A novel high-efficiency quantum joint signature method based on entanglement measurement

Abstract

This invention provides a novel and efficient quantum joint signature method based on entanglement measurement. After the signer performs multiple measurements on the qubits in the sequence and generates different sequences multiple times, under the action of the verifier, different sequences are generated by inserting decoy states. The signer then measures and compares the different sequences. After comparing the measurement results of the signers, the verifier combines the different sequences to form a signature. By comparing whether the values ​​of the superimposed sequences from different signers are the same, the validity of the joint signature is determined.

Description

Technical Field

[0001] This invention relates to the field of quantum secure communication technology, and specifically to a novel and efficient quantum joint signature method based on entanglement measurement. Background Technology

[0002] Quantum cryptography, as a novel interdisciplinary field, primarily utilizes the fundamental principles of quantum mechanics to establish a new cryptographic system that theoretically guarantees unconditional security. This has made research on quantum communication an important topic, including quantum secure direct communication (QSDC), quantum secret sharing protocol (QSS), quantum signature (QS), quantum privacy query protocol (QPQ), and quantum key negotiation (QKA). Among these, the main applications of quantum signature (QS) include, but are not limited to, financial transactions, e-government, and medical data sharing. For example, in electronic contract signing, quantum signatures can ensure the integrity of the contract content and the authenticity of the signatories' identities; in financial transactions, quantum signatures can prevent transaction information from being tampered with or forged; furthermore, quantum signature technology can also be used in multi-party collaboration scenarios, such as when hospital staff and patients jointly sign information and it is verified by a third party.

[0003] For example, Chinese patent application number 03146395.9, classification number H04K1 / 00, and publication date October 11, 2006, discloses a quantum state classical order rearrangement encryption method in quantum key distribution. This method primarily utilizes the no-cloning principle in quantum mechanics and the coherence and non-locality of entangled particles to encrypt the quantum key generation process. While ensuring security, it simultaneously transmits all particles in the entangled system, thereby increasing the transmission distance and simplifying the communication process. It is implemented using a control system controlled by control codes located at the sender and receiver ends respectively, a transmitting and receiving system connected via upper and lower channels, a corresponding transmission order rearrangement encryption and decryption system, a data processing system connected via classical channels, and a quantum coherent signal source. This allows the entangled pair-based quantum key distribution scheme to achieve maximum encoding capacity, simplifies the communication process, and, for the same coherence time, achieves a longer transmission distance than traditional methods.

[0004] The above literature mainly determines the transmission order rearrangement method and transmits the corresponding data group based on the value of each W bits of binary data in the control code at the sending and receiving ends. It encodes the data using the Bell ground state, removes uncounted measurement results, groups the remaining measurement results, and compares the groups with the results from the classical channel. The security of the key is determined by the error rate. This method also requires comparing the encoded data with the data from the classical channel to determine the security of the key. If the data transmitted in the classical channel is attacked, the final determination of key security will be inaccurate. Furthermore, it only verifies the data by performing entanglement measurement on the data in the control code. If the control code verification is successful, direct data transmission is prone to tampering. It does not add decoy states to both the message sequence and the control code sequence to ensure the stability of the signature from both aspects. Summary of the Invention

[0005] The purpose of this invention is to provide a novel and efficient quantum joint signature method based on entanglement measurement. By utilizing the non-cloning and quantum entanglement properties of quantum mechanics, the method ensures the non-forgeability and non-repudiation of the signature, thereby improving security. At the same time, by optimizing the quantum state preparation and measurement process, the method enhances the stability of the signature in noisy environments and improves the robustness of quantum communication.

[0006] To achieve the above objectives, this invention provides a novel, efficient quantum joint signature method based on entanglement measurement for joint signatures by participants. Before signing, the participants possess different sequences of quantum states and have measurement results for qubits. The participants include signer A, signer B, and verifier C. The method also includes the following steps:

[0007] S1 verifier C randomly arranges a preset number of Bell states and two-particle states into a sequence. ,sequence And according to the quantum state encoding rules, the sequences are respectively... ,sequence Encode the data to generate a string, then process the sequence according to the message sequence and encoding rules. ,sequence Corresponding generated sequence ,sequence ;

[0008] S2 verifier C inserts a decoy state into the sequence. and sequence The corresponding generated sequence and sequence Signer A and signer B measured respectively The deceptive state in the measurement When the decoy state in sequence C matches the decoy state in verifier C, verifier C inserts the decoy state into the sequence. Decomposed into And measured by signer A and signer B When the decoy state in the test matches the location of the decoy state published by verifier C, proceed to step S3;

[0009] S3 signer A and signer B respectively After extracting the decoy states, the Bell states in the sequence form a sequence. And measurements are performed; verifier C verifies the quantum state according to its encoding rules. , The qubits were measured and the results were obtained. The measurement results were then compared with... Generate signatures corresponding to signer A and signer B. S A , S B ;

[0010] S4 verifier C compares quantum one-way functions The value is used to determine the signature. S A , S B Is it effective?

[0011] The above method involves the signer measuring the qubits in the sequence, followed by the verifier randomly generating the sequence using Bell states and two-particle states, encoding the sequence using quantum states, and then combining the encoded sequence with the message sequence according to encoding rules. This encoded sequence serves as the verification code, with a decoy state added. Under the verifier's influence, different sequences are generated by inserting the decoy state, and the signer measures and compares these different sequences. After comparing the signer's measurement results, the verifier further divides the correctly verified sequence into two types and sends them to the sender and receiver respectively. Then, a decoy state is added to form a new sequence, which is compared again with the decoy state published by verifier C. This ensures the accuracy of the verification code through multiple entanglement measurements. Then, signers A and B confirm the verification code again. When the verification code is correct, the Bell state in the decoy state is extracted and qubit measurement is performed. The measurement results of verifier C and the sequence after extracting the decoy state are used to form a signature according to the quantum state encoding principle. Then, the signature value is compared to determine whether it is valid. This makes the original sequence robust because the verification code contains the superposition of Bell state and two-particle state. In addition, the reliability of the verification code transmission is determined by adding the decoy state and position verification during the sequence formation process. Furthermore, the addition of the decoy state makes the transmission more resistant to attacks. After extracting the decoy state from the correct verification code, the original signature is obtained by qubit measurement. Then, the signatures of signers A and B are compared to determine whether the signature is valid. Thus, the message sequence and verification code can be comprehensively verified to ensure the signature's unforgeability and non-repudiation.

[0012] Furthermore, step S1 includes: S1.1 to S1.5,

[0013] S1.1 Signer A, signer B, and verifier C possess quantum states. Then, signer A and signer B are made to pass through a set of induced mutations. The sequence contains qubits, and the different qubits in the corresponding sequences of signer A and signer B are compared. After informing each other of the measurement results, they are compared, and at the same time, verifier C measures the sequence. The qubits in the measurement data are then used to publish the measurement results to signer A and signer B.

[0014] S1.2 Verifier C will be from 2 n Bell states and 2 m A sequence is formed by random arrangement of two-particle states. ,sequence ;

[0015] S1.3 Verifier C verifies the sequence according to the quantum state encoding rules. ,sequence The Bell states in the code are encoded to generate binary strings. and ;

[0016] And order It contains the first and second particles of the Bell state and the two-particle state, respectively, and the order is... The first and second particles in Bell state and two-particle state;

[0017] S1.5 Verifier C, based on the encoding rules and message sequence .

[0018] The above settings facilitate signer A, signer B, and verifier C in measuring the qubits in their respective sequences and dividing the quantum state into two sequences. Signers A and B then extract the two sequences, making it convenient to send the two sequences to different signers for sequence verification, thus ensuring robustness.

[0019] The results of the second and third particles, and the comparison test between signer A and signer B.

[0020] The above settings allow signers to contain different particles in quantum states, forming different sequences that can be compared to identify the different positions of the qubits.

[0021] Furthermore, in step S1.2, the Bell state is obtained according to the following formula (2):

[0022] (2)

[0023] The ground state and excited state, the two-particle state from the set It was obtained from the middle.

[0024] The above settings facilitate the selection of Bell states and two-particle states, and ensure that the selected Bell states and two-particle states have a certain correlation.

[0025] Furthermore, step S2 also includes: S2.1-S2.4

[0026] And generate the corresponding The generated sequence is then sent to signer A and signer B respectively.

[0027] S2.2 Upon confirmation of receipt by signer A and signer B Afterwards, verifier C announced... The position of the deceptive state was determined, and then signer A and signer B measured it respectively. The system determines the position of the decoy state and informs verifier C of the measurement results. Verifier C verifies the measurement results. If the measurement results match, the system proceeds to step S2.3; otherwise, communication is terminated and the system exits.

[0028] S2.3 And generate corresponding sequences respectively. Send to signer B;

[0029] S2.4 After signers A and B confirm receipt of the corresponding sequence, verifier C publishes the sequence. The location is determined, and the measurement results are communicated to the verifier C, while the signer B measures the sequence. The system enters a deceptive state and informs verifier C of the measurement results. If the measurement results of signer A and signer B both match those of verifier C, then proceed to S3; otherwise, communication is terminated and the system exits.

[0030] The above setup uses decoy states to generate different sequences for measurement, and verifies the next sequence only when the previous sequence passes verification, and terminates communication when the previous sequence fails, thus achieving the initial verification of the authenticity of quantum communication between signers.

[0031] Furthermore, step S3 also includes: S3.1 to S3.4.

[0032] , ;

[0033] S3.2 Signer A determines the signature sequentially through local area operation and classic communication (LOCC). Are the particles in the sample Bell state particles? And retain the Bell state particles to obtain a length of... n of Meanwhile, signer B sequentially determines the signature through local area operation and classic communication (LOCC). Are the particles in the sample Bell state particles? And retain the Bell state particles to obtain a length of... n of ;

[0034] S3.3 Signer A Measurement The Bell state in the measurement results Inform verifier C, and simultaneously signer B measures. The Bell state in the measurement results The verifier C is informed, and then verifier C generates the corresponding quantum state according to the encoding rules. ;

[0035] Then the measurement results are obtained. , Meanwhile, signer B passed through the set Measurement The qubits are then used to obtain the measurement results. and generate a signature. .

[0036] The above settings involve inserting Bell states to form different sequences for measurement, and then forming a sequence from the CAPTCHA test results. Finally, the signature is confirmed by using qubits measured geometrically to reconfirm whether communication between the signers is feasible.

[0037] Furthermore, in step S4, the verifier C obtains the quantum one-way function. The value of the signature is calculated and compared with the two values. If they are the same, proceed to step S5; otherwise, the signature is invalid and return to step S3.

[0038] The above settings facilitate the verification of the signer's quantum signature sequence value through a quantum one-way function. The validity can be determined directly by comparing the magnitudes of the values, making the calculation simple and highly reliable.

[0039] Furthermore, it also includes step S5:

[0040] Verifier C will, according to the encoding rules Then make them respectively , Next, verify If the values ​​are the same, the signature is valid; otherwise, it is invalid.

[0041] The above settings, by reverse encoding and then superimposing the reverse encoded sequence, determine whether the values ​​of the signature sequence are the same, thereby determining whether it is valid and further improving the reliability of signature verification.

[0042] Furthermore, the encoding rule in step S1.5 is: if ; ,but .

[0043] The above settings associate the message sequence with the verification code by selecting the corresponding quantum state based on the value in the message sequence. Attached Figure Description

[0044] Figure 1 This is a flowchart of the present invention.

[0045] Figure 2 This is a schematic diagram illustrating the information transmission between signer A, signer B, and verifier C in this invention. Detailed Implementation

[0046] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0047] like Figure 1-2 As shown, a novel and efficient quantum joint signature method based on entanglement measurement is used for participants to jointly sign. Before signing, each participant has a different sequence of quantum states. The participants include signer A, signer B, and verifier C. In this embodiment, signer A is signer Alice, signer B is signer Bob, and verifier C is signer Charlie. The joint signature method is illustrated using signer Alice, signer Bob, and signer Charlie as an example.

[0048] The specific method includes the following steps:

[0049] S1, signer Alice, signer Bob, and verifier Charlie each measure the qubits in their respective sequences and obtain the corresponding measurement results. Then, verifier C randomly arranges the Bell state and the two-particle state to form a sequence. ,sequence And according to the encoding rules, the sequences are respectively... ,sequence Encode and generate a string. Specifically, this includes: S1.1 to S1.5;

[0050] S1.1 Signer Alice, signer Bob, and verifier Charlie possess quantum states. The three Each contains quantum states The first particle, the second particle, the third particle, and then make signer Alice and signer Bob pass through the induced state set. Measure separately The qubit in the middle, and asked verifier Charlie to measure it. The qubits in the quantum entanglement communicate the measurement results to each other. Then, signer Alice and signer Bob compare the measurement results using the following formula (1), which is derived from the principle of quantum entanglement. These represent three quantum sequences, one in the ground state and the other in the excited state. These are different states of two excited states;

[0051] (1);

[0052] This allows us to determine the different qubits in the sequences of signers Alice and Bob, while simultaneously enabling verifier Charlie to measure the sequence. The qubits in the measurement were then published to signer Alice and signer Bob; among them ;

[0053] S1.2 Verifier Charlie from 2 n Bell states and 2 m A sequence is formed by random arrangement of two-particle states. ,sequence , n , m are positive integers, and each sequence contains n A Bell state and m There are two-particle states, where the Bell state is obtained according to the following formula (2):

[0054] (2);

[0055] In the formula The ground state and excited state, The ground state and excited states, among which and For different states of the Bell state, the two-particle state is derived from the set Obtained from;

[0056] S1.3 Verifier Charlie verifies the quantum states according to the encoding rules in Table 1 below. , The Bell states in the code are encoded to generate binary strings. and ;

[0057] Table 1. Encoding rules for quantum states

[0058]

[0059] S1.4 Validator Charlie will All quantum states are divided into two ordered states. , It contains the first and second particles of the Bell state and the two-particle state, respectively. , , It contains the first particle and the second particle in the Bell state and the two-particle state, respectively;

[0060] S1.5 verifier Charlie, based on the encoding rules and message sequence... , The encoding rule is: if .

[0061] S2 validator Charlie inserts a decoy state. Corresponding generation and Signer Alice and signer Bob measured respectively The deceptive state in the measurement Communication terminates if the decoy state in the verifier does not match the result of Charlie's decoy state; otherwise, Charlie inserts the decoy state into the verifier's decoy state. and by Decomposed into , Signer Alice and signer Bob measured respectively The deceptive states in the process specifically include: S2.1-S2.4;

[0062] S2.1 Validator Charlie will use decoy state Randomly insert into the sequence of step S1.5 The generated sequence is then sent to signer Alice and signer Bob, respectively.

[0063] S2.2 Upon confirmation of receipt by signer Alice and signer Bob Afterwards, validator Charlie announced... The position of the decoy state was determined, and then signer Alice and signer Bob measured it respectively. The system identifies the decoy state and informs the verifier Charlie of the measurement results. Charlie checks the measurement results; if the results match, the system proceeds to step S2.3; otherwise, communication is terminated and the system exits.

[0064] S2.3 Validator Charlie will use deception. Randomly inserted into step S1.4 , , For the signer Alice, generate the corresponding Send to signer Bob;

[0065] S2.4 After signers Alice and Bob confirm receipt of the corresponding sequence, validator Charlie publishes it. The position of the deceptive state, then the signer Alice measures. The decoy state is located in the sequence, and the measurement result is given to the verifier Charlie; while the signer Bob measures... , The decoy state is determined, and the measurement results are communicated to verifier Charlie. If the measurement results of signer Alice and signer Bob are consistent with those published by verifier Charlie... If the position of the decoy state matches, proceed to S3; otherwise, terminate communication and exit.

[0066] S3 signer Alice and signer Bob respectively from After extracting the decoy state, we obtain Verifier C will generate a corresponding quantum state encoding rule. , will measure Quantum bits were used to obtain measurement results, and the measurement results were compared with... Generate signatures corresponding to signer A and signer B. Specifically, this includes: S3.1 to S3.4;

[0067] S3.1 Signer Alice from Signer Bob from ;

[0068] S3.2 The signer, Alice, determines the signature sequentially through local operations and classic communication (LOCC). Are the particles in the sample Bell state particles? And retain the Bell state particles to obtain a length of... n of Meanwhile, the signer Bob uses local area operations and classic communication (LOCC) to sequentially determine... Are the particles in the sample Bell state particles? And retain the Bell state particles to obtain a length of... n of In this embodiment, the local operation and classical communication for determining whether a particle is a Bell state are existing technologies and will not be elaborated further here.

[0069] S3.3 Signer Alice Measurement The Bell state in the measurement results Inform the verifier Charlie; simultaneously, signer Bob measures... The Bell state in the measurement results Inform the verifier Charlie, and then the verifier Charlie will generate the corresponding quantum state encoding rules according to Table 1 in step S1.3. In this embodiment, signer Alice and signer Bob respectively measured... The formula for the Bell state in the equation is shown in (2), where and The same logic applies to other states.

[0070] (2);

[0071] S3.4 Signer Alice through set The qubits are then used to obtain the measurement results. and generate a signature. Meanwhile, the signer Bob, through a set and generate a signature. The measurement results obtained in this embodiment The method is based on the principle of quantum entanglement.

[0072] S4 verifier Charlie compared quantum one-way functions. If the values ​​are the same, then the signature is... If valid, proceed to step S5; otherwise, if the signature is invalid, terminate communication and exit. In this embodiment, F is a quantum one-way function, which is existing technology and will not be described further here.

[0073] S5 Verifier Charlie will use the quantum state encoding rules in Table 1 of step S1.3 to complete step S3.3. , Next, verify. If the values ​​are the same, the signature is valid; otherwise, it is invalid.

[0074] In this embodiment, the robustness of the novel efficient quantum joint signature method based on entanglement measurement is described as follows:

[0075] If any attack results in the adversary gaining original non-zero information, it will inevitably introduce a detectable perturbation into the quantum channel. Assuming that the adversary Eve cannot gain any information without triggering detection, Eve's attack would be as follows:

[0076] 1) The adversary Eve intercepted the sequence sent by validator Charlie to signers Alice and Bob. and Then apply the joint probe operation. It acts on all qubits and their private auxiliary states. ;

[0077] 2) The adversary Eve forwards the processed qubits to signer Alice and signer Bob;

[0078] 3) The adversary Eve intercepts the sequence sent by validator Charlie again. Then apply a new probe It acts on all qubits and their private auxiliary states. ;

[0079] 4) Enemy Eve captures , The value is then returned to the verifier Charlie, who then obtains the valid signature information through the private auxiliary bits.

[0080] The first operation to obtain valid signature information using private auxiliary bits. Afterwards, the basic state is:

[0081] ;

[0082] in It is an arbitrary state in the adversary Eve's private auxiliary bits, and does not require normalization or orthogonality, and .

[0083] However, these states will be used for error detection with a non-zero probability; therefore, to avoid detection, the adversary Eve must set... All are zero vectors.

[0084] Throughout the entire quantum joint signature scheme, all decoy states originate from... Therefore, after the opponent Eve's entanglement operation, It will become an entangled state as follows:

[0085] ;

[0086] ;

[0087] because Therefore, we can obtain:

[0088] ;

[0089] The mutual information between signer Alice or signer Bob and verifier Charlie is as follows:

[0090] ;

[0091] If adversary Eve exploits an intermediate sequence, signer Alice or signer Bob and verifier Charlie will, with probability, [become] [they will be ... An incorrect measurement result was obtained, and the mutual information between signer Alice or signer Bob and verifier Charlie is:

[0092] ;

[0093] Clearly, under conditions of eavesdropping, the mutual information between signer Alice or signer Bob and verifier Charlie is less than the mutual information without eavesdropping:

[0094] ;

[0095] For the second operation The procedure is the same as the first one, so it will not be repeated here.

[0096] In this embodiment, the unforgeability of the novel efficient quantum joint signature method based on entanglement measurement is explained as follows:

[0097] If the adversary Eve wants to forge the signature of one of the signers, she can launch two forgery attacks: a no-message forgery attack and a message forgery attack.

[0098] a) No-message forgery attack

[0099] Suppose that adversary Eve generates a quantum-forged signature without receiving any messages from the three participants.

[0100] When the adversary Eve sends signature requests to both signer Alice and signer Bob, Alice and Bob will request a sequence measurement. The quantum bits in it, while the adversary Eve does not. Therefore, the probability that the adversary Eve successfully passes the verification by signers Alice and Bob in the initialization algorithm step S1 is: In other words, the adversary Eve cannot generate a quantum forged signature without receiving any messages from the three participants.

[0101] b) Message forgery attack

[0102] In demonstrating robustness, it has been shown that the adversary Eve cannot obtain any useful information about the signature by intercepting and retransmitting all quantum sequences. Furthermore, signers Alice and Bob eventually send the signature encrypted using a quantum one-way function to the verifier Charlie. Therefore, the enemy Eve cannot intercept To copy or obtain any useful information.

[0103] In this embodiment, the denial attack on the novel efficient quantum joint signature method based on entanglement measurement is described as follows:

[0104] In a secure quantum signature scheme, neither the signer nor the verifier can reject a valid quantum signature. In this embodiment, signer Alice and signer Bob request verifier Charlie to measure the quantum state. In the qubits, since the entangled quantum state collapses into a certain measurement result once it is measured, signer Alice and signer Bob cannot deny the measurement result of the quantum state. At the same time, signer Alice and signer Bob cannot deny the measurement result of the Bell state.

[0105] Therefore, a novel and efficient quantum joint signature method based on entanglement measurement can effectively resist denial attacks.

[0106] In this embodiment, the efficiency of the novel efficient quantum joint signature method based on entanglement measurement is described as follows:

[0107] The efficiency of the novel efficient quantum joint signature method based on entanglement measurement can be calculated using the following formula (3).

[0108] (3);

[0109] in This indicates the number of useful particles, while These represent the total number of sub-bits and the total number of classical bits used, respectively.

[0110] when n When large enough, the efficiency is .

[0111] To visually demonstrate the efficiency of this novel, highly efficient quantum joint signature method based on entanglement measurement, it is compared with similar quantum signature schemes. The results are shown in Table 2 below.

[0112] Table 2

[0113]

[0114] By comparison, it can be seen that the scheme of the present invention is significantly superior to other quantum signature schemes. Therefore, the novel efficient quantum joint signature method based on entanglement measurement has high efficiency.

[0115] In this embodiment, by introducing quantum efficient entanglement measurement technology, quantum resource consumption is reduced, and the signature generation and verification process is optimized to improve the efficiency of signature generation and verification. Furthermore, the non-cloning and quantum entanglement properties of quantum mechanics are fully utilized to ensure the unforgeability and non-repudiation of the joint signature, fundamentally improving security and avoiding security vulnerabilities (such as hash collisions and algorithm cracking) that may be introduced by classical encoding techniques. Simultaneously, the quantum state preparation and measurement process is optimized to enhance the stability of the joint signature in noisy environments, thereby improving its robustness in quantum noise environments and ensuring the reliability and stability of the joint signature in practical applications. This makes it easier to deploy and apply in practical systems, reducing implementation costs and technical complexity, and thus making it more suitable for practical application scenarios (such as multi-party collaboration and financial transactions).

[0116] The working principle of this invention is as follows: After the signer performs multiple measurements on the qubits in the sequence and generates different sequences multiple times, under the action of the verifier, different sequences are generated by inserting decoy states. The signer then measures and compares the different sequences. After comparing the measurement results of the signers, the verifier combines the different sequences to form a signature. By comparing whether the values ​​of the superimposed sequences from different signers are the same, the verifier determines whether the joint signature of the signers is valid.

Claims

1. A novel, efficient quantum joint signature method based on entanglement measurement, used for joint signature by participants, wherein before signing, the participants possess different sequences of quantum states and have measurement results of qubits, and the participants include signer A, signer B, and verifier C, characterized in that: It also includes the following steps: S1 verifier C randomly arranges a preset number of Bell states and two-particle states to form And according to the quantum state encoding rules, respectively Encode the data to generate a string, then process the sequence according to the message sequence and encoding rules. Corresponding generation Step S1 includes: S1.1~S1.5, S1.1 Signer A, signer B, and verifier C possess quantum states. The three sequences Then, signer A and signer B are made to pass through a set of induced mutations. Measure separately The sequence contains qubits, and the different qubits in the sequences corresponding to signer A and signer B are compared, while verifier C measures... The qubits in the measurement data are then used to publish the measurement results to signer A and signer B. S1.2 Verifier C from 2 n Bell states and 2 m Randomly arranged in two-particle states ; S1.3 Verifier C verifies the quantum states according to their encoding rules. The Bell states in the code are encoded to generate binary strings. and ; S1.4 Verifier C will ,and , It contains the first and second particles of the Bell state and the two-particle state, respectively, and the sequence is... The quantum states in the sequence are divided into two ordered sequences. ,sequence And sequence ,sequence These include the Bell state and the first and second particles in a two-particle system, respectively. S1.5 Verifier C, based on the encoding rules and message sequence , convert the sequence ,sequence Corresponding generated sequence , and ; S2 verifier C inserts a decoy state. Corresponding generation and sequence Signer A and signer B measured respectively The deceptive state in the measurement When the decoy state in verifier C matches the decoy state in verifier C, verifier C inserts the decoy state into the decoy state in verifier C. , In, and generate accordingly Signer A and signer B measured respectively The deceptive state in the text, and the measurement in signer A and signer B. When the decoy state in the test matches the location of the decoy state published by verifier C, proceed to step S3; S3 signer A and signer B respectively Bell states are formed in the sequence after the decoy states are extracted. And measurements are taken to generate measurement results. Verifier C will generate a corresponding quantum state encoding rule. and sequence , will measure Quantum bits were used to obtain measurement results, and the measurement results were compared with... Generate signatures corresponding to signer A and signer B. S A , S B Step S3 also includes: S3.1 to S3.

4. S3.1 Signer A from the sequence Signer B from ; S3.2 Signer A determines the signature sequentially through local area operation and classic communication (LOCC). Are the particles in the sample Bell state particles? And retain the Bell state particles to obtain a length of... n of Meanwhile, signer B sequentially determines the signature through local area operation and classic communication (LOCC). Are the particles in the sample Bell state particles? And retain the Bell state particles to obtain a length of... n of ; S3.3 Signer A Measurement The Bell state in the measurement results Inform verifier C, and simultaneously signer B measures. The Bell state in the measurement results The verifier C is informed, and then verifier C generates the corresponding quantum state according to the encoding rules. ; S3.4 Signer A through set The qubits are then used to obtain the measurement results. Meanwhile, signer B through a set The qubits are then used to obtain the measurement results. and generate a signature. ; S4 verifier C compares quantum one-way functions The value is used to determine the signature. S A , S B Is it effective? 2. The novel efficient quantum joint signature method based on entanglement measurement according to claim 1, characterized in that: In step S1.1, The first, second, and third particles, and the results of the comparison test between signer A and signer B.

3. The novel efficient quantum joint signature method based on entanglement measurement according to claim 1, characterized in that: In step S1.2, the Bell state is obtained according to the following formula (2): （2）； Two-particle state from set It was obtained from the middle.

4. The novel efficient quantum joint signature method based on entanglement measurement according to claim 1, characterized in that: Step S2 further includes: S2.1-S2.4 S2.1 Validator C will use deception. and will generate the corresponding The generated sequence is then sent to signer A and signer B respectively. S2.2 Upon confirmation of receipt by signer A and signer B Afterwards, verifier C announced... The position of the deceptive state was determined, and then signer A and signer B measured it respectively. The system determines the position of the decoy state and informs verifier C of the measurement results. Verifier C verifies the measurement results. If the measurement results match, the system proceeds to step S2.3; otherwise, communication is terminated and the system exits. S2.3 Validator C will use deception. Random insertion into a sequence The middle and each form a sequence and generate the corresponding sequence Send to signer A, corresponding to the generated sequence Send to signer B; S2.4 After signers A and B confirm receipt of the corresponding sequence, verifier C publishes it. Then signer A measures the sequence The decoy state is located in the sequence, and the measurement result is informed to the verifier C, while the signer B measures the sequence. The system enters a deceptive state and informs verifier C of the measurement results. If the measurement results of signer A and signer B both match those of verifier C, then proceed to S3; otherwise, communication is terminated and the system exits.

5. The novel efficient quantum joint signature method based on entanglement measurement according to claim 1, characterized in that: In step S4, verifier C obtains the quantum one-way function. The value of the signature is calculated and compared with the two values. If they are the same, proceed to step S5; otherwise, the signature is invalid.

6. The novel efficient quantum joint signature method based on entanglement measurement according to claim 5, characterized in that: It also includes step S5: Verifier C will, according to the encoding rules of quantum states, Then make them respectively Next, verify If the values ​​are the same, the signature is valid; otherwise, it is invalid.

7. The novel efficient quantum joint signature method based on entanglement measurement according to claim 1, characterized in that: The encoding rule in step S1.5 is: if ;if .

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