-07-17 | 2020-11-06 | 苏州大学 | Disorder high-capacity multiparty quantum key negotiation method based on high-energy level bell state |
| CN109150521B (en) * | 2018-10-22 | 2021-02-02 | 苏州大学 | Probability remote real coefficient quantum state preparation method based on unknown parameter GHZ channel |
| CN110098930B (en) * | 2019-05-27 | 2020-04-07 | 成都信息工程大学 | Bell state-based two-party quantum key negotiation method and system |
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