Novel quantum secret sharing method based on Bell state

Abstract

The invention relates to a novel quantum secret sharing method based on a Bell state. The method comprises the following steps that: firstly, a secret distributor sends a sequence of mixed Bell states and decoy particles to participants; secondly, the participants encode secret shares of the participants into corresponding Pauli operators, and the Pauli operators are applied to the received particle sequences; and finally, the participants recover the shared secret information through cooperation. And shared secret information can be obtained by executing Bell-based measurement by a secret distributor. Compared with other quantum secret sharing methods, the method has the advantages that the secret distributor does not grasp the secret share of the participant, even if the secret distributor grasp the shared secret information, the secret share of the participant cannot be deduced, and the privacy and benefits of the participant can be effectively protected. On the basis of meeting safety, a Bell state is used as a quantum carrier, and compared with an entangled state of n particles, the Bell state is easier to prepare; and meanwhile, various eavesdropping attacks can be effectively resisted. Compared with a traditional method, the method is more practical and higher in efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum communication, in particular to a novel quantum secret sharing method based on Bell states. BACKGROUND

[0002] Quantum secret sharing protocol is one of the research hotspots of quantum cryptography. It allows a secret distributor to divide its secret into several secret shares and distribute them to different participants. Only when all participants pool their secret shares together can the secret information be reconstructed. In theory, the security of quantum secret sharing protocol depends on quantum theory and technology. In particular, in quantum secret sharing protocol, the eavesdropping behavior of the attacker can be detected by checking the error rate of the quantum channel.

[0003] Therefore, quantum secret sharing protocol can provide high security for users who need to share certain secret information among certain participants. Quantum secret sharing protocol is also a useful tool in secure distributed quantum computing, joint sharing of quantum currency, etc.

[0004] Hillery et al. first proposed the concept of quantum secret sharing. Compared with traditional secret sharing based on computational mathematical problems, quantum secure secret system has higher security. In particular, users of quantum channel can check the eavesdropping behavior of the enemy. Although various quantum secret sharing schemes have been proposed, the quantum bit efficiency of the protocol is difficult to reach 100%. Moreover, complex quantum states are used as quantum carriers. At the same time, in many quantum secret sharing schemes, the secret distributor holds the secret share of each participant, which is not conducive to protecting the privacy and interests of the participants. Participants need to perform a large number of complex quantum operations.

[0005] The invention patent application with application number 201811272481.6 discloses a quantum key distribution method with bidirectional identity authentication function. The communication participants use a binary string representing the user's identity to prepare Bell states, encode according to the same agreement, exchange particles, complete Bell basis measurement to realize entanglement exchange of Bell state particles, and perform bitwise XOR operation. After that, any one of the communication parties performs Pauli gate operation to make the particles in their hands into Bell state particles as the particles in the hands of the other party. According to the same encoding rule, the communication parties can obtain a string of the same binary string to complete the key distribution. The present application improves the utilization rate of resources generated in the authentication process of the communication parties. According to the agreement published by the communication parties, identity authentication and key distribution can be realized without the intervention of a third party. The quantum state required is the Bell state of two particles, which is relatively easy to prepare. In this scheme, the secret distributor also holds the secret share of each participant, and the privacy and interests of the participants are difficult to be effectively protected.

[0006] In order to fundamentally protect the privacy and interests of participants, it is necessary to explore and improve the existing secret information transmission method to protect the privacy of participants. SUMMARY

[0007] The present application aims at the deficiencies of the prior art, and provides a novel quantum secret sharing method based on Bell state, which mainly uses Pauli operation to realize encrypted transmission of secret information in the quantum secret sharing scheme based on Bell state; the secret share is converted into Pauli operator to act on the transmitted particle sequence, so as to realize transmission of secret information; the secret distributor does not hold the secret share of the participants, which can effectively protect the privacy and interests of the participants and effectively resist various eavesdropping attacks.

[0008] The technical scheme adopted by the present application is as follows:

[0009] A novel quantum secret sharing method based on Bell state, which realizes transmission of secret information through the following steps:

[0010] S1, the secret distributor sends a sequence of mixed Bell state and decoy particles to the participants;

[0011] S2, the participants reorder the particle sequence and encode their secret share as a corresponding Pauli operator applied to the received particle sequence;

[0012] S3, the participants recover the original sequence by cooperation to obtain shared secret information;

[0013] S4, the secret distributor performs Bell base measurement to obtain the shared secret information.

[0014] The novel quantum secret sharing method based on Bell state, in step S1, the secret distributor prepares a Bell state sequence T, and the Bell state in the Bell state sequence T is randomly selected from { };

[0015] Then, the Bell state sequence T is divided into a first particle sequence A and a second particle sequence B; the first particle sequence A is a particle sequence composed of the first particles of all Bell states in T; the second particle sequence B is a particle sequence composed of the second particles of all Bell states in T;

[0016] Subsequently, the first particle sequence A and the second particle sequence B are reordered to obtain and , and decoy particles are inserted to obtain sequences A0 and B0;

[0017] The participants are divided into two groups, each group having multiple participants, and the first group receives the first particle sequence and the second group receives the second particle sequence.

[0018] Finally, the secret allocator sends sequence A0 to the participants in group one and sequence B0 to the participants in group two.

[0019] In the novel quantum secret sharing method based on Bell states, in step S2, the participants in group one receive A. i-1 The sender then publishes the location information of the decoy particles.

[0020] All receivers and corresponding senders test channel security using eavesdropping detection technology. If the eavesdropping detection passes, participants discard decoy particles, reorder the particle sequence, and simultaneously allocate the secret share 'a'. i The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence A is obtained by randomly inserting decoy particles. i ;

[0021] Finally, the participants will A i Send to the next participant in group one;

[0022] Perform this step sequentially for i=1,2,…n-1;

[0023] Similarly, participants in group two received B i-1 The sender then publishes the location information of the decoy particles.

[0024] All receivers and corresponding senders test channel security using eavesdropping detection technology. If the eavesdropping detection passes, participants discard decoy particles, reorder the particle sequence, and simultaneously allocate the secret share b. i The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence B is obtained by randomly inserting decoy particles. i ;

[0025] Finally, the participants will B i Send to the next participant in Group Two;

[0026] For i=1,2,…m-1, execute this step in sequence, where i, n, and m are all natural numbers greater than 1.

[0027] In the novel quantum secret sharing method based on Bell states, in step S2, the last participant in group one receives A. n-1 The sender then publishes the location information of the decoy particles.

[0028] Participants test channel security using eavesdropping detection technology. If the eavesdropping detection passes, the participants discard the decoy particles, reorder the particle sequence, and simultaneously encode the secret share 'a'. n The Pauli operator is applied to the corresponding particles to obtain the particle sequence. ,exist Sequence A is obtained by randomly inserting decoy particles. n Finally, the last participant in Group 1 will choose A. n Send to the secret distributor;

[0029] Similarly, the last participant in group two received B n-1 The sender then publishes the location information of the decoy particles.

[0030] Participants use eavesdropping detection technology to check channel security. If the eavesdropping detection is successful, the decoy particles are discarded, the particle sequence is reordered, and the secret share b is allocated. m The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence B is obtained by randomly inserting decoy particles. m Finally, the last participant in Group Two will be B. m Send to the secret distributor.

[0031] In the novel quantum secret sharing method based on Bell states, in step S3, the secret allocator receives A n and B m The location information of the decoy particles was disclosed, and the channel security was tested using eavesdropping detection technology.

[0032] The wiretapping detection has been passed, and the secret distributor has been revealed. and The original order; all participants in Group 1 and Group 2 announced A i and B i The original order;

[0033] The secret allocator rearranges the particles in his hand to obtain A. T and B T Secret allocators use Bell base { }Measurement A T and B T The particle at the corresponding position yields the measurement result. The shared secret information s is obtained according to the encoding method.

[0034] The novel quantum secret sharing method based on Bell states, and the method for judging the security of eavesdropping detection technology, are as follows: the sender prepares a sufficient number of decoy particles, and the decoy particles are randomly positioned... In one of two states, a decoy particle is randomly inserted into the quantum sequence to be transmitted. When the receiver receives the sequence mixed with the decoy particle, the sender tells the receiver the position of the decoy particle. The receiver measures the received decoy particle and checks the correctness of the measurement result. If the error rate of the measurement result of the decoy particle is lower than a predetermined threshold, it proves that the quantum channel is secure. To ensure the secure operation of the protocol, the participants use Z-based random decoy particles and, after performing the Pauli operation, randomly insert them into the sequence and send them to the next participant for subsequent eavesdropping detection.

[0035] The beneficial effects of this invention are:

[0036] 1. This invention is based on a novel quantum secret sharing method using Bell states. Compared with other quantum secret sharing methods, the secret allocator of this invention does not possess the secret share of the participants. Even if the secret allocator possesses the shared secret information, it cannot deduce the secret share of the participants. This effectively protects the privacy and interests of the participants and resists various eavesdropping attacks.

[0037] 2. The novel quantum secret sharing method of the present invention uses Bell states as quantum carriers to encode classical messages into corresponding Pauli operators and apply them to the transmitted quantum sequence to achieve secret information sharing; it is easier to prepare than entangled states of n particles.

[0038] 3. The novel quantum secret sharing method of this invention eliminates the need for participants to use long-term quantum memory technology to store unknown quantum states; it also eliminates the need for complex quantum operations and long-term quantum memory technology, making the operation relatively simple. While ensuring security, this invention uses Bell states as quantum carriers, which are easier to prepare than entangled states of n-particles; simultaneously, it effectively resists various eavesdropping attacks. Compared to traditional methods, this invention is more practical and more efficient. Attached Figure Description

[0039] Figure 1 This is a flowchart of the novel quantum secret sharing method based on Bell states according to the present invention;

[0040] Figure 2 This is a schematic diagram of the eavesdropping detection process according to the present invention. Detailed Implementation

[0041] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the following embodiments are only used to explain the preferred embodiments of the present invention and should not be regarded as limiting the scope of protection of the present invention.

[0042] Example 1

[0043] See Figure 1This invention presents a novel quantum secret sharing method based on Bell states, which achieves the transmission of secret information through the following steps:

[0044] S1, First, the secret allocator sends the sequence of mixed Bell states and decoy particles to the participants;

[0045] S2, Next, the participants reorder the particle sequence while encoding their secret share into the corresponding Pauli operator applied to the received particle sequence;

[0046] S3. Finally, the participants work together to recover the original sequence and obtain the shared secret information.

[0047] S4, the secret allocator can obtain the shared secret information by performing Bell basis measurements.

[0048] Bell states are the four maximally entangled states of a two-qubit system, consisting of { It consists of four Bell states. The four Bell states are represented as follows: , , , ; where subscript , These correspond to the first and second particles of the Bell state, respectively.

[0049] The Bell basis satisfies orthogonality (the inner product of any two Bell states is 0) and normalization (the modulus of each Bell state is 1).

[0050] The Pauli operator is , , , ;

[0051] The participants encode their secret shares into the corresponding Pauli operators in the following way:

[0052] Table 1. Secret Share Coding Method

[0053]

[0054] This invention presents a novel quantum secret sharing method using Bell states, which employs Pauli operations to achieve encrypted transmission of secret information.

[0055] The secret allocator prepares a Bell state sequence, divides it into a first particle sequence and a second particle sequence, performs rearrangement and decoy particle insertion operations, and sends them to the first participant in group one and the first participant in group two, respectively. Each participant, upon receiving the particle sequence, must first perform an eavesdropping detection. If no eavesdropping occurs, the rearrangement operation is performed. Then, the participant encodes their secret share with the corresponding Pauli operator and applies it to the particles in the rearranged sequence. Finally, it is sent to the next participant. This process continues until the last participant in each group has completed their operations and sends the particle sequence to the secret allocator. The secret allocator first performs an eavesdropping detection. If no eavesdropping occurs, all participants announce the rearranged order.

[0056] The secret allocator restores the original order and performs a measurement operation to obtain the shared secret information. All participants, based on the published rearrangement, restore the correct order of the secret shares, cooperating to recover the shared secret information.

[0057] This invention transforms the secret share into a Pauli operator that acts on the transmitted particle sequence to achieve the transmission of secret information; the secret allocator does not know the secret share of the participants, effectively protecting the privacy and interests of the participants.

[0058] Example 2

[0059] See Figure 1 The novel quantum secret sharing method based on Bell states in this embodiment differs from Embodiment 1 in that: in step S1, the secret allocator prepares a Bell state sequence T, and the Bell states in the Bell state sequence T are randomly selected from { Select from};

[0060] Then, the Bell state sequence T is divided into a first particle sequence A and a second particle sequence B; the first particle sequence A is a particle sequence composed of the first particles of all Bell states in T; the second particle sequence B is a particle sequence composed of the second particles of all Bell states in T.

[0061] Subsequently, the first particle sequence A and the second particle sequence B are reordered to obtain... and Inserting decoy particles yields sequences A0 and B0;

[0062] The participants are divided into two groups, with multiple participants in each group. Group 1 receives the first particle sequence, and Group 2 receives the second particle sequence.

[0063] Finally, the secret allocator sends sequence A0 to the participants in group one and sequence B0 to the participants in group two.

[0064] In step S2, the participants in group one receive A i-1The sender then publishes the location information of the decoy particles.

[0065] All receivers and corresponding senders test channel security using eavesdropping detection technology. If the eavesdropping detection passes, participants discard decoy particles, reorder the particle sequence, and simultaneously allocate the secret share 'a'. i The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence A is obtained by randomly inserting decoy particles. i ;

[0066] Finally, the participants will A i Send to the next participant in group one;

[0067] Perform this step sequentially for i=1,2,…n-1;

[0068] Similarly, participants in group two received B i-1 The sender then publishes the location information of the decoy particles.

[0069] All receivers and corresponding senders test channel security using eavesdropping detection technology. If the eavesdropping detection passes, participants discard decoy particles, reorder the particle sequence, and simultaneously allocate the secret share b. i The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence B is obtained by randomly inserting decoy particles. i ;

[0070] Finally, the participants will B i Send to the next participant in Group Two;

[0071] For i=1,2,…m-1, execute this step in sequence, where i, n, and m are all natural numbers greater than 1;

[0072] The last participant in Group 1 received A n-1 The sender then publishes the location information of the decoy particles.

[0073] Participants test channel security using eavesdropping detection technology. If the eavesdropping detection passes, the participants discard the decoy particles, reorder the particle sequence, and simultaneously encode the secret share 'a'. n The Pauli operator is applied to the corresponding particles to obtain the particle sequence. ,exist Sequence A is obtained by randomly inserting decoy particles. n Finally, the last participant in Group 1 will choose A. n Send to the secret distributor;

[0074] Similarly, the last participant in group two received B n-1 The sender then publishes the location information of the decoy particles.

[0075] Participants use eavesdropping detection technology to check channel security. If the eavesdropping detection is successful, the decoy particles are discarded, the particle sequence is reordered, and the secret share b is allocated. m The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence B is obtained by randomly inserting decoy particles. m Finally, the last participant in Group Two will be B. m Send to the secret distributor;

[0076] In step S3, the secret allocator receives A n and B m The location information of the decoy particles was disclosed, and the channel security was tested using eavesdropping detection technology.

[0077] The wiretapping detection has been passed, and the secret distributor has been revealed. and The original order; all participants in Group 1 and Group 2 announced A i and B i The original order;

[0078] The secret allocator rearranges the particles in his hand to obtain A. T and B T Secret allocators use Bell base { }Measurement A T and B T The particle at the corresponding position yields the measurement result. The shared secret information s is obtained according to the encoding method;

[0079] Participants are announced by the secret distributor. and The original order and all participants in Group 1 and Group 2 were announced. i and B i The original order was obtained by each participant reordering their secret share. and ;

[0080] All participants collaborated in the calculation. ,in, For the XOR symbol, first process the n bits. , , ..., Performing the XOR operation sequentially yields a single-bit result C;

[0081] Then, for m bits , , ..., Performing the XOR operation sequentially yields a single-bit result D;

[0082] Finally, perform an XOR operation on C and D to obtain the final secret information s.

[0083] Example 3

[0084] The novel quantum secret sharing method based on Bell states in this embodiment differs from Embodiments 1 or 2 in that: in step S4, the secret allocator randomly selects δ Bell states from the Bell state sequence T and compares their measurement results with the corresponding bits recovered by the participants, where δ is a natural number greater than 1; if the bit error rate in the sample bits is greater than a predefined threshold, the secret s is discarded; otherwise, it is accepted as shared secret information; the secret allocator uses Bell basis measurements A T and B T Measurement results of particles at corresponding positions The shared secret information s is obtained according to the encoding method in Table 2;

[0085] Table 2 Secret Reconstruction Encoding Method

[0086]

[0087] Example 4

[0088] Unlike the previous embodiments, this embodiment uses Trent as the secret allocator and {Alice1, Alice2, ..., Alice} as the group one participants. n Group 2 participants are {Bob1, Bob2, ..., Bob} m Taking Bell states as an example, the implementation process of the novel quantum secret sharing method based on Bell states in this invention is explained:

[0089] See Figure 1 The specific steps are as follows:

[0090] S1, Trent prepares the Bell state sequence. , where the Bell state in T is randomly selected from { Choose from}. Divide T into the first particle sequence. Second particle sequence Reorder A and B to get and And randomly insert decoy particles Obtain sequences A0 and B0. Send A0 to Alice1 in group one, and send B0 to Bob1 in group two.

[0091] Alice in Group 1, S2 i Received Ai-1 Alice i-1 Release the location information of the decoy particles. Alice i Z-basis measurements were performed on the decoy particles, and the results were sent to Alice. i-1 Alice i-1 The error rate is calculated; if it exceeds a predefined threshold, the protocol terminates. If the eavesdropping detection passes, the decoy particles are discarded, the particle sequence is reordered, and Alice... i secret share Encoded as Pauli operator And applied to the corresponding particles to obtain particle sequences. .exist Randomly inserted decoy particles Sequence A is obtained i Finally, Alice i A i Send to Alice i+1 Perform this step sequentially for i=1,2,…n-1.

[0092] Similarly, Bob in Group 2 i Received B i-1 Bob i-1 Release the location information of the decoy particles. (Bob) i Z-basis measurements were performed on the decoy particles, and the results were sent to Bob. i-1 Bob i-1 The error rate is calculated; if it exceeds a predefined threshold, the protocol terminates. If the eavesdropping detection passes, the decoy particles are discarded, the particle sequence is reordered, and Bob... i secret share Encoded as Pauli operator And applied to the corresponding particles to obtain particle sequences. .exist Randomly inserted decoy particles Sequence B is obtained i Finally, Bob i B i Send to Bob i+1 Perform this step sequentially for i=1,2,…m-1.

[0093] Alice in Group 1, S3 n Received A n-1 Alice n-1 Release the location information of the decoy particles. Alice n Z-basis measurements were performed on the decoy particles, and the results were sent to Alice. n-1 Alice n-1The error rate is calculated; if it exceeds a predefined threshold, the protocol terminates. If the eavesdropping detection passes, the decoy particles are discarded, the particle sequence is reordered, and Alice... n Encode the secret share Pauli operator And applied to the corresponding particles to obtain particle sequences. .exist Randomly inserted decoy particles Sequence A is obtained n Finally, Alice n A n Send to Trent.

[0094] Similarly, Bob in Group 2 m Received B n-1 Bob m-1 Release the location information of the decoy particles. (Bob) m Z-basis measurements were performed on the decoy particles, and the results were sent to Bob. m-1 Bob m-1 Calculate the error rate; if the error rate exceeds a predefined threshold, the protocol terminates. If the eavesdropping detection passes, discard the decoy particles, reorder the particle sequence, and Bob... m Encode the secret share Pauli operator And applied to the corresponding particles to obtain particle sequences. .exist Randomly inserted decoy particles Sequence B is obtained m Finally, Bob m B m Send to Trent.

[0095] S4, Trent received A n and B m Alice n and Bob m The location information of the decoy particles is published. Trent uses Z-basis measurements on the decoy particles and sends the results to Alice. n and Bob m Alice n and Bob m The error rate is calculated; if it exceeds a predefined threshold, the protocol terminates. If the eavesdropping detection passes, the decoy particles are discarded, and the secret allocator announces the results. and The original order. All participants announced A. i and B i The original order. Trent rearranged the particles in his hand to obtain A. T and BT Trent used the Bell base to measure A. T and B T The measurement result is obtained from the i-th particle in the sample. The shared secret information s is obtained according to the encoding method. i For example, if the measurement result , then s i =00.

[0096] S5, according to Trent's announcement and The original order and all participants published A i and B i The original order was obtained by each participant reordering their secret share. and All participants collaborated in the calculation. .

[0097] S6, Trent randomly selects from T. The system generates several Bell states and compares their measurements with the corresponding bits recovered by the participants. If the bit error rate in the sample bits is greater than a predefined threshold, the secret s is discarded; otherwise, it is accepted as shared secret information.

[0098] Trent Selective Preparation Forming a sequence Where t1(t2) represents the first (second) particle of the entangled system. T is divided into a sequence of first particles. Second particle sequence Reorder A and B to get and And randomly insert decoy particles The resulting sequences are A0 and B0. After receiving the particle sequences, Alice and Bob first perform an eavesdropping detection. If no eavesdropping activity is detected, the decoy particles are discarded. Assume Alice and Bob reorder the particles to obtain... and They each possess secret shares a∈{10, 11, 01, 00, 10} and b∈{01, 00, 10, 00, 11}, respectively. According to the encoding rules in Table 1, Alice (Bob) encodes his secret shares into the corresponding Pauli operators and applies them to particles t1(t2). Then, the state of the entangled system t1t2 will change. After Alice performs the Pauli operation, the particles become... After Bob performs the Pauli operation, the particle becomes... .

[0099] Alice (Bob) randomly inserts a decoy particle, Trent. Based on the rearranged order published by Alice (Bob) and measurements of the particle sequence, the shared secret information is s = {00, 11, 11, 00, 10}. Alice (Bob), using the original particle order published by Trent and her own rearranged order, reconstructs the original sequence's share of the secret information. ∈{11, 01, 10, 00, 10} and ∈{11, 10, 01, 00, 00}. Alice and Bob work together to recover s={00, 11, 11, 00, 10}.

[0100] Table 3 details the final state of the entangled system and the shared secret information.

[0101] Table 3 Final states of system t1t2

[0102]

[0103] like Figure 2 As shown, the novel quantum secret sharing method based on Bell states described in this invention uses the following method to determine the security of eavesdropping detection technology: the sender prepares a sufficient number of decoy particles, and the decoy particles are randomly positioned... In one of two states, decoy particles are randomly inserted into the quantum sequence to be transmitted. When the receiver receives the sequence mixed with decoy particles, the sender informs the receiver of the decoy particle's position. The receiver measures the received decoy particles, checks the accuracy of the measurement results, and publishes the results to the sender. The sender compares the published measurement results with the initial state of the prepared decoy particles and calculates the error rate. If the error rate of the decoy particle measurement results is below a predetermined threshold, the quantum channel is considered secure, and the protocol continues; if the error rate is above the predetermined threshold, eavesdropping is detected, and the protocol terminates. To ensure the protocol's security, participants randomly prepare decoy particles using a Z-basis and, after performing a Pauli operation, randomly insert them into the sequence and send them to the next participant for subsequent eavesdropping detection.

[0104] Compared to existing technologies, this invention utilizes Bell states as quantum carriers, which are easier to prepare than n-particle entangled states. This method encodes classical messages into corresponding Pauli operators and applies them to the transmitted quantum sequence to achieve the sharing of secret information. Participants do not need complex quantum operations or long-term quantum memory technology. The method of this invention is relatively simple to operate and can effectively resist various eavesdropping attacks, demonstrating good practicality, security, and qubit efficiency.

[0105] The above are merely preferred embodiments of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the protection scope of the present invention.

Claims

1. A novel quantum secret sharing method based on Bell states, characterized in that: The transmission of secret information is achieved through the following steps: S1, the secret allocator sends a sequence of mixed Bell states and decoy particles to the participants; S2, the participants reorder the particle sequence and encode their secret share into the corresponding Pauli operator applied to the received particle sequence; S3, participants work together to recover the original sequence and obtain shared secret information; S4, the secret allocator can obtain the shared secret information by performing Bell basis measurements.

2. The novel quantum secret sharing method based on Bell states according to claim 1, characterized in that: In step S1, the secret allocator prepares a Bell state sequence T, where the Bell states in the Bell state sequence T are randomly selected from { Select from}; Then, the Bell state sequence T is divided into a first particle sequence A and a second particle sequence B; the first particle sequence A is a particle sequence composed of the first particles of all Bell states in T; the second particle sequence B is a particle sequence composed of the second particles of all Bell states in T. Subsequently, the first particle sequence A and the second particle sequence B are reordered to obtain... and Inserting decoy particles yields sequences A0 and B0; The participants are divided into two groups, with multiple participants in each group. Group 1 receives the first particle sequence, and Group 2 receives the second particle sequence. Finally, the secret allocator sends sequence A0 to the participants in group one and sequence B0 to the participants in group two.

3. The novel quantum secret sharing method based on Bell states according to claim 2, characterized in that: In step S2, the participants in group one receive A i-1 The sender then publishes the location information of the decoy particles. All receivers and corresponding senders test channel security using eavesdropping detection technology. If the eavesdropping detection passes, participants discard decoy particles, reorder the particle sequence, and simultaneously allocate the secret share 'a'. i The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence A is obtained by randomly inserting decoy particles. i ; Finally, the participants will A i Send to the next participant in group one; Perform this step sequentially for i=1,2,…n-1; Similarly, participants in group two received B i-1 The sender then publishes the location information of the decoy particles. All receivers and corresponding senders test channel security using eavesdropping detection technology. If the eavesdropping detection passes, participants discard decoy particles, reorder the particle sequence, and simultaneously allocate the secret share b. i The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence B is obtained by randomly inserting decoy particles. i ; Finally, the participants will B i Send to the next participant in Group Two; For i=1,2,…m-1, execute this step in sequence, where i, n, and m are all natural numbers greater than 1.

4. The novel quantum secret sharing method based on Bell states according to claim 3, characterized in that: In step S2, the last participant in group one receives A. n-1 The sender then publishes the location information of the decoy particles. Participants test channel security using eavesdropping detection technology. If the eavesdropping detection passes, the participants discard the decoy particles, reorder the particle sequence, and simultaneously encode the secret share 'a'. n The Pauli operator is applied to the corresponding particles to obtain the particle sequence. ,exist Sequence A is obtained by randomly inserting decoy particles. n Finally, the last participant in Group 1 will choose A. n Send to the secret distributor; Similarly, the last participant in group two received B n-1 The sender then publishes the location information of the decoy particles. Participants use eavesdropping detection technology to check channel security. If the eavesdropping detection is successful, the decoy particles are discarded, the particle sequence is reordered, and the secret share b is allocated. m The code is encoded as a Pauli operator and applied to the corresponding particles to obtain a particle sequence. ,exist Sequence B is obtained by randomly inserting decoy particles. m Finally, the last participant in Group Two will be B. m Send to the secret distributor.

5. The novel quantum secret sharing method based on Bell states according to claim 4, characterized in that: In step S3, the secret allocator receives A n and B m The location information of the decoy particles was disclosed, and the channel security was tested using eavesdropping detection technology. The wiretapping detection has been passed, and the secret distributor has been revealed. and The original order; all participants in Group 1 and Group 2 announced A i and B i The original order; The secret allocator rearranges the particles in his hand to obtain A. T and B T Secret allocators use Bell base { }Measurement A T and B T The particle at the corresponding position yields the measurement result. The shared secret information s is obtained according to the encoding method.

6. The novel quantum secret sharing method based on Bell states according to claim 5, characterized in that: Participants are announced by the secret distributor. and The original order and all participants in Group 1 and Group 2 were announced. i and B i The original order was obtained by each participant reordering their secret share. and ; All participants collaborated in the calculation. ,in, For the XOR symbol, first process the n bits. , , ..., Performing the XOR operation sequentially yields a single-bit result C; Then, for m bits , , ..., Performing the XOR operation sequentially yields a single-bit result D; Finally, perform an XOR operation on C and D to obtain the final secret information s.

7. The novel quantum secret sharing method based on Bell states according to claim 5 or 6, characterized in that: In step S4, the secret allocator randomly selects δ Bell states from the Bell state sequence T and compares their measurement results with the corresponding bits recovered by the participants, where δ is a natural number greater than 1; if the bit error rate in the sample bits is greater than a predefined threshold, the secret s is discarded, otherwise it is accepted as shared secret information. Secret allocators use Bell base measurements A T and B T Measurement results of particles at corresponding positions The shared secret information s is obtained according to the encoding method in Table 2; Table 2 Secret Reconstruction Encoding Method 。 8. The novel quantum secret sharing method based on Bell states according to any one of claims 1-6, characterized in that: Bell states are the four maximally entangled states of a two-qubit system. The four Bell states are represented as follows: , , , ; where subscript , These correspond to the first and second particles of the Bell state, respectively.

9. The novel quantum secret sharing method based on Bell states according to claim 8, characterized in that: The Pauli operator is , , , ; The participants encode their secret shares into the corresponding Pauli operators in the following way: Table 1. Secret Share Coding Method 。 10. The novel quantum secret sharing method based on Bell states according to any one of claims 2-6 or 9, characterized in that: The method for determining the security of eavesdropping detection technology is as follows: the sender prepares a sufficient number of decoy particles, and the decoy particles are randomly positioned... In one of two states, a decoy particle is randomly inserted into the quantum sequence to be transmitted. When the receiver receives the sequence mixed with the decoy particle, the sender tells the receiver the position of the decoy particle. The receiver measures the received decoy particle and checks the correctness of the measurement result. If the error rate of the measurement result of the decoy particle is lower than a predetermined threshold, it proves that the quantum channel is secure. To ensure the secure operation of the protocol, the participants use Z-based random decoy particles and, after performing the Pauli operation, randomly insert them into the sequence and send them to the next participant for subsequent eavesdropping detection.

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