CN105915335A - Multi-party quantum private comparison method based on Bell state entanglement swapping - Google Patents

Multi-party quantum private comparison method based on Bell state entanglement swapping Download PDF

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CN105915335A
CN105915335A CN201610307854.3A CN201610307854A CN105915335A CN 105915335 A CN105915335 A CN 105915335A CN 201610307854 A CN201610307854 A CN 201610307854A CN 105915335 A CN105915335 A CN 105915335A
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CN105915335B (en
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叶天语
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Jiaxing shunkailu Technology Co.,Ltd.
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Zhejiang Gongshang 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
    • H04L9/0852—Quantum cryptography

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  • Optical Modulation, Optical Deflection, Nonlinear Optics, Optical Demodulation, Optical Logic Elements (AREA)

Abstract

The invention provides a multi-party quantum private comparison method based on Bell state entanglement swapping, which utilizes Bell state entanglement swapping to realize equality comparison on secrets of K different users. The method can realize equality comparison on secrets of any two parties among the K different users through once execution. A third party can know a comparison result of secrets of each two users but can not know true values. Each user can not know true values of secrets of other K-1 users.

Description

Quantum privacy comparative approach in many ways based on Bell state entanglement transfer
Technical field
The present invention relates to field of quantum security communication.The present invention designs a kind of quantum in many ways based on Bell state entanglement transfer Privacy comparative approach, the equality utilizing the entanglement transfer of Bell state to realize K different user secret compares.
Background technology
Multi-party computations (the Secure Multi-party that Yao A C [1] introduces first in millionaires' problem Computation, SMPC), it is a basic and important topic in classical cryptoraphy.Millionaires' problem at Yao A C In, two millionaires wish to know that who is more rich on the premise of not being leaked to each other by the exact amount of property.Then, Boudot F etc. [2] construct an equality comparative approach and judge that two millionaires are the most equal rich.SMPC can quilt Be applied to many occasions, such as concealed bid and auction, elect by secret ballot, ecommerce, data mining etc..
As a kind of special SMPC, classical privacy compares the mesh of (Classical Private Comparison, CPC) It is marked on the secret in the different both sides of judgement the most equal and do not reveal their actual value.Along with the development of quantum techniques, CPC is Produce quantum privacy compare (Quantum Private Comparison, QPC) through being generalized to quantum regime, the latter's Safety is based on principle of quantum mechanics rather than computational complexity.But, Lo H K [3] points out, under both sides' situation, and equality Function cannot be weighed safely.This situation be accomplished by some extra it is assumed that such as one third party (Third Party, TP)。
First QPC method by [4] such as Yang Y G by utilizing Einstein-Podolsky-Rosen (EPR) right Help with a TP designs.The safety of this method is based on one-way Hash function.Specifically, two users Secret encrypted by one-way Hash function after, they are coded into EPR pair by operation at local tenth of the twelve Earthly Branches.The same year, based on single photon QPC method is designed by [5] such as Yang Y G.In this approach, the secret two users is added by one-way Hash function After close, they are coded into single photon by operation at the tenth of the twelve Earthly Branches.In 2010, based on Greenberger-Horne-Zeilinger (GHZ) the QPC method of state is designed by [6] such as Chen X B, and the secret of two of which user is by by original GHZ state Particle carries out single-particle and measures the one time key encryption produced.In this approach, TP needs to perform operation at the tenth of the twelve Earthly Branches.2012 Year, a novel QPC method based on ERP pair is built by [7] such as Tseng H Y, wherein for two users of encryption Secret one time key result from the particle to original EPR pair and carry out single-particle measurement.Fortunately, this method was both Need not operation at the tenth of the twelve Earthly Branches and need not again one-way Hash function.In 2012, QPC method based on Bell state entanglement transfer was by Liu W Proposing Deng [8], wherein the secret one time key for two users of encryption is by original Bell state entanglement transfer The Bell state of rear generation carries out Bell base measurement and obtains.And, this method need not operation at the tenth of the twelve Earthly Branches.But, Liu W J etc. [9] Pointing out in the method for document [8], TP can measure to attack extract the secret of two users and the most tested by initiating Bell base Measure, and propose an improved method to make up this leak.So far, in addition to method mentioned above, many other Both sides' QPC method [10-34] are the most by utilizing different quantum states and quantum techniques to be devised.
About the role of TP, Chen X B etc. [6] is firstly introduced into half loyal model.It is to say, TP loyally performs whole Individual process, records all of intermediate calculation data but can attempt under the constraint that can not be included disloyal user's corrosion by opponent The secret of users is obtained from record.But, Yang Y G etc. [12] points out that this half loyal TP model is irrational, and Think that rational model should be as follows: TP can not be included disloyal user corrosion by opponent but be allowed to according to oneself Idea makes improper activity.It is true that so far, this hypothesis of TP is the most rational.
Assuming to there is K side, everyone has a secret.They wonder their K secret the most equal and not by Reveal.If two side's QPC methods are used for solving this equality comparison problem in many ways, two same side's QPC methods are had to It is performed (n-1) n (n-1)/2 time so that efficiency is not high enough.In 2013, Chang Y J etc. [35] utilized n particle GHZ class State proposition first quantum privacy in many ways compares (Multi-party Quantum Private Comparison, MQPC) side Method, can be achieved with the equality that in K user, any two sides are secret compare as long as being executed once.Subsequently, based on d Wiki state With the MQPC method [36] of Quantum fourier transform, MQPC method based on n level Entangled State and Quantum fourier transform [37] quilt Design.But, up to now, the most little several MQPC methods exist.
Analyzing based on above, the present invention proposes a kind of quantum privacy comparative approach in many ways based on Bell state entanglement transfer, The equality that the entanglement transfer utilizing Bell state realizes K different user secret compares.As long as the method is executed once with regard to energy Realize the equality that in K user, any two sides are secret to compare.Third party can know that the secret comparative result of each two user but Their actual value cannot be known.Each user cannot know the secret actual value of other K-1 user.
List of references
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Summary of the invention
It is an object of the invention to design a kind of quantum privacy comparative approach in many ways based on Bell state entanglement transfer, utilize The equality that the entanglement transfer of Bell state realizes K different user secret compares.
A kind of quantum privacy comparative approach in many ways based on Bell state entanglement transfer, includes following two process altogether:
S1) preparatory stage: (1) is similar with the QPC method of document [4-5], K user, P1、P2、...、PK, share in advance One secret one-way Hash function H.XiCryptographic Hash beI=1,2 ..., K.Pi By hisBinary representation be divided intoGroupThe most often group comprises two two and enters Bit processed.If N is mod 2=1, one 0 should be by PiIt is added to(2)PiPrepared by/TPIndividual all inQuantum state.Then, Pi/ TP picks out first particle from each quantum state and forms an ordered sequenceRemaining second particle of each quantum state automatically forms another ordered sequence(3) examine for safety Survey, P1/ TP prepares one again by all in | Φ+> the individual quantum state of L ' constitute sequence, be designated asThen P1/TP Respectively willIn first of each Bell state and second particle be inserted inWithIdentical bits Put.Correspondingly, P1/ TP obtainsWithThen, P1With TP exchanges between themWithIn order to ensure P1-TP/TP-P1The transmission security of quantum channel,In two differences of each Bell state are interparticle tangles dependency It is used for detecting whether to there is a listener-in.If there is no listener-in, P1Abandon sample particles with TP, and perform next Step.(4) forP1RightIn the every pair of particle apply Bell base measurement and measured knot accordingly ReallyIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenSo, in TP handsThe particle of reply mutually to be caved in be one of four Bell state.This in TP handsThe individual Bell state caved in is remembered For
S2) kth-1 is taken turns and is compared, k=2, and 3,4 ..., K:(1) PkWith TP preparation by all in | Φ+> L ' individual quantum state structure The sequence become is to guaranteeWithThe safety being exchanged.If there is no listener-in, PkAbandon sample particles with TP, and hold Go next step.(2) forPkRightIn the every pair of particle apply Bell base measurement and obtain accordingly Measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenSo, TP hands InThe particle of reply mutually to be caved in be one of four Bell state.TP is the most rightIn every pair of particle Apply Bell base measurement and obtain corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, then(3) forK user's cooperative computation togetherAnd will It is sent to TP.Here, m=1,2 ..., k-1.Pi(i=1,2 ..., m-1, m+1 ... k-2, k-1) and PmRespectively willWithResult be sent to PkFor calculatingThen, TP calculatesWithTP willIt is sent to PmAnd Pk.IfPmAnd PkDraw Xm=Xk；Otherwise, she Know Xm≠Xk。
The present invention proposes a kind of quantum privacy comparative approach in many ways based on Bell state entanglement transfer, utilizes entangling of Bell state Twine exchange to realize the equality of K different user secret and compare.Can be achieved with K user appoints as long as the method is executed once The equality of two sides' secrets of anticipating compares.Third party can know that the comparative result of each two user secret but cannot know the true of them Real-valued.Each user cannot know the secret actual value of other K-1 user.
Accompanying drawing explanation
Fig. 1 is the Bell state entanglement transfer process of four participants.Wherein, figure (a) represents Alice/Bob/Charlie/TP system Standby quantum state is inFigure (b) represents that Alice and TP exchanges their each hands Second particle A of middle Bell state2And T2；Figure (c) represents at Alice particle A1And T2After applying the measurement of Bell base, in TP hands Particle T1And A2Become tied up in knots；Figure (d) represents that TP and Bob exchanges particle A2And B2；Figure (e) represents at Bob particle B1And A2After applying the measurement of Bell base, the particle T in TP hands1And B2Become tied up in knots；Figure (f) represents TP and Charlie Exchange particle B2And C2；Figure (g) represents at Charlie particle C1And B2After applying the measurement of Bell base, the particle T in TP hands1With C2Become tied up in knots.
Detailed description of the invention
Below in conjunction with embodiment, technical scheme is described further.
1, coding rule
Assume have K user, P1、P2、...、PK, wherein PiHave a secret integer Xi, i=1,2 ..., K.Xi?Being represented in binary as of territoryHere,J=0,1 ..., L-1.They wonder The X that with the help of one and half loyal TP, each two is differentiThe most equal.They decide through consultation following rule with TP: | Φ+>、|Φ->、| Ψ+> and | Ψ-> represent two classical bits 00,01,10 and 11 respectively.
2, quantum privacy comparative approach in many ways
The method of the present invention includes following two process altogether:
S1) preparatory stage: (1) is similar with the QPC method of document [4-5], K user, P1、P2、...、PK, share in advance One secret one-way Hash function H.XiCryptographic Hash beI=1,2 ..., K。PiBy hisBinary representation be divided intoGroupThe most often group comprises two Binary bits.If N is mod 2=1, one 0 should be by PiIt is added to(2)PiPrepared by/TPIndividual all inQuantum state.Then, Pi/ TP picks out first particle from each quantum state and forms an ordered sequenceRemaining second particle of each quantum state automatically forms another ordered sequence(3) examine for safety Survey, P1/ TP prepares one again by all in | Φ+> the individual quantum state of L ' constitute sequence, be designated asThen P1/TP Respectively willIn first of each Bell state and second particle be inserted inWithIdentical bits Put.Correspondingly, P1/ TP obtainsWithThen, P1With TP exchanges between themWithIn order to ensure P1-TP/TP-P1The transmission security of quantum channel,In two differences of each Bell state are interparticle tangles dependency It is used for detecting whether to there is a listener-in.If there is no listener-in, P1Abandon sample particles with TP, and perform next Step.(4) forP1RightIn the every pair of particle apply Bell base measurement and measured accordingly ResultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenSo, in TP handsThe particle of reply mutually to be caved in be one of four Bell state.This in TP handsThe individual Bell state caved in is remembered For
S2) kth-1 is taken turns and is compared, k=2, and 3,4 ..., K:(1) PkWith TP preparation by all in | Φ+> L ' individual quantum state structure The sequence become is to guaranteeWithThe safety being exchanged.If there is no listener-in, PkSample particles is abandoned with TP, and Perform next step.(2) forPkRightIn the every pair of particle apply Bell base measurement and obtain phase The measurement result answeredIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenSo, In TP handsThe particle of reply mutually to be caved in be one of four Bell state.TP is the most rightIn every pair of grain Son applies Bell base measurement and obtains corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, that ?(3) forK user's cooperative computation togetherAnd will It is sent to TP.Here, m=1,2 ..., k-1.Pi(i=1,2 ..., m-1, m+1 ... k-2, k-1) and PmRespectively willWithResult be sent to PkFor calculatingThen, TP calculatesWithTP willIt is sent to PmAnd Pk.IfPmAnd PkDraw Xm=Xk；Otherwise, they Know Xm≠Xk。
3, analyze and discuss
1) correctness
About XmAnd Xk(m=1,2 ..., k-1 and k=2,3,4 ..., K) equality compare, k user needs to calculateAnd, TP needs CalculateWithMQPC method according to the present invention Entanglement transfer process, can obtain
Therefore, in the MQPC method of the present invention, XmAnd XkEquality comparative result be correct.
2) safety
Owing to using one-way Hash function that secret is encrypted, it is easy to finding, the MQPC method of the present invention is to external Attack, participant attacks and information leakage problem immunity.
3) with the comparison of previous QPC method
The method [8] of the method [6] of the method [4] of the MQPC method of the present invention and Yang etc., Chen etc., Liu etc. and Relatively being described in table 1 of the method [35] of Chang etc..
Must be it is further noted that in the MQPC method of current MQPC method [35-37] and the present invention, different quantum Method is used for realizing equality and compares.Specifically, the method [35] of Chang etc. utilizes two of a n particle GHZ class state Difference is interparticle tangles dependency；The method [37] of the method [36] of Liu etc. and Wang etc. all uses Quantum fourier transform. But, the method for the present invention employs quantum entanglement exchange.
The MQPC method of table 1. present invention and the contrast of previous QPC method
Embodiment:
1, quantum privacy comparative approach applicating example
Here illustrate as a example by K=3.Alice, Bob and Charlie have three secret integer X, Y and Z respectively, WhereinWithHere, xj, yj, zj∈ { 0,1}.One and half loyal TP's Under help, they wonder that in X, Y and Z, each two is the most equal.Alice, Bob, Charlie and TP decide through consultation following rule: | Φ+>、|Φ->、|Ψ+> and | Ψ-> represent two classical bits 00,01,10 and 11 respectively.They realize by performing following steps The equality of each two secret integer compares.
S1) preparatory stage: (1) is similar with the QPC method of document [4-5], and Alice, Bob and Charlie share one in advance One-way Hash function H of individual secret.The cryptographic Hash of X, Y and Z is respectively WithAlice/Bob/Charlie will S/he/her X#/Y#/Z#Binary representation be divided intoGroup The most often group comprises two binary bits.If N is mod 2=1, one 0 should When being added to by Alice/Bob/Charlie(2) prepared by Alice/Bob/Charlie/TPIndividual Quantum state is in Then, Alice/Bob/Charlie/TP is from each amount Sub-state is picked out first particle to form an ordered sequenceThe residue of each quantum state second Particle automatically forms another ordered sequence(3) for safety detection, Alice/TP prepares one again By all in | Φ+> the individual quantum state of L ' constitute sequence, be designated as DA′/DT′.Then Alice/TP is respectively by DA′/DT′In every First of individual Bell state and second particle are inserted inWithSame position.Correspondingly, Alice/TP obtains ArriveWithThen, Alice and TP exchanges between themWithIn order to ensure Alice-TP/TP- The transmission security of Alice quantum channel, DA′/DT′In each Bell state interparticle dependency that tangles of two differences be used for Detect whether to there is a listener-in.If there is no listener-in, Alice and TP abandons sample particles, and performs next step. (4) forAlice pairIn the every pair of particle apply Bell base measurement and obtain accordingly Measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, then So, TP hands InThe particle of reply mutually to be caved in be one of four Bell state.In TP hands thisThe individual Bell state quilt caved in It is designated as
S2) first round compares: (1) Bob/TP preparation is by all in | Φ+> the individual quantum state of L ' constitute sequence to guaranteeWithThe safety being exchanged.If there is no listener-in, Bob and TP abandons sample particles, and performs next step.(2) ForBob pairIn the every pair of particle apply Bell base measurement and obtain corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenSo, in TP handsThe particle of reply mutually to be caved in be one of four Bell state.TP is the most rightIn the every pair of particle apply Bell Base measurement obtains corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenThis in TP handsThe Bell state caved in is designated as(3) forCooperative computation together with Alice with Bob And willIt is sent to TP.Alice willResult be sent to Bob with calculateThen, TP calculatesWithThen, TP is by RABIt is published to Alice and Bob.If RAB =0, Alice and Bob draw X=Y；Otherwise, they know X ≠ Y.
S3) second take turns and compare: (1) Charlie/TP preparation is by all in | Φ+> the individual quantum state of L ' constitute sequence with GuaranteeWithThe safety being exchanged.If there is no listener-in, Charlie and TP abandons under sample particles, and execution One step.(2) forCharlie pairIn the every pair of particle apply Bell base measurement and obtain Corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenSo, In TP handsThe particle of reply mutually to be caved in be one of four Bell state.TP is the most rightIn every pair of grain Son applies Bell base measurement and obtains corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, that ?(3) forAlice, Bob close together with Charlie CalculateAnd willIt is sent to TP.Alice and Bob divides Will notWithResult be sent to Charlie with calculateThen, TP calculatesWithMeanwhile, for Alice, Bob be cooperative computation together with CharlieAnd willIt is sent to TP.Alice and Bob respectively willResult andIt is sent to Charlie to calculateThen, TP calculatesWithFinally, TP is by RBCBe sent to Bob and Charlie.If RBC=0, Bob and Charlie draw Y=Z；Otherwise, they know Y ≠ Z.On the other hand, TP is by RACSend To Alice and Charlie.If RAC=0, Alice and Charlie draw X=Z；Otherwise, they know X ≠ Z.
For clarity, the Bell state entanglement transfer process between above-mentioned four participants of tripartite's QPC method is depicted in In Fig. 1.
2, analyze and discuss
The most still discuss as a example by above-mentioned tripartite's QPC method.
1) correctness
For above-mentioned tripartite's QPC method, the correctness of a total of three kinds of situations needs to come into question.
(1) the secret equality of Alice and Bob compares
Equality about X and Y compares, Alice and Bob needs to calculate And, TP needs to calculateWithAccording to figure 1, can obtain following evolutionary process:
Therefore, in above-mentioned tripartite's QPC method, the equality comparative result of X and Y is correct.
(2) the secret equality of Bob and Charlie compares
Equality about Y and Z compares, and Alice, Bob and Charlie need to calculate And, TP needs to calculateWithAccording to Fig. 1, following evolutionary process can be obtained:
Therefore, in above-mentioned tripartite's QPC method, the equality comparative result of Y and Z is correct.
(3) the secret equality of Alice and Charlie compares
Equality about X and Z compares, and Alice, Bob and Charlie need to calculate And, TP needs to calculateWithAccording to Fig. 1, following evolutionary process can be obtained:
Therefore, in above-mentioned tripartite's QPC method, the equality comparative result of X and Z is correct.
3, sum up
The present invention proposes a kind of quantum privacy comparative approach in many ways based on Bell state entanglement transfer, utilizes entangling of Bell state Twine exchange to realize the equality of K different user secret and compare.Can be achieved with K user appoints as long as the method is executed once The equality of two sides' secrets of anticipating compares.Third party can know that the comparative result of each two user secret but cannot know the true of them Real-valued.Each user cannot know the secret actual value of other K-1 user.

Claims (1)

1. a quantum privacy comparative approach in many ways based on Bell state entanglement transfer, utilizes the entanglement transfer of Bell state to realize K The equality of individual different user secret compares；Secret equal of any two sides in K user is can be achieved with as long as being executed once Property compares；Third party can know that the comparative result of each two user secret but cannot know their actual value；Each user without Method knows the secret actual value of other K-1 user；Include following two process altogether:
S1) preparatory stage: (1) K user, P1、P2、...、PK, share secret one-way Hash function H in advance；XiKazakhstan Uncommon value is PiBy hisBinary representation be divided intoGroup The most often group comprises two binary bits；If N is mod2=1, one 0 should When by PiIt is added to(2)PiPrepared by/TPIndividual all inQuantum state；Then, Pi/ TP is from often Individual quantum state is picked out first particle and forms an ordered sequenceRemaining second particle of each quantum state is certainly Dynamic another ordered sequence of formation(3) for safety detection, P1/ TP prepares one again by all in | Φ+> L ' The sequence that individual quantum state is constituted, is designated asThen P1/ TP respectively willIn first of each Bell state and Second particle is inserted inWithSame position, correspondingly, P1/ TP obtainsWithThen, P1With TP exchanges between themWithIn order to ensure P1-TP/TP-P1The transmission security of quantum channel,In The interparticle dependency that tangles of two differences of each Bell state is used for detecting whether to there is a listener-in；If there is no stealing Hearer, P1Abandon sample particles with TP, and perform next step；(4) forP1RightIn Every pair of particle applies Bell base measurement and obtains corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, SoSo, in TP handsThe particle of reply mutually to be caved in be one of four Bell state； This in TP handsThe individual Bell state caved in is designated as
S2) kth-1 is taken turns and is compared, k=2, and 3,4 ..., K:(1) PkWith TP preparation by all in | Φ+> the individual quantum state of L ' constitute Sequence is to guaranteeWithThe safety being exchanged；If there is no listener-in, PkAbandon under sample particles, and execution with TP One step；(2) forPkRightIn the every pair of particle apply Bell base measurement and obtain accordingly Measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, thenSo, TP hands InThe particle of reply mutually to be caved in be one of four Bell state；TP is the most rightIn the every pair of particle apply Bell base measurement obtains corresponding measurement resultIfFor | Φ+>/|Φ->/|Ψ+>/|Ψ->, then(3) forK user's cooperative computation togetherAnd will It is sent to TP；Here, m=1,2 ..., k-1；Pi(i=1,2 ..., m-1, m+1 ... k-2, k-1) and PmRespectively willWithResult be sent to PkFor calculatingThen, TP calculates WithTP willIt is sent to PmAnd Pk；IfPmAnd PkDraw Xm=Xk, otherwise, she Know Xm≠Xk。
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