Novel efficient quantum joint signature method based on entanglement measurement

Abstract

The invention provides a novel efficient quantum joint signature method based on entanglement measurement, which comprises the following steps: after a signer measures quantum bits in a sequence for multiple times, generating different sequences for multiple times, and under the action of a verifier, generating different sequences by inserting a decoy state; according to the method and the device, a signer measures and compares different sequences, a verifier compares the measurement results of the signer and superposes the different sequences to form a signature, and whether the combined signature of the signer is valid or not is judged by comparing whether the superposed values of the different sequences of different signers are the same or not.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum secure communication, and particularly to a novel and efficient quantum joint signature method based on entanglement measurement. Background Art

[0002] As a new interdisciplinary subject, quantum cryptography mainly utilizes the basic principles of quantum mechanics to establish a new cryptographic system, which theoretically guarantees unconditional security. Therefore, the research on quantum communication has become an important topic, such as quantum secure direct communication (QSDC), quantum secret sharing protocol (QSS), quantum signature (QS), quantum private query protocol (QPQ), quantum key agreement (QKA), etc. The main application scenarios of quantum signature (QS) include but are not limited to financial transactions, e-government, medical data sharing, etc. For example, in the signing of electronic contracts, quantum signature can ensure the integrity of the contract content and the authenticity of the signatory's identity; in financial transactions, quantum signature can prevent transaction information from being tampered with or forged; in addition, quantum signature technology can also be used in multi-party collaboration scenarios, such as the scenario where both doctors and patients in a hospital jointly sign information and a third party verifies it.

[0003] For example, the patent document with the Chinese patent application number 03146395.9, the classification number H04K1 / 00, and the publication date October 11, 2006 discloses a classical sequential rearrangement encryption method for quantum states in quantum key distribution. It mainly uses the no-cloning principle in quantum mechanics and the quantum characteristics of coherence and non-locality between entangled particles to encrypt the generation process of quantum keys. While ensuring security, all particles of the entangled system are transmitted simultaneously to increase the transmission distance and simplify the communication process. It is realized by means of a control system controlled by a control code respectively located at the sender and receiver ends, a sending and receiving system connected by upper and lower channels, a corresponding transmission sequence rearrangement encryption and decryption system, a data processing system connected by a classical channel, and a quantum coherent signal source. It enables the quantum key distribution scheme based on entangled pairs to achieve maximum-capacity coding, and the communication process is simpler; and at the same coherence time, its transmission distance is longer than that of traditional methods.

[0004] The above-mentioned literature mainly determines the selection of the transmission order rearrangement method and transmits the corresponding data group according to the value of each W-bit binary in the control code at the sending end and the receiving end, encodes through the Bell basis state, removes the measurement results without counting, groups the remaining measurement results, and compares the groups with the results in the classical channel. Whether the key is secure is determined by the error rate. This method also needs to compare the encoded data with the data in the classical channel to determine whether the key is secure. If the data transmitted in the classical channel is attacked, the final determination of the key security is inaccurate. Moreover, it only verifies the data in the control code through entanglement measurement. In the case where the control code verification is okay, if data is directly transmitted, there is a possibility that the transmitted data is tampered with. It does not add decoy states to both the message sequence and the control code sequence, so as to ensure the stability of the signature in terms of both the control code and the message sequence. Summary of the Invention

[0005] The purpose of the present invention is to provide a new and efficient quantum joint signature method based on entanglement measurement, which utilizes the non-clonability of quantum mechanics and the characteristics of quantum entanglement to ensure the non-forgery and non-deniability of signatures, so as to enhance security. At the same time, by optimizing the preparation and measurement processes of quantum states, the stability of the signature in a noisy environment is enhanced, and the robustness of quantum communication is improved.

[0006] To achieve the above object, the present invention provides a new and efficient quantum joint signature method based on entanglement measurement for joint signature by participants. Before signature, the participants have different sequences of quantum states and measurement results of qubits. The participants include signer A, signer B, and verifier C, and further include the following steps: S1 The verifier C randomly arranges a preset number of Bell states and two-particle states to form sequences , sequence , and encodes sequences , sequence respectively according to the quantum state encoding rule to generate strings. Then, according to the message sequence and the encoding rule, sequences , sequence are correspondingly generated into sequences , sequence ; S2 The verifier C inserts decoy states into sequences and sequence to correspondingly generate sequences and sequence . Signer A and signer B respectively measure the decoy states in . When the decoy states measured in match the decoy states in the verifier C, the verifier C inserts the decoy states into the decomposed from sequence and enter step S3 when the decoy states measured by signer A and signer B match the positions of the decoy states announced by verifier C; in S3 Signer A and signer B respectively extract the Bell state formation sequence from the sequence after extracting the decoy states and perform measurements. Verifier C, according to the encoding rules of the quantum state, , on the qubits of to obtain the measurement results, and compare the measurement results with S A , S B ; S4 Verifier C compares the values of the quantum one-way function , and then judges the signatures S A , S B whether they are valid.

[0007] In the above method, after the signers measure the qubits in the sequence, the verifier randomly forms a sequence through Bell states and two-particle states, encodes the sequence in quantum states, then forms a sequence with the message sequence through the encoding rules, and this sequence is used as the verification code. Decoy states are added to the verification code, and under the action of the verifier, different sequences are generated by inserting decoy states, and the signers measure and compare different sequences respectively. After comparing the measurement results of the signers, the verifier further divides the verified correct sequences into two types and sends them to the sender and the receiver respectively, then adds decoy states here to form a new sequence and compares it with the decoy states announced by verifier C again, which can ensure the accuracy of the verification code through multiple entanglement measurements. Then, when signers A and B confirm that the verification code is correct again, they extract the Bell states in the decoy states and perform qubit measurements. Verifier C and the measurement results of the sequence after extracting the decoy states form signatures according to the quantum state encoding principle, and then compare the signature values to determine whether they are valid. This makes the verification code superimposed with Bell states and two-particle states, making the original sequence have a certain robustness, and determining the reliability of the verification code transmission through the addition and position verification of decoy states during the sequence formation process, and making the anti-attack ability stronger during the transmission process after adding decoy states. Then, after extracting the decoy states from the correct verification code, the original signature is obtained through qubit measurement, and then compare whether the signatures of signers A and B are consistent to determine whether the signature is qualified, so as to comprehensively verify the message sequence and the verification code, ensuring the non-forgery and non-denial of the signature.

[0008] Further, the step S1 includes: S1.1 to S1.5, S1.1 Signer A, Signer B, and Verifier C possess quantum states , then let Signer A and Signer B pass through the induced state set the qubits in the sequence, compare the different qubits in the corresponding sequences of Signer A and Signer B, inform each other of the measurement results and then compare them. At the same time, let Verifier C measure the qubits in the sequence and announce the measurement results to Signer A and Signer B; S1.2 Verifier C randomly arranges to form sequences n from 2 m Bell states and 2 sequences, ; S1.3 Verifier C encodes the Bell states in sequences , respectively according to the encoding rules of quantum states, and generates binary strings and respectively; And the sequence respectively contains the first particle and the second particle in the Bell state and the two-particle state. At the same time, the sequence the first particle and the second particle in the Bell state and the two-particle state; S1.5 Verifier C according to the encoding rules and the message sequence .

[0009] The above settings facilitate Signer A, Signer B, and Verifier C to measure the qubits in their respective sequences, divide the quantum states into two sequences, and Signer A and B take out two sequences from them, which is convenient for subsequent sending the two sequences to different signers and then performing sequence verification to ensure robustness.

[0010] The second particle, the third particle, and Signer A and Signer B compare the test results.

[0011] The above settings facilitate the signers to respectively contain different particles in the quantum state, and then form different sequences so as to compare different positions of the qubits.

[0012] Further, in the step S1.2, the Bell state is obtained according to the following formula (2): (2) The ground state and the excited state, and the two-particle state is obtained from the set .

[0013] The above settings facilitate the selection of Bell states and two-particle states, and make the selected Bell states and two-particle states have a certain correlation.

[0014] Furthermore, the step S2 further includes: S2.1 - S2.4 and generate the corresponding and send the generated sequences to signer A and signer B respectively; S2.2 After signer A and signer B confirm receipt of, verifier C announces the positions of the decoy states in, then signer A and signer B respectively measure the positions of the decoy states in, and inform verifier C of the measurement results. Verifier C checks the measurement results. If the measurement results are consistent, proceed to S2.3; otherwise, abort the communication and exit; S2.3 , and generate sequences respectively corresponding to and send them to signer B; S2.4 After signer A and signer B confirm receipt of the corresponding sequences, verifier C announces the sequences positions, and informs verifier C of the measurement results, while signer B measures the decoy states in the sequence and informs verifier C of the measurement results. If the measurement results of signer A and signer B are both consistent with verifier C, proceed to S3; otherwise, abort the communication and exit.

[0015] The above settings generate different sequences for measurement by inserting decoy states, and only perform the verification of the next sequence when the verification of each sequence is qualified, and abort the communication when it is unqualified, thereby realizing the authenticity verification of quantum communication between signers for the first time.

[0016] Furthermore, the step S3 further includes: S3.1 ~ S3.4 , ; S3.2 Signer A sequentially discriminates whether the particles in are Bell state particles through local operations and classical communication (LOCC), and retains the Bell state particles to obtain n with a length of ; At the same time, signer B sequentially discriminates whether the particles in are Bell state particles through local operations and classical communication (LOCC), and retains the Bell state particles to obtain n with a length of ; S3.3 Signer A measures the Bell state in, and sends the measurement result to Verifier C. Meanwhile, Signer B measures the Bell state in, and sends the measurement result to Verifier C. Then, Verifier C generates according to the encoding rule of the quantum state; , and then obtains the measurement result , Meanwhile, Signer B measures the qubits through the set and then obtains the measurement result , and generates a signature . .

[0017] With the above settings, different sequences are formed by inserting Bell states for measurement, and the verification code test results are formed into a sequence , and finally, the qubits are measured geometrically to determine the signature with doubts, so as to confirm again whether the communication between the signers is feasible.

[0018] Furthermore, in step S4, Verifier C obtains through a quantum one-way function and compares the values of the two. If they are the same, go to step S5; otherwise, the signature is invalid and return to step S3.

[0019] With the above settings, it is convenient to confirm the value of the signer's quantum signature sequence through a quantum one-way function, and it can directly determine whether it is valid by comparing the magnitudes of the values. The calculation is simple and the reliability is high.

[0020] Furthermore, it also includes step S5: Verifier C encodes according to the encoding rule, and then respectively makes , , and then verifies If the values are the same, the signature is legal; otherwise, it is illegal.

[0021] With the above settings, by reverse encoding and then superimposing the reverse-encoded sequence again, the value of the signature sequence is determined to be the same, so as to determine whether it is legal, further improving the reliability of signature verification.

[0022] Furthermore, in step S1.5, the encoding rule is: if ; , then .

[0023] With the above settings, the corresponding quantum state is selected according to the value in the message sequence, so that the message sequence is associated with the verification code. Description of the Drawings

[0024] Figure 1 This is a flowchart of the present invention.

[0025] Figure 2 This is a schematic diagram of information transmission among signer A, signer B, and verifier C in the present invention. Detailed Description of the Invention

[0026] The present invention will be further described in detail below in conjunction with the drawings and the detailed description of the invention.

[0027] As Figure 1-2 shown, a new and efficient quantum joint signature method based on entanglement measurement is used for joint signature by participants. Before signature, 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. Taking signer Alice, signer Bob, and signer Charlie as examples, the joint signature method is described.

[0028] The specific method includes the following steps: S1. Signer Alice, signer Bob, and verifier Charlie 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 sequences and sequence , and encodes sequences and sequence respectively according to the encoding rules to generate strings , which specifically includes: S1.1~S1.5; S1.1 Signer Alice, signer Bob, and verifier Charlie have three in the quantum state which respectively contain the first particle, the second particle, and the third particle in the quantum state . Then, signer Alice and signer Bob measure the qubits in respectively through the induced state set , and require verifier Charlie to measure the qubits in and inform each other of the measurement results. Then, signer Alice and signer Bob compare the measurement results through the following formula (1), and formula (1) is obtained according to the quantum entanglement principle, where respectively represent that the three quantum sequences are all in the ground state and all in the excited state, while are different states of two excited states; (1); Thus, different qubits in the sequences of signer Alice and signer Bob are obtained, and at the same time, the verifier Charlie measures the qubits in the sequence and announces the measurement results to signer Alice and signer Bob; where ; S1.2 The verifier Charlie randomly arranges 2 n Bell states and 2 m two-particle states to form sequences , sequence , n , m are positive integers, and each sequence contains n Bell states and m two-particle states, where the Bell states are obtained according to the following formula (2): (2); In the formula ground state and excited state of ground state and excited state of, where and are different states of the Bell state, and the two-particle state is obtained from the set ; S1.3 The verifier Charlie encodes the Bell states in , respectively according to the encoding rules of the quantum states in Table 1 below, and generates binary strings and respectively; Table 1 Encoding Rules of Quantum States

[0029] S1.4 The verifier Charlie divides all the quantum states in into two ordered , respectively containing the first particle and the second particle of the Bell state and the two-particle state, , , respectively containing the first particle and the second particle of the Bell state and the two-particle state; S1.5 The verifier Charlie, according to the encoding rules and the message sequences , ; where the encoding rule is: if .

[0030] Verifier Charlie inserts decoy states into to correspondingly generate and . Signer Alice and Signer Bob respectively measure the decoy states in . If the decoy states in the measurement do not match the decoy states of Verifier Charlie, the communication is aborted. If they match, then Verifier Charlie inserts decoy states into those decomposed by and by to , . Signer Alice and Signer Bob respectively measure the decoy states in , specifically including: S2.1 - S2.4; S2.1 Verifier Charlie randomly inserts the decoy state into the sequence in step S1.5 and sends the generated sequences to Signer Alice and Signer Bob respectively; S2.2 After Signer Alice and Signer Bob confirm receiving , Verifier Charlie announces the positions of the decoy states in . Then Signer Alice and Signer Bob respectively measure the positions of the decoy states in and inform Verifier Charlie of the measurement results. Verifier Charlie checks the measurement results. If the measurement results match, proceed to S2.3; otherwise, abort the communication and exit; S2.3 Verifier Charlie randomly inserts the decoy state into , in step S1.4, sends it to Signer Alice, and correspondingly generates to send to Signer Bob; S2.4 After Signer Alice and Signer Bob confirm receiving the corresponding sequences, Verifier Charlie announces the positions of the decoy states in . Then Signer Alice measures the position of the decoy state in and informs Verifier Charlie of the measurement result; while Signer Bob measures the decoy states in , and informs Verifier Charlie of the measurement result. If the measurement results of Signer Alice and Signer Bob both match the positions of the decoy states announced by Verifier Charlie in , proceed to S3; otherwise, abort the communication and exit.

[0031] S3 signer Alice and signer Bob respectively After extracting the decoy state from , the verifier C will generate the corresponding , the measurement The qubits are measured and the measurement results are compared with Generate signatures corresponding to signer A and signer B Specifically include: S3.1~ S3.4; S3.1 The signer Alice , the signer Bob from ; S3.2 The signer Alice uses local operations and classical communication (LOCC) to determine Is the particle in the Bell state particle, and retain the Bell state particle to obtain a length of n of ; At the same time, the signer Bob uses local operation and classical communication (LOCC) to determine Is the particle in the Bell state particle, and retain the Bell state particle to obtain a length of n of ; In this embodiment, local operation and classical communication to determine whether it is a Bell state particle are existing technologies; they will not be repeated here.

[0032] S3.3 Signer Alice measures The Bell state in the Tell the verifier Charlie; at the same time, the signer Bob measures The Bell state in the Tell the verifier Charlie, and then the verifier Charlie generates the corresponding quantum state encoding rules in step S1.3 Table 1 In this embodiment, the signer Alice and the signer Bob measure The formula of the Bell state in is shown as follows (2), where and , and so on for other states.

[0033] (2); S3.4 The signer Alice passes the set The quantum bit and then get the measurement result , and generate a signature , while the signer Bob passes the set , and generate a signature In this embodiment, the measurement results are obtained The method is obtained according to the principle of quantum entanglement.

[0034] S4 The verifier Charlie compares through a quantum one-way function If they are the same, the signature is valid and proceeds to step S5; otherwise, the signature is invalid, the communication is aborted and exited. In this embodiment, F is a quantum one-way function, which is a prior art and will not be elaborated here.

[0035] S5 The verifier Charlie encodes the quantum state in Table 1 of step S1.3 for step S3.3 , Then verify If they are the same, the signature is legal; otherwise, it is illegal.

[0036] In this embodiment, the robustness of the new and efficient quantum joint signature method based on entanglement measurement is described as follows: If any attack causes the adversary to obtain the original non-zero information, it will inevitably introduce detectable perturbations in the quantum channel. Assuming that the adversary Eve cannot obtain any information without triggering detection, the attack of the adversary Eve is as follows: 1) The adversary Eve intercepts the sequences and sent by the verifier Charlie to the signer Alice and the signer Bob, and then applies the joint probe operation , acting on all qubits and their private auxiliary states ; 2) The adversary Eve forwards the processed qubits to the signer Alice and the signer Bob; 3) The adversary Eve intercepts the sequence sent by the verifier Charlie again, and then applies a new probe , acting on all qubits and their private auxiliary states ; 4) The adversary Eve captures , values and returns them to the verifier Charlie, and then obtains the valid signature information through the private auxiliary bits.

[0037] After the first operation of obtaining the valid signature information from the private auxiliary bits , the basic state is: ; where is any state in the adversary Eve's private auxiliary bits, and does not require normalization or orthogonality, and .

[0038] However, with non - zero probability, these states will be used for error detection. Therefore, in order to avoid being detected, the adversary Eve must set to be all zero vectors.

[0039] In the whole quantum joint signature scheme, all decoy states are selected from Therefore, after the entanglement operation of the adversary Eve, will become the following entangled state: ; ; Since , it can be further obtained that: ; , the mutual information between the signer Alice or the signer Bob and the verifier Charlie is: ; If the adversary Eve uses the intermediate state sequence, the signer Alice or the signer Bob and the verifier Charlie will obtain incorrect measurement results with probability , and the mutual information between the signer Alice or the signer Bob and the verifier Charlie is: ; Obviously, in the case of eavesdropping, the mutual information between the signer Alice or the signer Bob and the verifier Charlie is less than that without eavesdropping: ; For the second operation , it is the same as the first operation and will not be elaborated here.

[0040] In this embodiment, the unforgeability of the new and efficient quantum joint signature method based on entanglement measurement is described as follows: If the adversary Eve wants to forge the signature of one of the signers, she can launch two types of forgery attacks, namely the no - message forgery attack and the message forgery attack; a) No - message forgery attack Suppose the adversary Eve generates a quantum forged signature without receiving any messages from the three participants.

[0041] When the adversary Eve sends signature requests to the signer Alice and the signer Bob respectively, the signer Alice and the signer Bob will require to measure the qubits in the sequence , while the adversary Eve does not have , therefore, the probability that the adversary Eve successfully passes the verification of signer Alice and signer Bob in the initialization algorithm step S1 is: , that is to say, the adversary Eve cannot generate a quantum forged signature without receiving any messages from the three participants.

[0042] b) Message forgery attack During the process of explaining the robustness, it has been proved that the adversary Eve cannot obtain any useful information about the signature by intercepting and resending all quantum sequences. In addition, signer Alice and signer Bob finally send the encrypted by the quantum one-way function to the verifier Charlie. Therefore, the adversary Eve cannot to copy or obtain any useful information.

[0043] In this embodiment, the denial attack on the new and efficient quantum joint signature method based on entanglement measurement is described as follows: In a secure quantum signature scheme, the signer and the verifier cannot reject a valid quantum signature. In this embodiment, signer Alice and signer Bob require the verifier Charlie to measure the qubits in the quantum state. Since the entangled quantum state will collapse into a certain definite measurement result once it is measured, therefore, signer Alice and signer Bob cannot deny the measurement result of the quantum state. At the same time, signer Alice and signer Bob also cannot deny the measurement result of the Bell state.

[0044] Therefore, the new and efficient quantum joint signature method based on entanglement measurement can effectively resist the denial attack.

[0045] In this embodiment, the efficiency of the new and efficient quantum joint signature method based on entanglement measurement is described as follows: The efficiency of the new and efficient quantum joint signature method based on entanglement measurement can be calculated by the following formula (3), (3); where represents the number of useful particles, and represent the total number of quantum bits and the total number of classical bits used respectively.

[0046] When n is large enough, the efficiency is .

[0047] To intuitively reflect the efficiency of this new and efficient quantum joint signature method based on entanglement measurement, a comparison with a similar quantum signature scheme is made, and the results are shown in Table 2 below. Table 2

[0048] Through comparison, it can be obtained that the solution of the present invention is significantly higher than other quantum signature solutions. Therefore, the new and efficient quantum joint signature method based on entanglement measurement has high efficiency.

[0049] In this embodiment, by introducing quantum efficient entanglement measurement technology, the consumption of quantum resources is reduced. At the same time, the signature generation and verification processes are optimized to improve the efficiency of signature generation and verification, and the no-cloning property and quantum entanglement characteristics of quantum mechanics are fully utilized to ensure the unforgeability and non-repudiation of the joint signature, fundamentally enhancing the security and avoiding security vulnerabilities (such as hash collisions, algorithm cracking, etc.) that may be introduced by classical coding techniques. At the same time, the quantum state preparation and measurement processes are optimized to enhance the stability of the joint signature in a noisy environment, so as to improve the robustness in a quantum noise environment and ensure the reliability and stability of the joint signature in practical applications, thus making it easy to be deployed and applied in an actual system, reducing the implementation cost and technical complexity, and further being more suitable for actual application scenarios (such as multi-party collaboration, financial transactions, etc.).

[0050] The working principle of the present invention: After the signer measures the qubits in the sequence multiple times and generates different sequences multiple times, under the action of the verifier, different sequences are generated by inserting decoy states, and the signer measures and compares different sequences respectively. After the verifier compares the measurement results of the signer, signatures are formed by superimposing different sequences, and then by comparing whether the superimposed values of different sequences of different signers are the same, it is judged whether the joint signature of the signer is valid.

Claims

1. A new and efficient quantum joint signature method based on entanglement measurement, which is used for joint signature by participants. Before signing, the participants have different sequences of quantum states and quantum bit measurement results. The participants include signer A, signer B and verifier C, which is characterized by: The following steps are also included: 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, Encode to generate a string, and then convert the sequence into Corresponding to the generation ; S2 validator C inserts the decoy state Corresponding to the generation and sequence , signer A and signer B measure The decoy state in the When the decoy state in matches the decoy state in verifier C, verifier C inserts the decoy state into , and generate the corresponding , signer A and signer B measure The decoy state in the , and measured at signer A and signer B When the decoy state in matches the decoy state position published by verifier C, proceed to step S3; S3 signer A and signer B will Bell states are formed in the sequence after extracting the decoy state And measure to form the measurement results , the verifier C will generate the corresponding and sequence , the measurement The qubits are measured and the measurement results are compared with Generate signatures corresponding to signer A and signer B S A , S B ; S4 Verifier C Comparison Quantum One-Way Functions The value of , and then judge the signature S A , S B Is it effective? 2. According to claim 1, a novel and efficient quantum joint signature method based on entanglement measurement is characterized in that: The step S1 includes: S1.1 to S1.5, S1.1 Signer A, Signer B and Verifier C have quantum states Three sequences of , then make signer A and signer B pass the mutagenesis state collection Measure separately The qubits in the sequence are compared with the different qubits in the sequence of signer A and signer B, and verifier C measures The quantum bits in the qubits and the measurement results are announced to signers A and B; S1.2 Validator C from 2 n Bell states and 2 m The two-particle state is randomly arranged to form ; S1.3 The verifier C respectively performs The Bell state in is encoded to generate binary strings respectively. and ; S1.4 Validator C will ,and , Contains the first particle and the second particle in the Bell state and the two-particle state respectively, and the sequence The quantum states in are divided into two ordered sequences ,sequence , and the sequence ,sequence They include Bell state and the first particle and the second particle in the binary particle respectively; S1.5 Verifier C according to the encoding rules and message sequence , convert the sequence ,sequence Corresponding to the generated sequence , and .

3. According to claim 2, a novel and efficient quantum joint signature method based on entanglement measurement is characterized in that: In step S1.1, The first particle, the second particle, and the third particle, signer A and signer B compare the test results.

4. According to claim 2, a novel and efficient quantum joint signature method based on entanglement measurement is characterized in that: In step S1.2, the Bell state is obtained according to the following formula (2): （2）； , the two-particle state is from the collection Obtained in.

5. According to claim 1, a novel and efficient quantum joint signature method based on entanglement measurement is characterized in that: The step S2 also includes: S2.1-S2.4 S2.1 Validator C will deceive the state , and the corresponding And send the generated sequence to signer A and signer B respectively; S2.2 After signer A and signer B confirm receipt After that, the verifier C announces The position of the decoy state in , and then signer A and signer B measure The position of the decoy state in the , and inform the verifier C of the measurement result, the verifier C checks the measurement result, if the measurement result is consistent, then enter S2.3; otherwise, terminate the communication and exit; S2.3 Validator C will deceive the state Randomly insert into the sequence and form sequences , and the corresponding generated sequence Sent to signer A, corresponding to the generated sequence Send to signer B; S2.4 After signer A and signer B confirm receipt of the corresponding sequence, verifier C announces , then signer A measures the sequence The position of the decoy state in the , and informs the verifier C of the measurement result, while the signer B measures the sequence The decoy state in the measurement is detected, and the measurement result is notified to the verifier C. If the measurement results of signer A and signer B are consistent with those of the verifier C, then S3 is entered; otherwise, the communication is terminated and the verifier exits.

6. According to claim 1, a novel and efficient quantum joint signature method based on entanglement measurement is characterized in that: The step S3 also includes: S3.1 to S3.4 S3.1 Signer A from sequence , signer B from ; S3.2 Signer A determines the signer through local operation and classical communication (LOCC) Is the particle in the Bell state particle, and retain the Bell state particle to obtain a length of n of ; At the same time, signer B uses local operation and classical communication (LOCC) to determine Is the particle in the Bell state particle, and retain the Bell state particle to obtain a length of n of ; S3.3 Signer A Measurement The Bell state in the Tell the verifier C, and the signer B measures The Bell state in the Inform the verifier C, and then the verifier C generates the corresponding ; S3.4 Signer A passes the set The quantum bit and then get the measurement result , while signer B passes the set The quantum bit and then get the measurement result , and generate a signature .

7. The novel and efficient quantum joint signature method based on entanglement measurement according to claim 1 is characterized in that: In step S4, the verifier C obtains the and compare the two values. If they are the same, go to step S5; otherwise, the signature is invalid.

8. The novel and efficient quantum joint signature method based on entanglement measurement according to claim 7 is characterized in that: The step S5 is also included: Verifier C will use the encoding rules of the quantum state to , and then respectively make , then verify If the values ​​are the same, the signature is legal; otherwise, it is illegal.

9. The novel and efficient quantum joint signature method based on entanglement measurement according to claim 2 is characterized in that: In step S1.5, the coding rule is: if ;if .

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