CN116599657A - Multipartite half-quantum secret size comparison method based on two-dimensional Bayer state - Google Patents

Multipartite half-quantum secret size comparison method based on two-dimensional Bayer state Download PDF

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CN116599657A
CN116599657A CN202310597815.1A CN202310597815A CN116599657A CN 116599657 A CN116599657 A CN 116599657A CN 202310597815 A CN202310597815 A CN 202310597815A CN 116599657 A CN116599657 A CN 116599657A
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stp
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王冰
杨小松
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Nanchang University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H04L9/0858—Details about key distillation or coding, e.g. reconciliation, error correction, privacy amplification, polarisation coding or phase coding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/085—Secret sharing or secret splitting, e.g. threshold schemes
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a multipartite half-quantum secret size comparison method based on a two-dimensional Bayer state, which comprises the following steps: 1) The participants encrypt the respective secret information; 2) Preparation of the two-dimensional bell state by the semi-honest Quantum third party (STP) and transmission of the particle sequence A n To participant P n Where n= {1,2,..n }; 3) Based on encrypted informationP n For particlesSelecting a corresponding operation; 4) STP record after passing security testAnd calculate5) Comparison ofAnd (3) withAnd then the size relationship of the secrets of the participants. A new method of secret size comparison can be performed. The secret size comparison can be completed based on the two-dimensional Bayer state, and compared with the traditional QPCS and SQPCS methods, the method is easier to realize under the existing quantum technical conditions. Meanwhile, based on the half quantum theory capable of saving quantum cost, the method can compare secrets of multiple participants at a time, and has more applicability and universality.

Description

Multipartite half-quantum secret size comparison method based on two-dimensional Bayer state
Technical Field
The invention relates to the technical field of quantum cryptography, in particular to a multipartite half-quantum secret size comparison method based on a two-dimensional Bayer state.
Background
Secret comparison refers to that two or more participants with secret values can confirm the magnitude relation of the secret values of the participants on the premise of not revealing the respective secrets by executing a cryptography protocol. Secret comparison originates from the megaphone problem of Yao Qizhi [1] Is an important special case of multiparty security computation. Quantum secret comparison (QPC) is a secret comparison method proposed based on techniques such as preparation and manipulation of quantum states. The security of which depends on quantum-specific physical properties rather than the complexity of mathematical calculations. It is in electronic bidding [2，3] Multiparty data summation [4] Electronic voting [5，6] And the like, there are many applications. Research into quantum secret comparison methods can be broadly divided into two categories: one is to compare if the secrets are equal (QPCE); the other is a size relation (QPCS) of the comparison secret. Obviously, the latter has wider application scenarios. Therefore, many quantum secret size comparison methods have been proposed over the last decade based on high-dimensional quantum states.
In 2011, jia et al proposed the first QPCS method [7] . In their method, the secret of each participant is encrypted into the phase of the Gao Weisan particle entangled state by a gate operation. For semi-honest third partiesThe operator sets measure the high-dimensional quantum states, and according to the measurement result, he can judge the secret size relationship of the two participants. Since Colbeck demonstrated that a secret comparison method involving only two parties is not possible to be absolutely secure [8] All secret comparison methods introduce a third party (which may be semi-honest or completely dishonest). The semi-honest third party (STP) means that he willThe program is executed faithfully and strictly, and no secret leakage is caused by the fact that the program is hooked with anyone, but the secret of each participant is particularly curious, and the secret of each participant is tried to be deduced from the mastered information. In 2013, lin et al also proposed a new QPCS method based on the high-Viebel state [9] . Based on the high-dimensional quantum state, a plurality of novel QPCS methods are also proposed in the year [10-12] . However, the above mentioned method can only compare the sizes of the two-party secrets. Fortunately, based on the high-dimensional maximum entanglement state, luo et al quickly designed the first multi-party QPCS method [13] . In this method STP prepares, 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. The STP can obtain the size relationship of the individual participant secrets by calculation without knowing the individual participant secrets. In 2018, two multipartite QPCS methods were also designed based on Gao Weishan particle states, ye, etc [14] . From this point on, the multiparty QPCS approach is getting more and more attention [15-17] 。
In 2007, boyer et al proposed a semi-quantum model that demonstrated that quantum communication could also be unconditionally secure with as little quantum resources and quantum operations as possible [18,19] . In a half quantum model, a quantum party usually has complete quantum capability, and can prepare and control quantum states, while a classical party has no quantum capability or only limited quantum capability, and can only complete a classical or limited quantum operation. Thus, quantum communication is no longer limited to advanced quantum laboratories and between quantum parties with full quantum operation capability. That is, classical participants without quantum devices can also communicate quantum-securely with quantum third parties anywhere via quantum channels with the help of quantum third parties. In recent years, many half-quantum secret comparison methods have been proposed due to the versatility and practicality of half-quantum models. However, early half-quantum secret comparison methods can only compare whether the secrets of two parties are equal [20-24] . Until 2021, the first half-quantum secret was proposed based on the d-Viebel state, peri-alikeSize comparison method (SQPCS), however, this method only involves two parties [25] .2022, luo et al have also proposed a novel two-way SQPCS method based on the high Viebel state [26] . In the same year, based on high-dimensional quantum state, wang et al and Li et al respectively propose a new two-side SQPCS method [27,28] 。
As described above, all quantum and half quantum methods capable of comparing secret sizes use a high-dimensional quantum state as a signal source. However, it is very difficult to prepare, transport, and measure high-dimensional quantum states in the laboratory. Therefore, this severely restricts the practical use of this type of technical approach.
Reference to the literature
[1]Yao,A.C.:Protocols for secure computations.In:Proceedings of 23rd IEEE Symposium on Foundations of Computer Science(SFCS’08),Washington,DC,USA,pp.160164(1982)
[2]Naseri,M.:Secure quantum sealed-bid auction.Opt.Commun.,282(9),193943(2009)
[3]He,L.B.,Huang,L.S.,Yang,W.,Xu,R.,Han,D.Q.:Cryptanalysis and melioration of secure quantum sealed-bid auction with post-confirmation.Quantum Inf.Process.,11(6),135969(2012)
[4]Chen,X.B.,Xu,G.,Yang,Y.X.,Wen,Q.Y.:An Efficient Protocol for the Secure Multi-party Quantum Summation.Int.J.Theor.Phys.,49(11),2793-804(2010)
[5]Hillery,M.,Ziman,M.,Buzek,V.,Bielikova,M.:Towards quantum-based privacy and voting.Phys.Lett.A,349(1),75-81(2006)
[6]Bonanome,M.,Buzek,V.,Hillery,M.,Ziman,M.:Toward protocols for quantum ensured privacy and secure voting.Phys.Rev.A,84(2),022331(2011)
[7]Jia,H.Y.,Wen,Q.Y.,Song,T.T.,Gao,F.:Quantum protocol for millionaire problem.Opt.Commun.,284(1),545-549(2011)
[8]Colbeck,R.:Impossibility of secure two-party classical computation.Phys.Rev.A,76(6),062308(2007)
[9]Lin,S.,Sun,Y.,Liu,X.,Yao,Z.:Quantum private comparison protocol with d-dimensional Bell states.Quantum Inf.Process.,12(1),559-568(2013)
[10]Guo,F.Z.,Gao,F.,Qin,S.J.,Zhang,J.,Wen,Q.Y.:Quantum private comparison protocol based on entanglement swapping of d-level Bell states.Quantum Inf.Process.,12(8),2793-2802(2013)
[11]Zhang,W.W.,Li,D.,Zhang,K.J.,Zuo,H.J.:A quantum protocol for millionaire problem with Bell states.Quantum Inf.Process.,12(6),2241-2249(2013)
[12]Yu,C.H.,Guo,G.D.,Lin,S.:Quantum private comparison with d-level single-particle states.Phys.Scr.,88(6),065013(2013)
[13]Luo,Q.B.,Yang,G.W.,She,K.,Niu,W.N.,Wang,Y.Q.:Multi-party quantum privacy comparison protocol based on d-dimensional entangled states.Quantum Inf.Process.,13(10),2343-2352(2014)
[14]Ye,C.Q,Ye,T.Y.:Multi-party quantum private comparison of size relation with d-level single-particle states.Quantum Inf.Process.,17,252(2018)
[15]Cao,H.,Ma,W.P.,Lu,L.D.,He,Y.F.,Liu,G.:Multi-party quantum privacy comparison of size based on d-level GHZ states.Quantum Inf.Process.,18(9),287(2019)
[16]Wang B,Gong L.H.,Liu S.Q.:Multi-party quantum private size comparison protocol with d-dimensional Bell states.Front.Phys.,10:981376(2022)
[17]Lian,J.Y.,Li,X.,Ye,T.Y.:Multi-party quantum private comparison of size relation with two third parties based on d-dimensional Bell states.Phys.Scr.,98.035011(2023)
[18]Boyer,M.,Kenigsberg,D.,Mor,T.:Quantum key distribution with classical Bob.Phys.Rev.Lett.,99(14),140501(2007)
[19]Boyer,M.,Gelles,R.,Kenigsberg,D.,Mor,T.:Semi-quantum key distribution.Phys.Rev.A,79(3),032341(2009)
[20]Chou,W.H.,Hwang,T.,Gu,J.:Semi-quantum private comparison protocol under an almost-dishonest third party.https://arxiv.org/abs/1607.07961(2016)
[21]Thapliyala,K.,Sharma,R.D.,Pathak,A.:Orthogonal-state-based and semi-quantum protocols for quantum private comparison in noisy environment.Int.J.Quantum Inf.,16(5),1850047(2018)
[22]Ye,T.Y.,Ye,C.Q.:Measure-resend semi-quantum private comparison without entanglement.Int.J.Theor.Phys.,57(12),3819-3834(2018)
[23]Lin,P.H.,Hwang,T.,Tsai,C.W.:Efficient semi-quantum private comparison using single photons.Quantum Inf.Process.,18(7),1-14(2019)
[24]Jiang,L.Z.:Semi-quantum private comparison based on Bell states.Quantum Inf.Process.,19(6),1-21(2020)
[25]Zhou,N.R.,Xu,Q.D.,Du N.S.,Gong L.H.:Semi-quantum private comparison protocol of size relation with d-dimensional Bell states.Quantum Inf.Process.,20,124(2021)
[26]Luo,Q.B.,Li,X.Y.,Yang,G.W.,Lin,C.:A mediated semi-quantum protocol for millionaire problem based on high-dimensional Bell states.Quantum Inf.Process.,21,257(2022)
[27]Li,Y.C.,Chen,Z.Y.,Xu,Q.D.,Gong,L.H.:Two Semi-Quantum Private Comparison Protocols of Size Relation Based on Single Particles.Int.J.Theor.Phys.,61,157(2022)
[28]Wang,B.,Liu,S.Q.,Gong,L.H.:Semi-quantum private comparison protocol of size relation with d-dimensional GHZ states.Chin.Phys.B.31,010302(2022)
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a multipartite half-quantum secret size comparison method based on a two-dimensional Bayer state, and the problem that the traditional quantum secret comparison method is difficult to be put into practical use is solved by designing a novel calculation method and comparing the secret sizes only based on the two-dimensional Bayer state.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a multipartite half-quantum secret size comparison method based on a two-dimensional Bayer state comprises the following steps:
step 1, before formal communication, the participants encrypt respective secret information;
step 2, STP preparation of N (L+1) bivilbeol states, and combining these Bell states into particle sequence A n Send to P n ；
Step 3, when P n Receiving particlesAfter that, P n Will be based on the encrypted information->For particles->Doing the corresponding operation if->Is 0, particle->Will be returned directly without any other action; otherwise, P n Will be about the particle>Performing a Brillouin operation, and returning particles through the quantum reverse channel;
step 4, when determining STP receives the particlesAfter that, P n Will announce the particle->Is performed according to the operation of (1); if P n Directly return to the particle, STP will give the particle +.>And->Performing Bell measurement, and judging whether eavesdropping behaviors exist in the output sub-channel according to a measurement result STP; in case of eavesdropping, the STP will give up this communication, otherwise the STP will record +>If P n For particles->By performing a certain Brix operation, STP will also be directed to the particles +.>And->Making Bell measurements and then repeating the above process for security detection, if no eavesdropping is performed, STP will record +.>When particle sequence A n After all particles are operated, STP will obtain a dataAnd further calculate C n ；
Step 5, after STP processes the particles in all the particle sequences, STP will obtain N data strings C 1 ,C 2 ,...,C N By sorting and comparing C 1 ,C 2 ,...,C N STP may obtain the individual participant secret p 1 ,p 2 ,...,p N Magnitude relation between the two.
Further, in step 1, the participants encrypt the respective secret information, and the encryption process is as follows:
first P n By the formula
Obtaining a data stringOr->
Then according to the formula
Completing binary logic operation to obtain a data string
In the formula (1), "+" is a binary addition operation with carry: if c n ≥c n′ Can be given by p n ≥p n′ Where n+.n'; if the data string c n Only L bit, P n Will be at c n Is preceded by a zero so that all c n Can be expressed asIn the formula (2), ∈>Is a logical operator.
Further, the STP in step 2 prepares N (L+1) bivilbeol states and combines these bell states into a particle sequenceSend to P n The specific process is as follows:
STP preparation of N (L+1) two-Viebel states:
wherein A and B represent respectively a first and a second particle in Bell states; STP combines these bell states into 2N particle sequences, where the particle sequence b= [ B ] 1 ,B 2 ,...B N ]The second particle containing all Bell states, and the particle sequence A= [ A ] 1 ,A 2 ,...A N ]Contains the first particle of all Bell states, anFinally STP will sequence A n Send to P n 。
Further, the STP in step 4 will obtain a dataAnd further calculate +.>The specific calculation process is as follows:
from F n ＝f n (4)
STP will be calculated by the following formula
By combining the formulas (2) and (4), it is possible to further obtain
Further, step 5 is performed by sorting and comparing C 1 ,C 2 ,...,C N STP may obtain the individual participant secret p 1 ,p 2 ,...,p N The size relation among the two is as follows:
STP processing of all particle sequencesAfter the particles, N data strings C are obtained 1 ,C 2 ,...,C N The method comprises the steps of carrying out a first treatment on the surface of the Available according to equations (1) and (6), if C n C is greater than or equal to C n′ Then p is n P is not less than n′ Where n+.n'; thus STP only compares C n And C n′ The magnitude relation of (2) can be obtained n And p is as follows n′ Is a size relationship of (2); STP takes out the same bits in all data strings for comparison and calculates by the following formula
If it isAnd->Is equal to the value of +.>Otherwise->Thus (2)
If it isDescription->And->One of the values of (2) is 0 and the other is 1;
STP can be further determined by the formula (9) and the formula (10)Whether a large number or a small number;
STP can then determine by equation (11)And->Is defined by the relation of the magnitudes of the (c) and (d),
finally, according to the above formula, STP can sort out C 1 ,C 2 ,...,C N To obtain the secret p of each participant 1 ,p 2 ,...,p N Magnitude relation between the two.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention designs a brand new algorithm, so that the technical method can complete secret size comparison based on the two-dimensional Bayer state, and compared with the traditional QPCS and SQPCS methods, the method is easier to realize under the existing quantum technical condition;
2. based on the half quantum theory capable of saving quantum cost, the method can compare secrets of multiple participants at a time, and has more applicability and universality;
3. the quantum communication process of the method is simulated on an IBM quantum platform, and the feasibility and effectiveness of the method are proved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a multipartite half-quantum secret size comparison method based on the two-dimensional Bayer state of the invention;
FIG. 2 is a graph of quantum circuits (left) and analog output results (right) without eavesdropping in an embodiment of the present invention;
FIG. 3 is a quantum circuit diagram (left) and analog output (right) with intercept-measure-retransmit attack in an embodiment of the present invention;
FIG. 4 is a graph of a quantum circuit (left) and analog output (right) for a Puali-X gate operation on a particle in an embodiment of the invention;
FIG. 5 is a quantum circuit diagram (left) and analog output result (right) of an intercept-repeat attack in an embodiment of the present invention;
FIG. 6 is a graph of a quantum circuit (left) and analog output (right) for a Puali-Y gate operation on a particle in an embodiment of the invention;
FIG. 7 is a graph of quantum circuits (left) and analog output (right) for Puali-Z gate operations on particles in an embodiment of the invention.
Detailed Description
For the purpose of promoting an understanding of the principles and advantages of the invention, reference will now be made in detail to specific examples, some but not all of which are illustrated in the accompanying drawings. All other embodiments, which can be made by one of ordinary skill in the art without inventive faculty, are intended to be within the scope of the present invention, based on the embodiments of the present invention.
Basic introduction:
1. two-dimensional bell state
The biverall state is the most common quantum entangled state, commonly used to describe the four largest entangled states in a two-particle system, expressed as:
experimentally, there are a number of ways in which the above bell state can be obtained. For example: when the laser is directed into an optical system consisting of BBO nonlinear crystals, a pair of entangled photons are generated.
2. Semi-quantum model
In this embodiment, STP can prepare and send the biveraber state, complete the biveraber measurement, and perform simple binary logic operation, while classical participants only need to complete the following restricted operations:
(i) The particles are directly returned through the quantum reverse channel, and no other operation is performed;
(ii) A brix gate operation is performed on the particles, which are then returned through the quantum reverse channel.
3. Preparation before communication
Assuming N classical participants, they are P 1 ,P 2 ,...P N Each participant has a secretWherein n.epsilon. {1,2,..N }, }>L e {1,2,., L }; if p is n Is less than L, P n Will be preceded by a sufficient zero, a string of keys k=k being shared in advance between the participants L ...K 2 K 1 Wherein K is l E {0,1}; in addition, STP and P n A string of keys is also shared in advance +.>Wherein->
Example 1
As shown in fig. 1, the invention provides a multipartite half-quantum secret size comparison method based on a bivbel state, which comprises the following steps:
step 1, before formal communication, the participants encrypt respective secret information;
step 2, STP preparation of N (L+1) bivilbeol states, and combining these Bell states into particlesSend to P n ；
Step 3, when P n Receiving particlesAfter that, P n Will be based on the encrypted information->For particles->Doing the corresponding operation if->Is 0, particle->Will be returned directly without any other action; otherwise, P n Will be about the particle>A brix gate operation was performed and then particles were returned through the quantum reverse channel, as shown in table 1 below;
table 1 participant pair particlesOperation table
Step 4, when determining STP receives the particlesAfter that, P n Will announce the particle->Is performed according to the operation of (1); if P n Directly return to the particle, STP will give the particle +.>And->Performing Bell measurement, and judging whether eavesdropping behaviors exist in the output sub-channel according to a measurement result STP; in case of eavesdropping, the STP will give up this communication, otherwise the STP will record +>If P n For particles->With a certain Brix operation, STP will also be given to the particles +>And->Making Bell measurements and then repeating the above process for security detection, if no eavesdropping is performed, STP will record +.>When particle sequence A n After all particles are operated, STP will obtain a dataAnd further calculate C n ；
Step 5, after STP processes the particles in all the particle sequences, STP will obtain N data strings C 1 ,C 2 ,...,C N By sorting and comparing C 1 ,C 2 ,...,C N STP may obtain the individual participant secret p 1 ,p 2 ,...,p N Magnitude relation between the two.
Further, in step 1, the participants encrypt the respective secret information, and the encryption process is as follows:
first P n By the formula
Obtaining a data stringOr->
Then according to the formula
Completing binary logic operation to obtain a data string
In the formula (1), "+" is a binary addition operation with carry: if c n ≥c n′ Can be given by p n ≥p n′ Where n+.n'; if the data string c n Only L bit, P n Will be at c n Is preceded by a zero so that all c n Can be expressed asIn the formula (2), ∈>Is a logical operator.
Further, the STP in step 2 prepares N (L+1) bivilbeol states and combines these bell states into a particle sequence A n Send to P n The specific process is as follows:
STP preparation of N (L+1) two-Viebel states:
wherein A and B represent respectively a first and a second particle in Bell states; STP combines these bell states into 2N particle sequences, where the particle sequence b= [ B ] 1 ,B 2 ,...B N ]The second particle containing all Bell states, and the particle sequence A= [ A ] 1 ,A 2 ,...A N ]Contains the first particle of all Bell states, anFinally STP will sequence A n Send to P n 。
Further, the STP in step 4 will obtain a dataAnd further calculate +.>The specific calculation process is as follows:
from F n ＝f n (4)
STP will be calculated by the following formula
By combining the formulas (2) and (4), it is possible to further obtain
Further, step 5 is performed by sorting and comparing C 1 ,C 2 ,...,C N STP may obtain the individual participant secret p 1 ,p 2 ,...,p N The size relation among the two is as follows:
after STP processing the particles in all the particle sequences, N data strings C are obtained 1 ,C 2 ,...,C N The method comprises the steps of carrying out a first treatment on the surface of the Available according to equations (1) and (6), if C n C is greater than or equal to C n′ Then p is n P is not less than n′ Where n+.n'; thus STP only compares C n And C n′ The magnitude relation of (2) can be obtained n And p is as follows n′ Is a size relationship of (2); STP takes out the same bits in all data strings for comparison and calculates by the following formula
If it isAnd->Is equal to the value of +.>Otherwise->Thus (2)
If it isDescription->And->One of the values of (2) is 0 and the other is 1;
STP can be further determined by the formula (9) and the formula (10)Whether a large number or a small number;
STP can then determine by equation (11)And->Is defined by the relation of the magnitudes of the (c) and (d),
finally, according to the above formula, STP can sort out C 1 ,C 2 ,...,C N To obtain the secret p of each participant 1 ,p 2 ,...,p N Magnitude relation between the two.
Example 2
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 an IBM quantum platform in this example.
1. Before simulation, several quantum gate operations to be used in the present embodiment are first given:
four types of Pauli gate operations are available,
when P n For particlesAfter a Pauli gate operation, the entire Bell state will become:
the Hadamard gate and CONT gate operations are respectively:
on IBM quantum platforms, the bell state in the circuit can be generated by Hadamard gates and CONT gates:
the bell state measurement in the circuit can be accomplished by Hadamard gates and CONT gates:
2. simulation process
According to P n For particlesIn this embodiment, the simulation is performed in two cases.
2.1.P n For particlesCompletion of operation (i)
Assuming that the Bell state prepared by STP isThe quantum circuit is shown in fig. 2 (left). If there is no eavesdropping in the quantum channel, the measurement must be 00, as shown in fig. 2 (right), as can be obtained from equation (20). When the analog output result is not 00, then the eavesdropping behavior is shown to exist in the quantum channel. For example, an eavesdropper Eve intercepts and measures the particle +.>Then return a new and particle +.>Particles with the same measurement (blocking-measurement-retransmission attack). For example STP vs particle->Is 1 according to ∈>Particle->Will collapse to 1. Thus, STP will return a new particle whose measurement is 1. The quantum circuit diagram and the simulation output result are shown in fig. 3. It is apparent that in the presence of eavesdropping, the analog output is not 00. Therefore, based on the analog output result, STP can determine whether eavesdropping exists in the output subchannel.
2.2.P n For particlesCompletion of operation (ii)
(1) When STP is prepared byAnd P is n For particles->The quantum circuit is shown in FIG. 4 (left) for Pauli-X gate operation. If there is no eavesdropping in the quantum channel, the measurement result must be 11 as shown in fig. 4 (right), as shown in equations (13) and (23). If the analog output result is not 11, then it indicates that there is certain eavesdropping behavior in the quantum channel. For example: eavesdropper Eve intercepts particles->And sends a new particle to STP (intercept-retransmit attack). The quantum circuit and analog output results are shown in fig. 5. From the figure, simulation results 00, 01, 10, 11 all appear with a probability of about 25%.
(2) When STP is prepared into |psi + > AB And P is n For particlesThe Pauli-Y gate operation is performed, the quantum circuit is shown on the left side of FIG. 6, and the corresponding output is 10, as shown on the right side of FIG. 6, which corresponds to the theoretical derivation of equations (15) and (22), i.e., the analog output verifies the theoretical derivation of the equations.
(3) When STP is prepared into |psi - > AB And P is n For particlesThe Pauli-Z gate operation is performed, the quantum circuit is shown on the left side of FIG. 7, the corresponding output result is 01, and as shown on the right side of FIG. 7, the result accords with the theoretical deduction result of formulas (16) and (23), namely the analog output verifies the theoretical deduction of the formulas.
From the above, it can be seen that the simulation output result and the theoretical derivation mutually verify, which indicates the feasibility and effectiveness of the method.
Example 3
In order to verify the security of the method of the present invention, the impact of both internal and external attacks on the method will be analyzed in detail in this embodiment. The problem of quantum channel loss is temporarily not considered in the communication process in this embodiment.
1. External attack
An external attacker Eve will launch a variety of attacks on the quantum channel in order to be able to obtain information about the secret. Such as intercept-repeat attacks, intercept-measure-repeat attacks, entanglement attacks. It can be seen from the simulation procedure in example 2 that both the intercept-retransmit and intercept-measure-retransmit attacks are ineffective for this approach.
Thus, the impact of entanglement attacks on the method of the present invention will be analyzed in detail in this embodiment.
Entanglement attack means Eve applying a unitary transformation U to particles in a quantum channel E So that the entangled state |E is assisted>Attached to the particles.
In the above, the pure auxiliary state |ε lk >Heel U only E Related, andwhen Eve is->When entanglement attack is implemented:
U E |0>|E>＝a 00 |0>|ε 00 >+a 10 |1>|ε 10 > (25)
U E |1>|E>＝a 01 |0>|ε 01 >+a 11 |1>|ε 11 > (26)
the entire initial bell state becomes
And once the state of the initial bell state changes, the result of the bell measurement will change accordingly. Therefore Eve has to set a in order not to be detected by STP 10 ＝a 01 =0 and a 00 |ε 00 >＝a 11 |ε 11 >。
Based on this, formulas (27) and (28) will become
It is known from formulas (29) and (30) that if it is not desired to be found, the entanglement attack by Eve has no effect on the method of the invention, i.e. the entanglement attack by Eve does not get any secret related information.
2. Internal attack,
2.1 dishonest P n Attack of (a)
Dishonest P n Some useful information can only be obtained in two ways:
(a)P n attack is initiated on the quantum channel;
(b)P n the secrets of the participants are derived from the known information.
In case (a), P n Will be detected as an external attacker. As described above, an external attacker cannot obtain any useful information.
In case (b), because of P n The shared secret between the other participants and the STP is not known, so he cannot decrypt the known information and derive the secrets of the participants.
2.2 dishonest STP attack
The semi-honest third party STP will strictly perform the steps of the present invention. Therefore, he will not prepare other quantum states (such as GHZ state or single particle state) to replace the Bell state required in the method to cause information leakage, and will not get hooked with other stealers in order to steal secret information. However he is very curious about the secrets of the participants, trying to derive the secrets of the participants from the known information.
STP is unaware of sharing the key k=k between the participants L ...K 2 K 1 He cannot derive the secrets of the participants from his own existing information. Thus, STP attacks on the method of the present invention are also ineffective.
In conclusion, the invention designs a novel multipartite half-quantum secret size comparison method based on the two-dimensional Bessel state; in the method, STP is a full quantum formula, and can prepare, send and measure the two-dimensional Bessel state, and a classical participant only needs to randomly return particles or do a British gate operation on the particles; after the bell measurement, the STP can judge whether eavesdropping exists in the communication process. If there is eavesdropping, the STP will relinquish the communication, otherwise proceed to the next operation. After security detection and binary logic operation, STP can obtain the secret size relation of each participant. In order to prove the correctness of the method, the present embodiment lists a number of examples in table 2 below.
Table 2 illustrates the correctness of the method of the invention
Furthermore, to demonstrate the feasibility and effectiveness of the method of the present invention, the inventors simulated the entire communication process of the method on an IBM quantum platform. At the same time, security analysis shows that the invention can resist internal and external attacks without revealing the secret of each participant. Compared with the existing quantum or semi-quantum secret size comparison method, the method only takes a two-dimensional quantum state as a signal source. The method is easier to realize under the existing quantum technology condition; finally, based on a half quantum model capable of saving quantum resources, the method can compare secrets of multiple participants at one time, and has more flexibility and universality.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (6)

1. The multipartite half-quantum secret size comparison method based on the two-dimensional Bayer state is characterized by comprising the following steps of:
step 1, before formal communication, the participants encrypt respective secret information;
step 2, preparing N (L+1) biville states by using a semi-honest quantum third party STP, and combining the biville states to form a particle sequence A n To the participant P n ；
Step 3, when P n Receiving particlesAfter that, P n Will be based on the encrypted information->For particles->Doing the corresponding operation ifIs 0, particle->Will be returned directly without any other action; otherwise, P n Will be about the particle>Performing a Brillouin operation, and returning particles through the quantum reverse channel;
step 4, when determining STP receives the particlesAfter that, P n Will announce the particle->Is performed according to the operation of (1); if P n Directly return to the particle, STP will give the particle +.>And->Performing Bell measurement, and judging whether eavesdropping behaviors exist in the output sub-channel according to a measurement result STP; in case of eavesdropping, the STP will give up this communication, otherwise the STP will record +>If P n For particles->By performing a certain Brix operation, STP will also be directed to the particles +.>And->Making Bell measurements and then repeating the above process for security detection, if no eavesdropping is performed, STP will record +.>When particle sequence A n After all particles are operated, STP will obtain a dataAnd further calculate C n ；
Step 5, after STP processes the particles in all the particle sequences, STP will obtain N data strings C 1 ,C 2 ,...,C N By sorting and comparing C 1 ,C 2 ,...,C N STP may obtain the individual participant secret p 1 ,p 2 ,...,p N Magnitude relation between the two.
2. The multi-party semi-quantum secret size comparison method based on the two-dimensional bell state according to claim 1, wherein the participants encrypt the respective secret information in the step 1, and the encryption process is as follows:
first P n By the formula
Obtaining a data stringOr->
Then according to the formula
Completing binary logic operation to obtain encrypted data string
3. The multi-party half-quantum secret size comparison method based on the two-dimensional bell state according to claim 2, wherein in the formula (1), "+" is a binary addition operation with carry: if c n ≥c n′ Can be given by p n ≥p n′ Where n+.n'; if the data string c n Only L bit, P n Will be at c n Is preceded by a zero so that all c n Can be expressed asIn the formula (2), ∈>Is a logical operator.
4. The method for comparing the sizes of multi-party half-quantum secrets based on the biville states according to claim 1, wherein the STP in step 2 prepares N (l+1) biville states and combines the bells to form a particle sequence a n Send to P n The specific process is as follows:
STP preparation of N (L+1) two-Viebel states:
wherein A and B represent respectively a first and a second particle in Bell states; STP combines these bell states into 2N particle sequences, where the particle sequence b= [ B ] 1 ,B 2 ,...B N ]The second particle containing all Bell states, and the particle sequence A= [ A ] 1 ,A 2 ,...A N ]Contains the first particle of all Bell states, anFinally STP will sequence A n Send to P n 。
5. The method of claim 1, wherein the STP in step 4 obtains a dataAnd further calculate +.>The specific calculation process is as follows:
from F n ＝f n (4) STP will be calculated by the following formula
By combining the formulas (2) and (4), it is possible to further obtain
6. The method for comparing the sizes of multiparty half-quantum secrets based on the two-dimensional bell state according to claim 1, wherein the step 5 is characterized by arranging and comparing C 1 ,C 2 ,...,C N STP may obtain the individual participant secret p 1 ,p 2 ,...,p N The size relation among the two is as follows:
after STP processing the particles in all the particle sequences, N data strings C are obtained 1 ,C 2 ,...,C N The method comprises the steps of carrying out a first treatment on the surface of the Available according to equations (1) and (6), if C n C is greater than or equal to C n′ Then p is n P is not less than n′ Where n+.n'; thus STP only compares C n And C n′ The magnitude relation of (2) can be obtained n And p is as follows n′ Is a size relationship of (2); STP takes out the same bits in all data strings for comparison and calculates by the following formula
If it isAnd->Is equal to the value of +.>Otherwise->Thus (2)
If it isDescription->And->One of the values of (2) is 0 and the other is 1;
STP can be further determined by the formula (9) and the formula (10)Whether a large number or a small number;
STP can then determine by equation (11)And->Is defined by the relation of the magnitudes of the (c) and (d),
finally, according to the above formula, STP can sort out C 1 ,C 2 ,...,C N To obtain the secret p of each participant 1 ,p 2 ,...,p N Magnitude relation between the two.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116996218A (en) * 2023-09-26 2023-11-03 山东高速建设管理集团有限公司 Semi-quantum secure multipartite summation method based on high-dimensional entangled state and single-particle state

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116996218A (en) * 2023-09-26 2023-11-03 山东高速建设管理集团有限公司 Semi-quantum secure multipartite summation method based on high-dimensional entangled state and single-particle state
CN116996218B (en) * 2023-09-26 2023-12-05 山东高速建设管理集团有限公司 Semi-quantum secure multipartite summation method based on high-dimensional entangled state and single-particle state

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