A verifiable quantum-safe multi-party XOR protocol based on superdense coding

Abstract

This invention belongs to the field of quantum-safe multi-party computation and discloses a verifiable quantum-safe multi-party XOR protocol based on hyperdense coding. The preprocessing stage is for n participants P. j Each participant holds two classical bits. Through an ultra-dense encoding method, P0 obtains specific aggregate information of each party's classical bits by transmitting only n qubits, while ensuring that P0 cannot access portions of the bits held by each party that P0 has no right to see. This method significantly reduces the communication overhead in multi-party computation. During the computation phase, the real input is hidden using the key and auxiliary values ​​generated in the preprocessing phase, and an XOR operation is performed without revealing the privacy of the input. The protocol does not require the participation of a trusted third party, eliminating trust dependencies and achieving decentralized security; it supports quantum state input, defending against future quantum computing threats; and it can verify whether anyone maliciously tampered with the calculated value during the XOR operation, making it suitable for sensitive scenarios such as privacy computation and joint analysis.

Description

Technical Field

[0001] This invention relates to the fields of quantum computing and cryptography, and in particular to a verifiable quantum-safe multi-party XOR protocol based on hyper-dense coding. Background Technology

[0002] Quantum-safe multi-party XOR protocols aim to allow multiple untrusted parties to collaboratively compute the XOR of multiple quantum states without revealing their private data. In classical cryptography, secure multi-party computation typically relies on difficult problems such as large number factorization and the discrete logarithm problem to ensure security. However, with the development of quantum computing technology, the cornerstones of classical cryptography face the potential threat of being broken.

[0003] Currently, research on quantum-safe multi-party XOR protocols mainly focuses on the following directions. The first is circuit implementation based on quantum logic gates. This involves designing specialized quantum circuits where participants encode their private bits into quantum states and jointly compute the XOR value through a series of quantum gate operations (such as CNOT gates). The second approach utilizes a third-party assisted computation framework, introducing one or more "semi-honest" third parties to assist in the computation. Summary of the Invention

[0004] To address the aforementioned shortcomings of existing technologies, this invention proposes a verifiable quantum-safe multi-party XOR protocol based on ultra-dense coding. This protocol reduces communication overhead between participants, eliminates the need for third-party intervention, and prevents arbitrary... The collusion attack by the participating parties and whether anyone maliciously tampered with the calculated value during the XOR process can be verified.

[0005] The technical solution of this invention is implemented as follows:

[0006] A verifiable quantum-safe multi-party XOR protocol based on superdense coding, which completes the process without the need for third-party intervention. The protocol includes an XOR operation between the quantum states held by each participant, whereby none of the participants obtain any information from the other participants other than the XOR result.

[0007] Preprocessing stage:

[0008] Each participant obtains the auxiliary values ​​and keys needed for the computation phase through the preprocessing phase;

[0009] Calculation phase:

[0010] Participants input real data and encrypt it using the key obtained in the preprocessing stage;

[0011] The participants sequentially send the results of executing the CONT gate to the next participant for XOR calculation, and aggregate the encrypted quantum state through chain transmission and finally send it to the first participant;

[0012] The first participant verifies the final result and then publishes the verification result.

[0013] Preferably,

[0014] Preprocessing phase: Each participant Generate random auxiliary values ​​of length n=2m and key ; Through ultra-dense coding methods, the first participant Obtain the aggregation key and the bit string of each participant , for and The index in the bit string, while ensuring It is impossible to know any single key. traversal To make get as well as ;

[0015] During the calculation phase, all participants utilize auxiliary values. and key and aggregation key Regarding the quantum states held by each party Encryption is performed, and the encrypted quantum states are aggregated through chain transmission in the execution order. Decryption is performed to obtain the XOR result, and auxiliary values ​​are used. Verify the correctness of the results.

[0016] Preferably, the calculation stage involves performing a secure multi-party XOR calculation according to the following steps:

[0017] 1) Each participant Use a pseudo-random function to assign auxiliary values The middle Bit extension to length of bit string, The former The position is denoted as The following The bit-extended bit string is denoted as ,Will , and Encoded as quantum states respectively , and Participants Using the same pseudo-random function, the auxiliary value The middle Bit extension to length of bit string and will , as well as Encoded as quantum states respectively , and ;

[0018] 2) Each participant Enter one quantum state of a bit , recorded as and will , and Perform a bitwise XOR operation, and the result is denoted as ;

[0019] 3) Participating parties Will Send to the participants ;

[0020] 4) Participating parties The calculated results are processed in sequence. With the participating parties Received After performing bitwise XOR, we get And send to the participants ;

[0021] 5) Participating parties The calculated With the participating parties Received After performing bitwise XOR, we get And send to the participants ;

[0022] 6) Participating parties get Then with Perform bitwise XOR to obtain ,Will and and Perform a bitwise XOR operation, and the first bit of the result will be... The states of each qubit are as follows: The XOR result, after The state of each qubit is used to... The comparison is used to verify whether the value has been modified during the calculation or transmission process.

[0023] Preferably, the target Each participating party And the two bits of data held by each participant. Through a super-dense coding method, only transmitting In the case of one quantum bit, make get and various At the same time ensure Unable to obtain a single The specific steps are as follows:

[0024] 1) Construct two sets of mutually non-orthogonal pairs. Bit entanglement basis , and from An entangled state Randomly select a state and use 1 quantum bit Prepare one of the selected states;

[0025] 2) The bits in the prepared quantum state Send to each in advance ;

[0026] 3) All Operation Acting on each received quantum bit Above, among which and These represent the actions performed on the qubits. Pauli-Z and Pauli-X operators on;

[0027] 4) Each Send the manipulated qubits to ;

[0028] 5) After receiving each qubit, they are measured using the basis corresponding to the initially selected entangled state; that is, assuming the initial... The selected entangled state belongs to the base Then use Perform measurements; assuming initially The selected entangled state belongs to the base Then use Take measurements. Calculate based on the measurement results and various .

[0029] Preferably, the two groups are not orthogonal to each other. Bit entanglement basis , for:

[0030] ,

[0031] in For one The computational basis of a quantum bit, whose corresponding eigenvalues ​​are integers. of The bit string determined by the binary representation; Indicates to Invert bits; and They represent and .

[0032] Preferably, the step (5) described Calculated based on measurement results and various The method is as follows:

[0033] if use The measurement was performed and the state of the qubit was determined to be... ,but , ;if use The measurement was performed and the state of the qubit was determined to be... ,but , .

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] It enables multiple parties to perform a joint XOR operation without the involvement of a trusted third party, and without disclosing any information other than the result:

[0036] It can securely exchange keys without using a QKD network, enables multi-participant XOR operations, and supports quantum state input.

[0037] This can verify whether someone maliciously tampered with the calculated value during the XOR process;

[0038] for A specific classic bit aggregation operation between the participants will transform what would otherwise be a transmission of... The communication of a classic bit is compressed to only one. Each quantum bit significantly reduces communication overhead. The required local Pauli operation is simple to implement and can be scaled to any number of participants.

[0039] By randomly selecting between two sets of non-orthogonal entangled bases and relying on base measurement results, the leakage resistance and eavesdropping resistance are enhanced. Attached Figure Description

[0040] Figure 1 This is the overall process of the verifiable quantum-safe multi-party XOR protocol based on ultra-dense coding in this invention;

[0041] Figure 2 To achieve high density in transmission using an ultra-dense coding method In the case of one quantum bit, the participants Obtain the classic bit combination for all four participants. and various At the same time ensure Unable to obtain a single A schematic diagram of the method;

[0042] Figure 3 This is a circuit diagram for preparing entangled states in the example;

[0043] Figure 4 The preparation of entangled states and the application of operations by each party in the examples are described. The circuit diagram for encoding. Detailed Implementation

[0044] The present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0045] like Figure 1 As shown, the protocol includes:

[0046] Preprocessing stage:

[0047] Each participant obtains the auxiliary values ​​and keys needed for the computation phase through the preprocessing phase;

[0048] Calculation phase:

[0049] Participants input real data and encrypt it using the key obtained in the preprocessing stage;

[0050] The participants sequentially send the results of executing the CONT gate to the next participant for XOR calculation, and aggregate the encrypted quantum state through chain transmission and finally send it to the first participant;

[0051] The first participant verifies the final result and makes the verification result public;

[0052] This invention reduces communication overhead between participants, eliminates the need for third-party involvement, and prevents arbitrary... The protocol verifies whether any participant maliciously tampered with the calculated value during the XOR operation, and includes two phases: a preprocessing phase and a computation phase. The preprocessing phase specifically includes the following steps:

[0053] Assume there is Each participating party Each participant holds two classic bit auxiliary values. and key Now it is necessary to transmit only In the case of one quantum bit, a secure communication method is used to enable get and various At the same time ensure Unable to obtain a single The following describes a specific approach to achieving this goal using an ultra-dense coding method:

[0054] First, construct two groups. Bit entanglement state:

[0055] ,

[0056] in For one The computational basis of a quantum bit, whose corresponding eigenvalues ​​are integers. of The binary representation determines the bit string, for example in In this case, express ; Indicates to Invert bits; and They represent and .

[0057] and Each constitutes a set of orthogonal bases, and through calculation and The inner product shows that the two sets of bases are not orthogonal to each other:

[0058] ,

[0059] For the sake of convenience in subsequent calculations, we define... ,

[0060] in bit string Middle (from highest to lowest position) Given the value of each bit, the entangled states can be written in the following form:

[0061] ,

[0062] Before the formal communication, from An entangled state Randomly select a state and use it Prepare 10 qubits, and then use 10 qubits of them. Send to each in advance .

[0063] After the communication begins, all Operation It acts on the respective received qubits. If initially... The chosen entangled state is a certain Then use operators and The following properties The effect can be achieved by changing the quantum state. The calculation neglects the global phase factor, which does not affect the measurement results. If from the beginning The chosen entangled state is a certain Then use operators and The following properties, You can get ,in Subsequently, each Send the manipulated qubits to . After receiving each qubit, measurements are performed using the basis corresponding to the initially selected entangled state. That is, assuming initially... The chosen entangled state is a certain Then use the base By taking measurements, we can ultimately obtain... ,because , and various for This is known, so Calculate based on measurement results and various Value: , If from the beginning The chosen entangled state is a certain Then use the base By taking measurements, we can ultimately obtain... ,because , , and various for This is known, so The key can also be calculated from the measurement results. and various auxiliary values Value: , .

[0064] 1) Each participant Traversal The next preprocessing stage generates a length of bit string and And use a pseudo-random function to convert the bit string The middle Bit extension to length of bit string, The former The position is denoted as The following The bit-extended bit string is denoted as ,Will , and Encoded as quantum states respectively , and Participants Use the same pseudo-random function to convert the bit string The middle Bit extension to length of bit string and will , as well as Encoded as quantum states respectively , and .

[0065] 2) Each participant Enter one quantum state of a bit , denoted as and will , and Perform a bitwise XOR operation, and the result is denoted as .

[0066] 3) Participating parties Will Send to the participants .

[0067] 4) Participating parties The calculated results are processed in sequence. With the participating parties Received After performing bitwise XOR, we get And send to the participants .

[0068] 5) Participating parties The calculated With the participating parties Received After performing bitwise XOR, we get And send to the participants .

[0069] 6) Participating parties get Then with Perform bitwise XOR to obtain ,Will and and Perform a bitwise XOR operation, and the first bit of the result will be... The states of each qubit are as follows: The XOR result, after The state of each qubit is used to... The comparison is used to verify whether the value has been modified during the calculation or transmission process.

[0070] Embodiments of the present invention:

[0071] Assume there is Each participating party All participants are traversed. The second preprocessing stage yields a bit string of length 4. .like Figure 2 As shown, this embodiment uses an ultra-dense encoding method to transmit only... In the case of one quantum bit, make get and various At the same time ensure Unable to obtain a single The specific steps to achieve this goal are described below.

[0072] Preprocessing stage:

[0073] Step 1: First, construct the following two sets of 4-bit entangled states:

[0074] ,in For a 3-qubit computational basis, the corresponding eigenvalues ​​are integers. The 3-bit binary representation determines the bit string; Indicates to Invert bits; and They represent and .

[0075] from An entangled state A state is randomly selected and four qubits are used. The entangled state prepared is denoted as . .like Figure 3 As shown, in entangled states For example, the preparation process is illustrated. The circuit diagram is shown, where X, Z, and H are the Pauli-X gate, Pauli-Z gate, and Hadamard gate, respectively.

[0076] Step Two: Will bits in Send to each in advance .

[0077] Step 3: All Operation Acting on each received quantum bit superior.

[0078] If at the beginning The chosen entangled state is a certain Then use operators and The following properties

[0079] This can achieve the effect of causing the quantum state to change ,in Each bit as well as for If from the beginning The chosen entangled state is a certain Then use operators and The following properties, You can get ,in, ,like Figure 4 The encoded portion shown uses the classical bits held by each party as... The initial entangled state is chosen as For example, the operations performed by each party are drawn. The circuit diagram is shown, where X, Z, and H are the Pauli-X gate, Pauli-Z gate, and Hadamard gate, respectively.

[0080] Step Four: Participants Send the manipulated qubits to .

[0081] Step 5: After receiving each qubit, measurements are performed using the basis corresponding to the initially selected entangled state. That is, assuming initially... The chosen entangled state is a certain Then use the base By taking measurements, we can ultimately obtain... , Calculated based on the measurement results as well as If from the beginning The chosen entangled state is a certain Then use the base By taking measurements, we can ultimately obtain... , Calculated based on the measurement results as well as .

[0082] Calculation phase:

[0083] Step Six: Participants Traversal The next preprocessing stage yields a length of... bit string and And use a pseudo-random function to convert the bit string The middle The bits are expanded into a bit string of length 4. The former The position is denoted as The following The bit-extended bit string is denoted as ,Will , and Encoded as quantum states respectively , and Participants Use the same pseudo-random function to convert the bit string The last two bits are expanded into a bit string of length 4. and will , as well as Encoded as quantum states respectively , and .

[0084] Step Seven: Each participant Input a 2-bit quantum state , recorded as and will , and Perform a bitwise XOR operation, and the result is denoted as .

[0085] Step 8: Participants Will Send to the participants .

[0086] Step Nine: Participants The calculated results are processed in sequence. With the participating parties Received After performing bitwise XOR, we get And send to the participants .

[0087] Step 10: Participants The calculated With the participating parties Received After performing bitwise XOR, we get And send to the participants .

[0088] Step Eleven: Participants get Then with Perform bitwise XOR to obtain ,Will and and Performing a bitwise XOR operation, the first two qubits in the result are in their respective states. The XOR result of the last two qubits is used to determine the state of the last two qubits. The comparison is used to verify whether the value has been modified during the calculation or transmission process.

[0089] As can be seen from the embodiments of this invention, this invention proposes a verifiable quantum-safe multi-party XOR protocol based on ultra-dense coding. This protocol enables multiple parties to jointly perform XOR operations without the involvement of a trusted third party, and does not disclose any information other than the result. It allows secure key exchange without a QKD network, supports multi-party XOR operations, and supports quantum state input. It also verifies whether anyone maliciously tampered with the calculated value during the XOR process. A specific classic bit aggregation operation between the participants will transform what would otherwise be a transmission of... The communication of a classic bit is compressed to only one. The single qubit significantly reduces communication overhead. The required local Pauli operation is simple to implement and can be scaled to any number of participants; leakage resistance and eavesdropping resistance are enhanced by randomly selecting between two sets of non-orthogonal entangled bases and relying on the base measurement results.

Claims

1. A verifiable quantum-safe multi-party XOR method based on superdense coding, characterized in that, completed without the need for third party involvement an exclusive or operation between quantum states held by the individual parties, and no party learns anything about any other party except the exclusive or result, the method comprising: Preprocessing stage: Each participant obtains the auxiliary values ​​and keys needed for the computation phase through the preprocessing phase; Calculation phase: Participants input real data and encrypt it using the key obtained in the preprocessing stage; The participants sequentially send the results of executing the CNOT gate to the next participant for XOR calculation, and aggregate the encrypted quantum state through chain transmission and finally send it to the first participant; The first participant verifies the final result and makes the verification result public. Preprocessing phase: Each participant Generate random auxiliary values ​​of length n=2m and key ; Through ultra-dense coding methods, the first participant Obtain the aggregation key and the bit string of each participant , for and The index in the bit string, while ensuring It is impossible to know any single key. traversal To make get as well as ; During the calculation phase, all participants utilize auxiliary values. and key and aggregation key Regarding the quantum states held by each party Encryption is performed, and the encrypted quantum states are aggregated through chain transmission in the execution order. Decryption is performed to obtain the XOR result, and auxiliary values ​​are used. Verify the correctness of the results. The computation phase involves performing a secure multi-party XOR computation according to the following steps: 1) Each participant Use a pseudo-random function to assign auxiliary values The middle Bit extension to length of bit string, The former The position is denoted as The following The bit-extended bit string is denoted as ,Will , and Encoded as quantum states respectively , and Participants Using the same pseudo-random function, the auxiliary value The middle Bit extension to length of bit string and will , as well as Encoded as quantum states respectively , and ; 2) Each participant Enter one quantum state of a bit , recorded as and will , and Perform a bitwise XOR operation, and the result is denoted as ; 3) Participating parties Will Send to the participants ; 4) Participating parties The calculated results are processed in sequence. With the participating parties Received After performing bitwise XOR, we get And send to the participants ; 5) Participating parties The calculated With the participating parties Received After performing bitwise XOR, we get And send to the participants ; 6) Participating parties get Then combine with Perform bitwise XOR to obtain ,Will and and Perform a bitwise XOR operation, and the first bit of the result will be... The states of each qubit are as follows: The XOR result, after The state of each qubit is used to... The comparison is used to verify whether the value has been modified during the calculation or transmission process. against Each participating party And the two bits of data held by each participant. Through a super-dense coding method, only transmitting In the case of one quantum bit, make get and various At the same time ensure Unable to obtain a single The specific steps are as follows: 1) Construct two sets of mutually non-orthogonal pairs. Bit entanglement basis , and from An entangled state Randomly select a state and use 1 quantum bit Prepare one of the selected states; 2) The bits in the prepared quantum state Send to each in advance ; 3) All Operation Acting on each received quantum bit Above, among which and These represent the actions performed on the qubits. Pauli-Z and Pauli-X operators on; 4) Each Send the manipulated qubits to ; 5) After receiving each qubit, they are measured using the basis corresponding to the initially selected entangled state; that is, assuming the initial... The selected entangled state belongs to the base Then use Perform measurements; assuming initially The selected entangled state belongs to the base Then use Take measurements. Calculate based on the measurement results and various .

2. The verifiable quantum-safe multi-party XOR method based on superdense coding as described in claim 1, characterized in that, The two groups are not orthogonal to each other. Bit entanglement basis , for: ， in For one The computational basis of a quantum bit, whose corresponding eigenvalues ​​are integers. of The bit string determined by the binary representation; Indicates to Invert bits; and They represent and .

3. The verifiable quantum-safe multi-party XOR method based on superdense coding as described in claim 2, characterized in that, The steps described in step (5) Calculated based on measurement results and various The method is as follows: if use The measurement was performed and the state of the qubit was determined to be... ,but , ;if use The measurement was performed and the state of the qubit was determined to be... ,but , .

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