CN115426108A

CN115426108A - Multiparty half-quantum privacy comparison method based on d-level single particle state

Info

Publication number: CN115426108A
Application number: CN202211061909.9A
Authority: CN
Inventors: 叶天语; 连江源
Original assignee: Zhejiang Gongshang University
Current assignee: Zhejiang Gongshang University
Priority date: 2022-09-01
Filing date: 2022-09-01
Publication date: 2022-12-02

Abstract

The invention provides a multiparty semi-quantum privacy comparison method based on a d-level single particle state, which can compare the magnitude relation of secret inputs of more than two classical users by executing one time. The method of the present invention requires the assistance of a quantum third party and a classical third party, both of which are allowed to misact at their own will, but are not allowed to collude with others. The method of the present invention requires neither quantum entanglement swapping nor unitary operation. Two third parties are only required to make a d-level single particle measurement. Correctness analysis shows that the method of the invention can obtain correct comparison results. The security analysis shows that the method of the invention can resist external attack and participant attack.

Description

Multiparty half-quantum privacy comparison method based on d-level single particle state

Technical Field

The present invention relates to the field of quantum cryptography. The invention designs a multiparty semi-quantum privacy comparison method based on a d-level single particle state, which can compare the magnitude relation of the secret inputs of more than two classical users by only one time.

Background

Quantum mechanics is known to be one of the greatest scientific discoveries to date. In 1984, a novel cryptography, namely quantum cryptography combining quantum mechanics with classical cryptography, was formally proposed [1]. In 1982, yao [2] presented a famous problem of millionaire, aiming to determine who is richer without revealing the wealth of two millionaire. The millionaire problem is essentially a classical privacy comparison problem, whose security is based on the computational complexity of solving the corresponding mathematical problem. Later, in 2009, yang and Wen [3] introduced Quantum mechanics in classical privacy comparisons to propose a new concept of "Quantum Private Comparison (QPC)". Thereafter, a series of QPC methods [4-20] were proposed in succession. Depending on function, QPC can be divided into two different types, namely QPC [4-10] for comparative size relationships and QPC [3,11-20] for comparative equality relationships. The QPC for comparing magnitude relationships can implement magnitude relationship (i.e. greater than, equal to, and less than) comparison of the secret inputs of different users, but the QPC for comparing equality relationships can only determine whether the secret inputs of different users are equal. To some extent, QPC with a more magnitude relationship may have wider application in practice than QPC with an equivalent relationship.

In fact, not all users have the ability to obtain various types of quantum devices. To overcome this problem, boyer et al [21] proposed an innovative concept of "half-quanta". In the half-quantum scheme, part of the users can be free from preparing and measuring the quantum superposition state and the quantum entanglement state. Later, ye et al [22,23] used a single photon with two degrees of freedom to design two novel half-quantum key distribution (SQKD) methods. In 2016, the first half-quantum privacy comparison (SQPC) method [24] was proposed by introducing the half-quantum concept to QPC. Like QPC, SQPCs can also be divided into two different types: SQPC [24-30] in an equal relationship and SQPC [31-35] in a magnitude relationship are compared. Regarding SQPC with comparative magnitude relationships, documents [32,33], documents [31,34] and documents [35] are based on d-level single particle states, d-level Bell states and d-level GHZ states, respectively. It is clear that each SQPC method in documents [31-35] is only applicable to two classical users. At present, an SQPC method which can compare the magnitude relation of secret inputs of more than two classical users only by performing one time does not appear.

Based on the analysis, the invention adopts a d-level single particle state to provide a Multi-party semi-quantum privacy comparison (MSQPC) method which can judge the magnitude relation of the secret inputs of more than two classical users only by one-time execution. A quantum Third Party (TP) assists in the comparison task with a classical TP, which is allowed to behave endlessly but cannot collude with others. The method of the present invention requires neither quantum entanglement swapping nor unitary operation. The method only needs two TPs to carry out d-level single particle measurement.

Reference to the literature

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Disclosure of Invention

The invention aims to design a multiparty semi-quantum privacy comparison method based on a d-level single particle state, which can compare the magnitude relation of the secret inputs of more than two classical users by only one time.

The multiparty semi-quantum privacy comparison method based on the d-level single particle state comprises the following eight processes:

s1) N classical users, P ₁ ,P ₂ ,...,P _N Intended to perform a privacy comparison, where P _n Having a sequence of secret integers of length L

Here, the

And i =1,2. Furthermore, N classical users previously passed through a secure SQKD with TP method [36 ]]Sharing a secret key sequence K = { K = ₁ ,k ₂ ,...,k _L In which k is _i E {0,1, ·, d-1} and i =1,2, ·, L.

S2) Quantum TP ₁ Preparing N single particle state sequences, wherein the particles are all from T ₁ And T ₂ And (5) randomly selecting the Chinese characters. Wherein, T ₁ ＝{|0>,|1>,...,|d-1>}，T ₂ ＝{F|0>,F|1>,...,F|d-1>F is a d-order discrete quantum fourier transform, and

TP ₁ is permitted to launch all types of attacks at her own will, but cannot collude with anyone. The N single particle state sequences are denoted S ₁ ,S ₂ ,...,S _N Wherein

Then, TP ₁ Through quantum channel, S _n Is sent to P _n . It is noted that TP in addition to the first particle ₁ Only at the slave TP ₂ Sending S after receiving the previous particle _n The next particle of (a).

S3)P _n Generating a random binary sequence r _n Wherein

And L =1,2. Upon reception of S _n After the first particle of (1), P _n According to

Enters either REFLRCT mode or MEASURE mode. In particular, when

When is, P _n Selecting a reflex mode; otherwise, P _n MEASURE mode is selected. Here, the REFLECT mode refers to returning the received particles to the sender without interference; while MEASURE mode refers to using T ₁ The received particles are measured, the same quantum state as the found state is prepared and returned to the sender. Note that when P is _n She needs to record the measurement when entering the measurement mode. P _n To S _n The new sequence formed after performing her operations is S _n ' is shown in

Finally, P _n Through quantum channel, S _n ' sending to TP ₂ 。

S4)TP ₂ Generating a random binary sequence v _n In which

And L =1,2. TP ₂ Is permitted to launch all types of attacks at her own will, but cannot collude with anyone. Upon reception of S _n ' after the first particle in, TP ₂ According to

Enters either REFLRCT mode or MEASURE mode. In particular, when

Time, TP ₂ Selecting a reflex mode; otherwise, P _n MEASURE mode is selected. It should be noted that when the MEASURE mode is selected, TP ₂ Her measurements were recorded. TP ₂ To S _n ' the new sequence obtained after the execution of the operation is denoted as S _n ", wherein

Finally, TP ₂ Through quantum channel, S _n "sent to TP ₁ 。

S5)TP ₁ Preparation at T in publication step S2 ₂ The position of the particles of the substrate. At the same time, P _n And TP ₂ Each publication r _n And v _n Where N =1,2. Based on published information, TP ₁ The corresponding operations listed in table 1 are performed.

Case 1: in this case, the starting particles are formed by TP ₁ Preparation at T in step S2 ₁ A group; p _n And TP ₂ The reflex mode is selected; and, TP ₁ By T ₁ The basis measures the corresponding particles in her hand. TP by comparing her measurements with the corresponding initial preparation states ₁ It is possible to judge whether there is an eavesdropper. If there is no eavesdropper, the communication will continue to be performed;

case 2: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₂ A group; p _n And TP ₂ The reflex mode is selected; and, TP ₁ By T ₂ The basis measures the corresponding particle in her hand. TP by comparing her measurements with the corresponding initial preparation states ₁ It is possible to judge whether there is an eavesdropper. If there is no eavesdropper, the communication will continue to be performed;

case 3: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₁ A group; p _n And TP ₂ The MEASURE mode and the REFLECT mode are respectively selected; and, TP ₁ By T ₁ The basis measures the corresponding particle in her hand. P _n Need to tell TP ₁ State of the freshly prepared particles. TP ₁ Compare her measurements with P _n The state of the freshly prepared particles was compared with the corresponding initial state of preparation. If there is no eavesdropper, the communication will continue to be performed;

case 4: in this case, the starting particles are formed by TP ₁ Preparation at T in step S2 ₁ A group; p is _n And TP ₂ Respectively selecting a REFLECT mode and a MEASURE mode; and, TP ₁ By T ₁ The basis measures the corresponding particle in her hand. TP ₂ Need to tell TP ₁ State of the freshly prepared particles. TP ₁ Compare her measurements to TP ₂ The state of the freshly prepared particles was compared with the corresponding initial state of preparation. If there is no eavesdropper, the communication will continue to be performed;

case 5, case 6, and case 7: in these three cases, the starting particle is formed by TP ₁ Preparation at T in step S2 ₂ A group; p _n And TP ₂ At least one party selects the MEASURE mode; and, TP ₁ No action is taken. It should be noted that these three situations are ignored.

Case 8: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₁ A base; p _n And TP ₂ The MEASURE mode is selected; and, TP ₁ By T ₁ The basis measures the corresponding particle in her hand. If TP ₁ In the case of a hand with a corresponding number of particles of less than 2L, the communication will be terminated.

S6)TP ₁ Pick L particles from her hand that belong to case 8 and publish the location of the picked particles. Then, P _n And TP ₂ And respectively publishing the measurement results of the selected positions. Then, TP ₁ By combining her measurements with P _n And TP ₂ The results of the measurements and the corresponding initial preparation states are compared to check the error rate of the selected particles. If the error rate is 0, the communication will be continued.

S7)P _n 、TP ₁ And TP ₂ The remaining L particles in case 8 were used for privacy comparisons. Note that P _n 、TP ₁ And TP ₂ The measurement results for the particles in case 8 are the same. P _n 、TP ₁ And TP ₂ The measurement results for the remaining L particles in case 8 are recorded as

Wherein

And i =1,2. P is _n Computing

Wherein the symbols

Denotes the modulo d sum, i =1,2. Finally, P _n By authenticating the classical channel _n Is sent to TP ₁ Wherein

TABLE 1 TP in different cases ₁ Operation of

S8) at reception of c _n Then, for N =1,2,.., N and i =1,2, ·, L, TP ₁ Computing

Then, TP ₁ Calculating out

Where N '=1,2.., N and N' ≠ N. TP ₁ Computing

Here, the first and second liquid crystal display panels are,

means that

Means that

Means that

Finally, TP ₁ To P ₁ ,P ₂ ,...,P _N The final comparison results are published.

Drawings

FIG. 1 is a flow chart of the method of the present inventionDrawing; FIG. 2 is Eve's with U _E And U _F Entanglement-measurement attack.

Detailed Description

The technical solution of the present invention is further described with reference to the following examples.

1 description of the method

In a d-scale quantum system, the Z and X radicals can each be described as

T ₁ ＝{|0>,|1>,...,|d-1>} (1)

And

T ₂ ＝{F|0>,F|1>,...,F|d-1>}, (2)

where F is a d-stage discrete quantum Fourier transform, and

T ₁ and T ₂ Two groups of conjugated groups are formed.

The MSQPC method proposed by the present invention is described below.

Here, the

And i =1,2. Furthermore, N classical users previously passed through a secure SQKD with TP method [36 ]]Sharing a secret key sequence K = { K = { (K) } ₁ ,k ₂ ,...,k _L In which k is _i E {0,1, ·, d-1} and i =1,2, ·, L.

S2) Quantum TP ₁ Preparing N single particle state sequences, wherein the particles are all from T ₁ And T ₂ And (4) randomly selecting the Chinese traditional medicines. TP ₁ Is permitted to launch all types of attacks at her own will, but cannot collude with anyone. The N single event state sequences are denoted S ₁ ,S ₂ ,...,S _N Wherein

S3)P _n Generating a random binary sequence r _n In which

Enters either REFLRCT mode or MEASURE mode. In particular, when

Finally, P _n Through quantum channel coupling S _n ' sending to TP ₂ 。

S4)TP ₂ Generating a random binary sequence v _n Wherein

And L =1,2. TP ₂ Is granted to launch all types of attacks at her own willBut not with anyone. Upon reception of S _n ' after the first particle in, TP ₂ According to

Enters either REFLRCT mode or MEASURE mode. In particular, when

Finally, TP ₂ Through quantum channel, S _n "sent to TP ₁ 。

S5)TP ₁ Preparation at T in publication step S2 ₂ The position of the particles of the substrate. At the same time, P _n And TP ₂ Each publication r _n And v _n Wherein N =1,2. Based on published information, TP ₁ The corresponding operations listed in table 1 are performed.

Case 1: in this case, the starting particles are formed by TP ₁ Preparation at T in step S2 ₁ A group; p _n And TP ₂ The reflex mode is selected; and, TP ₁ By T ₁ The basis measures the corresponding particle in her hand. TP by comparing her measurements with the corresponding initial preparation states ₁ It is possible to judge whether there is an eavesdropper. If there is no eavesdropper, the communication will continue to be performed;

case 2: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₂ A group; p _n And TP ₂ The reflex mode is selected; and, TP ₁ By T ₂ The basis measures the corresponding particle in her hand. TP by comparing her measurements with the corresponding initial preparation states ₁ Can judge whether toThere is an eavesdropper. If there is no eavesdropper, the communication will continue to be performed;

case 3: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₁ A base; p _n And TP ₂ The MEASURE mode and the REFLECT mode are respectively selected; and, TP ₁ By T ₁ The basis measures the corresponding particle in her hand. P _n Need to tell TP ₁ State of the freshly prepared particles. TP ₁ Compare her measurements with P _n The state of the freshly prepared particles was compared with the corresponding initial state of preparation. If there is no eavesdropper, the communication will continue to be performed;

case 4: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₁ A group; p _n And TP ₂ Respectively selecting a REFLECT mode and a MEASURE mode; and, TP ₁ By T ₁ The basis measures the corresponding particle in her hand. TP ₂ Need to tell TP ₁ State of the freshly prepared particles. TP ₁ Compare her measurements to TP ₂ The state of the freshly prepared particles was compared with the corresponding initial state of preparation. If there is no eavesdropper, the communication will continue to be performed;

case 5, case 6, and case 7: in these three cases, the starting particles are formed by TP ₁ Preparation at T in step S2 ₂ A group; p _n And TP ₂ At least one party selects the MEASURE mode; and, TP ₁ No action is taken. It should be noted that these three situations are ignored.

S6)TP ₁ Pick L particles from her hand that belong to case 8 and publish the location of the picked particles. Then, P _n And TP ₂ Are respectively publicThe measurements at the selected locations are laid out. Then, TP ₁ By combining her measurements with P _n And TP ₂ The results of the measurements and the corresponding initial preparation states are compared to check the error rate of the selected particles. If the error rate is 0, the communication will be continued.

S7)P _n 、TP ₁ And TP ₂ The remaining L particles in case 8 were used for privacy comparison. Note that P _n 、TP ₁ And TP ₂ The measurement results for the particles in case 8 are the same. P _n 、TP ₁ And TP ₂ The measurement results for the remaining L particles in case 8 are recorded as

Wherein

And i =1,2. P is _n Calculating out

Wherein, the symbol

Denotes modulo d and, i =1,2. Finally, P _n By authenticating classical channels _n Is sent to TP ₁ Wherein

Then, TP ₁ Computing

Where N '=1,2.., N and N' ≠ N. TP ₁ Computing

Here, the number of the first and second electrodes,

means that

Means that

Means that

2 analysis of correctness

Substituting the formula (3) and the formula (4) into the formula (5) can obtain

Here, N, N '=1,2, · N, N' ≠ N and i =1,2, ·, L. Due to the fact that

And

according toThe following points can be obtained by the following equations (6) and (7): when in use

When there is

Means that

When in use

When there is

Means that

And when

When there is

Means that

It can be concluded that the comparison results of the method of the invention are correct.

3 safety analysis

3.1 external attacks

The external attacker Eve can try to acquire p as best as possible by launching some well-known attacks, such as interception-retransmission attacks, measurement-retransmission attacks, entanglement-measurement attacks, and the like _n (n＝1,2,...,N)。

(1) Interception-retransmission attack

According to the flow of the method of the present invention, there are three types of interception-retransmission attacks. The detailed analysis will be made one by one.

First, in step S2, eve intercepts S _n And preparing her at T beforehand ₁ False of radicalSending of the particles to P _n (ii) a At P _n After performing her actions, eve intercepts S in step S3 _n ' and sending the original real particles to the TP ₂ . When P is present _n When the REFLECT mode is selected, regardless of the original true particle and TP ₂ Whatever the mode of operation selected, the attack of Eve will not be discovered. Consider P _n Case of selecting measurement mode: if the original real particles are prepared at T ₂ Basically, according to Table 1, it will be ignored, and the Eve attack will not be discovered in step S5; if the original real particles are prepared at T ₁ Base when TP ₂ Upon selection of REFLECT mode and MEASURE mode at step S4, eve' S attack will be at step S5 respectively

And in step S6 with

The probability of (a) is found.

Next, eve intercepts S in step S2 _n And preparing her beforehand at T ₁ Pseudo-particle of radicals to P _n (ii) a Then, in step S4, eve intercepts S _n "and sends the original real particles to TP ₁ . Considering that the original real particles are prepared at T ₁ Case of radical: if P is _n And TP ₂ The REFLECT mode and MEASURE mode are selected, respectively, and Eve will be selected in step S5

The probability of (a) is found; if P is _n And TP ₂ MEASURE mode is selected and Eve will be in step S6 to

Is detected; if P is _n And TP ₂ The MEASURE mode and REFLECT mode are selected, respectively, eve will be in step S5

The probability of (a) is found; if P is _n And TP ₂ The reflex mode is selected and Eve will not be found in step S5. Consider that the original real particle is prepared at T ₂ Case of radical: regardless of P _n And TP ₂ Selecting what operating mode, eve will not be found in step S5.

Again, eve intercepts S in step S3 _n ' and prepare her in advance at T ₁ Pseudo particle delivery of radicals to TP ₂ (ii) a At TP ₂ After the dummy particles have been operated, eve intercepts TP in step S4 ₂ The emitted particle and sends the original real particle to TP ₁ . Consider that the original real particle is prepared at T ₁ Case of radical: if P _n And TP ₂ Select MEASURE mode, eve will be in step S6

Is detected; if P is _n And TP ₂ The REFLECT mode and MEASURE mode are selected, respectively, and Eve will be selected in step S5

Is detected; if P is _n And TP ₂ Selecting a MEASURE mode and a REFLECT mode respectively, wherein the probability that Eve will be found in the step S5 is 0; if P is _n And TP ₂ The reflex mode is selected and the probability that Eve will be found in step S5 is also 0. Considering that the original real particles are prepared at T ₂ Radical, irrespective of P _n And TP ₂ Selecting what operating mode, eve will not be found in step S5.

(2) Measurement-retransmission attack

Three measurements are analyzed next-retransmission attacks.

Eve intercept S _n /S′ _n /S" _n Then with T ₁ Measure it and send the resulting status to P _n /TP ₂ / TP ₁ . If the primary particles are prepared at T ₁ Base no matterP _n And TP ₂ The attack by Eve will not be discovered, whatever mode of operation is selected. Consider a starting particle prepared at T ₂ Case of radical: if P is _n And TP ₂ At least one party selects the MEASURE mode, and the attack of Eve can not be discovered; if P is _n And TP ₂ The reflex mode is selected and the attack by Eve will be found in step S5 because the state of the primitive is corrupted by the measure of Eve.

(3) Entanglement-measurement attacks

Eve may be through the use of U, as shown in FIG. 2 _E And U _F These two unitary operations launch her entanglement-measurement attack, where U _E And U _F Sharing an initial state of | E>The common detection space of (1). Here, eve pairs are from TP ₁ Is sent to P _n Particle application U of _E To the slave P _n Is sent to TP ₂ Particle application U of _F . As in document [21]]As described, the shared probing state allows Eve to utilize the Slave U _E The obtained information attacks the returned particles.

Theorem 1, suppose Eve pairs TP ₁ Is sent to P _n Particle application U of _E And to P _n Is sent to TP ₂ Particle application U of _F . In order not to introduce errors in steps S5 and S6, the final state of the probe state of Eve should be independent of P not only _n And is also independent of P _n And TP ₂ The measurement result of (1). Thus, eve cannot acquire m _n 。

Prove for simplicity, use | t respectively>And | J _t >To represent a set T ₁ And T ₂ Of particles of (1), wherein

And t =0,1.

(1) Consider S _n Is prepared at T ₁ The case of radicals. When TP is present ₁ Send out S _n When Eve applies U to the particles of (1) _E Thus, it is possible to obtain [38 ]]

Wherein | e _tt' >(t, t' =0,1,. Ang., d-1) is represented by U _E A probing state of Eve is determined, and

when P is present _n When the MEASURE operation is applied, the global composite system is collapsed to gamma _tt' |t'>|e _tt' >. To avoid being discovered by the security checks in case 3 and case 8, U is applied at Eve _F Then, the global state of the composite system should satisfy

This implies

When P is present _n When the REFLECT operation is applied, U is applied in Eve according to the formula (8) and the formula (10) _F Thereafter, the global composite system is converted into

Here, t =0,1. Eve cannot change S in order to avoid being discovered by the security checks in case 1 and case 4 _n Of the primary particles. This requirement is automatically fulfilled according to equation (12).

(2) Consider S _n Is prepared at T ₂ The case of a base. Applying U in Eve _E Thereafter, the global composite system is evolved

When P is present _n When the REFLECT operation is selected, U is applied in Eve _F Thereafter, the global composite system is converted into

Substitution of formula (12) into formula (15) gives

From the inverse quantum Fourier transform

Wherein δ =0,1. Substitution of formula (16) into formula (15) can give

In order for Eve not to be discovered by the Security detection of case 2, it should suffice

Here, t ≠ α and t, α =0,1. Obviously, for t ≠ α, one can obtain

According to the formulae (18) and (19), the compounds are obtained

γ ₀₀ |F ₀₀ >＝γ ₁₁ |F ₁₁ >＝...＝γ _(d-1)(d-1) |F _(d-1)(d-1) >＝γ|F>。 (20)

(3) Substitution of formula (20) into formula (10) can give

Substitution of formula (20) into formula (12) can give

U _F [U _E (|t>|E>)]＝γ|t>|F>。 (22)

Substitution of formula (20) into formula (17) can give

U _F [U _E (|J _t >|E>)]＝γ|J _t >|F>。 (23)

When Eve applies to TP, according to equations (21), (22) and (23) ₁ Is sent to P _n Particle application U of _E And to P _n Is sent to TP ₂ Particle application U of _F In order not to introduce errors in steps S5 and S6, the final state of Eve' S probe state should be independent of P not only _n And is also independent of P _n And TP ₂ The measurement result of (1). Thus, eve cannot acquire m _n Let alone p _n 。

In addition, there are two other situations: one is that Eve is to TP ₁ Is sent to P _n Particle application U of _E And to TP ₂ Is sent to TP ₁ Particle application U of _F (ii) a The other is Eve to P _n Is sent to TP ₂ Particle application U of _E And to TP ₂ Is sent to TP ₁ Particle application U of _F . After similar proofs as above, it is readily found that in both cases Eve also cannot obtain m _n Even more need not to lift p _n 。

3.2 participant attack

In 2007, gao et al [39] presented for the first time a new attack called a "participant attack". Participant attacks are generally more serious and worth more attention. Four participant attacks will be analyzed next.

(1) Participant attack from an loyal user

In the method of the present inventionIt is readily seen that each user has equal importance. Without loss of generality, assume P ₁ Is an loyal user who intends to steal the cryptic input of the remaining N-1 users. P ₁ P will be obtained with the best effort possible by launching various possible attacks _j (j =2,3,.., N). In the process of the invention, P ₁ Independent of P _j 、TP ₁ And TP ₂ . Therefore, when P is ₁ When she is launched, she essentially plays the role of an external attacker. As set forth in section 3.1, her illegal activity will inevitably be discovered.

In addition, when P is _j In step S7, c is sent _j For TP ₁ When is, P ₁ Can hear c in a surreptitious way _j . However, although P is ₁ Knowing k _i But due to lack of

She still can not get according to

Obtaining

In step S8, P ₁ From TP ₁ The final comparison result is received. However, she still cannot know

(2) Participant attacks from two or more non-loyal users

Here, the extreme case where N-1 non-loyal users collude together to obtain the secret input of the remaining one is discussed. Without loss of generality, assume P ₁ ,P ₂ ,...,P _b-1 ,P _b+1 ,...,P _N Attempting to acquire P _b Where b =2,3, 1. In the process of the invention, P ₁ ,P ₂ ,...,P _b-1 ,P _b+1 ,...,P _N Is independent of P _b 、TP ₁ And TP ₂ . Due to the fact thatThis is when user P ₁ ,P ₂ ,...,P _b-1 ,P _b+1 ,...,P _N When collusion launches their attack, they in fact act as an external attacker. Thus, their attacks will inevitably be discovered, as demonstrated in section 3.1.

In addition, when P is _b In step S7, c is sent _b For TP ₁ When is, P ₁ ,P ₂ ,...,P _b-1 ,P _b+1 ,...,P _N Possibly hearing c _b . Although P is ₁ ,P ₂ ,...,P _b-1 ,P _b+1 ,...,P _N Knowing k _i But due to lack of

They still cannot get from

Decipher out

P ₁ ,P ₂ ,...,P _b-1 ,P _b+1 ,...,P _N From TP in step S8 ₁ The final comparison result is received. Unfortunately, they still have no access to

(3) From semi-loyal TP ₁ Attack of participants

In the method of the present invention, TP ₁ Is not allowed to collude with anyone. Apparently, TP ₁ Automatic know

Where N =1,2., N and i =1,2., L. In addition, when P is _n In step S7, c is _n Is sent to TP ₁ When she can get c _n . However, TP ₁ Cannot know k _i This means she cannot get from

Deduce

Furthermore, although TP ₁ The final comparison can be calculated in step S8, but she still does not get

(4) From semi-loyal TP ₂ Attack of participants

In the method of the present invention, TP ₂ Is not allowed to collude with anyone. TP ₂ Automatic know

Where N =1,2., N and i =1,2., L. In addition, when P is _n In step S7, c is sent _n For TP ₁ Time, TP ₂ Possibly hearing c _n . Unfortunately, due to lack of k _i ，TP ₂ Still cannot be obtained from

Decipher out

Furthermore, although TP ₂ Possibly from TP in step S8 ₁ Hear the final comparison, she still cannot know

Example (b):

1 examples of the application of the method of the present invention

The privacy comparison principle is now further explained with an example.

To further demonstrate the validity of the method of the present invention, a specific example is given here. Assume that the dimension of the quantum system is d =19; there are a total of four classical users, P ₁ ,P ₂ ,P ₃ ,P ₄ ；P ₁ ,P ₂ ,P ₃ ,P ₄ Respectively is

And

P ₁ ,P ₂ ,P ₃ ,P ₄ the first secret key shared in advance is an integer k ₁ ＝16；P ₁ ,P ₂ ,P ₃ ,P ₄ The measurement results for the first remaining particle in case 8 are respectively

And

according to formula (3), P ₁ ,P ₂ ,P ₃ ,P ₄ Can be respectively obtained

And

then, P ₁ ,P ₂ ,P ₃ ,P ₄ By authenticating classical channels respectively

Is sent to TP ₁ . Is receiving

Then, according to formula (4), TP ₁ Can obtain

And

then, according to formula (5), TP ₁ Can obtain

And

according to formula (6), TP ₁ Calculate out

And

respectively mean that

And

in a word, have

2 discussion and conclusions

Document [32] uses a quantum bottom special effect rate, which is derived from the quantum bit efficiency defined in document [40], to calculate the efficiency of a quantum communication method suitable for a d-dimensional system. According to document [32], quantum-base efficiencies can be described as

Where σ, μ, and θ represent the number of quantum bases used, the length of classical information consumed in classical communication, and the length of the stego input compared, respectively. Next, the quantum base efficiency of the method of the invention is calculated after ignoring the classical resources consumed by the security detection process and the resources consumed by the generation of the pre-shared key sequence K.

In the process of the invention, p _n The length of (N =1,2.., N) is L, so θ = L can be obtained. TP ₁ It is necessary to prepare S having a length of 16L _n (ii) a From TP ₁ After obtaining the quantum bottom, when P _n Upon entering the MEASURE mode, she needs to generate 8L quantum bases; from P _n After obtaining the quantum bottom, when TP ₂ When entering the MEASURE mode, she needs to generate 8L quantum bases; therefore, σ =16L × N +8L × N =32LN can be obtained. Furthermore, P _n Needs to send c _n For TP ₁ Therefore, μ = L × N = LN can be obtained. Therefore, the quantum-bottom specific efficiency of the method of the invention is equal to

In addition, the method of the present invention was compared in detail with the previous SQPC method, and the comparison results are described in Table 2. From Table 2, it can be easily understood that the method of the present invention surpasses the methods of documents [31], [34] and [35] in quantum resources, because the d-class single particle state is easier to prepare than the d-class Bell state and the d-class GHZ state; the method of the invention defeats the second method of document [33] in the use of unitary operation, since the method of the invention does not require the use of any unitary operation; the method of the invention exceeds the methods of documents [31], [34] and [35] in the quantum measurement of TP, because the method of the invention does not need d-level Bell state measurement or d-level GHZ state measurement; moreover, the method is the only MSQPC method which can judge the magnitude relation of the secret inputs of more than two classical users only by one-time execution.

In short, the invention provides a first MSQPC method capable of judging the magnitude relation of secret inputs of more than two classical users by using a d-level single particle state. The method of the present invention has two TPs, one with full quantum capability and the other with limited quantum capability. Both TPs may behave endlessly but not collude with others according to their own wishes. The method of the present invention requires neither quantum entanglement swapping nor unitary operation. The method of the invention only requires two TPs to perform d-level single particle measurement. The method of the invention can resist external attack and participant attack.

TABLE 2 comparison of the method of the present invention with the previous SQPC method

Claims

1. A multiparty semi-quantum privacy comparison method based on a d-level single particle state can compare the magnitude relation of secret inputs of more than two classical users by executing one time; requiring the assistance of a quantum third party and a classical third party, both of which are allowed to misact at their own will, but are not allowed to collude with others; quantum entanglement exchange and unitary operation are not needed; two third parties are only required to carry out d-level single particle measurement; the method comprises the following eight processes:

Here, the first and second liquid crystal display panels are,

and i =1,2, ·, L; moreover, N classical users share a secret key sequence K = { K } in advance through a safe half quantum key distribution method with a third party ₁ ,k ₂ ,...,k _L In which k is _i E {0,1, ·, d-1} and i =1,2, ·, L;

s2) Quantum TP ₁ Preparing N single particle state sequences, wherein the particles are all from T ₁ And T ₂ Selecting the Chinese characters randomly; wherein, T ₁ ＝{|0>,|1>,...,|d-1>}，T ₂ ＝{F|0>,F|1>,...,F|d-1>F is a d-order discrete quantum fourier transform, and

TP ₁ is permitted to launch all types of attacks at her own will, but cannot collude with anyone; the N single event state sequences are denoted S ₁ ,S ₂ ,...,S _N In which

Then, TP ₁ Through quantum channel, S _n Is sent to P _n (ii) a TP in addition to the first particle ₁ Only at the slave TP ₂ Sending S after receiving the previous particle _n The next particle of (a);

S3)P _n generating a random binary sequence r _n Wherein

And L =1,2, · 16L; upon receiving S _n After the first particle of (1), P _n According to

Enter either REFLRCT mode or MEASURE mode; when the temperature is higher than the set temperature

When is, P _n Selecting REFLECT mode, otherwise, P _n Selecting a MEASURE mode; here, REFLECT mode refers to returning the received particle to the sender without interference, and MEASURE mode refers to using T ₁ Based on the received particles, preparing the same quantum state as the found state and returning it to the sender; when P is present _n When entering measurement mode, she needs to record the measurement result; p _n To S _n New sequence formed after execution of her operation is S' _n Is shown in which

Finally, P _n S 'is converted through a quantum channel' _n Is sent to TP ₂ ；

S4)TP ₂ Generating a random binary sequence v _n Wherein

And L =1,2, ·,16L; TP ₂ Is permitted to launch all types of attacks at her own will, but cannot collude with anyone; upon reception of S' _n After the first particle in (1), TP ₂ According to

Enter either REFLRCT mode or MEASURE mode; when in use

Time, TP ₂ Selecting REFLECT mode, otherwise, P _n Selecting a MEASURE mode; when MEASURE mode is selected, TP ₂ Her measurements need to be recorded; TP ₂ To S' _n The new sequence obtained after the operation is executed is marked as S ″ _n Wherein

Finally, TP ₂ Through quantum channel, the S ″) _n Is sent to TP ₁ ；

S5)TP ₁ Preparation at T in publication step S2 ₂ The position of the particle of the substrate; at the same time, P _n And TP ₂ Each publication r _n And v _n Wherein N =1,2, ·, N; based on the published information, TP ₁ Performing the corresponding operations listed in table 1;

case 1: in this case, the starting particles are formed by TP ₁ Preparation at T in step S2 ₁ A group;P _n and TP ₂ The reflex mode is selected; and, TP ₁ By T ₁ Base measures the corresponding particle in her hand; TP by comparing her measurements with the corresponding initial preparation states ₁ Whether an eavesdropper exists can be judged; if there is no eavesdropper, the communication will continue to be performed;

case 2: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₂ A group; p is _n And TP ₂ The reflex mode is selected; and, TP ₁ By T ₂ Base measures the corresponding particle in her hand; TP by comparing her measurements with the corresponding initial preparation states ₁ Whether an eavesdropper exists can be judged; if there is no eavesdropper, the communication will continue to be performed;

case 3: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₁ A group; p is _n And TP ₂ The MEASURE mode and the REFLECT mode are respectively selected; and, TP ₁ By T ₁ Base measures the corresponding particle in her hand; p _n Need to tell TP ₁ The state of the freshly prepared particles; TP ₁ Compare her measurements with P _n Comparing the state of the freshly prepared particles with the corresponding initial state of preparation; if there is no eavesdropper, the communication will continue to be performed;

case 4: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₁ A group; p _n And TP ₂ Respectively selecting a REFLECT mode and a MEASURE mode; and, TP ₁ By T ₁ Base measures the corresponding particle in her hand; TP ₂ Need to tell TP ₁ The state of the freshly prepared particles; TP ₁ Compare her measurements to TP ₂ Comparing the state of the freshly prepared particles with the corresponding initial state of preparation; if there is no eavesdropper, the communication will continue to be performed;

case 5, case 6, and case 7: in these three cases, the starting particle is formed by TP ₁ Preparation at T in step S2 ₂ A group; p _n And TP ₂ At least one party selects the MEASURE mode; and is，TP ₁ No action is taken; these three situations are ignored;

case 8: in this case, the starting particle is formed by TP ₁ Preparation at T in step S2 ₁ A group; p _n And TP ₂ The MEASURE mode is selected; and, TP ₁ By T ₁ Base measures the corresponding particle in her hand; if TP ₁ In this case in the hand, the corresponding number of particles is less than 2L, and the communication will be terminated;

TABLE 1 TP in different cases ₁ Operation of

S6)TP ₁ Pick L particles from her hand that belong to case 8 and publish the location of the picked particles; then, P _n And TP ₂ Respectively publishing the measurement results of the selected positions; then, TP ₁ By combining her measurements with P _n And TP ₂ Comparing the measurement results with the corresponding initial preparation state to check the error rate of the selected particles; if the error rate is 0, the communication will be continued;

S7)P _n 、TP ₁ and TP ₂ Performing privacy comparison by using the remaining L particles in the case 8; p _n 、TP ₁ And TP ₂ The measurement results for the particles in case 8 are the same; p _n 、TP ₁ And TP ₂ The measurement results for the remaining L particles in case 8 are noted