A method for comparing the size of multi-party semi-quantum secrets based on two-dimensional Bell states

Abstract

The present invention discloses a multi-party semi-quantum secret size comparison method based on two-dimensional Bell state, comprising: 1) participants encrypt their respective secret information; 2) a semi-honest quantum third party (STP) prepares a two-dimensional Bell state and sends a particle sequence A n To Participant P n , where n = {1, 2, ... N}; 3) according to the encrypted information #imgabs0#P n Select the appropriate operation for particle #imgabs1#; 4) After passing the security check, the STP records #imgabs2# and calculates #imgabs3#; 5) Compare the sizes of #imgabs4# and #imgabs5#, and then determine the size relationship of each participant's secret. This is a new method for comparing secret sizes. This method, based solely on two-dimensional Bell states, can perform secret size comparisons. Compared to traditional QPCS and SQPCS methods, this method is much easier to implement with existing quantum technology. Furthermore, based on semi-quantum theory, which reduces quantum costs, this method can compare the secrets of multiple participants simultaneously, making it more applicable and universal.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum cryptography, and in particular to a multi-party half-quantum secret size comparison method based on two-dimensional Bell states. Background Art

[0002] Secret comparison refers to the process where two or more parties holding secret values ​​can confirm the size relationship of each party's secret values ​​by executing a cryptographic protocol without revealing their secrets. Secret comparison originated from Yao Qizhi's millionaire problem. [1] , is an important special case of multi-party secure computing. Quantum secret comparison (QPC) is a secret comparison method based on the preparation and manipulation of quantum states. Its security relies on the unique physical properties of quantum rather than the complexity of mathematical calculations. It is used in electronic bidding. [2，3] , summing up multiple data [4] , electronic voting elections [5，6] Quantum secret comparison methods have many applications in various fields. Research on quantum secret comparison methods can be roughly divided into two categories: one is comparing secret equality (QPCE); the other is comparing secret size relations (QPCS). Clearly, the latter has wider application scenarios. Consequently, over the past decade, numerous quantum secret size comparison methods have been proposed based on high-dimensional quantum states.

[0003] In 2011, Jia et al. proposed the first QPCS method [7] In their method, the secrets of each participant are encrypted into the phase of a high-dimensional three-particle entangled state through a gate operation. The operator measures these high-dimensional quantum states, and based on the measurement results, he can determine the size relationship between the secrets of the two participants. Since Colbeck proved that a secret comparison method involving only two parties is impossible to be absolutely secure, [8] All secret comparison methods introduce a third party (which may be semi-honest or completely dishonest). A semi-honest third party (STP) is one that strictly follows the procedure and does not collude with anyone to leak secrets. However, it is particularly curious about the secrets of the participants and attempts to deduce the secrets of each participant from the information it has. In 2013, Lin et al. also proposed a new QPCS method based on high-dimensional Bell states. [9] This year, many new QPCS methods were proposed based on high-dimensional quantum states. [10-12] However, the above mentioned methods can only compare the size of the secrets of two parties. Fortunately, based on high-dimensional maximally entangled states, Luo et al. quickly designed the first QPCS method that can compare the secrets of multiple parties.

[13] In this method, STP prepares and sends high-dimensional quantum states, while the participants measure these high-dimensional quantum states and convert the measured values ​​into keys for information encryption. Finally, the encrypted information is sent to STP through a secure classical authentication channel. Without knowing the secrets of each participant, STP can obtain the size relationship of the secrets of each participant through calculation. In 2018, based on high-dimensional single-particle states, Ye et al. also designed two multi-party QPCS methods.

[14] Since then, the multi-party QPCS method has attracted more and more attention. [15-17] .

[0004] In 2007, Boyer et al. proposed a semi-quantum model, which proved that quantum communication can be unconditionally secure under the condition of using as few quantum resources and quantum operations as possible. [18,19] . In the semi-quantum model, the quantum party usually has complete quantum capabilities and can prepare and control quantum states, while the classical party has no or only some limited quantum capabilities and can only perform certain classical or limited quantum operations. Therefore, quantum communication is no longer limited to advanced quantum laboratories and quantum parties with complete quantum operation capabilities. In other words, classical participants without quantum devices can also conduct quantum secure communication with quantum third parties through quantum channels anywhere with the help of quantum third parties. Due to the versatility and practicality of the semi-quantum model, many semi-quantum secret comparison methods have been proposed in recent years. However, early semi-quantum secret comparison methods could only compare whether the secrets of the two parties were equal. [20-24] Until 2021, Zhou et al. proposed the first semi-quantum secret size comparison method (SQPCS) based on the d-dimensional Bell state. However, this method is limited to two parties.

[25] In 2022, Luo et al. also proposed a new two-party SQPCS method based on high-dimensional Bell states.

[26] In the same year, based on high-dimensional quantum states, Wang et al. and Li et al. each proposed a new two-party SQPCS method. [27,28] .

[0005] As mentioned above, all quantum and semi-quantum methods capable of comparing secret sizes rely on high-dimensional quantum states as signal sources. However, currently, preparing, transmitting, and measuring high-dimensional quantum states in the laboratory is extremely difficult, severely restricting the practical application of these techniques.

[0006] References

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[0034]

[28] Wang, B., Liu, SQ, Gong, LH: Semi-quantum private comparison protocol of size relation with d-dimensional GHZ states.Chin.Phys.B.31,010302(2022) Summary of the Invention

[0035] The purpose of the present invention is to address the shortcomings of the existing technology and provide a multi-party semi-quantum secret size comparison method based on two-dimensional Bell states. By designing a new calculation method, secret size comparison is performed only based on two-dimensional Bell states to solve the problem that traditional quantum secret comparison methods are difficult to put into practical use.

[0036] To achieve the above object, the present invention adopts the following technical solutions:

[0037] A method for comparing the size of multi-party semi-quantum secrets based on two-dimensional Bell states, comprising the following steps:

[0038] Step 1: Before formal communication, participants encrypt their secret information;

[0039] Step 2: STP prepares N(L+1) two-dimensional Bell states and combines these Bell states into a particle sequence A n Send to P n ;

[0040] Step 3: When P n Receive particles After that, P n The encrypted information Particles Do the corresponding operation if is 0, particle Will be returned directly without any other operation; otherwise, P n The particles Perform a Pauli gate operation and then return the particle through the quantum back channel;

[0041] Step 4: When STP receives the particle After that, P n will publicly announce the operation; if P n Return particles directly, STP will and Perform Bell measurement, and according to the measurement results, STP will determine whether there is eavesdropping in the quantum channel; if there is eavesdropping, STP will abandon the communication, otherwise STP will record If P n Particles Doing a certain Pauli gate operation, STP will also affect the particle and Do Bell measurement, and then repeat the above process for security detection. If there is no eavesdropping, STP will record When the particle sequence A n After all particles in the STP are operated, the STP will obtain a data And further calculate C n ;

[0042] Step 5: After STP processes all particles in the particle sequence, STP will obtain N data strings C1, C2, ..., C N , by arranging and comparing C1, C2, ..., C NThe size relationship between them is that STP can obtain the secrets p1, p2, ..., p of each participant. N The size relationship between them.

[0043] Furthermore, the participants in step 1 encrypt their respective secret information. The encryption process is as follows:

[0044] First P n By formula

[0045]

[0046] Get data string or

[0047] Then according to the formula

[0048] Complete binary logic operations to obtain data strings

[0049] It should be noted that in formula (1), “+” is a binary addition operation with carry: if c n ≥c n′ , you can definitely get p n ≥p n′ , where n≠n′; if the data string c n Only L position, P n Will be in c n Add a zero before the highest bit of c, so all c n Can be expressed as In formula (2), is a logical operator.

[0050] Furthermore, the STP described in step 2 prepares N(L+1) two-dimensional Bell states, and combines these Bell states into a particle sequence Send to P n The specific process is as follows:

[0051] STP prepares N(L+1) two-dimensional Bell states:

[0052]

[0053] In the above formula, A and B represent the first and second particles in the Bell state respectively; STP combines these Bell states into 2N particle sequences, where the particle sequence B=[B1,B2,...B N ] contains all the second particles in the Bell state, and the particle sequence A=[A1,A2,...A N ] contains the first particle of all Bell states, and Finally, STP will particle sequence A nSend to P n .

[0054] Furthermore, the STP in step 4 will obtain a data And further calculated The specific calculation process is as follows:

[0055] By F n =f n (4)

[0056] STP will be calculated by the following formula

[0057]

[0058] Combining formulas (2) and (4), we can further obtain

[0059]

[0060] Furthermore, in step 5, by sorting and comparing C1, C2, ..., C N The size relationship between them is that STP can obtain the secrets p1, p2, ..., p of each participant. N The specific process is as follows:

[0061] After STP processes all particles in the particle sequence, it will obtain N data strings C1, C2, ..., C N According to formula (1) and formula (6), if C n Greater than or equal to C n′ , then p n Must be greater than or equal to p n′ , where n≠n′; therefore, STP only needs to compare C n with C n′ The relationship between the size of p n With p n′ Therefore, STP compares the same bits in all data strings and calculates them using the following formula

[0062]

[0063] if and The values ​​are equal, and after XOR operation we can get otherwise therefore

[0064]

[0065] if illustrate and One of the values ​​is 0 and the other is 1;

[0066] Therefore, STP can be further determined by formula (9) and formula (10): Is it a large number or a small number?

[0067]

[0068]

[0069] Then, through formula (11), STP can determine and The size relationship,

[0070]

[0071]

[0072]

[0073] Finally, according to the above formula, STP can sort out C1, C2, ..., C N The size relationship of each participant can be obtained by N The size relationship between them.

[0074] Compared with the prior art, the present invention has the following beneficial effects:

[0075] 1. This invention designs a brand-new algorithm, which enables this technical method to complete secret size comparison based only on two-dimensional Bell states. Compared with traditional QPCS and SQPCS methods, this method is easier to implement under existing quantum technology conditions;

[0076] 2. Based on semi-quantum theory that can save quantum costs, this method can compare the secrets of multiple participants at once, making it more applicable and universal;

[0077] 3. The quantum communication process of the method of the present invention was simulated on the IBM quantum platform, proving the feasibility and effectiveness of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0079] Figure 1This is a flow chart of a multi-party half-quantum secret size comparison method based on two-dimensional Bell states of the present invention;

[0080] Figure 2 The quantum circuit diagram (left) and simulation output results (right) without eavesdropping in an embodiment of the present invention are shown;

[0081] Figure 3 A quantum circuit diagram (left) and simulation output results (right) of an intercept-measure-retransmit attack in an embodiment of the present invention.

[0082] Figure 4 The quantum circuit diagram (left) and simulation output results (right) of performing Puali-X gate operations on particles in an embodiment of the present invention;

[0083] Figure 5 The quantum circuit diagram (left) and simulation output results (right) of the intercept-retransmit attack in an embodiment of the present invention;

[0084] Figure 6 The quantum circuit diagram (left) and simulation output results (right) of performing a Puali-Y gate operation on particles in an embodiment of the present invention;

[0085] Figure 7 The quantum circuit diagram (left) and simulation output results (right) of performing Puali-Z gate operations on particles in an embodiment of the present invention. DETAILED DESCRIPTION

[0086] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0087] Basic introduction:

[0088] 1. Two-dimensional Bell state

[0089] The two-dimensional Bell state is the most common quantum entangled state, usually used to describe the four maximum entangled states in a two-particle system, expressed as:

[0090]

[0091]

[0092] Experimentally, there are several ways to obtain the above Bell states. For example, when laser light is irradiated into an optical system composed of a BBO nonlinear crystal, a pair of entangled photons is generated.

[0093] 2. Semi-quantum model

[0094] In this embodiment, STP can prepare and transmit two-dimensional Bell states, perform two-dimensional Bell measurements, and perform simple binary logic operations, while classical participants only need to complete the following restricted operations:

[0095] (i) Return the particle directly through the quantum reverse channel without performing any other operations;

[0096] (ii) Perform a Pauli gate operation on the particle and then return it to the particle through the quantum reverse channel.

[0097] 3. Preparation before communication

[0098] Assume there are N classical participants, they are P1, P2, ...P N , each participant has a secret Where n∈{1,2,...N}, l∈{1,2,...,L}; if p n The length is less than L, P n Add enough zeros before the highest bit, and all participants share a key K=K L ...K 2 K 1 , where K l ∈{0,1}; In addition, STP and P n Also share a key in advance in

[0099] Example 1

[0100] like Figure 1 As shown, the present invention provides a multi-party half-quantum secret size comparison method based on two-dimensional Bell states, comprising the following steps:

[0101] Step 1: Before formal communication, participants encrypt their secret information;

[0102] Step 2: STP prepares N(L+1) two-dimensional Bell states and combines these Bell states into particles Send to P n ;

[0103] Step 3: When P n Receive particles After that, P n The encrypted information Particles Do the corresponding operation if is 0, particle Will be returned directly without any other operation; otherwise, Pn The particles Perform a Pauli gate operation and then return the particle through the quantum reverse channel, as shown in Table 1 below;

[0104] Table 1 Participants' opinions on particles Action Sheet

[0105]

[0106] Step 4: When STP receives the particle After that, P n will publicly announce the operation; if P n Return particles directly, STP will and Perform Bell measurement, and according to the measurement results, STP will determine whether there is eavesdropping in the quantum channel; if there is eavesdropping, STP will abandon the communication, otherwise STP will record If P n Particles After a certain Pauli gate operation, STP will also affect the particle and Do Bell measurement, and then repeat the above process for security detection. If there is no eavesdropping, STP will record When the particle sequence A n After all particles in the STP are operated, the STP will obtain a data And further calculate C n ;

[0107] Step 5: After STP processes all particles in the particle sequence, STP will obtain N data strings C1, C2, ..., C N , by arranging and comparing C1, C2, ..., C N The size relationship between them is that STP can obtain the secrets p1, p2, ..., p of each participant. N The size relationship between them.

[0108] Furthermore, the participants in step 1 encrypt their respective secret information. The encryption process is as follows:

[0109] First P n By formula

[0110]

[0111] Get data string or

[0112] Then according to the formula

[0113] Complete binary logic operations to obtain data strings

[0114] It should be noted that in formula (1), “+” is a binary addition operation with carry: if c n ≥c n′ , you can definitely get p n ≥p n′ , where n≠n′; if the data string c n Only L position, P n Will be in c n Add a zero before the highest bit of c, so all c n Can be expressed as In formula (2), is a logical operator.

[0115] Furthermore, the STP described in step 2 prepares N(L+1) two-dimensional Bell states, and combines these Bell states into a particle sequence A n Send to P n The specific process is as follows:

[0116] STP prepares N(L+1) two-dimensional Bell states:

[0117]

[0118] In the above formula, A and B represent the first and second particles in the Bell state respectively; STP combines these Bell states into 2N particle sequences, where the particle sequence B=[B1,B2,...B N ] contains all the second particles in the Bell state, and the particle sequence A=[A1,A2,...A N ] contains the first particle of all Bell states, and Finally, STP will particle sequence A n Send to P n .

[0119] Furthermore, the STP in step 4 will obtain a data And further calculated The specific calculation process is as follows:

[0120] By F n =f n (4)

[0121] STP will be calculated by the following formula

[0122]

[0123] Combining formulas (2) and (4), we can further obtain

[0124]

[0125] Furthermore, in step 5, by sorting and comparing C1, C2, ..., C N The size relationship between them is that STP can obtain the secrets p1, p2, ..., p of each participant. N The specific process is as follows:

[0126] After STP processes all particles in the particle sequence, it will obtain N data strings C1, C2, ..., C N According to formula (1) and formula (6), if C n Greater than or equal to C n′ , then p n Must be greater than or equal to p n′ , where n≠n′; therefore, STP only needs to compare C n with C n′ The relationship between the size of p n With p n′ Therefore, STP compares the same bits in all data strings and calculates them using the following formula

[0127] if and The values ​​are equal, and after XOR operation we can get otherwise therefore

[0128]

[0129] if illustrate and One of the values ​​is 0 and the other is 1;

[0130] Therefore, STP can be further determined by formula (9) and formula (10): Is it a large number or a small number?

[0131]

[0132]

[0133] Then, through formula (11), STP can determine and The size relationship,

[0134]

[0135]

[0136]

[0137] Finally, according to the above formula, STP can sort out C1, C2, ..., C N The size relationship of each participant can be obtained by N The size relationship between them.

[0138] Example 2

[0139] In order to verify the feasibility and effectiveness of the method of the present invention, the communication process of the method of the present invention will be simulated on the IBM quantum platform in this embodiment.

[0140] 1. Before simulation, several quantum gate operations that will be used in this example are first given:

[0141] There are four types of Pauli door operations:

[0142]

[0143] When P n Particles After doing a Pauli gate operation, the entire Bell state will become:

[0144]

[0145]

[0146]

[0147]

[0148] The Hadamard gate and CONT gate operations are:

[0149]

[0150] On the IBM quantum platform, Bell states in circuits can be generated by Hadamard gates and CONT gates:

[0151]

[0152]

[0153]

[0154]

[0155] The measurement of Bell states in a circuit can be accomplished using Hadamard gates and CONT gates:

[0156]

[0157]

[0158]

[0159]

[0160] 2. Simulation process

[0161] According to P n Particles In this embodiment, two cases are simulated.

[0162] 2.1.P n Particles Complete operation (i)

[0163] Assume that the Bell state prepared by STP is Quantum circuits such as Figure 2 (left). If there is no eavesdropping in the quantum channel, according to formula (20), the measurement result must be 00, just as Figure 2 (right) When the simulation output is not 00, it indicates that there is eavesdropping in the quantum channel. For example, the eavesdropper Eve intercepts and measures the particle Then return a new one that matches the particle Particles with the same measurement value (intercept-measure-retransmit attack). The measured value is 1, according to particle will collapse to 1. Therefore, STP will return a new particle with a measurement value of 1. The quantum circuit diagram and simulation output are as follows Figure 3 As shown in the figure, it is obvious that when eavesdropping occurs, the simulation output is not 00. Therefore, based on the simulation output, STP can determine whether there is eavesdropping in the quantum channel.

[0164] 2.2.P n Particles Complete operation (ii)

[0165] ① When STP is prepared And P n Particles To perform Pauli-X gate operations, the quantum circuit is as follows Figure 4 (left). If there is no eavesdropping in the quantum channel, according to formulas (13) and (23), the measurement result must be 11, as Figure 4(right). If the simulation output is not 11, it means there must be eavesdropping in the quantum channel. For example: the eavesdropper Eve intercepts the particle And send a new particle to STP (intercept-retransmit attack). The quantum circuit and simulation output results are as follows Figure 5 As shown in the figure, the simulation results 00, 01, 10, and 11 all appear with a probability of about 25%.

[0166] ② When STP prepares |ψ + > AB , and P n Particles Performing Pauli-Y gate operation, quantum circuits such as Figure 6 As shown on the left, the corresponding output result is 10, as shown in Figure 6 As shown on the right, this is consistent with the theoretical derivation results of formulas (15) and (22), that is, the simulation output verifies the theoretical derivation of the formula.

[0167] ③ When STP prepares |ψ - > AB , and P n Particles To perform Pauli-Z gate operation, the quantum circuit is as follows Figure 7 As shown on the left, the corresponding output result is 01, such as Figure 7 As shown on the right, this is consistent with the theoretical derivation results of formulas (16) and (23), that is, the simulation output verifies the theoretical derivation of the formula.

[0168] According to the above content, the simulation output results and theoretical derivation verify each other, indicating the feasibility and effectiveness of this method.

[0169] Example 3

[0170] In order to verify the security of the method of the present invention, this embodiment will analyze in detail the impact of two types of attacks on the method. In this embodiment, the loss of quantum channels during communication is not considered.

[0171] 1. External attacks

[0172] An external attacker, Eve, could launch various attacks on the quantum channel to obtain secret-related information. These attacks include intercept-and-retransmit, intercept-measure-and-retransmit, and entanglement attacks. The simulations in Example 2 show that intercept-and-retransmit and intercept-measure-and-retransmit attacks are ineffective against this method.

[0173] Therefore, this embodiment will analyze in detail the impact of entanglement attack on the method of the present invention.

[0174] Entanglement attack refers to Eve performing a unitary transformation U on the particles in the quantum channel.E , so that the auxiliary entangled state |E> is attached to the particle.

[0175]

[0176] In the above formula, the pure auxiliary state |ε lk >Only follow U E related, and When Eve When performing an entanglement attack:

[0177] U E |0>|E>=a 00 |0>|ε 00 >+a 10 |1>|ε 10 > (25)

[0178] U E |1>|E>=a 01 |0>|ε 01 >+a 11 |1>|ε 11 > (26)

[0179] Then the entire initial Bell state becomes

[0180]

[0181]

[0182] Once the initial Bell state changes, the result of the Bell measurement will also change accordingly. Therefore, in order not to be detected by STP, Eve has to set a 10 =a 01 =0 and a 00 |ε 00 >=a 11 |ε 11 >.

[0183] Based on this, formulas (27) and (28) will become

[0184]

[0185]

[0186] From formulas (29) and (30), it can be seen that if one wants to remain undetected, the entanglement attack initiated by Eve will have no effect on the method of the present invention, that is, the entanglement attack initiated by Eve cannot obtain any information related to the secret.

[0187] 2. Internal attacks,

[0188] 2.1 Dishonest P n Attack

[0189] Dishonest P n There are only two ways to get some useful information:

[0190] (a)P n Launch an attack on the quantum channel;

[0191] (b)P n Deducing the secrets of each participant from known information.

[0192] In case (a), P n It will be detected as an external attacker. As mentioned above, the external attacker cannot obtain any useful information.

[0193] In case (b), because P n He does not know the shared secret between other participants and STP, so he cannot decrypt known information and cannot deduce the secrets of each participant.

[0194] 2.2 Dishonest STP Attack

[0195] The semi-honest third party (STP) strictly follows the steps of the present invention. Therefore, it neither prepares other quantum states (such as GHz states or single-particle states) to replace the Bell states required by the method, thereby leaking information, nor colludes with other thieves to steal secret information. However, it is very curious about the secrets of each participant and attempts to deduce them from the known information.

[0196] But STP does not know the key K=K shared among all participants L ...K 2 K 1 , so he cannot deduce the secrets of each participant from the information he already has. Therefore, the attack of STP on the method of the present invention is also invalid.

[0197] In summary, the present invention designs a new multi-party method for comparing the magnitude of half-quantum secrets based on two-dimensional Bell states. In this method, the STP is a fully quantum party capable of preparing, transmitting, and measuring two-dimensional Bell states, while the classical participants only need to randomly return particles or perform Pauli gate operations on them. After performing Bell measurements, the STP can determine whether eavesdropping occurs during the communication process. If eavesdropping occurs, the STP aborts the communication; otherwise, it proceeds to the next step. After security checks and binary logic operations, the STP can determine the magnitude of each participant's secret. To demonstrate the correctness of this method, this embodiment lists several examples in Table 2 below.

[0198] Table 2 illustrates the correctness of the method of the present invention

[0199]

[0200] Furthermore, to demonstrate the feasibility and effectiveness of the method, the inventors simulated the entire communication process on an IBM quantum platform. Security analysis also demonstrated that the method can withstand both internal and external attacks without revealing the secrets of any participant. Compared to existing quantum or semi-quantum secret size comparison methods, the method of the present invention utilizes only two-dimensional quantum states as a signal source. This makes it easier to implement under existing quantum technology. Finally, based on the semi-quantum model, which conserves quantum resources, the method of the present invention can compare the secrets of multiple participants simultaneously, making it more flexible and universal.

[0201] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for comparing the size of multi-party semi-quantum secrets based on two-dimensional Bell states, characterized in that: The following steps are involved: Step 1: Before formal communication, participants encrypt their secret information; Step 2: The semi-honest quantum third party STP prepares N(L+1) two-dimensional Bell states and combines these Bell states into a particle sequence A n Sent to participant P n ; Step 3: When P n Receive particles After that, P n The encrypted information Particles Do the corresponding operation if is 0, particle Will be returned directly without any other operation; otherwise, P n The particles Perform a Pauli gate operation and then return the particle through the quantum back channel; Step 4: When STP receives the particle After that, P n will publicly announce the operation; if P n Return particles directly, STP will and Perform Bell measurement, and according to the measurement results, STP will determine whether there is eavesdropping in the quantum channel; if there is eavesdropping, STP will abandon the communication, otherwise STP will record If P n Particles Doing a certain Pauli gate operation, STP will also affect the particle and Do Bell measurement, and then repeat the above process for security detection. If there is no eavesdropping, STP will record When the particle sequence A n After all particles in the STP are operated, the STP will obtain a data And further calculate C n ; Step 5: After STP processes all particles in the particle sequence, STP will obtain N data strings C1, C2, ..., C N , by arranging and comparing C1, C2, ..., C N The size relationship between them is that STP can obtain the secrets of each participant p1, p2, ..., p N The size relationship between them.

2. The method for comparing the size of multi-party half-quantum secrets based on two-dimensional Bell states according to claim 1, characterized in that: The participants in step 1 encrypt their secret information. The encryption process is as follows: First, all participants share a key K=K l ...K 2 K 1 , where K l ∈{0,1}, In addition, STP and P n Also share a key in advance in Then P n By formula Get data string or Then according to the formula Complete binary logic operations to obtain the encrypted data string 3. The method for comparing the size of multi-party half-quantum secrets based on two-dimensional Bell states according to claim 2, characterized in that: In formula (1), "+" is a binary addition operation with carry: if c n ≥c n′ , you can definitely get p n ≥p n′ , where n≠n′; if the data string c n Only L position, P n Will be in c n Add a zero before the highest bit of c, so all c n Can be expressed as In formula (2), is a logical operator.

4. The method for comparing the size of multi-party half-quantum secrets based on two-dimensional Bell states according to claim 1, characterized in that: In step 2, the STP prepares N(L+1) two-dimensional Bell states and combines these Bell states into a particle sequence A. n Send to P n The specific process is as follows: STP prepares N(L+1) two-dimensional Bell states: In the above formula, A and B represent the first and second particles in the Bell state respectively; STP combines these Bell states into 2N particle sequences, where the particle sequence B=[B1,B2,...B N ] contains all the second particles in the Bell state, and the particle sequence A=[A1,A2,...A N ] contains the first particle of all Bell states, and the particle sequence particle sequence Finally, STP will particle sequence A n Send to P n .

5. The method for comparing the size of multi-party half-quantum secrets based on two-dimensional Bell states according to claim 2, characterized in that: In step 4, STP will get a data And further calculated The specific calculation process is as follows: By F n =f n (4) STP will be calculated by the following formula Combining formulas (2) and (4), we can further obtain 6. The method for comparing the size of multi-party half-quantum secrets based on two-dimensional Bell states according to claim 2, characterized in that: As described in step 5, by sorting and comparing C1, C2, ..., C N The size relationship between them is that STP can obtain the secrets p1, p2, ..., p of each participant. N The specific process is as follows: After STP processes all particles in the particle sequence, it will obtain N data strings C1, C2, ..., C N According to formula (1) and formula (6), if C n Greater than or equal to C n′ , then p n Must be greater than or equal to p n′ , where n≠n′; therefore, STP only needs to compare C n with C n′ The relationship between the size of p n With p n′ Therefore, STP compares the same bits in all data strings and calculates them using the following formula if and The values ​​of are equal, and after XOR operation we can get otherwise therefore if illustrate and One of the values ​​is 0 and the other is 1; Therefore, STP can be further determined by formula (9) and formula (10): Is it a large number or a small number? Then, through formula (11), STP can determine and The size relationship, Finally, according to the above formula, STP can sort out C1, C2, ..., C N The size relationship of each participant can be obtained by N The size relationship between them.

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