Quantum security vector dominance judgment method based on privacy protection

Abstract

The invention provides a quantum security vector dominance judgment method based on privacy protection, which comprises the following steps that: a first participant and a second participant respectively carry out input camouflage on own private vectors, and carry out encoding and replacement operations to obtain a result after replacement and random number encryption; the semi-honest third party generates an entangled state sequence; the semi-honesty third party retains a first particle sequence in the entangled state sequence, respectively distributes a second particle and a third particle to the first participant and the second participant in sequence, carries out corresponding processing to obtain comparison results, and if the obtained comparison results are all 2, the semi-honesty third party sends the second particle sequence to the second participant; and the semi-honest third party declares that the vector of the first participant dominates the vector of the second participant, otherwise, declares that the vector of the first participant is not dominated. According to the method, input camouflage attacks carried out by the participants are prevented at the same time. According to the method, efficient judgment of vector dominance can be realized under polynomial complexity, various attacks can be resisted, and privacy leakage is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of privacy protection computing in quantum cryptography, and in particular relates to a quantum security vector dominance determination method based on privacy protection. Background Art

[0002] Against the backdrop of the rapid development of quantum information technology, secure computational geometry (SCG) based on computational complexity assumptions has gradually exposed its security limitations under the powerful computing power of quantum computers. However, combining quantum mechanisms with encryption technology can break through these limitations and achieve unconditional security of SCG. This combination has spawned a new field called Quantum Secure Computational Geometry (QSCG). In recent years, solutions to geometric problems have mostly relied on dividing geometric shapes into grids and using private set calculations to achieve approximate geometric calculations. However, these methods have problems such as difficulty in accurately identifying boundary nodes and high resource consumption. Summary of the invention

[0003] Purpose of the invention: The technical problem to be solved by the present invention is to provide a privacy-preserving quantum security vector domination determination method in response to the deficiencies of the prior art, aiming to solve the security limitations of traditional secure computational geometry (SCG) faced by the powerful computing power of quantum computers, and overcome the accuracy and resource consumption problems in existing geometric problem solutions. The method uses a quantum private permutation method to scramble the participant information encoded into an entangled state, and to perform domination determination on the scrambled information, while ensuring the privacy of the information of both parties. Compared with traditional methods, the quantum security vector domination protocol of the present invention has achieved significant improvements in computing efficiency and communication costs, and has expanded its application in privacy-preserving computing. In addition, the method of the present invention also has the advantages of high efficiency, scalability and flexibility, and can meet the security computing needs in various complex scenarios, especially in distributed computing, cloud computing platforms, Internet of Things devices, and occasions with special requirements for privacy protection.

[0004] The method of the present invention comprises the following steps:

[0005] Step 1: The first participant Alice and the second participant Bob disguise their own private vectors respectively;

[0006] Step 2: Alice, the first participant, encodes each element in the private vector into a quantum entangled state, selects the first and second particle sequences and sends them to Bob, the second participant, for permutation operation.

[0007] Step 3, the second participant Bob performs a permutation operation on the first particle sequence and sends it back to the first participant Alice, adds the prepared random vector elements to the phase of the second particle sequence and performs a permutation operation, and then sends it back to the first participant Alice;

[0008] Step 4: Alice, the first participant, measures the final quantum state and obtains the result after being permuted and encrypted with random numbers.

[0009] Step 5: The second participant Bob performs random vector addition and permutation operations on his own private vector, and performs random vector permutation operations on the fixed vector Permutate and get the vector ;

[0010] Step 6: The first participant Alice and the second participant Bob share a random bit string to encrypt their respective private information when performing the phase shift operation in step 7, and the semi-honest third party Trent generates an entangled state sequence;

[0011] Step 7, the semi-honest third party Trent retains the first particle sequence in the entangled state sequence, and distributes the second and third particles to the first participant Alice and the second participant Bob in order, respectively. The first participant Alice and the second participant Bob apply a phase shift operation with private vector information to the sequence;

[0012] Step 8: The semi-honest third party Trent measures the final quantum state with encrypted information on the phase and sends the measured encoding result R i Inform the first participant Alice;

[0013] Step 9: The first participant Alice encodes the result R i XOR with the random bit string and invert it bit by bit to get the comparison result U;

[0014] Step 10: The first participant Alice and the second participant Bob compare the result U and the vector Send it to the semi-honest third party Trent for repeated private comparison. If the comparison result R i All are 2, and the semi-honest third party Trent declares that the first participant's vector dominates the second participant's vector, otherwise it declares that it does not dominate.

[0015] Step 1 includes: Setting , , where n is the number of elements in the vector, N is the element dimension, and D is the dimension of the quantum state; the first participant Alice enters a private vector , the second participant Bob enters a private vector , a permutation operation , , , is the i-th element in the private vector A, It is the i-th element in the private vector B, where i ranges from 1 to n;

[0016] The first participant Alice disguises the input of her private vector A:

[0017] (1)

[0018] Get the disguised private vector , with a length of 4n, The i-th element of the 4n elements in is defined as , i takes the value of 1~4n, and we get ;

[0019] The second participant Bob performs input disguise on his private vector B:

[0020] (2)

[0021] Get the disguised private vector , with a length of 4n, The i-th element of the 4n elements in is defined as ,get ; and let the vector .

[0022] Step 2 includes: the first participant Alice sends the private vector Each element in Encoded as quantum state, i takes the value of 1~4n, the formula is:

[0023] (3)

[0024] in The first participant, Alice, adds the i-th element in the private vector Encoded quantum state; is a complex phase factor, usually used to describe the phase change in the quantum state, , It is a quantum state The ground state in Stored in particles middle, Stored in particles middle; is an index variable;

[0025] and Respectively represent particles storing two different d-qubits, particles The quantum bits on ,particle The quantum bits on , , e is the Euler number, is an imaginary unit;

[0026] Then, the first participant Alice selects the first particle and the second particle from each quantum state, forming two ordered particle sequences, the first sequence H and the second sequence T. , ,in, It means that the first participant Alice obtains the disguised private vector The 4nth element in The first particle selected from the encoded quantum state, It means that the first participant Alice obtains the disguised private vector The 4nth element in The second particle selected from the quantum state encoded.

[0027] Step 2 also includes: the first participant Alice initializes a particle g, using a two-particle addition gate The operation calculates the sum of the quantum bits of the particles in the first sequence H and sends the first sequence H to the second participant Bob;

[0028] Said The formula for the operation is:

[0029] (4)

[0030] (5)

[0031] in It means that a two-particle addition gate operation is performed on particles t and h. The colon ":" in formula 4 is meaningless. are two particles used to demonstrate the effect of BSUM. In operation, the quantum state is transformed into , the quantum state of quantum bit y is added to quantum bit x through BSUM operation to form a new quantum state ;

[0032] Represents the particle and particles Apply the BSUM operation to turn the quantum bit on particle g into particle and particles The sum of the quantum bits; then arrive , so that the quantum bit on particle g is ;

[0033] Indicates application After that, the quantum bit on particle g becomes , It means that the first participant Alice adds the 4nth element in the private vector Encoded quantum state The first particle in .

[0034] Step 3 includes: the second participant Bob replaces the particles in the first sequence H Operation, and record the result as , and then sent to the first participant Alice; the first participant Alice receives the result The particles in the single particle modular multiplication gate Operation to calculate ;

[0035] Then apply The gates sequentially subtract the received result from particle g The quantum bits of particles in the

[0036] Finally, the particle g is measured. If the measurement result is , it means that the second participant Bob has not carried out any attack on the particle to destroy the entangled state, such as measurement or forgery, and the total particle verification is correct after the replacement operation, and the protocol continues; otherwise, the protocol terminates;

[0037] The single particle modular multiplication gate The formula for the operation is:

[0038] (6)

[0039] (7)

[0040] Where D is the modulus; is an operation example, which means that the particle t is modularly multiplied by parameter m, and the quantum state is The particle t passes through Operation results , Represents the particle Perform modular multiplication (D-1). mod (modulo) means modular arithmetic, which is to calculate the remainder after dividing two numbers.

[0041] The application The gates subtract the received The formula for the particle in is:

[0042] (8)

[0043] Then, the first participant Alice sends the second sequence Sent to the second participant Bob, the second participant Bob prepares a random vector ,in, , is a random vector The i-th element in the second sequence is 1~4n. The second participant Bob Apply phase manipulation to each particle , after the permutation operation, the result is , and then send it back to the first participant Alice;

[0044] The operation The formula is: (9) (10)

[0045] in It is a single-particle revolving door operation; This is an example operation with parameter m, acting on particle t, where parameter m represents the magnitude of the rotation; Indicates that the phase factor of the quantum bit x is adjusted by performing a phase rotation with parameter m, where y is the control factor of the rotation operation. is the quantum state with qubit x; Represents the particle The parameters are Phase rotation operation.

[0046] Step 4 includes: the quantum state in the hand of the first participant Alice is:

[0047] (11)

[0048] in When the second participant Bob adds a random vector element to the phase of the second sequence of particles, and , second sequence The result obtained after applying the same permutation operation; is the ith element of the private vector of the first participant Alice after input disguise, and is the i-th quantum state entangled particles in

[0049] Then the first participant Alice applies a two-particle XOR gate to the result Operation, quantum inverse Fourier transform operate: (12) (13) (14) (15)

[0050] in is the conventional notation for the inverse Fourier transform, The symbol in the upper right corner represents the inverse transformation, represents the inverse quantum Fourier transform operation on particle t, It means that a double-particle XOR gate operation is performed on particles t and h. After the operation, particle h will XOR the value of the quantum state in particle t. Among them, particles t and h and the quantum bits x and y on their particles are used as examples to more clearly describe the process and function of quantum gate operation. Similarly, After performing a double particle XOR gate, we get , that is ; is an XOR operation, 0 1=1,1 1=0,0 0=0,1 0=1, It is a particle Performing an inverse quantum Fourier transform Operation to obtain particles Information stored on the phase;

[0051] Finally, the first participant Alice Perform inverse quantum Fourier transform to extract phase data and measure , and the resulting vector ,in yes The ith element of .

[0052] Step 5 includes: the second participant Bob converts the vector Add to Vector Then, and Replace operate:

[0053] (16)

[0054] in refers to After the i-th element is privately replaced, it is replaced from the i-th element to the elements, the mapping of i in the permutation operation is ;

[0055] Then the second participant Bob gets , , ; yes Add random vector And the result vector obtained after the overall permutation; For vector The i-th element in yes The result after the permutation operation.

[0056] Step 6 includes: the first participant Alice privately shares a set of random bits with the second participant Bob , among which , ; Semi-honest third party Trent generation A sequence of three-particle entangled states, where the i-th entangled state is of the form:

[0057] (17)

[0058] in is the i-th entangled state among the 4n entangled states generated by the semi-honest third party Trent, in which the three entangled particles are the particles retained by the semi-honest third party Trent. , the particle sent to the first participant Alice , the particle sent to the second participant Bob , Represents particles The quantum state of Represents particles The quantum state of Represents particles The quantum state of represents the i-th three-particle entangled state generated by the semi-honest third party Trent The second particle in represents the i-th three-particle entangled state generated by the semi-honest third party Trent The third particle in .

[0059] Step 7 includes: the semi-honest third party Trent selects the second and third particles from each entangled state to form an ordered sequence and ; then the semi-honest third party Trent will and Send to the first participant Alice and the second participant Bob respectively; Represents the 4nth three-particle entangled state generated by the semi-honest third party Trent The second particle in The calculation formula is: , represents the third particle in the 4nth three-particle entangled state generated by the semi-honest third party Trent;

[0060] The first participant, Alice, receives Afterwards, Applying a phase shift operator , add your own private information : ,in, It means that the particle The phase shift operation is performed. Representation Operator The operation performed is to multiply the phase by ,and Same, but represents the operations performed on particles; represents the phase factor, which is used to control the phase change of the quantum state. ;

[0061] The second participant, Bob, Applying a phase shift operator : ,in, It means that the particle The phase shift operation is performed. Representation Operator The operation performed is to multiply the phase by ;

[0062] Then the first participant Alice and the second participant Bob will and Sent to the semi-honest third party Trent.

[0063] Step 8 includes: After integrating all received particles, the semi-honest third party Trent obtains the following quantum state:

[0064] ,

[0065] in is the initial i-th quantum state The overall quantum state form after the first participant Alice and the second participant Bob respectively perform phase shift operations on the received particles;

[0066] Then the semi-honest third party Trent imposes Door and Operation, then Particles for measurement:

[0067] ,

[0068] in It is a particle and The two-particle XOR gate operation is performed to convert the quantum state Processed as , It is a particle and The two-particle XOR gate operation converts the quantum state Processed as , It is a particle The quantum inverse Fourier transform operation is performed because the two particles behind and Use a two-particle XOR gate to process Only then can the inverse quantum Fourier transform be performed to obtain phase information, otherwise the result obtained is meaningless random information;

[0069] The results after measurement ;

[0070] Step 9 includes: the semi-honest third party Trent counts the results. If , the semi-honest third party Trent will Recorded as 0; if Trent will Recorded as 2, otherwise Record it as 1, and then Inform the first participant Alice, who and Applying XOR operation and bitwise inversion yields and The comparison result U;

[0071] Step 10 includes: the first participant Alice and the second participant Bob repeat steps 7 to 9, but the first participant Alice inputs U and the second participant Bob inputs ; After the protocol is executed, the semi-honest third party Trent outputs the result ; If all are all equal to 2, then , the semi-honest third party Trent publishes the results , that is, vector A dominates vector B, symbol It means that for i=1,2,…,n, there is the i-th element in vector A Greater than the i-th element in vector B Otherwise, the semi-honest third party Trent publishes the results , that is, vector A does not dominate vector B, the symbol It means that for i=1,2,…,n, there is at least one .

[0072] Beneficial effects: The present invention proposes a privacy-preserving quantum-safe vector dominance determination method, which uses a quantum private permutation protocol to permute the private input vector of the participant while ensuring that the dominance determination is not affected, thereby preventing other participants from stealing information. Compared with other perturbation methods, this method also prevents input camouflage attacks by the participant himself. This method can achieve efficient determination of vector dominance under polynomial complexity, and can resist various attacks and reduce privacy leakage. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a flow chart of the method of the present invention.

[0074] Figure 2 It is a schematic diagram of the quantum security vector control process.

[0075] Figure 3 It is a schematic diagram of quantum private comparison. DETAILED DESCRIPTION

[0076] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0077] The embodiment of the present invention provides a privacy protection-based quantum security vector dominance determination method, including:

[0078] Step 1, such as Figure 1 As shown ( Figure 1U represents the result obtained by the first participant Alice and the second participant Bob adding the same random vector to the disguised input private vector, performing a permutation operation and then performing a private comparison). The first participant Alice and the second participant Bob disguise their respective private vectors and set the vector length to , the dimension of a quantum system The first participant, Alice, enters a private vector , the second participant Bob enters a private vector and a permutation operation .like Figure 2 As shown, both parties perform input camouflage operations at the same time, and Alice performs input camouflage on her private vector, which is recorded as , where according to the input camouflage rule, we get , Bob performs the input disguise operation mentioned above on his private vector and obtains , and prepare a .

[0079] Step 2: Alice transfers the private vector Each element in Encoded as quantum states: , for example, the first element is encoded as:

[0080] (1)

[0081] The 8th element is encoded as:

[0082] (2)

[0083] The same is true for other elements. . Then, Alice selects Select the first particle and the second particle respectively to form two ordered particle sequences and .

[0084] Alice initializes a particle g, namely ,use The operation calculates the sum of particles in the first sequence H and sends H to Bob:

[0085] (3)

[0086] Step 3: Bob permutes the first sequence H received Operation, and record the result as ,in, , and then send it back to Alice. Alice is happy with the received The particles in Operation to calculate :

[0087] (4)

[0088] (5)

[0089] Then apply The gate subtracts these particles in turn:

[0090] (6)

[0091] Finally, the particle g is measured. If the measurement result is , it means that Bob has not carried out any attack on the particles that destroy the entanglement state, such as measurement or forgery, and the total particle verification is correct after the replacement operation, and the protocol continues; otherwise, the protocol terminates.

[0092] Alice will sequence Send to Bob. Bob prepares a random vector . Bob has a sequence Each particle is operated on ,in , after the permutation operation, the change of the first particle is: , the change of the second particle is: , and the same is true for other particles, and the particles after the phase rotation operation are permuted to obtain: , and send it back to Alice.

[0093] Step 4, the quantum state in Alice's hand is as follows:

[0094] (7)

[0095] Right now: ;

[0096] Alice then applies , :

[0097] (8)

[0098] (9)

[0099] Finally, Alice Take measurements, get results ,in , so we get .

[0100] Step 5: Bob converts the vector Add to Vector Then, compare it with Replace Operation, where , , that is, , .

[0101] Step 6, such as Figure 3 As shown in Figure 2, at this point, a semi-honest third party begins to assist the two participants in the private comparison. Alice privately shares a set of random bit strings with Bob. =1010111. Trent generated A sequence of three-particle entangled states:

[0102] (10)

[0103] Subscript The corresponding particles are sent to Trent, Alice and Bob respectively. Trent selects the second and third particles from each quantum state to form an ordered sequence. and . Trent then sends them to Alice and Bob respectively.

[0104] Step 7: Alice receives Then, the particles Applying a phase shift operator ,like Figure 3 As shown, add your own private information : , for example, for particles Applying a phase shift operator , we can get , similarly, Bob also applies his own phase shift operator : , for example, for particles Applying a phase shift operator , we can get: , and then after the operation is completed and The sequence is sent back to Trent.

[0105] Step 8, such as Figure 3 As shown, Trent obtains a quantum state that combines the private information of the two participants. in, , ,……, .

[0106] Trent then applies Door and Operation, then The particle is measured and we get:

[0107] , ,

[0108] That is , ;

[0109] right , ;

[0110] After measuring these, we get the results . , , , , , , , .

[0111] Step 9: Trent counts the results. Trent will Recorded as 0; if Trent will Recorded as 2, otherwise Recorded as 1, the calculated result is , and then inform Alice of the result, and Alice XOR operation is performed with the pre-shared key: ,get , and bitwise invert to get , denoted as U, such as Figure 1 shown.

[0112] Step 10: Alice and Bob repeat steps 7 to 9, but Alice inputs U and Bob inputs That is, Alice and Bob call the above steps to let Trent compare U and After the protocol is executed, Trent calculates , due to U and Same , so all are all equal to 2. According to the protocol steps, Trent found , so the results are published: . The problem of information leakage of a single vector element pair in the comparison process in reality is solved. Compared with the prior art, when dealing with similar problems, the present invention uses input camouflage technology to enhance the confidentiality of vector elements, while being able to resist internal and external attacks, ensuring the security of secret information of both parties during the comparison process, and maintaining the privacy of information even with the participation of a third party. The use of a semi-quantum model reduces the user's requirements for quantum resources, reduces the demand for expensive quantum equipment, and saves hardware costs.

[0113] The present invention provides a privacy-protected quantum security vector dominance determination method. There are many methods and ways to implement the technical solution. The above is only a preferred implementation of the present invention. It should be pointed out that for ordinary technicians in this technical field, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A privacy-preserving quantum security vector dominance determination method, characterized in that: The following steps are involved: Step 1: The first participant Alice and the second participant Bob disguise their own private vectors respectively; Step 2: Alice, the first participant, encodes each element in the private vector into a quantum entangled state, selects the first and second particle sequences and sends them to Bob, the second participant, for permutation operation. Step 3, the second participant Bob performs a permutation operation on the first particle sequence and sends it back to the first participant Alice, adds the prepared random vector elements to the phase of the second particle sequence and performs a permutation operation, and then sends it back to the first participant Alice; Step 4: Alice, the first participant, measures the final quantum state and obtains the result after being permuted and encrypted with random numbers. Step 5: The second participant Bob performs random vector addition and permutation operations on his own private vector, and performs random vector permutation operations on the fixed vector Permutate and get the vector ; Step 6: The first participant Alice and the second participant Bob share a random bit string, and the semi-honest third party Trent generates an entangled state sequence; Step 7, the semi-honest third party Trent retains the first particle sequence in the entangled state sequence, and distributes the second and third particles to the first participant Alice and the second participant Bob in order, respectively. The first participant Alice and the second participant Bob apply a phase shift operation with private vector information to the sequence; Step 8: The semi-honest third party Trent measures the final quantum state with encrypted information on the phase and sends the measured encoding result R i Inform the first participant Alice; Step 9: The first participant Alice encodes the result R i XOR with the random bit string and invert it bit by bit to get the comparison result U; Step 10: The first participant Alice and the second participant Bob compare the result U and the vector Send it to the semi-honest third party Trent for repeated private comparison. If the comparison result R i All are 2, and the semi-honest third party Trent declares that the first participant's vector dominates the second participant's vector, otherwise it declares that it does not dominate.

2. The method according to claim 1, characterized in that Step 1 includes: Setting , , where n is the number of elements in the vector, N is the element dimension, and D is the dimension of the quantum state; the first participant Alice enters a private vector , the second participant Bob enters a private vector , a permutation operation , , , Is a private vector The i-th element in Is a private vector The i-th element in , i ranges from 1 to n; The first participant Alice disguises the input of her private vector A: (1)， Get the disguised private vector , with a length of 4n, The i-th element of the 4n elements in is defined as , i ranges from 1 to 4n, and we get ; The second participant Bob performs input disguise on his private vector B: (2)， Get the disguised private vector , with a length of 4n, The i-th element of the 4n elements in is defined as ,get ; and let the vector .

3. The method according to claim 2, characterized in that Step 2 includes: the first participant Alice sends the private vector Each element in Encoded as quantum state, i takes the value of 1~4n, the formula is: (3)， in The first participant, Alice, adds the i-th element in the private vector Encoded quantum state; is a complex phase factor, , It is a quantum state The ground state in Stored in particles middle, Stored in particles middle; is an index variable; and Respectively represent particles storing two different d-qubits, particles The quantum bits on ,particle The quantum bits on , , e is the Euler number, is an imaginary unit; Then, the first participant Alice selects the first particle and the second particle from each quantum state, forming two ordered particle sequences, the first sequence H and the second sequence T. , ,in, It means that the first participant Alice obtains the disguised private vector The 4nth element in The first particle selected from the encoded quantum state, It means that the first participant Alice obtains the disguised private vector The 4nth element in The second particle selected from the quantum state encoded.

4. The method according to claim 3, characterized in that Step 2 also includes: the first participant Alice initializes a particle g, using a two-particle addition gate Operation on the first sequence The sum of the quantum bits of the particles in the first sequence is calculated and Sent to the second participant Bob; Said The formula for the operation is: (4)， (5)， in represents the double particle addition gate operation performed on particles t and h. are two particles used to demonstrate the effect of BSUM. In operation, the quantum state is transformed into , the quantum state of quantum bit y is added to quantum bit x through BSUM operation to form a new quantum state ; Represents the particle and particles Apply the BSUM operation to turn the quantum bit on particle g into particle and particles The sum of the quantum bits; then arrive , so that the quantum bit on particle g is ; Indicates application After that, the quantum bit on particle g becomes , It means that the first participant Alice adds the 4nth element in the private vector Encoded quantum state The first particle in .

5. The method according to claim 4, characterized in that Step 3 includes: the second participant Bob takes the first sequence Replace the particles in Operation, and record the result as , and then sent to the first participant Alice; the first participant Alice receives the result The particles in the single particle modular multiplication gate Operation to calculate ; Then apply The gates sequentially subtract the received result from particle g The quantum bits of particles in the Finally, the particle g is measured. If the measurement result is , it means that the second participant Bob did not attack the particle to destroy the entanglement state, and the total particle verification is correct after the replacement operation, and the protocol continues; otherwise, the protocol terminates; The single particle modular multiplication gate The formula for the operation is: (6)， (7)， Where D is the modulus; It means to multiply the particle t by parameter m, and the quantum state is The particle t passes through Operation results , Represents the particle Perform modular multiplication D-1, mod represents modular operation; The application The gates subtract the received The formula for the particle in is: (8)， Subsequently, the first participant Alice sends the second sequence T to the second participant Bob, who prepares a random vector ,in, , is a random vector The second participant Bob applies a phase operation to each particle of the second sequence T. , after the permutation operation, the result is , and then send it back to the first participant Alice; The operation The formula is: (9)， (10)， in This is an example operation with parameter m, acting on particle t, where parameter m represents the magnitude of the rotation; Indicates that the phase factor of the quantum bit x is adjusted by performing a phase rotation with parameter m on the quantum bit x. is the quantum state with qubit x; Represents the particle The parameters are Phase rotation operation.

6. The method according to claim 5, characterized in that Step 4 includes: the quantum state in the hand of the first participant Alice is: (11)， in When the second participant Bob adds a random vector element to the phase of the second sequence of particles, and , second sequence The result obtained after applying the same permutation operation; is the i-th element of the private vector of the first participant Alice after input disguise; Then the first participant Alice applies a two-particle XOR gate to the result Operation, quantum inverse Fourier transform operate: (12)， (13)， (14)， (15)， in The symbol in the upper right corner represents the inverse transformation, represents the inverse quantum Fourier transform operation on particle t, It means that a double-particle XOR gate operation is performed on particles t and h. After the operation, particle h will XOR the value of the quantum state in particle t. After performing a double particle XOR gate, we get , that is ; is an XOR operation, It is a particle Perform inverse quantum Fourier transform operations to obtain particles Information stored on the phase; Finally, the first participant Alice Perform inverse quantum Fourier transform to extract phase data and measure , and the resulting vector ,in yes The ith element of .

7. The method according to claim 6, characterized in that Step 5 includes: the second participant Bob converts the vector Add to Vector Then, and Replace operate: (16)， in refers to After the i-th element is privately replaced, it is replaced from the i-th element to the elements, the mapping of i in the permutation operation is ; Then the second participant Bob gets , , ; yes Add random vector And the result vector obtained after the overall permutation; For vector The i-th element in yes The result after the permutation operation.

8. The method according to claim 7, characterized in that Step 6 includes: the first participant Alice privately shares a set of random bits with the second participant Bob , among which , ; Semi-honest third party Trent generation A sequence of three-particle entangled states, where the i-th entangled state is of the form: (17)， in is the i-th entangled state among the 4n entangled states generated by the semi-honest third party Trent, in which the three entangled particles are the particles retained by the semi-honest third party Trent. , the particle sent to the first participant Alice , the particle sent to the second participant Bob , Represents particles The quantum state of Represents particles The quantum state of Represents particles The quantum state of represents the i-th three-particle entangled state generated by the semi-honest third party Trent The second particle in represents the i-th three-particle entangled state generated by the semi-honest third party Trent The third particle in .

9. The method according to claim 8, characterized in that Step 7 includes: the semi-honest third party Trent selects the second and third particles from each entangled state to form an ordered sequence and ; then the semi-honest third party Trent will and Send to the first participant Alice and the second participant Bob respectively; Represents the 4nth three-particle entangled state generated by the semi-honest third party Trent The second particle in The calculation formula is , represents the third particle in the 4nth three-particle entangled state generated by the semi-honest third party Trent; The first participant, Alice, receives Afterwards, Applying a phase shift operator , add your own private information : ,in, It means that the particle The phase shift operation is performed. Representation Operator The operation performed is to multiply the phase by ; represents the phase factor, which is used to control the phase change of the quantum state. ; The second participant, Bob, Applying a phase shift operator : ,in, It means that the particle The phase shift operation is performed. Representation Operator The operation performed is to multiply the phase by ; Then the first participant Alice and the second participant Bob will and Sent to the semi-honest third party Trent.

10. The method according to claim 9, characterized in that Step 8 includes: After integrating all received particles, the semi-honest third party Trent obtains the following quantum state: ， in is the initial i-th quantum state The overall quantum state form after the first participant Alice and the second participant Bob respectively perform phase shift operations on the received particles; Then the semi-honest third party Trent imposes Door and Operation, then Particles for measurement: ， in It is a particle and The two-particle XOR gate operation converts the quantum state Processed as , It is a particle and The two-particle XOR gate operation converts the quantum state Processed as , It is a particle The inverse quantum Fourier transform operation performed; The results after measurement ; Step 9 includes: the semi-honest third party Trent counts the results. If , the semi-honest third party Trent will Recorded as 0; if Trent will Recorded as 2, otherwise Record it as 1, and then Inform the first participant Alice, who and Applying XOR operation and bitwise inversion yields and The comparison result U; Step 10 includes: the first participant Alice and the second participant Bob repeat steps 7 to 9, but the first participant Alice inputs U and the second participant Bob inputs ; After the protocol is executed, the semi-honest third party Trent outputs the result ; If all are all equal to 2, then , the semi-honest third party Trent publishes the results Otherwise, the semi-honest third party Trent publishes the results .

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