Multi-party information exchange method and device based on GHZ state and medium

Abstract

The invention discloses a multi-party information exchange method and device based on a GHZ state and a medium, and relates to the technical field of quantum communication. The method comprises the steps that firstly, GHZ state particles are prepared through STTP for distribution, a user applies a bit unitary operator and then returns the bit unitary operator, the STTP jointly measures and publishes a result, and the user is assisted in determining a coding mode; in the information exchange stage, the STTP prepares GHZ state particles again for distribution, the user encodes the particles according to the plaintext, secondarily applies operators after exchange and returns the operators, the STTP jointly measures and publishes a result, and the user deduces plaintexts of other parties; and finally, each party calculates and broadcasts the hash value, and if the hash value is consistent, switching success is confirmed. The method depends on GHZ state non-local entanglement, guarantees status, content and time fairness, supports multi-user integrated exchange, and resists quantum and classical attacks.

Description

Technical Field

[0001] The present invention relates to the field of quantum communication technology, and more specifically, to a multi-party information exchange method, device and medium based on GHZ states. Background Art

[0002] With the rapid development of quantum information science, the fields of information security and communications are experiencing unprecedented transformation. The fundamental principles of quantum mechanics, particularly quantum entanglement and the no-cloning theorem, have laid a solid physical foundation for a new generation of secure communications systems, driving rapid progress in cutting-edge technologies such as quantum cryptography and quantum key distribution. These breakthroughs offer new approaches to solving traditional information security challenges and create unprecedented opportunities for the innovative design of fundamental protocols such as fair exchange.

[0003] Fair exchange protocols, as fundamental security protocols in scenarios such as the digital economy, e-commerce, and financial settlement, aim to ensure the secure and fair exchange of information or digital assets between mutually distrusting parties. To achieve this goal, a variety of classic fair exchange protocol models have been proposed, including incremental release (IR-FE), online trusted third party (Online-TTP-FE), offline trusted third party (Offline-TTP-FE), and blockchain-based fair exchange (Blockchain-FE). These protocols have been continuously refined in both theory and practice, significantly advancing the field of information security. For example, the IR-FE model lowers the trust threshold through sequential shard exchange, the TTP model enhances fairness by introducing a third party, and the blockchain approach leverages smart contracts for automated penalties and transparent execution.

[0004] However, with the continuous advancement of informatization and the booming digital economy, the demand for secure and fair exchanges is growing across all sectors of society. Traditional fair exchange protocols have exposed a series of fundamental challenges in practical application. First, most existing solutions rely on ex post punishment mechanisms to deter dishonest behavior, but when the value of the exchanged information significantly exceeds the cost of the applicable punishment, the mechanism may fail. Second, classical protocols cannot completely eliminate the "first-mover disadvantage" dilemma. That is, in the process of peer-to-peer exchange, one party must always release valuable information first, making absolute fairness difficult to achieve. Furthermore, with the development of emerging technologies such as quantum computing, classical protocols based on traditional cryptographic assumptions are also at risk of being compromised, and their security urgently needs to be further improved.

[0005] In recent years, with breakthroughs in quantum communication and quantum computing, researchers have begun exploring the integration of quantum mechanical properties into fair exchange protocols, attempting to leverage the non-locality and measurement uncloning properties of quantum entanglement to construct a physical-level fairness guarantee mechanism. Although research is still in its infancy, quantum fair exchange protocols have shown the potential to fundamentally eliminate first-mover disadvantage and repudiation, potentially breaking the theoretical bottlenecks of the classical paradigm. However, this field currently faces challenges such as imperfect theoretical models, a scarcity of practical protocols, and significant technical implementation challenges, necessitating further in-depth research and innovative exploration. Summary of the Invention

[0006] In order to solve the above technical problems, the present invention provides a multi-party information exchange method, device and medium based on GHZ state.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions:

[0008] In a first aspect, the present invention provides a multi-party information exchange method based on GHZ state, the method comprising:

[0009] A semi-trusted third party prepares multiple pairs of GHZ state particles and distributes each GHZ state particle to multiple user terminals according to their location. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results.

[0010] The semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. Each user terminal encodes the received GHZ state particles according to the corresponding plaintext information using the determined encoding method, exchanges the encoded particles in sequence, and applies the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the results to the user terminals of each party. The user terminals calculate and obtain the plaintext of the other party based on the results.

[0011] Each user terminal calculates a hash value based on its own plaintext and the plaintext of the other party obtained, and broadcasts the hash value to other user terminals. If the hash values ​​calculated by all user terminals are equal, it is confirmed that the current round of information exchange is successful.

[0012] Furthermore, the GHZ state particles are in the multi-particle maximal entangled state, which is expressed as:

[0013]

[0014] Where n is the number of entangled particles, |GHZ> n represents the GHZ entangled state composed of n particles, |0> and |1> represent the basic quantum state of a single quantum bit, represents the tensor product symbol;

[0015] The GHZ state particles include four expressions of three-particle GHZ states:

[0016]

[0017] Where, and They represent four different three-qubit entangled states.

[0018] Furthermore, there are three user terminals, namely user terminal Alice, user terminal Bob and user terminal Charlie.

[0019] Furthermore, a semi-trusted third party prepares multiple pairs of GHZ state particles, and distributes each GHZ state particle to multiple user terminals according to position. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results, including:

[0020] A semi-trusted third party prepares 40 pairs of entangled states The GHZ state particles are extracted bit by bit from the first, second and third positions to form quantum sequences S1, S2 and S3 respectively, and sent to user end Alice, user end Bob and user end Charlie respectively through the quantum channel.

[0021] Alice, Bob, and Charlie randomly select bit unitary operators Act on each quantum in quantum sequences S1, S2 and S3 respectively, and return the quantum sequences after the action to the semi-trusted third party;

[0022] The semi-trusted third party extracts the particles at the same position in the quantum sequence after the action and performs joint measurement, and then publishes the measurement results, which are determined by the entangled state. Combined in order;

[0023] Each user terminal will The position of the corresponding bit unitary operator is determined by In the emergence When there are more than three positions, determine the 3-bit classical information, and determine the encoding method of the current round exchange based on the classical information; if there is If the number of positions is less than three, repeat the above steps until it appears.

[0024] Furthermore, the encoding method is a determined mapping relationship f, which is expressed as:

[0025] f:f(K,M)=C

[0026] Where f(K, M) represents the operation process and result of taking the elements in the key set K and the elements in the plaintext set M as input and outputting the ciphertext after the mapping f operation, C represents the ciphertext set, They represent different three-qubit GHZ entangled states respectively, M represents the plaintext set, M = {m1, m2,…, m8}, m1, m2 and m8 represent the first, second to eighth plaintext respectively, K represents the key set, K = {k1, k2,…, k8}, k1, k2 and k8 represent the first, second to eighth keys respectively.

[0027] In the encoding method, when the key is unknown, the probability that any plaintext is mapped to any ciphertext is equal, and the probability that any ciphertext corresponds to any plaintext is equal.

[0028] Furthermore, the semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. The user terminals of each party encode the received GHZ state particles according to the corresponding plaintext information in a determined encoding method, exchange the encoded particles in sequence, and apply the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party jointly measures and publishes the results to the user terminals of each party. The user terminals calculate and obtain the plaintext of the other party based on the results, including:

[0029] A semi-trusted third party prepares 40 pairs of entangled states The GHZ state particles are extracted bit by bit from the first, second and third positions to form quantum sequences S1, S2 and S3 respectively, and sent to user end Alice, user end Bob and user end Charlie through the quantum channel respectively;

[0030] User-side Alice applies Ua to quantum sequence S1 to obtain quantum sequence S1'; user-side Bob applies Ub to quantum sequence S2 to obtain quantum sequence S2'; user-side Charlie applies Uc to quantum sequence S3 to obtain quantum sequence S3'. Ua, Ub, and Uc are the quantum operator sequences of length n1 constructed by user-side Alice, user-side Bob, and user-side Charlie according to their respective n1-bit plaintexts Pa, Pb, and Pc, according to the set correspondence relationship.

[0031] User end Alice sends quantum sequence S1' to user end Bob; user end Bob sends quantum sequence S2' to Charlie; user end Charlie sends quantum sequence S3' to Alice.

[0032] User end Alice applies Ua to quantum sequence S3' to obtain quantum sequence S3"; user end Bob applies Ub to quantum sequence S1' to obtain quantum sequence S1"; user end Charlie applies Uc to quantum sequence S2' to obtain quantum sequence S2". Each user end sends the corresponding quantum sequence to a semi-trusted third party.

[0033] The semi-trusted third party extracts particles at the same position from the quantum sequences S1", S2" and S3" for joint measurement, and announces the measurement results Cabc to all parties' user terminals in sequence through broadcasting.

[0034] Each user terminal calculates the plaintext of the other party based on its own quantum operator sequence and the published measurement result Cabc; among them, the user terminal Alice calculates Pb' and Pc'; the user terminal Bob calculates Pa' and Pc"; the user terminal Charlie calculates Pa" and Pb"; Pa' and Pc' are the plaintexts of user terminals Bob and Charlie calculated by user terminal Alice, Pa' and Pc" are the plaintexts of user terminals Alice and Charlie calculated by user terminal Bob, and Pa" and Pb" are the plaintexts of user terminals Alice and Bob calculated by user terminal Charlie.

[0035] Furthermore, each user terminal calculates a hash value based on its own plaintext and the other party's plaintext obtained by calculation, and broadcasts the hash value to other user terminals. If the hash values ​​calculated by all user terminals are equal, it is confirmed that the current round of information exchange is successful, including:

[0036] Each user terminal calculates the hash value using the following formula:

[0037] Ca=HASH(Pa||Pb'||Pc'||sid)

[0038] Cb=HASH(Pa'||Pb||Pc"||sid)

[0039] Cc=HASH(Pa"||Pb"||Pc||sid)

[0040] Where Ca, Cb, and Cc are the hash values ​​calculated by user Alice, user Bob, and user Charlie respectively, HASH is a cryptographic hash function, sid is the current fair exchange round number, and || is data splicing;

[0041] When Ca=Cb=Cc, it is confirmed that the current round of information exchange is successful.

[0042] Furthermore, the method further comprises:

[0043] Every time a quantum sequence is transmitted in a quantum channel, both the sender and the receiver will use decoy particles to perform an eavesdropping detection.

[0044] In a second aspect, the present invention provides a multi-party information exchange device based on GHZ state, the device comprising:

[0045] A semi-trusted third party prepares multiple pairs of GHZ state particles and distributes each GHZ state particle to multiple user terminals according to their location. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results.

[0046] The semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. Each user terminal encodes the received GHZ state particles according to the corresponding plaintext information using the determined encoding method, exchanges the encoded particles in sequence, and applies the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the results to the user terminals of each party. The user terminals calculate and obtain the plaintext of the other party based on the results.

[0047] Each user terminal calculates a hash value based on its own plaintext and the plaintext of the other party obtained, and broadcasts the hash value to other user terminals. If the hash values ​​of all user terminals are equal, it is confirmed that the current round of information exchange is successful.

[0048] In a third aspect, the present invention provides a readable storage medium, wherein the readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method as described above.

[0049] The present invention has at least the following beneficial effects:

[0050] 1. Theoretical Breakthrough and Cryptographic Modeling of GHZ States: This paper systematically explains for the first time how the indivisibility and global correlation of GHZ states naturally enable fair multi-party exchange. It also uses cryptographic language to compare and model the physical properties of GHZ states with classical fair exchange protocols. The cooperative collapse mechanism of GHZ states is essentially equivalent to the "atomicity" and "synchronicity" of classical fair exchange, providing a theoretical foundation for achieving complete fairness at the physical level.

[0051] 2. Multi-dimensional fairness guarantee: This invention achieves all-round fairness among participants in terms of status, content, and time, ensuring that all users are completely equal in identity, information content, and exchange time, effectively overcoming the first-mover disadvantage and identity asymmetry problems in classic protocols.

[0052] 3. Efficient multi-user integrated exchange and identity discrimination: The present invention supports integrated information exchange among multiple users in a single round of operation (e.g., user a can obtain information about users b and c at one time, user b obtains information about users a and c, and user c obtains information about users a and b). Furthermore, information ownership can be naturally discriminated through quantum coding, eliminating the need to embed identifiers in the information, thereby improving efficiency and traceability.

[0053] 4. Dedicated Coding and Mathematical Modeling: This paper proposes a specialized quantum coding method by deducing the characteristics of the three-particle GHZ state, transforming the multi-party fair exchange problem into a discrimination problem, laying a solid theoretical foundation for the feasibility and verifiability of the protocol.

[0054] 5. Engineering feasibility and experimental verification: This invention has good engineering feasibility and can be directly verified on mainstream quantum platforms such as IBM, promoting the practical implementation of quantum security protocols.

[0055] 6. Balancing Classical and Quantum Security: This paper not only systematically analyzes the classical security of the protocol, but also comprehensively explores security protection under quantum attacks, including various threats such as quantum eavesdropping, interference, and internal collusion, to ensure the integrity and robustness of the protocol in a quantum environment.

[0056] In summary, the present invention has achieved a major breakthrough in traditional multi-party fair exchange schemes in terms of theoretical modeling, method design, and engineering implementation, providing a new idea and technical foundation for quantum secure communication and information security protection in the digital economy era. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 An application scenario diagram according to the prior art is shown;

[0058] Figure 2 A flowchart of a multi-party information exchange method based on GHZ state according to an embodiment of the present invention is shown;

[0059] Figure 3 FIG2 shows a data structure diagram obtained by selecting different measurement bases for particles at three positions in a three-particle GHZ state according to an embodiment of the present invention;

[0060] Figure 4 The embodiment of the present invention is shown. Figure 3 The data structure diagram obtained by performing the interactive particle sequence;

[0061] Figure 5 shows a structural diagram of data 1 according to an embodiment of the present invention;

[0062] Figure 6 It shows a structural diagram of data 2 according to an embodiment of the present invention;

[0063] Figure 7shows a structural diagram of data 3 according to an embodiment of the present invention;

[0064] Figure 8 shows a structural diagram of data 4 according to an embodiment of the present invention;

[0065] Figure 9 shows a structural diagram of data 5 according to an embodiment of the present invention;

[0066] Figure 10 shows a structural diagram of data 6 according to an embodiment of the present invention;

[0067] Figure 11 shows a structural diagram of data 7 according to an embodiment of the present invention;

[0068] Figure 12 shows a structural diagram of data 8 according to an embodiment of the present invention;

[0069] Figure 13 shows a structural diagram of a quantum circuit according to an embodiment of the present invention;

[0070] Figure 14 shows a diagram of theoretical measurement results according to an embodiment of the present invention;

[0071] Figure 15 shows a diagram of actual measurement results according to an embodiment of the present invention;

[0072] Figure 16 The figure shows a structural diagram of a multi-party information exchange device based on GHZ state according to an embodiment of the present invention. DETAILED DESCRIPTION

[0073] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments of the present invention are further described in detail below with reference to the accompanying drawings and specific embodiments, but are not intended to limit the present invention. For the various steps described herein, if there is no necessity for a contextual relationship between each other, the order in which they are described as examples herein should not be regarded as limiting, and those skilled in the art should know that they can be adjusted in order as long as the logic between them is not destroyed, resulting in the inability to implement the entire process.

[0074] The embodiments of the present invention first introduce the technologies that may be relied upon when implementing the present invention.

[0075] 1. Quantum Key Distribution (QKD) – focuses on eavesdropping detection.

[0076] QKD is the earliest practical technology in quantum communications. Its core goal is to securely distribute cryptographic keys. Its security is based on the quantum no-cloning theorem of quantum mechanics, which effectively detects eavesdropping. If eavesdropping is detected, both communicating parties can terminate the session immediately, ensuring the absolute security of the key.

[0077] 2. Quantum teleportation (QT) – the role of the unitary matrix.

[0078] Quantum teleportation allows a quantum state to be transferred from a sender to a receiver without directly transmitting the qubits. This process relies on the pre-shared existence of entangled pairs and the precise recovery of the quantum state through unitary matrix operations. QT technology provides the foundation for the efficient and secure transfer of quantum information over long distances in quantum networks.

[0079] 3. Quantum Secure Direct Communication (QSDC) – information transfer.

[0080] QSDC goes beyond key distribution to enable direct and secure information transmission. By directly sending confidential messages over quantum channels and combining quantum entanglement, single-photon technology, and other technologies, it effectively prevents eavesdropping and tampering, achieving end-to-end information security. QSDC is suitable for multi-party scenarios with extremely high communication security requirements.

[0081] 4. Quantum Fair Exchange (QFE) - Information Fairness.

[0082] QFE focuses on fairness in multi-party information exchange, ensuring that all parties receive information or none at all during protocol execution, preventing unilateral profit or information asymmetry. QFE typically combines quantum entanglement with authentication mechanisms to enhance security and fairness in multi-party collaboration, and is a key development direction for quantum-safe protocols.

[0083] Example 1: Multi-party information exchange method based on GHZ state

[0084] Figure 1 An application scenario diagram according to the prior art is shown, such as Figure 1 As shown, the application scenario includes a semi-trusted third-party STTP and multiple user terminals, wherein the multiple user terminals and the user terminals of each party are signal-connected to each other and to the semi-trusted third-party STTP. In this embodiment, there are three examples of multiple user terminals, namely user terminal Alice, user terminal Bob, and user terminal Charlie.

[0085] based on Figure 1 The application scenario shown, Figure 2 The flowchart of a multi-party information exchange method based on GHZ state according to an embodiment of the present invention is shown. The embodiment of the present invention provides a multi-party information exchange method based on GHZ state, such as Figure 2As shown, the method includes the following steps S100-S300.

[0086] S100: A semi-trusted third party prepares multiple pairs of GHZ state particles, and distributes each GHZ state particle to multiple user terminals according to location. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results.

[0087] In this embodiment, the GHZ state, i.e., the Greenberger-Horne-Zeilinger state, is a multi-particle maximally entangled state, and its form is:

[0088]

[0089] Among them, |GHZ> n represents the GHZ entangled state composed of n particles, |0> and |1> represent the basic quantum state of a single quantum bit, represents the tensor product symbol, and n represents the number of entangled particles. Its most common form is the three-particle GHZ state, and this example uses four of these expressions:

[0090]

[0091]

[0092] Where, and They represent four different three-qubit entangled states.

[0093] GHZ states have the following properties: maximum entanglement, meaning that all particles are nonlocally correlated, and the state of any particle is closely related to all others. They also possess symmetry, meaning that permutations of particles do not alter the GHZ state, making them suitable for multi-user symmetric communication. Furthermore, they exhibit measurement sensitivity, meaning that any measurement of any particle affects the state of the entire system.

[0094] Single-qubit unitary operator for user-encoded classical information Defined as:

[0095] in, is the unit operator, is the Pauli-X operator: And it satisfies two properties:

[0096]

[0097] The data obtained by selecting different measurement bases for the three particles at the three positions of the three-particle GHZ state are as follows: Figure 3 As shown, then the particle sequence is exchanged and the data obtained is as follows Figure 4 shown.

[0098] In some embodiments, the construction principle of the encoding method is as follows:

[0099] The user terminals Alice, Bob, and Charlie construct quantum operator sequences Ua, Ub, and Uc of length n1 according to their respective n1-bit plaintexts Pa, Pb, and Pc, according to the corresponding relationship shown in Table 1.

[0100] Table 1 Correspondence between plaintext and quantum operator sequence

[0101]

[0102] The structures of data 0 to data 7 in Table 1 are as follows: Figures 5 to 12 shown.

[0103] Suppose the plaintext set is M = {m1,m2,…,m8}, where m1, m2, and m8 represent the first, second, and eighth plaintext respectively, and the ciphertext set is C = {|φ0>,|φ1>,|φ2>,|φ3>}, Each represents a different three-qubit GHZ entangled state. The key (encoding scheme) set is K = {k1, k2, …, k8}, where k1, k2, and k8 represent the first, second, and eighth keys, respectively. Each encoding scheme defines a mapping f: f(K, M) = C. Here, f(K, M) represents the process and result of taking the elements of the key set K and the elements of the plaintext set M as input and outputting the ciphertext after the mapping f is calculated.

[0104] This encoding method has three characteristics, namely characteristic 1, characteristic 2 and characteristic 3.

[0105] Characteristic 1: Uniformity and symmetry.

[0106] It ensures that all plaintext distribution and ciphertext distribution are uniformly distributed, reflecting good uniformity and symmetry.

[0107] For any plaintext m, any ciphertext c: Where p(C=c|M=m) represents the probability that the ciphertext is c under the condition that the plaintext is m.

[0108] For any ciphertext c: Where P(C=c) represents the probability that the ciphertext is c when other conditions such as the plaintext are not considered.

[0109] Property 2: Equal probability mapping of plaintext to ciphertext.

[0110] In the case of an unknown key, the probability that any plaintext is mapped to any ciphertext is equal. Similarly, the probability that any ciphertext corresponds to any plaintext is also equal.

[0111] For any plaintext m and any ciphertext c:

[0112]

[0113] Here, p(M=m|C=c) represents the probability that the plaintext is m under the condition that the ciphertext is c.

[0114] Feature 3: Unique decryption.

[0115] Assume there are three clients, Alice, Bob, and Charlie, each of whom possesses a secret message, namely plaintext ma, mb, and mc, and a key k. After encryption, a unique ciphertext c is generated.

[0116] 1. Generate ciphertext c = Ek(ma,mb,mc), where Ek represents the encryption function.

[0117] 2. Decryption process: For any party, such as user Alice, knowing the key k, user Alice's plaintext ma and ciphertext c, the plaintexts of the other two parties can be calculated: (mb,mc) = D(k,c,ma); (ma,mc) = D(k,c,mb); (ma,mb) = D(k,c,mc), where D(k,c,ma), D(k,c,mb) and D(k,c,mc) represent the decryption functions of the three users respectively, and ma, mb and mc represent the plaintexts of user Alice, Bob and Charlie respectively.

[0118] In some embodiments, each time a quantum sequence is transmitted in a quantum channel, both the sender and the receiver perform an eavesdropping detection using decoy states to prevent potential external eavesdropping.

[0119] The purpose of step S100 is to determine the encoding method. In some embodiments, step S100 can determine the encoding method through the following steps S101-S104.

[0120] S101: STTP prepared 40 pairs of The GHZ state particles are extracted bit by bit from the particles at the 1st / 2nd / 3rd positions to form quantum sequences S1, S2 and S3, and are sent to the user terminals Alice, Bob and Charlie respectively through the quantum channel.

[0121] S102: User Alice, Bob, and Charlie randomly select Act on each quantum in quantum sequences S1, S2 and S3 respectively, and then return it to STTP.

[0122] S103: STTP extracts particles at the same position in the quantum sequence for joint measurement and then publishes the measurement results. Assembled in sequence.

[0123] S104: The user responds to the measurement result. Determine the position of your hand Then the 3-bit classic information is determined, and based on this information, the encoding method of this exchange is determined. Then repeat steps S101-S104 until it appears.

[0124] S200: The semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. The user terminals of each party encode the received GHZ state particles according to the corresponding plaintext information in a determined encoding method, exchange the encoded particles in sequence, and apply the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the results to the user terminals of each party. The user terminals calculate and obtain the plaintext of the other party based on the results.

[0125] Step S200 implements fair exchange of user information. In some embodiments, step S200 can implement fair exchange of user information through the following steps S201-S206:

[0126] Step 1: STTP prepares multiple pairs of The GHZ state particles are extracted bit by bit from the particles at the 1st / 2nd / 3rd positions to form quantum sequences S1, S2 and S3, which are then sent to the user terminals Alice, Bob and Charlie respectively through the quantum channel.

[0127] Step 2: User terminals Alice, Bob, and Charlie encode their own plaintext information respectively. User terminal Alice applies Ua to quantum sequence S1 to obtain quantum sequence S1'; Bob applies Ub to quantum sequence S2 to obtain quantum sequence S2'; Charlie applies Uc to quantum sequence S3 to obtain quantum sequence S3'.

[0128] Step 3: User end Alice sends quantum sequence S1' to user end Bob; user end Bob sends quantum sequence S2' to user end Charlie; user end Charlie sends quantum sequence S3' to user end Alice.

[0129] Step 4: User-side Alice applies Ua to quantum sequence S3' to obtain quantum sequence S3", user-side Bob applies Ub to quantum sequence S1' to obtain quantum sequence S1", and user-side Charlie applies Uc to quantum sequence S2' to obtain quantum sequence S2". These are sent to the STTP respectively. Ua, Ub, and Uc are the quantum operator sequences of length n1 constructed by user-side Alice, user-side Bob, and user-side Charlie according to their respective n1-bit plaintexts Pa, Pb, and Pc, according to the set correspondence.

[0130] Step 5: STTP extracts particles at the same position from the quantum sequences S1", S2", and S3", performs joint measurement, and publishes the measurement results Cabc in sequence through broadcasting.

[0131] Step 6: Users Alice, Bob, and Charlie calculate the other parties' plaintexts based on their respective Ui and the published Cabc. Alice calculates Pb' and Pc'; Bob calculates Pa' and Pc", and Charlie calculates Pa" and Pb". Pa' and Pc' are the plaintexts for Bob and Charlie calculated by Alice, Pa' and Pc" are the plaintexts for Alice and Charlie calculated by Bob, and Pa" and Pb" are the plaintexts for Alice and Bob calculated by Charlie.

[0132] S300: Each user terminal calculates a hash value based on its own plaintext and the plaintext of the other party obtained by calculation, and broadcasts the hash value to other user terminals. If the hash values ​​calculated by all user terminals are equal, it is confirmed that the current round of information exchange is successful.

[0133] The purpose of step S300 is to implement consistency verification. In some embodiments, the method of implementing consistency verification in step S300 includes:

[0134] Each user terminal calculates the hash value using the following formula:

[0135] Ca=HASH(Pa||Pb'||Pc'||sid)

[0136] Cb=HASH(Pa'||Pb||Pc"||sid)

[0137] Cc=HASH(Pa"||Pb"||Pc||sid)

[0138] Where Ca, Cb, and Cc are the hash values ​​calculated by user Alice, user Bob, and user Charlie respectively, HASH is a cryptographic hash function, sid is the current fair exchange round number, and || is data splicing;

[0139] When Ca=Cb=Cc, it is confirmed that the current round of information exchange is successful.

[0140] The feasibility and advancement of the multi-party information exchange method based on the GHZ state will be analyzed from various perspectives through the following multiple embodiments.

[0141] Example 2: Encoding Analysis

[0142] This embodiment analyzes the encoding method through probability analysis and effectiveness analysis.

[0143] Probability analysis. Suppose there are 3 users, each of whom randomly selects an operation Encode the particles. According to the probability theory analysis, this process obeys the binomial distribution. The probability is p,

[0144]

[0145] If in n2 joint measurements, at least 3 The probability of is P(n2), then:

[0146]

[0147] in, Represents the number of combinations. When n=40, P(n2)>99.95%.

[0148] Validity analysis. When users randomly select When three users select the same When the joint measurement result is When observed When the position of the item in the sequence is determined, the user can know the corresponding item in his hand. 's specific location, thereby further inferring the And then obtain the secret information they hold.

[0149] When 3 When , three users can share 3 bits of classical information. Based on this classical information, users can choose the encoding method for this round and prepare for the subsequent fair exchange operation.

[0150] Example 3: Effectiveness Analysis

[0151] Known initial GHZ state:

[0152]

[0153] Apply the operator to each particle separately Get the intermediate state

[0154]

[0155] Once again, the operators are applied to each particle, but this time the order of the operators is changed. Acting on particle 2 Acting on particle 3 Get the final state

[0156]

[0157] Total Operator It can be expressed as the product of the second and first step operators

[0158]

[0159] Since the operators acting on different particles are reciprocal, the operators in the tensor product can be rearranged.

[0160]

[0161] Therefore, the proof of its validity is transformed into a discrimination problem, that is, in the Hilbert space, the initial state is known. Final state and any operator Is it possible to uniquely determine the other two operators The solution is expressed as:

[0162]

[0163] Suppose there are two different combinations of operators that both satisfy

[0164] or

[0165] Since the joint measurement does not consider the global phase, this equality holds.

[0166]

[0167] Consider the following:

[0168]

[0169] Known is reciprocal, so

[0170]

[0171] and

[0172]

[0173] but

[0174]

[0175] It contradicts the assumption, so the assumption is not true and the solution must be unique.

[0176] Example 4: Fairness Analysis

[0177] This embodiment analyzes the fairness of the method proposed in the present invention from the perspectives of status fairness, content fairness, and time fairness.

[0178] Status Fairness Analysis. In the proposed method, all users participate with equal roles and responsibilities at every stage of the protocol—including determining the encoding method, exchanging information, and checking consistency. Throughout the entire process, no participant has priority or special status. This demonstrates that the protocol mechanically guarantees status fairness, ensuring that every user enjoys equal rights and influence throughout the protocol's execution.

[0179] Content fairness requires that, assuming all participants are honest and persist in completing the exchange, each party will be able to successfully obtain the other party's secret information at the end of the protocol. Conversely, if any participant fails to obtain useful information, no party can obtain the other party's secret information, thus ensuring the fairness of the exchange content.

[0180] When the protocol completes successfully—that is, when all participants execute the protocol honestly—the multi-particle GHZ state, as the maximally entangled state, ensures that any measurement of any single particle instantly affects the states of the remaining particles. According to the protocol design (property 2), no user can access the exchanged information of other users before the joint measurement results are published. However, after the joint measurement results are broadcast (property 3), combined with the aforementioned validity analysis, all users can infer the secret information of other participants, thus achieving fair information exchange. This fairness is guaranteed by the physical properties of quantum entanglement itself, rather than relying on punitive mechanisms.

[0181] If the protocol fails to complete, all participants will not be able to obtain useful information. In the present invention, the secret information of the participants is embedded in the three-particle entangled state, and no single particle can extract all the secret information (property 2). During the execution of the protocol, the entangled particles carrying the secret information need to be passed to a semi-trusted third party (STTP), but in the actual transmission process, the protocol may be terminated due to reasons such as link interruption or channel occupancy. In addition, based on the quantum properties of entangled particles in the GHZ state, the plaintext information cannot be extracted individually, effectively ensuring the content fairness requirements of quantum fair exchange.

[0182] Analysis of temporal fairness. Unlike traditional fair exchange protocols that rely on mechanisms such as sequential operations to achieve temporal fairness, the quantum fair exchange protocol of the present invention relies on the characteristics of quantum entanglement and broadcast mechanisms to achieve it. The GHZ state ensures that the information of all participants is highly non-local when measured, that is, the measurement of any particle will immediately affect the state of other particles. The key is that due to the design of the encoding method (characteristic 3), no participant can unilaterally decode useful information, and must rely on a semi-trusted third party (STTP) to perform synchronous measurements and inform all users of the measurement results at the same time through broadcasting. In this way, before the joint measurement results are announced, no user can obtain the information of others, and the measurement results are transmitted synchronously by broadcasting to ensure that all participants obtain the information at the same time. This mechanism effectively circumvents the timing unfairness problem caused by different sending orders in the IR-FE model, and eliminates the situation where any party is at a disadvantage due to being the first to start.

[0183] In summary, the multi-party information exchange method based on GHZ state can effectively achieve time fairness, ensuring that all participants obtain information at the same time, and eliminating the unfairness existing in traditional information exchange.

[0184] Example 5: Safety Analysis

[0185] This embodiment analyzes the security of the method proposed in the present invention from the perspectives of leakage, eavesdropping detection, interception measurement attack, man-in-the-middle attack, entanglement attack central node analysis and false signal attack.

[0186] The leakage is analyzed from two perspectives: encoding information leakage and plaintext information leakage.

[0187] Encoding information leakage

[0188] In this invention, the key is collected one bit at a time from each of the three participants, ultimately obtaining a random bit sequence of length 3. Since the collection process of each bit is completely independent and repetitive, we only need to analyze the collection process of a single bit, and the conclusions can be directly extended to the case of 3 bits.

[0189] Suppose three participants choose bits x1, x2, and x3, respectively, where each xi∈{0,1}, i=1,2,3, and the choices are all independent and identically distributed (IID) Bernoulli distributed (with probability 0.5). Only when the three participants agree on the same choice ((0,0,0) or (1,1,1)) is the bit collected in that round recorded as valid; otherwise, it is discarded. We are interested in the information that an external observer obtains about the valid bit.

[0190] Before the collection, there are only two possibilities for the three people to choose unanimously, and the probability is equal P(X=(0,0,0))=P(X=(1,1,1))=0.5. Therefore, the prior entropy H(x) of the three people's unanimous choice is:

[0191]

[0192] Where P(Xi) is the probability that the discrete random variable X takes the value Xi, which is the value of the probability mass function (Probability Mass Function, for discrete random variables).

[0193] An external observer can only determine that the three people's choices in this round are consistent, but cannot distinguish whether they are all 0 or all 1, that is:

[0194] I(x;C)=0

[0195] Where I(x; C) is the mutual information between random variables x and random variables C.

[0196] In summary, the present invention does not leak information to external observers in the sense of information theory.

[0197] Plaintext information is leaked. Since the encoding method is completely confidential to the eavesdropper, each ciphertext may correspond to all 8 plaintext bit combinations from the eavesdropper's perspective. At this time, the posterior distribution of the plaintext is uniform, and the conditional entropy p(plaintext|ciphertext) = 3H(plaintext|ciphertext) = 3 (bits), achieving the maximum information entropy and fully ensuring the security of the protocol. According to the design of the scheme, non-participants, including STTP, can only obtain the joint measurement result sequence. According to information theory analysis, the conditional probability in each case can be known.

[0198] Let the plaintext bit combination be M and the ciphertext be C. For the eavesdropper, given the ciphertext C, the posterior distribution of the plaintext M is uniform:

[0199]

[0200] So the conditional entropy H(M|C) of the ciphertext is:

[0201]

[0202] Where, P(M i |C) is the conditional probability, which means that under the condition that the ciphertext is C, the plaintext is M i The probability of M i is the i-th plaintext element in the plaintext set.

[0203] Information entropy of plaintext:

[0204]

[0205] I(M;C)=H(A)-H(A|E)=0

[0206] Where H(M) is the information entropy of the plaintext, P(M i ) is the plaintext M i The prior probability of occurrence, I(M;C) is the mutual information between plaintext M and ciphertext C, H(A) is the information entropy of variable A, and H(A|E) is the conditional entropy, where E is the conditional variable.

[0207] Therefore, the technical solution adopted by the present invention will not cause information leakage.

[0208] Eavesdropping Detection:

[0209] Throughout the operation of the proposed method, whenever a quantum sequence is transmitted through a quantum channel, decoy particles prepared from Z and X bases are randomly inserted. These particles are distributed at random positions in the quantum sequence. Because an eavesdropper cannot predict the specific location and preparation basis of the decoy particles, once eavesdropping on the quantum sequence, their operation will inevitably introduce abnormal disturbances. When the user and the trusted third party (STTP) conduct collaborative detection, they will find that the bit error rate of the decoy particles is significantly higher than that in the absence of eavesdropping, effectively identifying the eavesdropping behavior and immediately terminating the protocol. As a result, the eavesdropper (Eve) cannot obtain any useful information, and the security of the protocol is guaranteed.

[0210] Intercept measurement attack:

[0211] Even if the eavesdropper (Eve) is still determined to steal the user's secret information after being detected, she may attempt to directly intercept and measure one or more quantum sequences containing the secret information. However, the superposition properties of particles in the GHZ state determine that even using single-particle measurements, Eve cannot obtain meaningful information. If Eve attempts to perform a joint measurement on multiple particles, because she does not have the key and the protocol design ensures that the joint measurement results are symmetric (see Property 1), Eve still cannot infer valid secret information from the measurement results. Therefore, the present invention can effectively resist interception measurement attacks and prevent information leakage.

[0212] Man-in-the-middle attacks:

[0213] To counter man-in-the-middle attacks, Eve might attempt to replace the original quantum sequence with entangled particles she has prepared to steal information from both communicating parties. However, because the present invention inserts decoy particles at random locations in the quantum sequence, and Eve cannot know the specific locations of these particles or their preparation basis, she can only randomly select a basis for measurement. According to the quantum no-cloning theorem, when Eve selects the wrong basis to measure the decoy particles, their state collapses, leading to an increase in the bit error rate of the decoy particles. Once this bit error rate exceeds a set threshold, the STTP and the user detect the anomaly and terminate communication promptly. This shows that the present invention can effectively prevent man-in-the-middle attacks and ensure communication security.

[0214] Entanglement attack:

[0215] Assume that Eve introduces an auxiliary particle |e> on each particle and performs a joint unitary operation on each pair of particles (denoted as ), making the entire system a larger Hilbert space, The matrix representation of is:

[0216]

[0217] in a, b, a', b' are complex coefficients that satisfy the normalization condition:

[0218] |a| 2 +|b| 2 =1

[0219] |a'| 2 +|b'| 2 =1

[0220] ab * =(a') * b'

[0221] where b * is the conjugate of the complex number b, (a') * is the conjugate of the complex coefficient a'.

[0222] Then Eve's operation on the decoy particle can be written as:

[0223]

[0224] where |e 00 >,|e 01 >,|e 10 >,|e 11 > is the orthogonal state of Eve’s auxiliary particles. In order to ensure the probability conservation of the entire system, the orthogonal states of these auxiliary particles must satisfy the normalization condition:

[0225]

[0226] Among them, e α,β is the quantum state of Eve auxiliary particle, α and β are index parameters for labeling the quantum state.

[0227] According to the derivation, we can get:

[0228] |a| 2 =|a'| 2 ,|b| 2 =|b'| 2

[0229] During the eavesdropping detection process, Eve’s interference will inevitably introduce errors, so the probability of Eve being detected is:

[0230] P=|b| 2 =1-|a| 2 =|b'| 2 =1-|a'| 2

[0231] When no errors are introduced, the signal particle and Eve's auxiliary particle can only be in a direct product state. A direct product state means there is no correlation between the signal particle and the auxiliary particle, so Eve cannot obtain any useful information.

[0232] Central node analysis:

[0233] In this paper, the semi-trusted third party (STTP) is primarily responsible for the preparation of the initial entangled particles, channel eavesdropping detection, joint measurement, and result publication. Although the STTP undertakes these key steps, it never directly accesses the key or plaintext information throughout the entire process, whether during the key distribution phase or the subsequent information transmission phase.

[0234] Therefore, the STTP is effectively equivalent to an external eavesdropper. If it does not possess the key k or the plaintext content, even if it participates in all operations, it cannot obtain any useful information. Based on the above analysis, the scheme can ensure that the information security of the communicating parties is not affected by the STTP in the semi-trusted model.

[0235] False signal attack:

[0236] In a false signal attack, STTP may attempt to obstruct information exchange between users by publishing false ciphertext or preparing an incorrect initial state. However, the present invention introduces a consistency detection mechanism: all users will sequentially concatenate their plaintext information and exchange round numbers, calculate a hash value, and broadcast it.

[0237] Due to the irreversibility and uniqueness of hash functions, if either party's input differs, the output hash value will inevitably be different. Thus, any STTP spoofing will cause the hash values ​​of all parties to be inconsistent, thus being discovered promptly. Therefore, the present invention can effectively resist spoofing attacks and ensure communication reliability.

[0238] Example 6: Performance Analysis

[0239] This embodiment analyzes the performance of the method proposed in the present invention from two aspects: transmission efficiency analysis and coding efficiency analysis.

[0240] Transmission efficiency analysis:

[0241] Without considering decoy particles and key transmission, from the perspective of information theory, the information utilization rate of quantum cryptography schemes can be measured by transmission efficiency. Transmission efficiency is defined as the ratio of the number of useful information bits actually exchanged between the communicating parties to the total number of bits consumed during the communication process (including quantum bits and classical bits). For the method proposed in this invention, the number of useful information bits b s =2, number of quantum bits q t =2, the number of classic bits b t =2, so the transmission efficiency ξ is:

[0242]

[0243] This shows that under this protocol, for every 4 bits transmitted (including quantum and classical), 2 bits are valid information, reflecting a high information utilization rate.

[0244] Coding efficiency analysis:

[0245] Coding efficiency refers to the ratio of the number of useful information bits actually transmitted to the number of quantum bits consumed during quantum communication. This indicator reflects the efficiency of quantum resource utilization. For the method proposed in this invention, the number of information bits exchanged between the two communicating parties is b s =2, the number of quantum bits in the communication process n=2, so the coding efficiency is:

[0246]

[0247] This shows that every qubit is fully utilized for information transmission, and the coding efficiency is optimized. In summary, the method proposed in the present invention performs well in both transmission efficiency and coding efficiency, and has certain practical application value.

[0248] Example 7: Experiment

[0249] Based on the multi-party information exchange method based on GHZ state proposed in Example 1, an experiment is conducted using an IBM-Sherbrooke quantum computer, wherein an IBM-Sherbrooke quantum computer is configured in each of the semi-trusted third party and the multi-party user terminal. The IBM-Sherbrooke quantum computer can be based on the following example: Figure 13 The quantum circuit shown performs a multi-party exchange experiment. Figure 13 In the figure, q[0], q[1], and q[2] represent three quantum bits (qubits), which are carriers of quantum information and can be in the |0>, |1>, or superposition states. c3 represents a classical register (3 bits) used to store the measurement results of the qubits (recorded after the quantum state collapses to the classical 0 / 1). This quantum circuit can implement GHZ state preparation, unitary operator encoding, joint measurement, and hash consistency verification. GHZ state preparation can be achieved through H gate 1301, first CNOT gate 1302, and second CNOT gate 1303. First CNOT gate 1302 and second CNOT gate 1303 are controlled NOT gates. Unitary operator encoding can be achieved through RX gate 1304 and I gate 1305. Joint measurement and hash consistency verification can be achieved through RZ gate 1306 and measurement gate 1307. H gate 1301 changes q[0] from |0> to a superposition state, preparing for entanglement. The control bit q[0] of the first CNOT gate 1302 corresponding to q[1] is q[1]. If q[0]=|1>, the state of q[1] is flipped. If q[0]=|0>, q[1] remains unchanged. The control bit q[0] of the second CNOT gate 1303 corresponding to q[2] and the target bit q[2] are logically the same as the CNOT of q[1], realizing the entanglement of q[0] and q[2]. The three bits form a GHZ state, that is, state.

[0250] based on Figure 13 The theoretical predictions and actual results are shown in the following table. Figure 14 and Figure 15 shown. Figure 14 In the figure, the vertical axis (Probability of the states) represents the probability of the quantum state appearing, ranging from 0 to 100, which measures the probability of each computational basis state being observed. The horizontal axis (Computational basis states) lists 8 computational basis states, corresponding to all possible states of the three-qubit system (represented by three-digit binary numbers 000-111), representing the classical states that the quantum system may collapse into. The figure shows that the 011 and 100 states have probability values, indicating that after evolution / measurement, the quantum system mainly presents these two computational basis states, and the probabilities of other basis states are close to 0, reflecting the probability distribution characteristics of quantum states under the computational basis.

[0251] Figure 15 In the figure, the horizontal axis is labeled "Computational Basis States," listing the computational basis states (quantum states represented by three binary digits) of a three-qubit system, such as 000, 001, 010, 011, 100, 101, 110, and 111. These correspond to the classical states to which the quantum system might collapse. The vertical axis, labeled "Probability," indicates the probability of observing each computational basis state, measuring the likelihood of that quantum state occurring. The inclusion of columns corresponding to the 011 and 100 states in the figure indicates that, after evolution / measurement, the quantum system primarily appears in these two computational basis states, with the probabilities of the other basis states approaching zero. This reflects the probabilistic distribution of quantum states under the computational basis.

[0252] contrast Figure 14 and Figure 15 As can be seen, the target state (011, 100) probability in the theoretical graph is concentrated, and the histogram is highly regular, indicating the high purity of the ideal quantum state (the quantum state is free of spurious signals and fully conforms to the theoretical design). The target state probability still dominates the actual graph, but other ground states have a weak distribution, reflecting the loss of purity of the actual quantum state. This is because the quantum state in the experiment is difficult to completely isolate from environmental interference, resulting in a diffuse probability distribution and minor results outside the theory. However, the target state is still the main result, which is consistent with theoretical expectations and proves the applicability of the theoretical model in real-world scenarios.

[0253] Example 8: Multi-party information exchange device based on GHZ state

[0254] The embodiment of the present invention also provides a multi-party information exchange device based on GHZ state, such as Figure 16 As shown, the apparatus includes a first terminal 1601 and multiple second terminals 1602, wherein the first terminal 1601 serves as a semi-trusted third party, and the multiple second terminals 1602 serve as multiple user terminals;

[0255] A semi-trusted third party prepares multiple pairs of GHZ state particles and distributes each GHZ state particle to multiple user terminals according to their location. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results.

[0256] The semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. Each user terminal encodes the received GHZ state particles according to the corresponding plaintext information using the determined encoding method, exchanges the encoded particles in sequence, and applies the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the results to the user terminals of each party. The user terminals calculate and obtain the plaintext of the other party based on the results.

[0257] Each user terminal calculates a hash value based on its own plaintext and the plaintext of the other party obtained, and broadcasts the hash value to other user terminals. If the hash values ​​of all user terminals are equal, it is confirmed that the current round of information exchange is successful.

[0258] It should be noted that the structures of the various GHZ-state-based multi-party information exchange devices described in this embodiment belong to the same technical concept as the previously described GHZ-state-based multi-party information exchange method, and achieve the same beneficial effects through the same principles, which will not be repeated here.

[0259] Example 9: Readable storage medium

[0260] An embodiment of the present invention further provides a readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the method described in any of the above embodiments.

[0261] The above embodiments are only used to illustrate the present invention, and are not intended to limit the present invention. Ordinary technicians in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also fall within the scope of the present invention. The scope of patent protection of the present invention should be defined by the claims.

Claims

1. A multi-party information exchange method based on GHZ state, characterized in that: The method comprises: A semi-trusted third party prepares multiple pairs of GHZ state particles and distributes each GHZ state particle to multiple user terminals according to their location. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results. The semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. Each user terminal encodes the received GHZ state particles according to the corresponding plaintext information using the determined encoding method, exchanges the encoded particles in sequence, and applies the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the results to the user terminals of each party. The user terminals calculate and obtain the plaintext of the other party based on the results. Each user terminal calculates a hash value based on its own plaintext and the plaintext of the other party obtained, and broadcasts the hash value to other user terminals. If the hash values ​​calculated by all user terminals are equal, it is confirmed that the current round of information exchange is successful.

2. The multi-party information exchange method based on GHZ state according to claim 1, characterized in that: The GHZ state particles are the multi-particle maximum entangled state, which is expressed as: Where n is the number of entangled particles, |GHZ> n represents the GHZ entangled state composed of n particles, |0> and |1> represent the basic quantum state of a single quantum bit, represents the tensor product symbol; The GHZ state particles include four expressions of three-particle GHZ states: Where, and They represent four different three-qubit entangled states.

3. The multi-party information exchange method based on GHZ state according to claim 1, characterized in that: There are three user terminals, namely user terminal Alice, user terminal Bob and user terminal Charlie.

4. The multi-party information exchange method based on GHZ state according to claim 3, characterized in that: A semi-trusted third party prepares multiple pairs of GHZ state particles, and distributes each GHZ state particle to multiple user terminals according to their location. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results, including: A semi-trusted third party prepares 40 pairs of entangled states The GHZ state particles are extracted bit by bit from the first, second and third positions to form quantum sequences S1, S2 and S3 respectively, and sent to user end Alice, user end Bob and user end Charlie respectively through the quantum channel. Alice, Bob, and Charlie randomly select bit unitary operators Act on each quantum in quantum sequences S1, S2 and S3 respectively, and return the quantum sequences after the action to the semi-trusted third party; The semi-trusted third party extracts the particles at the same position in the quantum sequence after the action and performs joint measurement, and then publishes the measurement results, which are determined by the entangled state. Combined in order; Each user terminal will The position of the corresponding bit unitary operator is determined by In the emergence When there are more than three positions, determine the 3-bit classical information, and determine the encoding method of the current round exchange based on the classical information; if there is If the number of positions is less than three, repeat the above steps until it appears.

5. The multi-party information exchange method based on GHZ state according to claim 4, characterized in that: The encoding method is a determined mapping relationship f, which is expressed as: f:f(K,M)=C Where f(K, M) represents the operation process and result of taking the elements in the key set K and the elements in the plaintext set M as input and outputting the ciphertext after the mapping f operation, C represents the ciphertext set, They represent different three-qubit GHZ entangled states respectively, M represents the plaintext set, M = {m1, m2,…, m8}, m1, m2 and m8 represent the first, second to eighth plaintext respectively, K represents the key set, K = {k1, k2,…, k8}, k1, k2 and k8 represent the first, second to eighth keys respectively. In the encoding method, when the key is unknown, the probability that any plaintext is mapped to any ciphertext is equal, and the probability that any ciphertext corresponds to any plaintext is equal.

6. The multi-party information exchange method based on GHZ state according to claim 3, characterized in that: The semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. The user terminals of each party encode the received GHZ state particles according to the corresponding plaintext information using the determined encoding method, exchange the encoded particles in sequence, and apply the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the results to the user terminals of all parties. The user terminals calculate and obtain the plaintext of other parties based on the results, including: A semi-trusted third party prepares 40 pairs of entangled states The GHZ state particles are extracted bit by bit from the first, second and third positions to form quantum sequences S1, S2 and S3 respectively, and sent to user end Alice, user end Bob and user end Charlie through the quantum channel respectively; User-side Alice applies Ua to quantum sequence S1 to obtain quantum sequence S1'; user-side Bob applies Ub to quantum sequence S2 to obtain quantum sequence S2'; user-side Charlie applies Uc to quantum sequence S3 to obtain quantum sequence S3'. Ua, Ub, and Uc are the quantum operator sequences of length n1 constructed by user-side Alice, user-side Bob, and user-side Charlie according to their respective n1-bit plaintexts Pa, Pb, and Pc, according to the set correspondence relationship. User end Alice sends quantum sequence S1' to user end Bob; user end Bob sends quantum sequence S2' to Charlie; user end Charlie sends quantum sequence S3' to Alice. User end Alice applies Ua to quantum sequence S3' to obtain quantum sequence S3"; user end Bob applies Ub to quantum sequence S1' to obtain quantum sequence S1"; user end Charlie applies Uc to quantum sequence S2' to obtain quantum sequence S2". Each user end sends the corresponding quantum sequence to a semi-trusted third party. The semi-trusted third party extracts particles at the same position from the quantum sequences S1", S2" and S3" for joint measurement, and announces the measurement results Cabc to all parties' user terminals in sequence through broadcasting. Each user terminal calculates the plaintext of the other party based on its own quantum operator sequence and the published measurement result Cabc; among them, the user terminal Alice calculates Pb' and Pc'; the user terminal Bob calculates Pa' and Pc"; the user terminal Charlie calculates Pa" and Pb"; Pa' and Pc' are the plaintexts of user terminals Bob and Charlie calculated by user terminal Alice, Pa' and Pc" are the plaintexts of user terminals Alice and Charlie calculated by user terminal Bob, and Pa" and Pb" are the plaintexts of user terminals Alice and Bob calculated by user terminal Charlie.

7. The multi-party information exchange method based on GHZ state according to claim 6, characterized in that: Each client calculates a hash value based on its own plaintext and the other client's plaintext, and broadcasts the hash value to the other client. If the hash values ​​calculated by all clients are equal, the current round of information exchange is confirmed to be successful, including: Each user terminal calculates the hash value using the following formula: Ca=HASH(Pa||Pb'||Pc'||sid) Cb=HASH(Pa'||Pb||Pc"||sid) Cc=HASH(Pa"||Pb"||Pc||sid) Where Ca, Cb, and Cc are the hash values ​​calculated by user Alice, user Bob, and user Charlie respectively, HASH is a cryptographic hash function, sid is the current fair exchange round number, and || is data splicing; When Ca=Cb=Cc, it is confirmed that the current round of information exchange is successful.

8. The multi-party information exchange method based on GHZ state according to any one of claims 1 to 7, characterized in that: The method further comprises: Every time a quantum sequence is transmitted in a quantum channel, both the sender and the receiver will use decoy particles to perform an eavesdropping detection.

9. A multi-party information exchange device based on GHZ state, characterized in that: For executing the method according to any one of claims 1 to 8, the apparatus comprises a first terminal and a plurality of second terminals, wherein the first terminal serves as a semi-trusted third party and the plurality of second terminals serve as multi-party user terminals; A semi-trusted third party prepares multiple pairs of GHZ state particles and distributes each GHZ state particle to multiple user terminals according to their location. Each user terminal applies a bit unitary operator to the received GHZ state particles and returns them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the measurement results to each user terminal. Each user terminal determines an encoding method based on the measurement results. The semi-trusted third party again prepares multiple pairs of GHZ state particles and distributes them to the user terminals of each party. The user terminals of each party encode the received GHZ state particles according to the corresponding plaintext information using the determined encoding method, exchange the encoded particles in sequence, and apply the bit unitary operator again before sending them to the semi-trusted third party. The semi-trusted third party conducts joint measurements and publishes the results to the user terminals of each party, and the user terminals calculate and obtain the plaintext of the other party based on the results; Each user terminal calculates a hash value based on its own plaintext and the plaintext of the other party obtained, and broadcasts the hash value to other user terminals. If the hash values ​​of all user terminals are equal, it is confirmed that the current round of information exchange is successful.

10. A non-transitory computer-readable storage medium storing instructions, characterized in that: When the instructions are executed by a processor, the method according to any one of claims 1 to 8 is performed.

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