Dynamic network adaptive multi-party quantum key exchange method based on GHZ state

Abstract

The invention discloses a dynamic network adaptive multi-party quantum key exchange method based on a GHZ state, and belongs to the field of quantum cryptography. The method mainly comprises the following steps: introducing an election algorithm to fairly select an initial leader, taking a four-particle GHZ state as a core resource, and flexibly switching to use a three-particle GHZ state and a Bell state according to the number of actual participants. In a quantum key agreement QKA stage, four initial leaders are elected through an election algorithm, and quantum key agreement is realized by adopting a four-particle GHZ state and Pauli operation; in a quantum key distribution QKD stage, a four-particle GHZ state is preferentially considered, different quantum resources are adaptively adopted according to the number of participants, and consumption of the quantum resources is reduced. Quantum key exchange QKE is realized by using QKA and QKD, and a simulation result shows that the method does not need to share a key in advance and supports Ngt; 4, the number of participants is dynamically expanded, and the number can be further expanded to a multi-particle GHZ state.

Description

Technical Field

[0001] The present invention belongs to the field of quantum cryptography, and in particular to a secure communication protocol. Background Art

[0002] With the rapid development of quantum computing, traditional cryptographic systems (such as RSA and ECC) are facing severe challenges. Quantum algorithms (such as Shor's algorithm) can crack encryption schemes based on large prime number factorization and discrete logarithm problems in multiple times, fundamentally shaking the foundation of information security. Against this backdrop, quantum cryptography combines classical cryptography with quantum mechanics, leveraging quantum mechanical principles such as the non-cloning principle of quantum states and the collapse of measured states to provide a new security paradigm.

[0003] At the same time, with the dynamic development of multi-node quantum networks, quantum protocols based on entangled states have attracted much attention due to their high efficiency and strong correlation characteristics. Quantum entanglement is a core phenomenon in quantum mechanics and a key resource in quantum information theory. Bell states and GHZ states are typical representatives of this. QKD and QKA, as core technologies in quantum cryptography, combine quantum entanglement to lay the theoretical foundation for unconditionally secure communication. CN110557250B and the present invention have the following differences:

[0004] (1) Different quantum resources: In CN110557250B, the four-particle χ state is used as the quantum resource required for key negotiation; the present invention preferentially uses the four-particle GHZ state, and then flexibly selects the three-particle GHZ state or Bell state as the quantum resource required for key negotiation based on the remaining participants, which is more flexible in quantum resource selection.

[0005] (2) The number of participants is different: In CN110557250B, each user is authenticated by the network center server in advance to achieve multi-participant key negotiation; the present invention can be In the first round, N participants conduct quantum key negotiation and finally obtain the same key. For example, in the first round, 4 people conduct quantum key negotiation and obtain the same key. In the second round, 16 people obtain the same key by combining quantum key distribution. In the third round, 64 people obtain the same key by combining quantum key distribution. And so on. Implementation 4 in round People can obtain the same key, achieving exponential growth in the number of participants, which can be flexibly applied to dynamic quantum networks.

[0006] (3) Different operation and encoding methods: In CN110557250B, each participant needs to obtain quantum resources from the network center server, perform U matrix on it, perform unitary operation on the exchange sequence with the private key, and finally perform U twice. +Operation; The present invention combines the entanglement characteristics of several quantum resources, uses Pauli I operation and Pauli X operation to realize the encoding of private keys 0 and 1, and uses election algorithm, quantum key agreement and quantum key distribution technology among N participants to realize multi-participant key agreement, and performs fewer operations on quantum resources.

[0007] (4) Whether there is classical bit exchange: In CN110557250B, the private key is encoded into the exchange sequence, and then the negotiated key is obtained through two-bit measurement, without the need to exchange classical bits. The present invention takes the keys obtained by the initial four leaders as the basis. When the leader obtains multiple keys, it is necessary to publish the positions of different keys. For example, K=1100, K1=0101, the first and fourth bits announced by the leader are different. The private key cannot be further inferred based on the positions of the first and fourth bits alone. The published classical information will not disclose any key-related content.

[0008] (5) Whether there is third-party participation: In CN110557250B, quantum resources are prepared by a third-party network center server, and participants use private keys to operate the quantum resources and obtain the key. In the present invention, quantum resources are prepared by participants, without the need for third-party preparation. The generation of quantum resources by participants is more secure. Summary of the Invention

[0009] The present invention aims to use four-particle GHZ states as the core resource, while flexibly using three-particle GHZ states or Bell states according to the actual number of participants, to ensure efficient collaboration between QKA and QKD, improve the scalability and efficiency of dynamic quantum networks, reduce quantum resource consumption, optimize quantum resources, and enable dynamic participant entry and exit. The technical solution of the present invention is as follows:

[0010] A GHZ state-based dynamic network adaptive multi-party quantum key exchange method comprises the following steps:

[0011] Step 1: Use the election algorithm to select four initial leaders, prepare a four-particle GHZ state and divide it into four quantum sequences. Some sequences are inserted into the decoy state and then exchanged;

[0012] Step 2: The four initial leaders remove the decoy state from the received sequence, further perform the Pauli operation with the private key, and randomly insert the decoy state again before exchanging;

[0013] Step 3: The four initial leaders remove the decoy state from the received sequence and perform GHZ state measurement to derive the initial shared session key.

[0014] Step 4: The four leaders first use the four-particle GHZ state to distribute quantum keys with the remaining participants. Then, based on the number of participants, they dynamically switch to the three-particle GHZ state or Bell state to continue distribution. The initial leader compares the keys and announces the differences, ultimately ensuring that all participants obtain the same key.

[0015] The advantages and beneficial effects of the present invention are as follows:

[0016] 1. This invention leverages the entangled nature of GHZ and Bell states, flexibly selecting quantum resources based on the number of participants. Furthermore, combined with QKA and QKD technologies, it proposes a dynamic network-adaptive multi-party quantum key exchange method based on GHZ states. This method uses an election algorithm to fairly and randomly select an initial leader. During the QKA and QKD phases, the four-particle GHZ state is used as the core resource, while adaptively switching between the three-particle GHZ state and Bell state based on the number of participants. This method eliminates the need for pre-shared keys and supports dynamic expansion to a number of participants N > 4. This not only reduces quantum resource consumption but also allows for expansion to multiple GHZ states.

[0017] 2. Quantum bit efficiency calculation formula c, q, and b represent the shared key, the quantum bits used, and the number of classical bits used to decode the partial key, respectively. In steps A1-A2, B1-B3, and C1-C4, the final shared key K is of length M, so c=M; P1-P4 prepares M groups of |G4> and inserts d|D> into the three transmission sequences, obtaining q1=16M+12d; P1-P4 announces the position of |D> and inserts |D> into 12 execution sequences, obtaining q2=12d and b1=12d; P1-P4 announces the position of |D> again, obtaining b2=12d. So When M is large enough, d can be ignored.

[0018] In steps D1-D3, K 2,8 The length of is M, c = M; P2 and P8 prepare M groups of Bell states and insert d|D> in the transmission sequence, q = 4M + 4d; then, they announce the insertion position of d|D>, b = 4d; therefore, the quantum bit efficiency of P2 and P8 is And K 2,8,9 The length of |G3> is M, c = M; P2, P8 and P9 prepare M groups of |G3> and insert d|D> into the transmission sequence, q = 9M + 12d; then, they announce the insertion position of d|D>, b = 6d; therefore, the quantum bit efficiency of P2, P8 and P9 is

[0019] 3. In the intercept-retransmit attack, the probability that Eve correctly obtains the position of the decoy photon is A represents the arrangement; the probability that Eve correctly chooses the measurement basis (X-basis or Z-basis) to measure each set of sequences is Eve guesses The probability of Eve successfully obtains The probability of In the interception-entanglement attack, Eve uses the auxiliary particle |e> to identify quantum resources, unitary operations Uniquely determine the four pure states {|e 00 >,|e 01 >,|e 10 >,|e 11 >}, and the normalization condition is met Calculate |a| 2 =|a′| 2 , |b| 2 =|b′| 2 Eve cannot determine the specific location of |D> and will inevitably entangle |D>. The probability that Eve's attack on |D> will be detected is |b| 2 In Eve's attack analysis on Bell states, P2(P8) measures |Φ + >2 and |ψ + >2, |a|=|a′|, the probability of eavesdropping being detected is 1-|a| 2 =1-|a′| 2 . In Eve's attack analysis on |G3> and |G4>, Eve's measurement of the auxiliary particles |e1> and |e2> (|e1>, |e2> and |e3>) cannot determine the state of the first particle of |G3> (|G4>), nor can it infer the complete encoding of the receiver's operation or GHZ state. In addition, participants use error detection and privacy amplification techniques to improve communication security. In information leakage, using classical channels to announce the insertion position and measurement basis of |D> will not leak the private key; the leader informs the participants of the different positions of the key through the classical channel, and Eve cannot infer K from these position information, so there is no information leakage problem.

[0020] 4. Overall, with one or two participants remaining, the qubit efficiencies of the Bell state and three-particle GHZ state reached 25% and 11.11%, respectively, significantly higher than the 6.25% achieved by the four-particle GHZ state. This invention flexibly selects quantum resources based on the number of participants, reducing quantum resource consumption and improving quantum network flexibility. Combining Pauli operations with single-photon states effectively resists interception-measurement-retransmission attacks, interception-entanglement-retransmission attacks, and information leakage. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1The present invention provides a preferred embodiment for performing QKA and QKD with different numbers of participants;

[0022] Figure 2 This is the overall flow chart of the present invention using the four-particle GHZ state QKA.

[0023] Explanation of the attached table

[0024] Table 1 shows the measurement results of the four-particle GHZ state |G4>;

[0025] Table 2 is the derivation of P1

[0026] Table 3 shows the correspondence between Bell states and Pauli operations;

[0027] Table 4 is the derivation of P2 DETAILED DESCRIPTION

[0028] The following will describe the technical solutions in the embodiments of the present invention in detail with reference to the accompanying drawings. The described embodiments are only a part of the embodiments of the present invention.

[0029] The technical solution of the present invention to solve the above technical problems is:

[0030] A GHZ state-based dynamic network adaptive multi-party quantum key exchange method comprises the following steps:

[0031] Step 1: Use the election algorithm to select four initial leaders, prepare a four-particle GHZ state and divide it into four quantum sequences. Some sequences are inserted into the decoy state and then exchanged;

[0032] Step 2: The four initial leaders remove the decoy state from the received sequence, further perform the Pauli operation with the private key, and randomly insert the decoy state again before exchanging;

[0033] Step 3: The four initial leaders remove the decoy state from the received sequence and perform GHZ state measurement to derive the initial shared session key.

[0034] Step 4: The four leaders first use the four-particle GHZ state to distribute quantum keys with the remaining participants. Then, based on the number of participants, they dynamically switch to the three-particle GHZ state or Bell state to continue distribution. The initial leader compares the keys and announces the differences, ultimately ensuring that all participants obtain the same key.

[0035] Furthermore, the step 1: using an election algorithm to select four initial leaders, preparing a four-particle GHZ state and dividing it into four quantum sequences, inserting some sequences into the decoy state and then exchanging them, specifically includes the following steps:

[0036] A1. Use the election algorithm to select four initial leaders P1-P4. Leader P i M groups of |G4>states were randomly prepared and divided into A i , B i , C i and D i Four sequences, where i∈{1,2,3,4}.

[0037] A2, P i In B i , C i and D i Insert d decoy states |D> into the sequence and record the insertion position and measurement base. These sequences are represented as B i ′,C i ′ and D i ′, where |D>∈{|0>,|1>,|+>,|->}. Subsequently, P1 sends B1′, C1′, and D1′ to P2(P3, P4); P2 sends B2′, C2′, and D2′ to P1(P3, P4); P3 sends B3′, C3′, and D3′ to P1(P2, P4); and P4 sends B4′, C4′, and D4′ to P1(P2, P3).

[0038] Furthermore, step 2: the four initial leaders remove the decoy state from the received sequence, further perform the Pauli operation in combination with the private key, and randomly insert the decoy state again before exchanging, specifically including the following steps:

[0039] B1, after confirming that P1-P4 received the sequence, P i Announce the insertion position and measurement basis of the decoy state. P1-P4 use the correct insertion position and measurement basis to measure |D> and send the measurement results to the corresponding sender P i .P i Calculate the error rate: If the error rate is lower than the threshold, it means the channel is secure and the protocol continues; otherwise, it means there is an eavesdropper and the protocol terminates and restarts.

[0040] B2. Assuming the error rate is lower than the threshold, P1, P2, P3 and P4 remove |D> and perform Pauli operations on {B2, B3, B4}, {B1, C3, C4}, {C1, C2, D4} and {D1, D2, D3} respectively, to obtain and Randomly insert d |D> again, record the insertion position and measure the base.

[0041] B3, P1 will Send to P2(P3, P4); P2 will Send to P1(P3, P4); P3 will Send to P1(P2, P4); P4 will Send to P1(P2, P3).

[0042] Furthermore, step 3: the four initial leaders remove the decoy state from the received particle sequence and perform GHZ state measurement to derive the initial shared session key, which specifically includes the following steps:

[0043] C1, remove |D> according to B1, P1, P2, P3 and P4 and perform Pauli operation on the received sequence according to the private key to obtain and

[0044] C2, P1-P4 randomly select Z-basis or X-basis to measure four groups of GHZ state sequences, and the measurement results are recorded as and

[0045] C3, P1-P4 derive the XOR result of the private keys of the other three parties based on the measurement results. Table 2 derives the j-th private key of P2-P4 from P1 For example, referring to Table 1, if the measurement result of the first particle is 0, the XOR result of the measurement results of the remaining three particles is 0, indicating that the number of Pauli-X operations is even (III, IXX, XIX, XXI); if the XOR result of the measurement results of the remaining three particles is 1, it indicates that the number of Pauli-X operations is odd (XII, IXI, IIX, XXX). When the measurement result of the first particle is 1, the above principle also applies.

[0046] P1 passed Derived Thus we get Similarly, P2-P4 are derived respectively and Finally, P1-P4 get the same key

[0047] Furthermore, step 4: The four leaders first use the four-particle GHZ state to complete quantum key distribution with the remaining participants, and then dynamically switch to the three-particle GHZ state or Bell state to continue distribution based on the remaining number of participants. The initial leader compares the keys and announces the difference position, so that all participants eventually obtain the same key. Specifically, the following steps are included:

[0048] D1. When (N-4) mod 3 = 0, assume N = 7. First, in the first round, P1-P4 execute the above steps to obtain the same K. Then, in the second round, P1, P5, P6 and P7 execute the above steps to obtain the same key Finally, P1 compares the K and K held 1,5,6,7, inform P5-P7 of the different positions, and P5-P7 perform bit conversion operations to obtain the same K. Finally, the 7 participants perform 2 rounds in total to obtain the same K.

[0049] D2. When (N-4) mod 3 = 1, assume N = 8. First, in the first round, P1-P4 perform the above steps to obtain K. Then, in the second round, P1, P5, P6 and P7 perform the above steps to obtain the key The steps for obtaining K in P1, P5, P6 and P7 are the same as those in D1; P2 and P8 use |Φ + > and |ψ + >Get specific:

[0050] (1) P2 and P8 from |Φ + > and |ψ + > randomly prepare M groups of Bell states, group them into {A2, B2} and {A8, B8}, P 2,j (1),P 2,j (2)∈{|Φ + >,|ψ + P2 and P8 randomly insert d |D> into B2 and B8 to obtain B2′ and B8′, while recording the insertion positions and measuring the bases, and then exchange B2′ and B8′;

[0051] (2) After confirming that the other party has received the sequence, P2 and P8 measure and remove |D> in the same way as B1. Assuming that the error rate is lower than the threshold, P2 and P8 remove |D> to obtain B8 and B2 respectively. According to K2 and K8, Pauli operations are performed on B8 and B2 to obtain and Randomly insert d |D> and then swap and

[0052] (3) After confirming that the other party has received the sequence, P2 and P8 measure and remove |D> in the same way as B1. P2 (P8) performs Bell state measurement on the held sequence to obtain measurement results MA2 and (MA8 and );

[0053] (4) P2 and P8 compare the initial Bell state with the measurement results to deduce K8 and K2. Table 3 takes P2's derivation of K8 as an example, specifically:

[0054] ① When the jth group of Bell states is |Φ + >, This means that P8 performs the Pauli I operation on the jth particle, that is,

[0055] ② When the jth group of Bell states is |Φ+ >, This means that P8 performs the Pauli X operation on the jth particle, that is,

[0056] ③ When the jth group of Bell states is |ψ + >, This means that P8 performs the Pauli I operation on the jth particle, that is,

[0057] ④ When the jth group of Bell states is |ψ + >, This means that P8 performs the Pauli X operation on the jth particle, that is,

[0058] Similarly, P8 combined with MA8, Derivation of K2, P2 and P8 calculations P2 vs. K and K 2,8 , inform P8 of the different positions. P8 is 2,8 Perform bit conversion to get the same K. Finally, 8 participants can get the same K after performing 2 rounds in total.

[0059] D3. When (N-4) mod 3 = 2, assume N = 9. First, in the first round, P1-P4 perform the above steps to obtain K. Then, in the second round, P1, P5, P6 and P7 perform the above steps to obtain the key P1, P5, P6 and P7 obtain K in the same way as D1; P2, P8 and P9 use |G3> to obtain the key specific:

[0060] (1) P2, P8, and P9 prepare M groups of |G3> and divide them into three sequences: {A2, B2, C2}, {A8, B8, C8}, and {A9, B9, C9}. P2, P8, and P9 randomly insert d |D> into {B2, C2}, {B8, C8}, and {B9, C9}, respectively, to obtain B2′, C2′, B8′, C8′, B9′, and C9′, while recording the insertion positions and measuring the base. P2 then sends B2′ and C2′ to P8 and P9, respectively. Similarly, P8 (P9) sends B8′ and C8′ (B9′ and C9′) to P2 and P9 (P2 and P8), respectively.

[0061] (2) After confirming the received sequence, P2, P8, and P9 measure and remove |D> in the same way as B1. Assuming the error rate is lower than the threshold, P2, P8, and P9 remove |D>, perform the Pauli operation on the received sequence according to K2, K8, and K9, and insert |D> again to obtain and And return the sequence to the corresponding sender.

[0062] (3) After confirming the sequence, P2, P8 and P9 measure and remove |D> in the same way as B1. Assuming the error rate is lower than the threshold, P2, P8 and P9 remove |D> and obtain and They randomly select Z-basis or X-basis to measure and get the measurement results and

[0063] (4) The measurement results of |G3> are similar to those in Table 1. If the first particle is measured as 0 and the XOR result of the other two particles is 0, it means that the number of Pauli-X operations is even, such as II or XX, and the XOR result of the private keys of the other two people can be deduced to be 0; if the XOR result is 1, it means that the number of Pauli-X operations is odd, such as IX, and the XOR result of the private keys of the other two people can be deduced to be 1. Table 4 is derived based on P2 For example, then P2, P8 and P9 are calculated

[0064] P2 vs. K and K 2,8,9 , then inform P8 and P9 of the different positions in the key. P8 and P9 2,8,9 The bit conversion operation is performed and the same key K is obtained. Finally, the 9 participants obtain the same key K.

[0065] As attached Figure 1 As shown in the figure, a dynamic network adaptive multi-party quantum key exchange method based on GHZ state includes the following four steps. In combination with Qiskit, some Python software codes are given:

[0066] 1. As attached Figure 1 As shown in step 1, the election algorithm selects four initial leaders to prepare a four-particle GHZ state and divide it into four quantum sequences. Each initial leader exchanges part of the GHZ state sequence inserted into the decoy state:

[0067] 1) Use the election algorithm to select P1-P4, P i Prepare M group|G4> state to obtain A i , B i , C i and D i ;

[0068] participants=[{'id':i}for iin range(1,N)]

[0069] leaders=elect_leaders(participants)

[0070] sequence=[]

[0071] seq_name={1:'A',2:'B',3:'C',4:'D'}[seq_type]

[0072] 2)P i In B i , C i and D i Insert d decoy states |D> into the molecule, record the insertion positions and measure the substrate.

[0073]

[0074] 2. As attached Figure 2 As shown in step 2, the four initial leaders remove the decoy state from the received sequence, further perform the Pauli operation with the private key, and randomly insert the decoy state again before exchanging:

[0075] 1) After confirming that P1-P4 receives the sequence, P i Announce the insertion position and measurement basis of the decoy state. P1-P4 use the correct insertion position and measurement basis to measure |D> and send the measurement results to the corresponding sender P i ;P i Calculate the error rate: If the error rate is lower than the threshold, the channel is secure and the protocol continues; otherwise, there is an eavesdropper, and the protocol is terminated and restarted;

[0076]

[0077] P i Calculate the error rate: If the error rate is below the threshold, the channel is secure and the protocol continues;

[0078] Otherwise, it indicates that there is an eavesdropper, and the protocol is terminated and restarted;

[0079]

[0080] 2) Assuming the error rate is below a threshold, P1, P2, P3, and P4 remove |D> and perform Pauli operations on {B2, B3, B4}, {B1, C3, C4}, {C1, C2, D4}, and {D1, D2, D3}.

[0081]

[0082] The sequence that has performed the Pauli operation and inserted the decoy state

[0083] and Send to corresponding participants;

[0084]

[0085] 3. As attached Figure 2 As shown in step 3, the four initial leaders remove the decoy state from the received sequence and perform GHZ state measurement to derive the initial shared session key:

[0086] 1) Remove |D> from B1, P1-P4 and perform Pauli operation, randomly selecting Z-basis or X-basis to measure the GHZ state;

[0087]

[0088] 2) P1-P4 derive the XOR result of the private keys of the other three parties based on the measurement results and calculate the same key K;

[0089]

[0090] 4. The four leaders first use the four-particle GHZ state to complete quantum key distribution with the remaining participants, and then dynamically switch to the three-particle GHZ state or Bell state to continue distribution based on the remaining number of participants. The initial leader compares the keys and announces the difference position, and eventually all participants obtain the same key:

[0091] Determine the remaining number of participants and decide whether to use the GHZ state |G4> or |G3> or the Bell state |Φ + > and |ψ + >:

[0092]

[0093]

[0094] 1) When (N-4) mod 3 = 0, use |G4> to obtain the same key;

[0095]

[0096] 2) When (N-4) mod 3 = 1, use |Φ + > and |ψ + >Get the same key;

[0097]

[0098]

[0099] 3) When (N-4) mod 3 = 2, use |G3> to obtain the same key;

[0100]

[0101] The present invention utilizes quantum key negotiation and quantum key distribution technologies to achieve flexible, efficient, adaptive, dynamic, key-sharing, and resource-optimized multi-party communication in dynamic networks. By combining single-photon decoy states to achieve secure detection and complete sequence transmission, it can effectively combat eavesdropping attacks and information leakage in communications. By utilizing the entanglement properties of GHZ and Bell states, flexible and efficient key sharing between communicating parties is achieved under different measurement bases, with feasible quantum bit efficiency. Compared with other quantum key exchange methods, the present invention achieves dynamic network adaptive multi-party quantum key exchange, reduces quantum resource consumption, supports dynamic expansion of the number of participants N>4, and can be expanded to multi-particle GHZ states, providing a solid foundation for large-scale quantum communication.

[0102] Table 1 Measurement results of the four-particle GHZ state |G4>

[0103]

[0104] Table 2P1 specific derivation

[0105]

[0106]

[0107] Table 3 Bell state and Pauli operation

[0108]

[0109] Table 4P2 Specific derivation

[0110]

[0111] The systems, devices, modules, or units described in the above embodiments may be implemented by computer chips or entities, or by products having certain functions. A typical implementation device is a computer. Specifically, the computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0112] It should also be noted that the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, commodity, or apparatus that includes a series of elements includes not only those elements but also other elements not explicitly listed, or includes elements inherent to such process, method, commodity, or apparatus. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, commodity, or apparatus that includes the element.

[0113] The above embodiments should be understood as merely illustrating the present invention and not as limiting the scope of protection of the present invention. After reading the contents of the present invention, technicians may make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A dynamic network adaptive multi-party quantum key exchange method based on GHZ state, characterized in that: The following steps are involved: Step 1: Use the election algorithm to select four initial leaders, prepare a four-particle GHZ state and divide it into four quantum sequences. Some sequences are inserted into the decoy state and then exchanged; Step 2: The four initial leaders remove the decoy state from the received sequence, perform the Pauli operation with the private key, and randomly insert the decoy state again before exchanging; Step 3: The four initial leaders remove the decoy state from the received sequence and perform GHZ state measurement to derive the initial shared session key. Step 4: The four leaders first use the four-particle GHZ state to complete quantum key distribution with the remaining participants, and then dynamically switch to the three-particle GHZ state or Bell state to continue distribution according to the remaining number of people. The initial leader compares the keys and announces the difference positions, and finally all participants obtain the same key.

2. A GHZ state-based dynamic network adaptive multi-party quantum key exchange method according to claim 1, characterized in that: The four-particle GHZ state and Bell state are specifically: Three-particle GHZ state Four-particle GHZ state according to Formula (1) can be obtained: In the |G4> measurement result, 0 represents the measurement result |0> or |+>, and 1 represents the measurement result |1> or |->. Here, the Z-basis is a rectangular basis with polarization in two orthogonal directions, such as |0> or |1>; the X-basis is a diagonal basis with polarization in two orthogonal directions, such as |+> or |->. Pauli I operation = |0><0|+|1><1|, Pauli X operation = |0><1|+|1><0|, Pauli I operation is performed when the private key is 0, and Pauli X operation is performed when the private key is 1. U is used to represent the two Pauli operations; for Bell states and Performing the Pauli operation yields formula (2): Φ + , ψ + They represent two Bell states respectively; I and X represent two Pauli operations respectively.

3. The method for dynamic network adaptive multi-party quantum key exchange based on GHZ state according to claim 1, characterized in that: Step 1: Use the election algorithm to select four initial leaders, prepare a four-particle GHZ state and divide it into four quantum sequences, insert some sequences into the bait state and then exchange them, specifically including the following steps: A1. Use the election algorithm to select four initial leaders P1-P4. Leader P i M groups of |G4>states were randomly prepared and divided into A i , B i , C i and D i Four sequences, where i∈{1,2,3,4}; A2, P i In B i , C i and D i Randomly insert d decoy states |D>, |D>∈{|0>,|1>,|+>,|->}, and record the insertion position and measurement basis to obtain B i ′,C i ′ and D i ’, then P1 sends B1’, C1’ and D1’ to P2 (P3, P4); P2 sends B2’, C2’ and D2’ to P1 (P3, P4); P3 sends B3’, C3’ and D3’ to P1 (P2, P4); P4 sends B4’, C4’ and D4’ to P1 (P2, P3).

4. A GHZ state-based dynamic network adaptive multi-party quantum key exchange method according to claim 3, characterized in that: Step 2: The four initial leaders remove the decoy state from the received sequence, perform a Pauli operation based on the private key, and randomly insert the decoy state again before exchanging. Specifically, the following steps are included: B1, after confirming that P1-P4 received the sequence, P i Announce the insertion position and measurement basis of the bait state. P1-P4 use the correct insertion position and measurement basis to measure |D> and send the measurement results to the corresponding sender P i ;P i Calculate the error rate: If the error rate is lower than the threshold, it means the channel is secure and the protocol continues; otherwise, it means there is an eavesdropper and the protocol terminates and restarts. B2. Assuming the error rate is lower than the threshold, P1, P2, P3 and P4 remove |D> and perform Pauli operations on {B2, B3, B4}, {B1, C3, C4}, {C1, C2, D4} and {D1, D2, D3} respectively, to obtain and Insert d |D randomly again, record the insertion position and measure the base; the superscript numbers of A, B, C, and D represent P i The Pauli operation performed, The sequence D3 representing P3 is Pauli-operated by P4; B3, P1 will Send to P2(P3, P4); P2 will Send to P1(P3, P4); P3 will Send to P1(P2, P4); P4 will Send to P1(P2, P3).

5. A GHZ state-based dynamic network adaptive multi-party quantum key exchange method according to claim 4, characterized in that: Step 3: The four initial leaders remove the decoy state from the received sequence and perform GHZ state measurement to derive the initial shared session key, which specifically includes the following steps: C1, remove |D> according to B1, P1, P2, P3 and P4 and perform Pauli operation on the received sequence according to the private key to obtain and C2, P1-P4 randomly select Z-basis or X-basis to measure four groups of GHZ state sequences, and the measurement results are recorded as and C3, P1-P4 derive the XOR result of the private keys of the other three parties based on the measurement results, and P1 derives the j-th private key of P2-P4 When the measurement result of the first particle is 0, the XOR result of the measurement results of the other three particles is 0, indicating that the number of Pauli-X operations is an even number (III, IXX, XIX, XXI); the XOR result of the measurement results of the other three particles is 1, indicating that the number of Pauli-X operations is an odd number (XII, IXI, IIX, XXX); when the measurement result of the first particle is 1, the above principle also applies; P1 passed Derived Thus we get Similarly, P2-P4 are derived respectively and Finally, P1-P4 get the same key 6. A GHZ state-based dynamic network adaptive multi-party quantum key exchange method according to claim 5, characterized in that: Step 4: The four leaders first use the four-particle GHZ state to complete quantum key distribution with the remaining participants, and then dynamically switch to the three-particle GHZ state or Bell state to continue distribution according to the remaining number of participants. The initial leader compares the keys and announces the difference position. Ultimately, all participants obtain the same key. The specific steps include the following: N participants execute a total of The same K can be obtained in each round. Indicates rounding up; D1. When (N-4) mod 3 = 0, assuming N = 7, first, in the first round, P1-P4 execute the above steps to obtain the same K. Then, in the second round, P1, P5, P6 and P7 execute the above steps to obtain the same key. Finally, P1 compares the K and K held 1,5,6,7 , inform P5-P7 of the different positions, P5-P7 perform bit conversion operations to obtain the same K; D2. When (N-4) mod 3 = 1, assume N = 8. First, in the first round, P1-P4 perform the above steps to obtain K. Then, in the second round, P1, P5, P6 and P7 perform the above steps to obtain the key The steps for obtaining K in P1, P5, P6 and P7 are the same as those in D1; P2 and P8 use |Φ + > and |ψ + >Get specific: (1) P2 and P8 from |Φ + > and |ψ + > randomly prepare M groups of Bell states, group them into {A2, B2} and {A8, B8}, P 2,j (1),P 2,j (2)∈{|Φ + >>,|ψ + >>}; P2 and P8 randomly insert d |D> into B2 and B8 to obtain B2′ and B8′, while recording the insertion positions and measuring the bases, and then exchanging B2′ and B8′. (2) After confirming that the other party has received the sequence, P2 and P8 measure and remove |D> in the same way as B1; assuming that the error rate is lower than the threshold, P2 and P8 remove |D> to obtain B8 and B2 respectively, and perform Pauli operations on B8 and B2 according to K2 and K8 to obtain and Randomly insert d |D> and then swap and (3) After confirming that the other party has received the sequence, P2 and P8 measure and remove |D> in the same way as B1; and See formula (10) for the expression of P2(P8) performs Bell state measurement on the holding sequence to obtain measurement results MA2 and ( and ), (4) P2 and P8 are derived from the initial Bell state by comparing it with the measurement results according to formula (2). Specifically, when deriving K8 from P2: ① When the jth group of Bell states is |Φ + >, This means that P8 performs the Pauli I operation on the jth particle, that is, ② When the jth group of Bell states is |Φ + >, This means that P8 performs the Pauli X operation on the jth particle, that is, ③ When the jth group of Bell states is |ψ + >, This means that P8 performs the Pauli I operation on the jth particle, that is, ④ When the jth group of Bell states is |ψ + >, This means that P8 performs the Pauli X operation on the jth particle, that is, Similarly, P8 combined with MA8, Derivation of K2, P2 and P8 calculations P2 vs. K and K 2,8 , inform P8 of different positions; P8 2,8 Perform bit conversion to get the same K; eventually, 8 participants can get the same K after performing 2 rounds in total; D3. When (N-4) mod 3 = 2, assume N = 9; First, in the first round, P1-P4 perform the above steps to obtain K. Then, in the second round, P1, P5, P6 and P7 perform the above steps to obtain the key P1, P5, P6 and P7 obtain K in the same way as D1; P2, P8 and P9 use |G3 to obtain the key specific: (1) P2, P8 and P9 prepared M group |G3> and divided it into three sequences: {A2, B2, C2}, {A8, B8, C8} and {A9, B9, C9}. P2, P8, and P9 randomly insert d |Ds into {B2, C2}, {B8, C8}, and {B9, C9}, respectively, to obtain B2′, C2′, B8′, C8′, B9′, and C9′, while recording the insertion positions and measuring the basis. P2 then sends B2′ and C2′ to P8 and P9, respectively. Similarly, P8 (P9) sends B8′ and C8′ (B9′ and C9′) to P2 and P9 (P2 and P8), respectively. (2) After confirming the received sequence, P2, P8, and P9 measure and remove |D> in the same way as B1. Assuming the error rate is lower than the threshold, P2, P8, and P9 remove |D>, perform the Pauli operation on the received sequence according to K2, K8, and K9, and insert |D> again to obtain and And return the sequence to the corresponding sender. (3) After confirming the sequence, P2, P8 and P9 measure and remove |D> in the same way as B1. Assuming the error rate is lower than the threshold, P2, P8 and P9 remove |D> and obtain and They randomly select Z-basis or X-basis to measure and get the measurement results and (4) The measurement result of |G3> is: if the first particle is measured as 0, and the XOR result of the other two particles is 0, it means that the number of Pauli-X operations is even, such as II or XX, and the XOR result of the private keys of the other two people can be deduced to be 0; if the XOR result is 1, it means that the number of Pauli-X operations is odd, such as IX, and the XOR result of the private keys of the other two people can be deduced to be 1; deduced by P2 For example, then P2, P8 and P9 are calculated P2 vs. K and K 2,8,9 , then notify P8 and P9 of the different positions in the key; P8 and P9 2,8,9 The bit conversion operation is performed and the same key K is obtained. Finally, the 9 participants obtain the same key K.

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