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CN110932848B - Multi-party quantum key agreement method based on non-maximally entangled Bell states with known parameters - Google Patents

Multi-party quantum key agreement method based on non-maximally entangled Bell states with known parameters Download PDF

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CN110932848B
CN110932848B CN201911182080.6A CN201911182080A CN110932848B CN 110932848 B CN110932848 B CN 110932848B CN 201911182080 A CN201911182080 A CN 201911182080A CN 110932848 B CN110932848 B CN 110932848B
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李太超
姜敏
李华阳
周刘蕾
陈虹
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Suzhou 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
    • H04L9/0852—Quantum cryptography
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/70—Photonic quantum communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/80—Optical aspects relating to the use of optical transmission for specific applications, not provided for in groups H04B10/03 - H04B10/70, e.g. optical power feeding or optical transmission through water
    • H04B10/85—Protection from unauthorised access, e.g. eavesdrop protection
    • 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
    • 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
    • H04L9/0852—Quantum cryptography
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Abstract

本发明公开了一种基于参数已知的非最大纠缠Bell态的多方量子密钥协商方法。本发明一种基于参数已知的非最大纠缠Bell态的多方量子密钥协商方法，包括：整个方案中包含m个参与者，并且网络中心服务器要确保每个参与者都已经通过量子身份安全认证。本发明的有益效果：1、本发明是首次使用参数已知的非最大纠缠Bell态进行多方密钥协商方法，很大程度上提高了密钥协商的安全性，提高了粒子的利用效率。2、本发明只涉及单粒子测量，参与协商的用户不需要实施复杂的多比特态测量，降低了用户端的测量难度和设备需求，使得本方法更易实现。

Figure 201911182080

The invention discloses a multi-party quantum key negotiation method based on a non-maximally entangled Bell state with known parameters. The present invention is a multi-party quantum key agreement method based on non-maximally entangled Bell state with known parameters, including: the whole scheme includes m participants, and the network center server must ensure that each participant has passed the quantum identity security authentication . Beneficial effects of the present invention: 1. The present invention is the first to use the non-maximally entangled Bell state with known parameters for multi-party key negotiation method, which greatly improves the security of key negotiation and improves the utilization efficiency of particles. 2. The present invention only involves single particle measurement, and users participating in the negotiation do not need to perform complex multi-bit state measurement, which reduces the measurement difficulty and equipment requirements at the user end, and makes the method easier to implement.

Figure 201911182080

Description

Multi-party quantum key negotiation method based on non-maximum entanglement Bell state with known parameters
Technical Field
The invention relates to the field of quantum secret communication, in particular to a parameter-known non-maximum entangled Bell state-based multi-party quantum key negotiation method.
Background
Quantum cryptography is a novel interdisciplinary, mainly utilizes the basic principle of quantum mechanics to establish a novel cryptosystem, and theoretically ensures unconditional security. At present, quantum cryptography generally uses a quantum state as an information carrier for two communication parties, and utilizes the quantum mechanics principle to establish a shared key between the two communication parties through quantum channel transmission, which is called quantum key distribution. The safety is ensured by the uncertainty relation in quantum mechanics and quantum cloning theorem. At present, quantum key distribution is one of the most promising technologies in quantum information technology, and with the development of quantum technology, information transmission can be realized in an optical fiber channel or a space channel of several kilometers. Many schemes have been proposed for various cryptographic tasks, including quantum key distribution [1-2], Quantum Signatures (QS), quantum secret sharing (QSs) [3-4], Quantum Secure Direct Communication (QSDC) [5], Quantum Bit Commitment (QBC), quantum absence transfer (QOT), and the like.
Quantum Key Agreement (QKA) [6-8] is an important branch of Quantum cryptography and Quantum information technology, which is different from traditional Quantum Key distribution, where one participant distributes a predetermined Key to other participants, and QKA allows participants to share secret Key Agreement via a traditional public Quantum channel. Furthermore, each participant in the QKA also facilitates the generation of a shared key that cannot be completely determined by any one of the participants. Since the traditional undecipherable classical password is not undecipherable under the development of quantum information technology, the research of the password technology in the field of quantum information has been greatly developed, and a plurality of quantum secret sharing methods such as multi-party quantum secret sharing, quantum secret sharing based on the Chinese remainder theorem, high-efficiency multi-party quantum secret sharing and the like are presented. The method makes up the defects of the classical field and greatly improves the safety and reliability of communication.
The traditional technology has the following technical problems:
although several QKA schemes based on Bell regime have been proposed in recent years [9-10], it is still believed that these schemes can be further improved in terms of efficiency, quantum and classical resource consumption. In a practical environment, due to decoherence and the presence of noise, a channel is easy to evolve into a non-maximally entangled state. Common solutions to this problem are therefore quantum distillation [11] and local filtering [12 ]. But such operation inevitably increases the operational complexity. To date, many quantum communication schemes have been proposed that directly use non-maximally entangled states, such as probabilistic quantum stealth states [13], secure quantum dialogues [14], probabilistic remote state preparation [15-16], quantum state sharing [17], and the like.
[1]Bennett,C.H.,Brassard,G.:Quantum cryptography:public key distribution and coin tossing.In:Proceedings of IEEE International Conference on Computers,Systems,and Signal Processing,Bangalore,India,pp.175–179(1984)
[2]Curty,M.,Santos,D.J.:Quantum authentication of classical messages.Phys.Rev.A 64,062309(2001)
[3]Yin,X.R.,Ma,W.P.,Liu,W.Y.:Ablind quantum signature scheme withχ-type entangled states.Int.J.Theory.Phys.51,455–461(2012)
[4]Zhang,Z.,Man,Z.:Multiparty quantum secret sharing of classical messages based on entanglement swapping.Phys.Rev.A 72,022303(2005)
[5]Chang,Y.,Xu,C.X.,Zhang,S.B.,et al.:Quantum secure direct communication and authentication protocol with single photons.Chin.Sci.Bull.58,4571–4576(2013)
[6]Zhou,N.,Zeng,G.,Xiong,J.:Quantum key agreement protocol.Electron.Lett.40,1(2004)
[7]He,Y.F.,Ma,W.P.:Two-party quantum key agreement against collective noise.Quantum Inf.Process.15,5023–5035(2016)
[8]Cai,B.B.,Guo,G.D.,Lin,S.:Multi-party quantum key agreement without entanglement.Int.J.Theory.Phys.56,1039(2016)
[9]Huang,W.,Wen,Q.-Y.,Liu,B.,Gao,F.,Sun,Y.:Quantum key agreement with EPR pairs and single-particle measurements.Quantum Inf.Process.13,649–663(2014)
[10]Liu,W.-J.,Xu,Y.,Yang,C.-N.,Gao,P.-P.,Yu,W.-B.:An efficient and secure arbitrary N-party quantum key agreement protocol using Bell states.Int.J.Theory.Phys.57,195–207(2018)
[11]Bennett,C.H.,Brassard,G.,Popescu,S.,et al.:Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels.Phys.Rev.Lett.76(5),722-725(1996)
[12]Gisin,N.:Hidden quantum nonlocality revealed by local filters.Phys.Lett.A 210(3),151-156(1996)
[13]Agrawal,P.,Pati,A.K.:Probabilistic Quantum Teleportation.Phys.Lett.A 305(1),12-17(2002)
[14]Xia,Y.,Song,J.,Song,H.S.:Quantum dialogue using non-maximally entangled states based on entanglement swapping.Phys.Scripta 76(4),363(2007)
[15]Wei,J.H.,Dai,H.Y.,Zhang,M.:Two efficient schemes for probabilistic remote state preparation and the combination of both schemes.Quantum Inf.Process.13:2115–2125(2014)
[16]Ma,P.C.,Zhan,Y.B.:Scheme for remotely preparing a four-particle entangled cluster-type state.Opt.Communications.283(12),2640-2643(2010)
[17]Jiang,M.,Huang,X.,Zhou,L.L.,et al.:An efficient scheme for multi-party quantum state sharing via non-maximally entangled states.Chin.Sci.Bull.57(10),1089-1094(2012)
Disclosure of Invention
The invention aims to provide a parameter-known non-maximum entangled Bell state-based multi-party quantum key negotiation method.
In order to solve the technical problem, the technical scheme adopted by the invention is that m participating users P existiAnd (i ═ 1,2, …, m) participates in quantum key agreement, and each participating user passes identity security authentication of the network center server. Each participating user has a set of key sequences K of length 2l (l being an integer)i(ki,1,ki,2,…,ki,2l) Wherein 2l is an integer and
Figure BDA0002291535530000041
(ηiprobability of success measured using pomm for each user).
Step 1: implementation preparation because all participants negotiate to generate 2l bit quantum negotiation key in the method, each legal user participating in key negotiation needs to prepare l non-maximum entangled Bell states, and the basic form is
Figure BDA0002291535530000042
Then each participating user PiThe one piece
Figure BDA0002291535530000043
Representation of state sequence as
Figure BDA0002291535530000044
(wherein the small superscripts A and B of the superscript denote each
Figure BDA0002291535530000045
2 bits of state, the small subscripts of the superscript denoting each
Figure BDA0002291535530000046
The order of the states). Then each party participant respectively has own
Figure BDA0002291535530000047
The first particle and the second particle in the state are combined into two sequences as follows:
Figure BDA0002291535530000048
since each user is required to encode the received particle sequence according to the own key sequence in the method, each user needs to know the corresponding relationship among the encoding position, the key and the encoding unitary operation of the method before the protocol, as follows
Figure BDA0002291535530000051
Figure BDA0002291535530000052
Figure BDA0002291535530000053
Figure BDA0002291535530000054
The corresponding table is as follows
TABLE 1 negotiated Key and Final after unitary operation on particle B
Figure BDA0002291535530000055
State correspondence table
Figure BDA0002291535530000056
Step 2: sequential transmission user PiSequence of oriented particles
Figure BDA0002291535530000057
Randomly inserting decoy single-photon sequence ZiForming a transmission sequence
Figure BDA0002291535530000058
These baits are single photon random from { |0>,|1>,|+>,|->Selected from the states, wherein
Figure BDA0002291535530000059
User PiTransmitting sequences over quantum channels
Figure BDA00022915355300000510
Sent to the next participating user
Figure BDA00022915355300000511
(
Figure BDA00022915355300000512
Representing modulo m plus).
And step 3: security detection while validating a user
Figure BDA00022915355300000513
Receiving a transmission sequence
Figure BDA00022915355300000514
After, user PiTo the user
Figure BDA00022915355300000515
Publishing the position of a bait single photon in the quantum sequence, and simultaneously publishing a corresponding measuring base; wherein |0>,|1>Measured by Z base, | +>,|->And selecting an X base for measurement. User' s
Figure BDA00022915355300000516
According to user PiPublished information is from { |0>,|1>,|+>,|->Selecting corresponding measurement base to measure bait single photon, and sending measurement result to user PiUser PiWhether an eavesdropper exists or not can be detected through a threshold value set in advance;
if the error rate is lower than the preset threshold value, no eavesdropper exists, and the step 4 is continuously executed;
otherwise, if the error rate exceeds the preset threshold value, discarding all previous operations and restarting the scheme;
and 4, step 4: after the code security detection is passed, the user
Figure BDA00022915355300000517
Discarding bait single photons and recovering particle sequences
Figure BDA00022915355300000518
User' s
Figure BDA00022915355300000519
According to its own secret key
Figure BDA00022915355300000520
Then by referring to the correspondence among the coding position, the key and the coding unitary given in table 1,
Figure BDA00022915355300000521
are respectively paired
Figure BDA00022915355300000522
In sequence
Figure BDA0002291535530000061
Execute
Figure BDA0002291535530000062
(j is equal to {1,2, …, l }) operation to obtain a new particle sequence
Figure BDA0002291535530000063
Then the user
Figure BDA0002291535530000064
Random particle sequence
Figure BDA0002291535530000065
Inserting bait single-photon sequences to form transmission sequences
Figure BDA0002291535530000066
Sending to next user through quantum channel
Figure BDA0002291535530000067
And 5: repeatedly executing step 3 and step 4
Figure BDA0002291535530000068
Repeating steps 3 and 4 for security detection and message encoding, if all sequences are secure, they will encode their keys on the corresponding qubits of each sequence and randomly insert decoy single-photon sequences in the sequences, and then send them to the next participant, otherwise they will terminate this key implementation and start over.
Step 6: generating transmission sequence of negotiation key received after all other user encryption operations
Figure BDA0002291535530000069
After, user PiAt the user
Figure BDA00022915355300000610
With the help of (1) to perform safety inspectionAnd (6) measuring. After the security detection is passed, the user PiDiscarding bait single photons and recovering particle sequences
Figure BDA00022915355300000611
Then according to its own key pair sequence
Figure BDA00022915355300000612
Execute
Figure BDA00022915355300000613
(j is equal to {1,2, …, l }) operation to obtain a new particle sequence
Figure BDA00022915355300000614
And finally, restoring the sequence.
Then PiTo pair
Figure BDA00022915355300000615
Particles A in the statej、BjPerforming a CNOT operation, j takes 1,2, …, l; t is 0, 1,2 and 3. After all CNOT operations are completed, PiNew l ordered states are obtained:
Figure BDA00022915355300000616
Figure BDA00022915355300000617
the following were used:
Figure BDA00022915355300000618
Figure BDA00022915355300000619
Figure BDA00022915355300000620
Figure BDA00022915355300000621
wherein
Figure BDA00022915355300000622
Then PiAre sequentially firstly aligned
Figure BDA00022915355300000623
Particles B in the state (j takes 1,2, …, l)jMaking single bit measurement, the measurement base is { |0>,|1>}, particles A thereofjCollapse into
Figure BDA00022915355300000624
Or
Figure BDA00022915355300000625
j is 1,2, …, l. Then PiThen for the particle AjPOVM measurements were made as follows:
firstly, taking a measuring base
Figure BDA00022915355300000626
Wherein
Figure BDA0002291535530000071
Wherein x is
Figure BDA0002291535530000072
Is such that p is2Becomes a positive operator.
p0,p1,p2The matrix representations of (a) are respectively as follows:
Figure BDA0002291535530000073
when P is presentiFor particle AjMeasured as p0Then, the particles A can be distinguishedjIn a state of
Figure BDA0002291535530000074
The probability of success at this time is
Figure BDA0002291535530000075
When the particle AjMeasured as p1Then, the particles A can be distinguishedjIs in a state of | phi1>When the success probability is
Figure BDA0002291535530000076
When for the particle AjMeasured as p2This is an invalid result and no inference can be made.
To sum up, the particle A is obtainedjThe probability of success of POVM measurement is 4a2b2/x。
TABLE 2 Pair of particles AjPOVM measurement result and last state mapping table
Figure BDA0002291535530000077
Finally, user PiWith ηiMeasurement success probability for particle Aj(j ═ 1,2, …, l) the POVM measurements were made and the locations where the POVM measurements succeeded were published according to a look-up table 2 (1,2, …,2 l). Then each user PiSelecting a public position in the POVM successfully measured positions published by other m-1 participating users and the position which is successfully measured by the public position as a final n-bit negotiation key
Figure BDA0002291535530000078
The invention has the beneficial effects that:
1. the invention uses the non-maximum entanglement Bell state with known parameters to carry out the multi-party key agreement method for the first time, thereby greatly improving the security of the key agreement and improving the utilization efficiency of the particles.
2. The invention only relates to single particle measurement, and users participating in negotiation do not need to implement complex multi-bit state measurement, thereby reducing the measurement difficulty and equipment requirements of a user side and ensuring that the scheme is easier to realize.
Drawings
FIG. 1 is a flow chart of a multi-party quantum key agreement method based on a non-maximal entanglement Bell state with known parameters.
Fig. 2 is a schematic diagram of a three-party quantum key agreement scheme in the parameter-known non-maximally entangled Bell-state-based multi-party quantum key agreement method of the present invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
Referring to fig. 1 and fig. 2, in this patent, a multiparty QKA scheme based on non-maximal entangled Bell state is proposed, and the protocol is obtained to be able to resist external attacks and participant attacks, and is a secure QKA scheme. The scheme provides a multi-party quantum key negotiation method using the non-maximum entanglement Bell state and POVM measurement with known parameters, breaks through the conventional mode of quantum key negotiation by using the maximum entanglement Bell state as a quantum channel, and can resist external and internal attacks, thereby greatly improving the communication security.
The technical terms of the invention explain:
1. z radical, X radical
{ |0>, |1> } form the Z radical, { | + >, | - >, form the X radical, where { | + >, forms the X radical
Figure BDA0002291535530000091
2. Channel selection
The non-maximum entanglement Bell state form is selected from the channels: a |00>+b|11>And the parameters a, b are known, | a tint2+|b|2＝1
3. Quantum controlled not gate
A quantum controlled NOT gate (CNOT gate) having two input qubits, a control qubit and a target qubit. The function is as follows: when the control qubit is |0>, the target qubit state is unchanged; when the control qubit is |1>, then the target bit state flips. The corresponding matrix form is:
Figure BDA0002291535530000092
4. pauli array
Some unitary matrices, also known as Pauli matrices, are also used in the present invention. The specific form is as follows:
Figure BDA0002291535530000093
Figure BDA0002291535530000094
Figure BDA0002291535530000095
Figure BDA0002291535530000096
the implementation case is as follows: a multi-party quantum key agreement protocol method based on a parameter-known non-maximum entangled Bell state realizes the three-party quantum key agreement based on the parameter-known non-maximum entangled Bell state by taking a three-party participating user as an example, and comprises the following steps:
step 1: suppose that three users, Alice, Bob and Charlie, participate in the key agreement, they all pass the identity authentication of the network center server in advance, and the three participating users want to negotiate out 2-bit information. It is assumed in advance that the probability of success of the POVM measurement of each party and the user is 0.6, 0.7 and 0.8 respectively. Each party participating in the user needs to provide a length of
Figure BDA0002291535530000101
The key sequence of (1). The key sequences of three participating users, namely Alice, Bob and Charlie, are respectively as follows: kA＝001011,KB＝010110,KC101011. Each user then has to prepare 3 parameters known as non-maximal entangled Bell states, the basic form of which is:
Figure BDA0002291535530000102
then, Alice, Bob and Charlie will receive 3 respectively
Figure BDA0002291535530000103
The states are divided into two particle sequences, which are respectively designated as:
Figure BDA0002291535530000104
Figure BDA0002291535530000105
wherein the subscripts a, B, C indicate that the particle sequence belongs to users Alice, Bob and Charlie, respectively. Sequence of
Figure BDA0002291535530000106
(i ═ A, B, C) respectively represent
Figure BDA0002291535530000107
A first particle of a state, a second particle.
Step 2: alice-oriented particle sequence
Figure BDA0002291535530000108
In which a bait single-photon sequence Z is randomly insertediForming a transmission sequence
Figure BDA0002291535530000109
Then transmitting the sequence through quantum channel
Figure BDA00022915355300001010
Is sent to Bob. Bob receives the transmission sequence
Figure BDA00022915355300001011
Then, firstly, safety detection is carried out, the bait single photon sequence is discarded after confirming that no eavesdropper exists, and the particle sequence is recovered
Figure BDA00022915355300001012
Bob then will have a key sequence KBEvery two of the key pairs are divided into three key pairs { (01), (01), (10) }, and the corresponding particle sequences of the keys are known according to the look-up table 1
Figure BDA00022915355300001013
Perform corresponding unitary operation
Figure BDA00022915355300001014
After the unitary operation, Bob follows the particle sequence
Figure BDA00022915355300001015
Medium random inserting bait single photon sequence ZiForming a transmission sequence
Figure BDA00022915355300001016
Then transmitting the sequence through quantum channel
Figure BDA00022915355300001017
And sending the information to Charlie.
TABLE 1 negotiated Key and Final after unitary operation on particle B
Figure BDA00022915355300001018
State correspondence table
Figure BDA00022915355300001019
And step 3: charlie receives transmission sequence
Figure BDA0002291535530000111
Then, firstly, safety detection is carried out, the bait single photon sequence is discarded after confirming that no eavesdropper exists, and the particle sequence is recovered
Figure BDA0002291535530000112
Charlie will then possess the key sequence KCThe two groups are divided into two key pairs { (10), (10), (11) }, and the key pair particle sequences are known according to the view of Table 1
Figure BDA0002291535530000113
Perform corresponding unitary operation
Figure BDA0002291535530000114
After the unitary operation, Charlie is to the particle sequence
Figure BDA0002291535530000115
Medium random inserting bait single photon sequence ZiForming a transmission sequence
Figure BDA0002291535530000116
Then transmitting the sequence through quantum channel
Figure BDA0002291535530000117
And sending the data to Alice.
And 4, step 4: alice receives the transmission sequence
Figure BDA0002291535530000118
Then, firstly, safety detection is carried out, the bait single photon sequence is discarded after confirming that no eavesdropper exists, and the particle sequence is recovered
Figure BDA0002291535530000119
Then Alice receives the particle sequence according to the own secret key (00), (10), (11) }
Figure BDA00022915355300001110
To carry out
Figure BDA00022915355300001111
And (5) performing a unitary operation.
TABLE 2 Pair of particles AjPOVM measurement result and last state mapping table
Figure BDA00022915355300001112
After Alice performs unitary operation on the particles received by Alice, the particles in the hands are immediately recovered to non-maximum entangled Bell state forms with known parameters, namely the non-maximum entangled Bell state forms are respectively
Figure BDA00022915355300001113
Figure BDA00022915355300001114
And
Figure BDA00022915355300001115
then separately for AjAnd Bj(j ═ 1,2,3) particles obtained by performing a CNOT operation
Figure BDA00022915355300001116
And
Figure BDA00022915355300001117
and for the particle BjProceed to { |0>,|1>Measurement, for AjPOVM measurement is carried out, and the accurate measurement positions are published as a second group and a third group, namely, the second group and the third group respectively correspond to each other according to the table 2
Figure BDA0002291535530000121
And
Figure BDA0002291535530000122
the state, key corresponds to 01 and 10, respectively.
The same procedure as the above scheme, the sequential operations, which are initially issued from Bob and Charlie, respectively, Bob → Charlie → Alice → Bob and Charlie → Alice → Bob → Charlie, also enable Bob and Charlie to perform single-particle measurement and POVM measurement in the last step, and respectively publish that the respective measurement correct positions are the first and third groups and the corresponding measurement results are 11 and 10 and the second and third groups and the corresponding measurement results are 01 and 10, respectively. And finally, selecting a public position in the POVM measurement success positions published by three users of Alice, Bob and Charlie, wherein the public position is the final 2-bit negotiation key K-10.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.

Claims (1)

1.一种基于参数已知的非最大纠缠Bell态的多方量子密钥协商方法，其特征在于，包括：整个方案中包含m个参与者Pi，其中，i＝1,2,…,m，并且网络中心服务器要确保每个参与者都已经通过量子身份安全认证；1. A multi-party quantum key agreement method based on a known non-maximally entangled Bell state of parameters, characterized in that, comprising: the whole scheme contains m participants P i , wherein i=1,2,...,m , and the network center server must ensure that each participant has passed the quantum identity security authentication; 经所有参与者协商出本次方案所需协商密钥的长度为n，n为整数，由于在最后各参与者需要利用POVM测量各自接收到的未知Bell态并进行相应的解码操作，所以每一方参与者Pi都需各自生成长度为2l的密钥Ki，其中，ki,1,ki,2,…,ki,2l，其中l为整数且
Figure FDA0003163742810000011
其中，ηi为每位用户使用POVM测量成功的概率；相邻参与者通过检查窃听和协商并对变换后的非最大纠缠Bell态中的量子位分别执行各自密钥对应的幺正操作；After negotiated by all participants, the length of the negotiated key required for this scheme is n, and n is an integer. Since each participant needs to use POVM to measure the unknown Bell state received by each party and perform corresponding decoding operations, each party needs to use POVM. Each participant Pi needs to generate a key K i of length 2l, where k i ,1 ,ki ,2 ,...,ki ,2l , where l is an integer and
Figure FDA0003163742810000011
Among them, η i is the probability of each user using POVM to measure the success; adjacent participants perform unitary operations corresponding to their respective keys by checking eavesdropping and negotiation and performing the qubits in the transformed non-maximally entangled Bell states; 最后各参与者把经幺正操作过的粒子恢复出Bell态形式，并对每一组Bell态进行CNOT操作；然后再分别对受控粒子进行单粒子测量，对控制粒子进行POVM测量；Finally, each participant restores the unitary-operated particles to the form of Bell state, and performs CNOT operation on each group of Bell states; 各参与用户在参照原始协商密钥Each participating user is referring to the original negotiated key
Figure FDA0003163742810000012
的基础上公布POVM测量成功的位置；选取各用户公布的POVM测量成功的公共位置，所有参与者可以获得最终长度为n的协商密钥
Figure FDA0003163742810000012
Publish the position where the POVM measurement is successful on the basis of the value of
Figure FDA0003163742810000013
Figure FDA0003163742810000013
 具体如下：details as follows: 步骤1：实施准备：由于本方法中所有参与者需要协商生成2l比特量子协商密钥，因此每一位参与密钥协商的合法用户都需制备l个非最大纠缠Bell态，其基本形式为
Figure FDA0003163742810000014
其中参数ai和bi为用户Pi已知；Step 1: Implementation preparation: Since all participants in this method need to negotiate to generate a 2l-bit quantum negotiation key, each legitimate user participating in the key negotiation needs to prepare l non-maximally entangled Bell states, whose basic form is
Figure FDA0003163742810000014
Wherein the parameters a i and b i are known by the user P i ; 然后每个参与用户Pi将这l个
Figure FDA0003163742810000015
态顺序的表示为
Figure FDA0003163742810000016
其中，上标的小上标A和B表示每个
Figure FDA0003163742810000017
态的2个比特，上标的小下标表示每个
Figure FDA0003163742810000018
态的顺序；随后每一方参与者分别将自己所拥有的
Figure FDA0003163742810000021
态中的第一个粒子，第二个粒子分别组合成两个序列如下：
Figure FDA0003163742810000022
Then each participating user P i puts these l
Figure FDA0003163742810000015
The state order is expressed as
Figure FDA0003163742810000016
Among them, the superscript small superscript A and B indicate that each
Figure FDA0003163742810000017
2 bits of the state, the superscript small subscript indicates each
Figure FDA0003163742810000018
the order of states; each participant then assigns the
Figure FDA0003163742810000021
The first particle in the state and the second particle are combined into two sequences as follows:
Figure FDA0003163742810000022
 由于需要各用户根据自己的密钥序列对接收到的粒子序列进行编码，所以各用户需要在方案实施前了解本方法编码位置、密钥和编码幺正操作之间的对应关系；Since each user needs to encode the received particle sequence according to his own key sequence, each user needs to understand the corresponding relationship between the encoding position, key and encoding unitary operation of this method before the implementation of the scheme; 具体如下：details as follows:
Figure FDA0003163742810000023
Figure FDA0003163742810000023
Figure FDA0003163742810000024
Figure FDA0003163742810000024
Figure FDA0003163742810000025
Figure FDA0003163742810000025
Figure FDA0003163742810000026
Figure FDA0003163742810000026
 对应表格如下The corresponding table is as follows 表1经对粒子B幺正操作后的协商密钥和最终
Figure FDA0003163742810000027
态对应表Table 1 Negotiated key and final key after unitary operation on particle B
Figure FDA0003163742810000027
state correspondence table
Figure FDA0003163742810000028
Figure FDA0003163742810000028
 步骤2：序列传输：用户Pi向粒子序列
Figure FDA0003163742810000029
中随机地插入诱骗单光子序列Zi，形成传输序列
Figure FDA00031637428100000210
这些诱饵单光子随机的从{|0>,|1>,|+>,|->}这些状态中选取，其中
Figure FDA00031637428100000211
用户Pi通过量子信道将传输序列
Figure FDA00031637428100000212
发送给下一个参与用户
Figure FDA00031637428100000217
其中，
Figure FDA00031637428100000213
表示模m加；Step 2: Sequence transfer: User Pi sends particle sequence
Figure FDA0003163742810000029
Randomly insert decoy single-photon sequence Z i into the transmission sequence
Figure FDA00031637428100000210
These decoy single photons are randomly selected from {|0>,|1>,|+>,|->} states, where
Figure FDA00031637428100000211
User Pi transmits the sequence through the quantum channel
Figure FDA00031637428100000212
Send to next participating user
Figure FDA00031637428100000217
in,
Figure FDA00031637428100000213
means modulo m plus; 步骤3：安全检测：当确认用户
Figure FDA00031637428100000218
接收到传输序列
Figure FDA00031637428100000214
后，用户Pi向用户
Figure FDA00031637428100000215
公布量子序列中的诱饵单光子的位置，同时公布相应的测量基；其中|0>,|1>采用Z基测量，|+>,|->选取X基测量；用户
Figure FDA00031637428100000216
根据用户Pi公布的信息从{|0>,|1>,|+>,|->}中选择相应的测量基对诱饵单光子进行测量，并将测量结果发送给用户Pi，用户Pi可以通过提前设定的阈值来检测是否存在窃听者；Step 3: Security Detection: When confirming the user
Figure FDA00031637428100000218
transmission sequence received
Figure FDA00031637428100000214
After that, user Pi sends user
Figure FDA00031637428100000215
The position of the decoy single photon in the quantum sequence is announced, and the corresponding measurement base is announced at the same time; where |0>, |1> use Z-based measurement, |+>, |-> select X-based measurement; user
Figure FDA00031637428100000216
Select the corresponding measurement base from {|0>,|1>,|+>,|-> } to measure the decoy single photon according to the information published by the user Pi, and send the measurement result to the user Pi , the user P i can detect whether there is an eavesdropper through a threshold set in advance; 如果错误率低于预设的阈值，表示没有窃听者，继续执行步骤4；If the error rate is lower than the preset threshold, it means that there is no eavesdropper, and proceed to step 4; 如果错误率超出了提前设定的阈值，就舍弃之前的全部操作重新开始方案；If the error rate exceeds the threshold set in advance, all previous operations will be discarded and the plan will be restarted; 步骤4：编码：安全检测通过后，用户
Figure FDA0003163742810000031
丢弃诱饵单光子并恢复出粒子序列
Figure FDA0003163742810000032
用户
Figure FDA0003163742810000033
根据自己的密钥
Figure FDA0003163742810000034
然后通过参考表1中给出的编码位置、密钥和编码幺正操作之间的对应关系，
Figure FDA0003163742810000035
分别对
Figure FDA0003163742810000036
序列中的
Figure FDA0003163742810000037
执行
Figure FDA0003163742810000038
其中，j∈{1,2,…,l}，操作得到新的粒子序列
Figure FDA0003163742810000039
然后用户
Figure FDA00031637428100000310
随机向粒子序列
Figure FDA00031637428100000311
中插入诱饵单光子序列，形成传输序列
Figure FDA00031637428100000312
通过量子信道发送给下一位用户
Figure FDA00031637428100000313
Step 4: Encoding: After passing the security check, the user
Figure FDA0003163742810000031
Discard the decoy single photon and recover the particle sequence
Figure FDA0003163742810000032
user
Figure FDA0003163742810000033
according to your own key
Figure FDA0003163742810000034
Then by referring to the correspondence between encoding positions, keys and encoding unitary operations given in Table 1,
Figure FDA0003163742810000035
respectively
Figure FDA0003163742810000036
in sequence
Figure FDA0003163742810000037
implement
Figure FDA0003163742810000038
Among them, j∈{1,2,…,l}, the operation gets a new particle sequence
Figure FDA0003163742810000039
then the user
Figure FDA00031637428100000310
random particle sequence
Figure FDA00031637428100000311
Insert a decoy single-photon sequence into the transmission sequence
Figure FDA00031637428100000312
Send to next user via quantum channel
Figure FDA00031637428100000313
 步骤5：重复执行步骤3和步骤4：用户
Figure FDA00031637428100000314
重复执行步骤3和步骤4进行安全检测和消息编码，如果所有的序列都是安全的，它们就会在每个序列相应的量子位上编码它们的密钥，并在序列中随机插入诱饵单光子序列，然后发送给下一位参与者，否则，它们将终止本次密钥协议并重新开始；Step 5: Repeat Step 3 and Step 4: User
Figure FDA00031637428100000314
Repeat steps 3 and 4 for security detection and message encoding, if all sequences are secure, they encode their keys on the corresponding qubits of each sequence and randomly insert decoy single photons into the sequence sequence, and then send it to the next participant, otherwise, they will terminate this key agreement and start over; 步骤6：生成协商密钥：接收到经过所有其他用户加密操作后的传输序列
Figure FDA00031637428100000315
后，用户Pi在用户
Figure FDA00031637428100000316
的帮助下进行安全检测；安全检测通过后，用户Pi丢弃诱饵单光子并恢复出粒子序列
Figure FDA00031637428100000317
然后再根据自己的密钥对序列
Figure FDA00031637428100000318
执行
Figure FDA00031637428100000319
操作得到新的粒子序列
Figure FDA00031637428100000320
最后恢复出序列，其中，j∈{1,2,…,l}；Step 6: Generate Negotiated Key: Receive the transmission sequence encrypted by all other users
Figure FDA00031637428100000315
After the user P i is in the user
Figure FDA00031637428100000316
With the help of the security detection; after the security detection is passed, the user Pi discards the decoy single photon and restores the particle sequence
Figure FDA00031637428100000317
Then according to your own key pair sequence
Figure FDA00031637428100000318
implement
Figure FDA00031637428100000319
operation to get a new particle sequence
Figure FDA00031637428100000320
Finally, recover the sequence, where j∈{1,2,…,l}; 接着Pi对
Figure FDA00031637428100000321
态中的粒子Aj、Bj执行CNOT操作，j取1、2、…、l；t取0、1、2、3；所有的CNOT操作完成后，Pi得到新的l个有序的态：
Figure FDA00031637428100000322
Figure FDA00031637428100000323
如下：Then Pi pair
Figure FDA00031637428100000321
The particles A j and B j in the state perform the CNOT operation, j takes 1, 2, ..., l; t takes 0, 1, 2, 3; after all the CNOT operations are completed, P i gets a new l ordered state:
Figure FDA00031637428100000322
Figure FDA00031637428100000323
as follows:
Figure FDA0003163742810000041
Figure FDA0003163742810000041
 其中，
Figure FDA0003163742810000042
in,
Figure FDA0003163742810000042
 随后Pi依次先对
Figure FDA0003163742810000043
态中的粒子Bj做单比特测量，其中，j取1，2，…，l，测量基为{|0>,|1>}，其粒子Aj将坍缩为
Figure FDA0003163742810000044
或
Figure FDA0003163742810000045
j取1、2、…、l；然后Pi再以测量成功概率ηi对其粒子Aj做POVM测量并结合单比特测量结果和POVM测量结果可以确定自己目前所拥有的粒子处在
Figure FDA0003163742810000046
态，其中，j＝1,2,…,l；再根据
Figure FDA0003163742810000047
与
Figure FDA0003163742810000048
是一一对应的关系，即可确定自己所拥有的密钥；Then P i is paired first
Figure FDA0003163742810000043
The particle B j in the state is measured by a single bit, where j is 1, 2, ..., l, and the measurement basis is {|0>, |1>}, and its particle A j will collapse into
Figure FDA0003163742810000044
or
Figure FDA0003163742810000045
j takes 1, 2, .
Figure FDA0003163742810000046
state, where j=1,2,...,l; and then according to
Figure FDA0003163742810000047
and
Figure FDA0003163742810000048
It is a one-to-one correspondence, and you can determine the key you own; 最后，用户Pi公布自己POVM测量成功的位置1,2,…,2l；各用户Pi选取其他m-1个参与用户公布的POVM测量成功的位置与自己测量成功的位置中的公共位置作为最终的n比特协商密钥Finally, the user P i announces the positions 1, 2, . Final n-bit negotiated key
Figure FDA0003163742810000049
Figure FDA0003163742810000049
 Pi再对其粒子Aj做POVM测量，具体如下：首先取测量基
Figure FDA00031637428100000410
P i then performs POVM measurement on its particle A j , as follows: First, take the measurement basis
Figure FDA00031637428100000410
 其中
Figure FDA00031637428100000411
in
Figure FDA00031637428100000411
 其中x取
Figure FDA00031637428100000412
中的最大值，它能够使得p2成为一个正定算子；where x is taken
Figure FDA00031637428100000412
The maximum value in , which can make p 2 a positive definite operator; p0,p1,p2的矩阵表示分别如下：The matrix representations of p 0 , p 1 , and p 2 are as follows:
Figure FDA00031637428100000413
Figure FDA00031637428100000413
 当Pi对粒子Aj的测量结果为p0时，可区分出粒子Aj的状态为|φ0>，此时成功的概率为
Figure FDA0003163742810000051
当粒子Aj的测量结果为p1时，可区分出粒子Aj的状态为|φ1>，此时成功的概率为
Figure FDA0003163742810000052
当对粒子Aj的测量结果为p2时，此为无效结果，无法做出推断。When the measurement result of P i on particle A j is p 0 , it can be distinguished that the state of particle A j is |φ 0 >, and the probability of success at this time is
Figure FDA0003163742810000051
When the measurement result of particle A j is p 1 , the state of particle A j can be distinguished as |φ 1 >, and the probability of success at this time is
Figure FDA0003163742810000052
When the measurement result for particle A j is p 2 , this is an invalid result and no inference can be made.
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