Quantum private comparison protocol based on photon two degrees of freedom

Abstract

Quantum private comparison (QPC) is a basic relational operation in quantum cryptography, and can compare whether two pieces of data are equal or not on the premise of not leaking specific numerical values of private data; an existing QPC protocol does not have the defects that the requirement for the quantum capacity of a user is high, that is, the steps are complex, the quantum bit efficiency is low, and the quantum bit efficiency is not higher than 100%; the technical difficulty and the cost are challenged; according to the invention, a QPC protocol is realized by using single photons with two degrees of freedom, and in the whole QPC process, only preparation and measurement of photons and quantum operations such as unitary operations on partial degrees of freedom of partial photons before measurement are involved; in this way, the implementation difficulty and cost of the protocol are greatly reduced, but the quantum bit efficiency of the protocol is extremely high and reaches up to 400%; according to the invention, the main defects of the existing QPC protocol are overcome; analysis shows that the method has the security and correctness of the QPC protocol.

Description

TECHNICAL FIELD

[0001] The application relates to a quantum private comparison method for comparing four bits by using single photons with two degrees of freedom as quantum resources. BACKGROUND

[0002] Quantum cryptography has theoretically unconditional security [1, 2]. Quantum private comparison (QPC) is a branch of quantum cryptography, which can protect the privacy of private data while comparing whether two data are equal. At present, various QPC protocols have appeared [3-32]. However, the quantum bit efficiency of these protocols is not higher than 100%.

[0003] The application uses single photons with polarization and vacuum mode degrees of freedom as quantum resources to design a new QPC protocol. The quantum states of the photons in the polarization and vacuum mode degrees of freedom are maximally utilized, but this utilization does not need to perform unitary operations on each photon or on both degrees of freedom of the photon, that is, only one degree of freedom is randomly selected to perform unitary operation. In this way, the number of unitary operations is greatly reduced. From the perspective of probability statistics, the number of unitary operations is only one fourth of the number of comparison photons. This can greatly reduce the use cost. In addition, the quantum bit efficiency of the application is as high as 400%, far exceeding the quantum bit efficiency of the prior art - not highly 100%.

[0004] Lo

[35] once pointed out that it is impossible to design a secure equality function in a scenario with only two participants. Therefore, an additional third party (TP) is needed to participate in the QPC protocol. The application will involve a semi-honest third party (STP) in the invented QPC protocol. "Semi-honest" means that the STP may steal the private data of the users itself, but it will faithfully execute the protocol process and will not be bribed by external eavesdroppers to corrupt and collude with any internal user to steal the private data of another user. In this way, there will be three QPC participants in the invented QPC protocol: two users and one STP.

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[0044] In view of the defects of the prior art, that is, the quantum bit efficiency of the existing quantum privacy comparison protocol is not higher than 100%, the present application creates a quantum privacy comparison protocol with a quantum bit efficiency of 400%. The present application uses a single photon with two degrees of freedom to realize the content of the application. This single photon is a photon with polarization degrees of freedom and spatial-mode degrees of freedom, abbreviated as PSDF photon. According to the literature [33-34], the quantum state of the PSDF photon can be expressed as Where |phi> P and |phi> S are the states of the polarization degrees of freedom and the spatial-mode degrees of freedom, respectively. We use the symbols |H> and |V> to represent the horizontal polarization and the vertical polarization of the photon, respectively. In this way, the preparation basis / measurement basis of the two non-orthogonal polarization degrees of freedom can be written as Z P = {|H>, |V>} and X P = {|R>, |A>}, wherein

[0045] According to the literature [33-34], the states of the polarization degrees of freedom and the spatial-mode degrees of freedom of a photon are interchangeable, that is, we can independently operate the quantum states of the two degrees of freedom, which do not affect each other. The literature

[33] discusses four kinds of polarization degrees of unitary operations, two of which do not change the measurement basis of the photon, which are represented by equations (1) and (2); the other two change the measurement basis of the photon, which are represented by equations (3) and (4). Table 1 lists 16 kinds of operation results of the four polarization degrees of states |H>, |V>, |R> and |A> under the action of the unitary operations shown in equations (1), (2), (3) and (4).

[0046] U P00 = |H><H| + |V><V| (1)

[0047] U P01 = |V><H| - |H><V| (2)

[0048]

[0049] Table 1 Action results of the four polarization degrees of unitary operations

[0050]

[0051] In the spatial-mode degrees of freedom, we use |b1> and |b2> to represent the upper spatial mode and the lower spatial mode of the photon, respectively. In this way, the preparation basis / measurement basis of the two non-orthogonal spatial-mode degrees of freedom can be written as Z S = {|b1>, |b2>} and X S = {|s>, |a>}, wherein and

[0052] Document

[34] shows that there are also 4 unitary operations on the spatial mode degree of freedom, which are represented by equations (5), (6), (7) and (8). The unitary operations represented by equations (5) and (6) do not change the measurement basis of the photon on the spatial mode degree of freedom; the unitary operations represented by equations (7) and (8) change the measurement basis of the photon on the spatial mode degree of freedom. The expressions of the 4 unitary operations acting on the 4 spatial mode degree states |b1>, |b2>, |s> and |a> are represented by equations (9), (10), (11) and (12). Table 2 lists the 16 quantum states produced by the 4 unitary operations represented by equations (5), (6), (7) and (8) acting on the 4 spatial mode degree states |b1>, |b2>, |s> and |a>.

[0053]

[0054]

[0055] Table 2 Results of the action of the unitary operations on the 4 spatial mode degrees

[0056]

[0057] According to the above discussion, a PSDF photon has at least 16 quantum states as shown in Table 3. The photon has Z P = { |H>, |V>} and X P = { |R>, |A>} measurement bases on the polarization degree; and Z S = { |b1>, |b2>} and X S = { |s>, |a>} measurement bases on the spatial mode degree. The 16 quantum states correspond to 4 measurement bases and The correspondence between the 16 quantum states and the 4 measurement bases is shown in Table 3.

[0058] Table 3 Correspondence between the 16 quantum states and the 4 measurement bases

[0059] DETAILED DESCRIPTION

[0060] Quantum private comparison (QPC) can not leak the specific value of private data in the whole process of comparing whether the private data is equal; the quantum bit efficiency of the existing QPC technology is not higher than 100%; in order to improve the quantum bit efficiency and reduce the implementation cost, the present application uses a single photon with polarization and vacuum mode degree of freedom to create a quantum private comparison method with a quantum bit efficiency of 400%, and the name of the method is quantum private comparison protocol based on photon double degree of freedom; the protocol is that two private data comparison parties Alice and Bob compare whether the private data is equal under the hosting of a semi-loyal third party STP, Alice and Bob respectively own private data AC={a j c j} and BD={b j d j}, wherein a j ,b j ,c j ,d j ∈{00,01,10,11}, j∈{0,1,...,L-1}, 2 4L-1 ≤max{AC,BD}<2 4L . Alice and Bob also agree on the correspondence between the quantum state shown in formula (13) and (14) and two-bit.

[0061]

[0062] The specific steps of the protocol are as follows:

[0063] Step 1: Bob prepares L single photons CP={cp j d j} with polarization and vacuum mode degree of freedom according to the private data BD={b j}, the quantum state of photon cp j in the polarization degree is prepared according to b j and formula (13), and the quantum state in the vacuum mode degree is prepared according to d j and formula (14). In addition, Bob also prepares a sufficient number of decoy photons, the quantum state of which is randomly selected from one of the 16 quantum states , here |φ P ∈{|H>,|V>,|R>,|A>}, |φ S ∈{|b1>,|b2>,|s>,|a>}. Bob divides these decoy photons into two parts DP0 and DP1 and randomly inserts them into the quantum sequence CP to form a new quantum sequence DCP. Only Bob knows the corresponding measurement basis and quantum initial state of each photon in DCP. Bob sends the quantum sequence DCP to STP in the form of quantum data block through a quantum channel.

[0064] Step 2: After receiving the quantum sequence DCP, Bob announces the position and measurement basis of the decoy photon DP0; STP performs quantum measurement on DP0 according to the announced information; after the measurement, STP tells Bob the measurement result of DP0 in a public way through a classical channel; Bob compares the measurement result of DP0 with the quantum initial state of DP0 and calculates the error rate, and determines whether there is eavesdropping in the quantum channel from Bob to STP according to the error rate; if the error rate is lower than the normal threshold, the protocol continues to step 3; otherwise, the protocol terminates this run and then restarts.

[0065] Step 3: After Bob announces the position, measurement basis and quantum initial state of the decoy photon DP1, STP randomly selects part of photons from DP1 and CP to perform random unitary operations U P01 , U P10 , U P11 , and on them, and records the photons in CP as follows: if the photon cp j with subscript j is not subjected to unitary operation in both polarization and vacuum mode degrees of freedom, record e j =00, f j =00 and mu j =00; if the unitary operation performed on cp j is U P01 , U P10 , U P11 , and , record e j =01, e j =10, e j =11, f j =01, f j =10 and f j =11 respectively, and record mu j =00, mu j =10, mu j =10, mu j =00, mu j =01 and mu j =01 respectively as the flag of the change of measurement basis of the photon subjected to unitary operation. In this way, STP can obtain two private number sequences UR={e j f j} and MU={mu j}, where e j , f j ∈{00,01,10,11} and mu j∈ {00, 01, 10}, j e {0, 1,..., L - 1}. The unitary operation evolves the quantum sequences DP1and CPinto UDP1and UCP= {ucp j}, respectively. The quantum sequence UDP1is reinserted into the quantum sequence UCPto form a new quantum sequence UDCP. At this time, only STP knows the positions of the decoy photons, the measurement bases, and the quantum states in the quantum sequence UDCP. Subsequently, STP sends the quantum sequence UDCPto Alice through the quantum channel.

[0066] Step 4: When Alice receives the quantum sequence UDCP, STP announces the positions of the decoy photons and the measurement bases. Alice measures the decoy photons according to the information announced by STP and tells STP the measurement results in a public way through the classical channel. STP compares the measurement results of Alice with the quantum states of the decoy photons and calculates the error rate of the quantum states. If the error rate is normal, i.e., there is no eavesdropper in the quantum channel, the protocol enters step 5; otherwise, the current run of the protocol is terminated and the protocol is restarted.

[0067] Step 5: When Alice discards the decoy photons in the UDCPand restores the quantum sequence UCP, Alice informs STP and Bob to announce the values of the MU and the measurement bases of the photons in CP, respectively. Since the unitary operation U P01 and does not change the measurement bases of the photons, while the unitary operation U P10 , U P11 , and changes the measurement bases of the photons, and the photons have only two measurement bases in the polarization and the vacuum mode degrees of freedom, when mu j = 00, Alice measures ucp j using the measurement bases of the polarization and the vacuum mode announced by Bob; when mu j = 10, Alice switches the measurement base of the polarization announced by Bob while keeping the measurement base of the vacuum mode to measure ucp j ; when mu j = 01, Alice switches the measurement base of the vacuum mode announced by Bob while keeping the measurement base of the polarization to measure ucp j . The photons ucp j have four measurement results |H>, |V>, |R>, and |A> in the polarization degree, which are recorded as rp j = 00, 01, 10, and 11, respectively; and four measurement results |b1>, |b2>, |s>, and |a> in the vacuum mode degree, which are recorded as rs j = 00, 01, 10, and 11, respectively. After the quantum measurement, Alice obtains a private number sequence MR= {rp jrs j}, where rp j , rs j ∈ {00, 01, 10, 11}, j ∈ {0, 1,..., L-1}. Alice performs the following two-bit XOR operation on the MR and the secret data AC: and Here uab j , ucd j ∈ {00, 01, 10, 11}, j ∈ {0, 1,..., L-1}, is the binary XOR operator, and publishes the result, the sequence UABCD = {uab j ucd j}.

[0068] Step 6: After receiving the sequence UABCD value published by Alice, the STP compares the UABCD with the UR in the hand of the STP. If they are equal, the STP publishes that the secret data of Alice and Bob are equal; otherwise, publishes that the secret data of the two users are not equal.

[0069] The switching in step 5 means that, in the polarization degree of freedom, if the published photon measurement basis is Z P = { |H>, |V>}, then the measurement basis is changed to X P = { |R>, |A>} when measuring; if the published photon measurement basis is X P = { |R>, |A>}, then the measurement basis is changed to Z P = { |H>, |V>} when measuring. In the vacuum mode degree of freedom, if the published photon measurement basis is Z S = { |b1>, |b2>}, then the measurement basis is changed to X S = { |s>, |a>} when measuring; if the published photon measurement basis is X S = { |s>, |a>}, then the measurement basis is changed to Z S = { |b1>, |b2>} when measuring.

[0070] Embodiment

[0071] To facilitate the understanding of the above protocol, the following is an example illustrating the flow of the protocol. Here, we assume that AC = 00101101 and BD = 00101101, i.e., a1 = 00, c1 = 10, a0 = 11, c0 = 01; b1 = 00, d1 = 10, b0 = 11, d0 = 01. Here, L = 2.

[0072] Step 1*: Bob prepares a quantum sequence of two photons The measurement basis of the two photons is and

[0073] Step 3*: STP chooses cp1 to perform a unitary operation, which randomly selects U P11 ; while cp0 does not perform a unitary operation. In this way, STP can obtain two private number sequences UR=(e1f1)(e0f0)=(11000000) and MU=(mu1)(mu0)=(10)(00).

[0074] Step 5*: Alice informs STP and Bob to respectively publish MU=(mu1)(mu0)=(10)(00) and the measurement basis of photon cp1 and the measurement basis of photon cp0 Since mu1=10 and mu0=00, Alice switches the measurement basis to measure photon ucp1 and still uses to measure photon ucp0. After the measurement, Alice obtains a private number sequence MR=(rp1rs1)(rp0rs0)=(1110)(1101). Alice uses MR and the private data AC to perform the following two-bit bitwise XOR operation: and and In this way, UABCD=(uab1ucd1)(uab0ucd0)=(1100)(0000)=(11000000).

[0075] Step 6*: When STP receives the value UABCD=(11000000) published by Alice, STP compares UABCD and UR=(11000000). Since UABCD=UR=(11000000), STP declares that the private data of Alice and Bob are the same.

[0076] In the above example, Alice's private data AC=00101101 is indeed equal to Bob's private data BD=00101101, which is consistent with the content of STP's declaration. It can be seen that the protocol has the correct function.

[0077] Quantum bit efficiency

[0078] According to reference [6], if we use the symbol η to represent the quantum bit efficiency, its definition is shown in formula (15).

[0079]

[0080] where c represents the number of bits of data to be compared in a comparison stage; and q represents the number of photons used for comparison in a comparison stage, here excluding the number of decoy photons, because the number of decoy photons can be considered as belonging to another independent operation process. In the protocol, 1 photon cp j is used to compare 4 bits of data, i.e. Alice's 4-bit data a j c j and Bob's 4-bit data b j d j . Thus, q = 1 and c = 4. Therefore, without considering the security check link,

[0081] Correctness analysis

[0082] According to the method of preparing photons cp j by Bob according to formula (13) and (14), the recording method of STP for 6 unitary operations: U P01 , U P10 , U P11 , and , and the recording and calculation method of Alice for the measurement results of photons ucp j , the comprehensive effect of the three-party operations is equivalent to formula (16) and (17).

[0083]

[0084]

[0085] According to formula (16) and (17), if uab j = e j and ucd j = f j , it means that and which means a j is equal to b j and c j is equal to d j . If two or one of uab j = e j and ucd j = f j do not hold, we can deduce that a j c j ≠ b j d j . Therefore, STP can determine whether the private data of Alice and Bob are equal by comparing whether UABCD received and UR held by it are the same. It can be seen that the invented QPC protocol has correct function.

[0086] Security analysis

[0087] The security of the protocol is analyzed from both external attacks and internal attacks.

[0088] External attack analysis

[0089] In the invented QPC protocol, there are totally 6 steps, and in 3 steps, i.e. steps 1, 3 and 5, there are security risks, while in the remaining three steps, there are no external attacks, because in steps 1 and 3, the photons are transmitted through quantum channels, and in step 5, the quantum measurement results and the calculated values of the secret data are announced through classical channels. Therefore, in these 3 steps, it is easy to be attacked by external attackers. As to steps 1 and 3, both quantum sequences DCP and UDCP contain decoy photons; the decoy photons in these two quantum sequences can be used to detect whether there is an external attacker. According to references [37, 38], the decoy photon technology can provide theoretically unconditional security for the above-mentioned photon communication, because this technology is considered to be a copy of the method for detecting eavesdropping in the famous BB84 protocol, which is proved to have theoretically unconditional security [2].

[0090] Although the decoy photons DP1 are prepared by Bob, they are subjected to unitary operations by STP, the measurement bases and initial states of the decoy photons are changed, and the positions, i.e. the orders in quantum sequence UDCP, are also adjusted by STP. Therefore, as long as STP does not announce the positions, measurement bases and initial states of UDP1 photons, no one knows the positions, measurement bases and initial states of decoy photons UDP1 in UDCP except STP. Therefore, UDP1 can still be safely used as decoy photons. Based on this, the quantum communication in steps 1 and 3 is protected by the decoy photon technology. Therefore, steps 1 and 3 are both secure.

[0091] In step 5, because the external attacker knows nothing about UR, only STP knows the value of UR, according to equations (16) and (17), the external attacker is impossible to deduce the secret data AC and BD of the users from UABCD encrypted by UR. In summary, the invented QPC protocol can prevent external attacks.

[0092] Internal attack analysis

[0093] As to internal attacks, there are two cases: the first case is that STP wants to steal the secret data of the two users; the second case is that the two users steal each other's secret data. Therefore, we only need to analyze the above two cases.

[0094] Case 1: Attack of STP

[0095] If the STP wants to steal the user's private data, it can only attack the quantum sequence DCP. Since the STP does not know the measurement bases of the individual photons in the quantum sequence CP, the STP cannot accurately obtain Bob's private data, and thus cannot succeed in stealing Bob's private data BD. Without the data BD, it is impossible for the STP to derive Alice's private data AC from UABCD using equations (16) and (17). Therefore, the protocol is not threatened by the STP attack.

[0096] Case 2: Mutual attack between users

[0097] First, we analyze the first scenario, i.e., Alice stealing Bob's private data. To achieve this goal, Alice can intercept the quantum sequence DCP. However, if this is done, the decoy photon technique will discover Alice as an external attacker. Since the STP is semi-loyal, the STP cannot collude with Alice to steal Bob's private data. This means that the STP cannot leak the UR value in the STP's possession to Alice. In this way, if Alice wants to derive Bob's private data from its quantum measurement results MR, it is impossible to derive Bob's private data BD according to equations (16) and (17) because Alice has no knowledge of the UR value. Therefore, Alice's attack is not successful.

[0098] Now we analyze the second scenario, i.e., Bob stealing Alice's private data. To do this, Bob can only steal Alice's private data according to the announced UABCD. However, the announced UABCD contains the private number sequence UR that is private to the STP. Since the STP is semi-loyal, the STP is prohibited from colluding with any party in the protocol to steal private data. Therefore, the STP cannot leak the UR value known to itself to Bob. Since Bob does not know the UR value, Bob cannot derive Alice's private data AC from UABCD according to equations (16) and (17).

[0099] In summary, the above analysis shows that Alice and Bob are not likely to steal each other's private data.

[0100] Based on the above security analysis of the two internal attacks, we can conclude that the invented QPC protocol is also capable of resisting internal attacks.

[0101] In summary, the protocol can prevent both external attacks and internal attacks, and is secure.

[0102] Comparison with previous QPC protocols

[0103] In terms of qubit efficiency, the QPC protocol surpasses all existing QPC protocols - its qubit efficiency reaches 400%. In order to more fully evaluate the invented protocol, we compare the QPC protocol with some existing QPC protocols. We compare them from five aspects: quantum resources, quantum entanglement, quantum unitary operations, quantum measurements and qubit efficiency. The comparison results are listed in Table 1. From Table 1, we can see that the invented QPC protocol achieves 400% qubit efficiency using only two degrees of freedom of photons.

[0104] Table 1 Comparison of the QPC protocol of the present application with some existing QPC protocols

[0105]

[0106] Compared with the prior art, the qubit efficiency of the QPC protocol of the present application is as high as 400%. It is also lower than many existing QPC protocols in terms of implementation difficulty and cost, because it only uses two degrees of freedom of single photons and unitary operations on only some degrees of freedom of some photons. It can be implemented without obstacles and at low cost using existing conventional quantum technology. Therefore, the present application has the creativity, practicality and novelty required by the Patent Law. This is the reason why the present patent application can be granted a patent.

Claims

1. Quantum Private Comparison (QPC) can ensure that the specific value of private data is not disclosed during the entire process of comparing whether private data is equal. The existing QPC technology has a quantum bit efficiency of less than 100%. To improve the quantum bit efficiency and reduce the implementation cost, this application invents a quantum private comparison method with a quantum bit efficiency of 400% using single photons with polarization and empty mode degrees of freedom. The method is called "Quantum Private Comparison Protocol Based on Photon Dual Degrees of Freedom". The protocol is that two private data comparison parties, Alice and Bob, compare whether private data is equal under the auspices of a semi-loyal third party, STP. Alice and Bob each have private data AC = {a j c j } and BD={b j d j }, where a j ,b j ,c j ,d j ∈{00,01,10,11},j∈{0,1,...,L-1},2 4L-1 ≤max{AC,BD}<2 4L , L is a positive integer; Alice and Bob also agree on the correspondence between the two quantum states and the two bits: Correspondence 1 is " and ", and the corresponding relationship 2 is " and "; The protocol is characterized as a whole by the following 6 steps: Step 1: Bob uses the private data BD = {b j d j } Prepare L single photons with polarization and empty mode degrees of freedom, namely the quantum sequence CP={cp j }, photon cp j The quantum state in terms of polarizability is determined by b j Prepared in accordance with the corresponding relationship 1, photon cp j The quantum state on the empty mode is determined by d j and the corresponding relationship 2; In addition, Bob also prepares a sufficient number of decoy photons, whose quantum states are randomly selected from 16 quantum states One, here |φ> P ∈{|H>,|V>,|R>,|A>},|φ> S ∈{|b1>,|b2>,|s>,|a>}; Bob divides these decoy photons into two parts DP0 and DP1 and randomly inserts them into the quantum sequence CP to form a new quantum sequence DCP; only Bob knows the measurement basis and quantum initial state corresponding to each photon in the DCP; Bob sends the quantum sequence DCP to the STP in the form of quantum data blocks through the quantum channel; Step 2: After receiving the quantum sequence DCP, Bob announces the position and measurement basis of the DP0 decoy photon in the quantum sequence DCP. STP performs quantum measurement on the DP0 decoy photon based on the announced information. After the measurement, STP informs Bob of the DP0 measurement result through the classical channel in an announcement. Bob compares the DP0 measurement result with the DP0 quantum initial state and calculates the error rate. Based on the error rate, it determines whether there is any eavesdropping in the quantum channel from Bob to STP. If the error rate is lower than the normal threshold, the protocol continues and enters step 3. Otherwise, the protocol terminates this operation and then restarts the protocol. Step 3: After Bob announces the position, measurement basis and quantum initial state of the DP1 decoy photon in the quantum sequence DCP, STP randomly selects some photons from DP1 and CP and performs the following 6 unitary operations: P01 , U P10 , U P11 , and And record the photons in CP as follows: If the photon cp with subscript j j No unitary operation is performed on the polarization degrees of freedom and the null mode degrees of freedom, so record e j =00, f j =00 and mu j =00; if in cp j The unitary operation on P01 、U P10 、U P11 、 and Then record e separately j =01,e j =10, e j =11, f j =01, f j =10 and f j =11, and record mu respectively j =00, mu j =10, mu j =10, mu j =00, mu j =01 and mu j = 01 as the unitary operation to change the sign of the photon measurement basis; thus, STP obtains two private number sequences UR = {e j f j } and MU={mu j }, where e j ,f j ∈{00,01,10,11},mu j ∈{00,01,10},j∈{0,1,...,L-1};Unitary operation transforms quantum sequences DP1 and CP into UDP1 and UCP={ucp j The quantum sequence UDP1 is randomly reinserted into the quantum sequence UCP to form a new quantum sequence UDCP. At this point, only the STP knows the position, measurement basis, and quantum state of each decoy photon in the quantum sequence UDCP. Subsequently, the STP sends the quantum sequence UDCP to Alice through the quantum channel. Step 4: After Alice receives the quantum sequence UDCP, STP announces the position and measurement basis of the decoy photon. Alice measures the decoy photon based on the information announced by STP and announces the measurement result to STP via the classical channel. STP compares Alice's measurement result with the quantum state of the decoy photon and calculates the error rate of the quantum state. If the error rate is normal, that is, there is no eavesdropper in the quantum channel, the protocol proceeds to step 5. Otherwise, the current run of the protocol is terminated and restarted. Step 5: After Alice discards the decoy photons in the UDCP and recovers the quantum sequence UCP, Alice notifies STP and Bob to publish the value of MU and the measurement basis of each photon in CP respectively; P01 and The measurement basis of the photon will not be changed, and the unitary operation U P10 、U P11 、 and It will change the measurement basis of the photon, and the photon has only two measurement bases in terms of polarization and empty mode freedom. Therefore, when mu j = 00, Alice uses the polarization and empty mode measurement basis published by Bob to measure ucp j ; When mu j = 10, Alice switches the polarization measurement basis announced by Bob and keeps the measurement basis of the empty mode to measure ucp j ; When mu j = 01, Alice switches to the empty mode measurement basis announced by Bob and keeps the polarization measurement basis to measure ucp j ; Photon UCP j There are four measurement results in polarization: |H>, |V>, |R> and |A>, respectively expressed as rp j = 00, 01, 10 and 11 records; there are also 4 measurement results on the empty mode |b1>, |b2>, |s> and |a>, respectively, using rs j =00, 01, 10 and 11 records; after quantum measurement, Alice obtains a private sequence MR = {rp j rs j }, where rp j ,rs j ∈{00,01,10,11}, j∈{0,1,...,L-1}; Alice uses the MR and the private data AC to perform the following two-bit bitwise exclusive OR operation: uab j =rp j ⊕a j and UCD j =rs j ⊕c j , here uab j ,ucd j ∈{00,01,10,11}, j∈{0,1,...,L-1}, ⊕ is the binary exclusive OR operator, and the calculation result is announced, that is, the sequence UABCD={uab j ucd j }; Step 6: After receiving the value of the sequence UABCD published by Alice, STP compares the UABCD with the UR in STP's hand to see if they are equal; if they are equal, STP announces that the private data of Alice and Bob are equal; otherwise, the private data of the two users are unequal.

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