CN108599933A - A kind of two side's quantum information control methods based on bell bases - Google Patents
A kind of two side's quantum information control methods based on bell bases Download PDFInfo
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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
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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
- H04L9/002—Countermeasures against attacks on cryptographic mechanisms
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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
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/0643—Hash functions, e.g. MD5, SHA, HMAC or f9 MAC
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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
- H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
- H04L9/3236—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials using cryptographic hash functions
Abstract
Two side's quantum information control methods based on bell bases that the present invention provides a kind of.The present invention makes the two share a hash function, and calculate separately the cryptographic Hash of respective secret information first when the secret information to Alice and Bob compares;The cryptographic Hash of respective secret information is grouped;Later according to the cryptographic Hash in each group, the secret information of two sides is compared;If the secret information for comparing the two according to the cryptographic Hash in any group differs, then it is assumed that the secret information of two sides differs;If the secret information for comparing the two according to the cryptographic Hash in all groups is equal, then it is assumed that the secret information of two sides is equal.State is inveigled by insertion in comparison process, may detect that with the presence or absence of attacker so that comparison process is safe and reliable.Moreover, the present invention is a kind of efficient quantum secret information control methods, operation is mainly measurement and the rotation process of light particle so that the efficiency of calculating is higher.
Description
Technical field
The present invention relates to field of information security technology, specifically a kind of two side's quantum informations comparison based on bell bases
Method.
Background technology
Multi-party computations are that the theoretical foundation of distributed cryptography and one of Distributed Calculation research ask substantially
Topic.Since Yao Qi intelligence academicians propose the concept of multi-party computations the eighties in last century, which has become modern password
One of important research content.With the birth of quantum algorithm, the safety of the classical password based on computational complexity by
It threatens.The quantum both sides of one of important branch as Secure quantum calculation calculate the pass for also resulting in numerous scholars
Note.There are many two side's quantum calculation agreements of safety of specific use to occur.
Safety two side's quantum informations comparison agreement is a kind of scheme with special applications function.Utilize quantum-mechanical reason
By a kind of scheme of design so that the both sides of participation compare under the premise of not announcing secret information, and comparing result selection is public
It opens or maintains secrecy.Common scheme belongs to semi-honesty model mostly, that is, exist one and half honest third parties (Third Party,
TP) agreement is assisted to complete.Half honesty refers to that TP verily executes agreement, and records all results of intermediate calculations, but he may
It can attempt the steal information from record.But there are some defects for the existing the third Protocol based on half honesty, first in reality
In the case of border, TP can attempt the secret of eavesdropping participant by various attack patterns.Secondly, the presence of TP increases to the realization of agreement
Add difficulty, reduces efficiency.
Invention content
Two side's quantum information control methods based on bell bases that it is an object of the invention to provide a kind of, this method can not have
Have and realize in the presence of TP the quantum secret information of both sides is compared, safe and reliable and efficiency is higher.
The object of the present invention is achieved like this:A kind of two side's quantum information control methods based on bell bases, including such as
Lower step:
A, there is Alice secret information x, Bob to have secret information y;Both Alice and Bob arrange a hash function
H, and the cryptographic Hash of respective secret information is calculated separately, it obtainsWith
B, the cryptographic Hash of respective secret information is divided by Alice and BobIt is a group, precedingEvery group of m member in group
Element, k element in last group, m≤n, k≤m;
C, according to the cryptographic Hash in first group, the secret information of Alice and Bob is compared;
According to m cryptographic Hash in first group, the secret information of Alice and Bob is compared, is specifically comprised the following steps:
C1, Alice (Bob) prepare m Bell state, and each Bell state isOr
It is S that Alice (Bob), which records m Bell state prepared by it,A(SB);By SA(SB) in each Bell state first grain it is molecular
Sequence is denoted asBy SA(SB) in the sequence of residual particles composition of each Bell state be denoted as
C2, Alice (Bob) prepare single-photon state and are inserted into as trick stateIt is middle to form new sequenceAnd by new sequenceIt is sent to Bob (Alice);Single-photon state isOr
C3, when confirm Bob (Alice) receive sequenceAfterwards, Alice (Bob) informs that other side inveigles state
Position and measurement base;Bob (Alice) is from sequenceMiddle extraction inveigles state and measurement result is sent to Alice
(Bob), Alice (Bob) compares measurement result and original state, and calculates error rate;If error rate is less than the threshold value of setting,
Then show that attacker is not present, executes step c4;Otherwise, show that, there are attacker, return to step c1 restarts;
The particle sequence that c4, Bob (Alice) will be receivedIn trick state removal, obtain sequenceAnd according to m cryptographic Hash in its first group, to particle sequenceIn m particle execute one respectively
Direct transform;IfTransform then is executed to corresponding particle, Z=| 1><0|+|0><1|;IfI transformation then is executed to corresponding particle, I=| 0><0|+|1><1|;It is Bob secret information cryptographic Hash
I-th of cryptographic Hash in first group,It is i-th of cryptographic Hash in first group of Alice secret informations cryptographic Hash, i=1,
2、……、m;Sequence is obtained after having executed unitary transformation
C5, Bob (Alice) prepare single-photon state and are inserted into sequence as trick stateIt is middle to form new sequence And by sequenceIt is sent to Alice (Bob);Single-photon state is
Or
C6, when confirm Alice (Bob) receive sequenceAfterwards, Bob (Alice) informs that other side inveigles state
Position and measurement base;Alice (Bob) is from sequenceMiddle extraction inveigles state and measurement result is sent to Bob
(Alice), Bob (Alice) compares measurement result and original state, and calculates error rate;If error rate is less than the thresholding of setting
Value then shows that attacker is not present, executes step c7;Otherwise, then show that, there are attacker, return to step c1 restarts;
The particle sequence that c7, Alice (Bob) will be receivedIn trick state removal, obtain sequenceAnd according to m cryptographic Hash in its first group, to sequenceIn m particle execute unitary respectively
Transformation;IfTransform then is executed to corresponding particle, Z=| 1><0|+|0><1|;IfI transformation then is executed to corresponding particle, I=| 0><0|+|1><1|;It is Alice secret information Hash
I-th of cryptographic Hash in first group of value,It is i-th of cryptographic Hash in first group of Bob secret informations cryptographic Hash, i=1,
2、……、m;Sequence is obtained after having executed unitary transformation
C8, Alice (Bob) are according to sequenceAnd sequenceObtain state SA′(SB′);Alice
(Bob) by state SA′(SB') and state SA(SB) be compared, if SA'=SA(SB'=SB), then it is assumed that according to the Hash in first group
It is equal to be worth comparison result, executes step d;Otherwise then think unequal according to the cryptographic Hash comparison result in first group, execute step
Rapid e;
D, according to method in step c, sequentially according to second group, third group ...,Cryptographic Hash in group, respectively
Compare the secret information of Alice and Bob;If when according to cryptographic Hash comparison result is unequal in any group, step is directly executed
e;If according to when cryptographic Hash comparison result is equal in all groups, it is concluded that the equal knot of the secret information of both Alice and Bob
Fruit;
E, the unequal result of the secret information of both Alice and Bob is obtained.
The present invention makes the two shared one first when the secret information y of secret information x and Bob to Alice are compared
A hash function H, and calculate separately the cryptographic Hash of respective secret information;The cryptographic Hash of respective secret information is grouped;It
Afterwards according to the cryptographic Hash in each group, the secret information of Alice and Bob is compared;If comparing two according to the cryptographic Hash in any group
The secret information of person differs, then it is assumed that the secret information of Alice and Bob differs;If comparing two according to the cryptographic Hash in all groups
The secret information of person is equal, then it is assumed that the secret information of Alice and Bob is equal.State is inveigled by insertion in comparison process, it can
It detects and whether there is attacker so that comparison process is safe and reliable.Moreover, the present invention is a kind of efficient quantum secret information
Control methods, operation are mainly measurement and the rotation process of light particle so that the efficiency of calculating is higher.
The present invention is a kind of two side's quantum information control methods designed based on quantum physics principle, and security performance is main
Tangling property based on quantum state can resist external attack and dishonest internal attack.In addition, the present invention contains only quantum physics
In common Bell state and single-photon state, these operations experimentally with had been carried out in business application, so the invention can be
It is run in existing quantum devices.
Specific implementation mode
Two side's quantum information control methods provided by the present invention based on bell bases, concrete methods of realizing are as follows:
Assuming that Alice is gathered around and is gathered around that there are one secret information y there are one secret information x, Bob.Alice and two sides of Bob are according to such as
Lower step carries out the comparison of secret information:
The first step:Alice and two sides of Bob arrange one --- the hash function H of mapping:{0,1}n→{0,1}n;Alice
The cryptographic Hash for calculating its secret information x, obtainsBob calculates the cryptographic Hash of its secret information y, obtains
Second step:The cryptographic Hash H (x) of its secret information x is divided by AliceIt is a group, precedingEvery group m in group
Element, k element in last group, m≤n, k≤m;The cryptographic Hash grouping situation of Alice secret informations x is as follows:
The cryptographic Hash H (y) of its secret information y is also divided by BobIt is a group, precedingEvery group of m element in group, most
K element in later group, m≤n, k≤m;The cryptographic Hash grouping situation of Bob secret informations y is as follows:
Third walks:According to the cryptographic Hash in first group of Alice and Bob, the secret information of Alice and Bob is compared.
This step is specific as follows:
1., Alice (Bob) prepare m Bell state as initial state, each Bell state isOrIt is S that Alice (Bob), which records the initial state prepared by it,A(SB);By SA(SB) in each Bell state head
A molecular sequence of grain is denoted asBy SA(SB) in residual particles form in addition to first particle in each Bell state
Sequence is denoted as
2., Alice (Bob) prepare single-photon state as inveigle state radom insertion arriveIt is middle to form new sequenceAnd by new sequenceIt is sent to Bob (Alice).Single-photon state be fromWithIn it is randomly selected.
3., when confirm Bob (Alice) receive sequenceAfterwards, Alice (Bob) is informed by classical channel
Bob (Alice) step 2. in the position of trick state be inserted into and measurement base.Bob (Alice) is from sequenceIn carry
It takes and state is inveigled to obtain sequenceBob (Alice) is gone to measure corresponding trick photon with correct measurement base, and will be surveyed
Amount result is sent to Alice (Bob) by classical channel.Alice (Bob) compares measurement result and inveigles the initial shape of photon
State, and calculate error rate;If error rate shows the presence of not attacker less than the threshold value of setting, step is executed 4.;It is no
Then, then show the presence for having attacker, terminate the comparison of secret information at this time, 1. return to step restarts.
4., Bob (Alice) is according to its first group of Y1(X1) in m cryptographic Hash, to particle sequenceIn m
A particle executes unitary transformation respectively;IfThen to sequenceIn i-th of particle execute Z become
Change, Z=| 1><0|+|0><1|;IfThen to sequenceIn i-th of particle execute I transformation,
I=| 0><0|+|1><1|;It is first group of Y of Bob secret information y cryptographic Hash1In i-th of cryptographic Hash,It is Alice secrets
First group of X of information x cryptographic Hash1In i-th of cryptographic Hash, i=1,2 ..., m;To particle sequenceUnitary is executed
Sequence is obtained after transformation
5., Bob (Alice) prepare single-photon state as inveigle state radom insertion to sequenceIt is middle to be formed newly
SequenceAnd by sequenceIt is sent to Alice (Bob).Single-photon state be fromWithIn it is randomly selected.
6., when confirm Alice (Bob) receive sequenceAfterwards, Bob (Alice) is informed by classical channel
Alice (Bob) step 5. in the position of trick state be inserted into and measurement base.Alice (Bob) is from sequenceIn carry
It takes and state is inveigled to obtain sequenceAlice (Bob) is gone to measure corresponding trick photon with correct measurement base, and will
Measurement result is sent to Bob (Alice) by classical channel.Bob (Alice) compares measurement result and inveigles the initial shape of photon
State, and calculate error rate;If error rate shows the presence of not attacker less than the threshold value of setting, step is executed 7.;It is no
Then, then show the presence for having attacker, terminate the comparison of secret information at this time, 1. return to step restarts.
7., Alice (Bob) is according to its first group of X1(Y1) in m cryptographic Hash, to sequenceIn m grain
Son executes unitary transformation respectively;IfThen to sequenceIn i-th of particle execute transform, Z
=| 1><0|+|0><1|;IfThen to sequenceIn i-th of particle execute I transformation, I=
|0><0|+|1><1|;It is first group of X of Alice secret information x cryptographic Hash1In i-th of cryptographic Hash,It is Bob secret informations
First group of Y of y cryptographic Hash1In i-th of cryptographic Hash, i=1,2 ..., m;To particle sequenceUnitary change is executed
Sequence is obtained after changing
8., Alice (Bob) is according to sequenceAnd sequenceObtain state SA′(SB′);Alice
(Bob) by state SA′(SB') and state SA(SB) Bell state measurement is carried out, if SA'=SA(SB'=SB), then it is assumed that according in first group
Cryptographic Hash compare secret information the result is that equal, continue to carry out secret information according to the cryptographic Hash in second group later
It compares, that is, executes the 4th following step;If SA′≠SA(SB′≠SB), then it is assumed that it is compared according to the cryptographic Hash in first group secret
Information the result is that unequal, do not have to carry out subsequent comparison again at this time, directly give two side's secret information of Alice and Bob
It is unequal as a result, i.e. directly execution the 5th step.
4th step:Method in being walked according to third compares the secret letter of Alice and Bob according to the cryptographic Hash in second group
Breath;If according to the cryptographic Hash in second group, it is equal to compare the secret information of Alice and Bob, then then according in third group
Cryptographic Hash, compare Alice and Bob secret information;And so on.If according to the not phase of cryptographic Hash comparison result in any group
Whens equal, the 5th step is directly executed;If according to when cryptographic Hash comparison result is equal in all groups, it is concluded that both Alice and Bob
The equal result of secret information.
It should be noted that due in last group of secret information cryptographic Hash there are k element, according to most
Should prepare k when 1. middle preparation Bell state is as initial state for step when cryptographic Hash compares two side's secret informations in later group
Bell state is as initial state.
5th step:Obtain the unequal result of both Alice and Bob secret information.
The method in the present invention is described in detail with a specific example below.
Assuming that Alice is gathered around there are one secret information 101, Bob gathers around that there are one secret informations 100.Alice and two sides of Bob press
The comparison of secret information is carried out according to following steps:
The first step:Alice and two sides of Bob arrange a hash function based on system conversion;Alice calculates its secret letter
The cryptographic Hash of breath 101, obtains H (101)=011;Bob calculates the cryptographic Hash of its secret information 100, obtains H (100)=010.
Second step:The cryptographic Hash of its secret information is divided into a group by Alice and Bob, three elements in every group.
Third walks:According to the cryptographic Hash in Alice and first group of Bob (and unique one group), compare Alice's and Bob
Secret information, it is specific as follows:
1., Alice prepare three Bell states at random as initial state, three Bell states prepared by Alice are respectively | α+
>、|β+>、|α+>, and it is recorded as SA.Bob prepares three Bell states and is used as initial state at random, and three Bell states prepared by Bob are divided
It is not | β+>、|β+>、|β+>, and it is recorded as SB.Wherein,
Alice is by SAIn the molecular sequence of first grain of each Bell state be denoted asBy SAIn remove first particle in each Bell state
The sequence of outer residual particles composition is denoted asBob is by SBIn the molecular sequence of first grain of each Bell state be denoted asIt will
SBIn residual particles form in addition to first particle in each Bell state sequence be denoted as
2., Alice randomly choose three single-photon statesIt is inserted into sequenceIt is middle to form one
A new particle sequence In new particle sequenceIn position be respectively the 1st, the 2nd
Position and the 4th;Alice is by new particle sequenceIt is sent to Bob.Bob randomly chooses three single-photon states It is inserted into sequenceOne new particle sequence of middle formation
In new particle sequenceIn position be respectively the 2nd, the 4th and the 5th;Bob is by new particle sequenceIt is sent to
Alice。
3., when Alice and Bob respectively by classical channel announce received other side transmission particle sequence after, according to
The position for the trick state that other side announces and measurement base recover the particle sequence for being not inserted into and inveigling state.Alice and Bob difference
Whether detecting has the presence of attacker;If without attacker, next step is continued to execute;Otherwise step is returned to 1. again
Start.
4., Alice according to three cryptographic Hash in its first group to (eliminate inveigle state) after received recovery
Particle sequence in particle execute I, Z, Z operations successively;Bob according to three cryptographic Hash in its first group to after recovery (i.e.
Eliminate inveigle state) particle sequence in particle execute I, Z, I operations successively.Z=| 1><0|+|0><1 |, I=| 0><0|+|
1><1|。
5., Alice and Bob randomly choose three single photons respectively again and states inveigled to be inserted into quanta particle sequence, and
It is sent to other side.
6., when Alice and Bob respectively by classical channel announce received other side transmission particle sequence after, according to
The position for the trick state that other side announces and measurement base recover the particle sequence for being not inserted into and inveigling state.Alice and Bob difference
Whether detecting has the presence of attacker;If without attacker, next step is continued to execute;Otherwise step is returned to 1. again
Start.
7., Alice I, Z, Z unitary transformations are executed to the particle sequence that receives againObtain | α+>,|β+>,|β+>.By measuring
And it is unequal with original record comparison discovery, then Alice announces that two side's secret information comparing results are unequal.In addition Bob pairs
The particle sequence received executes I, Z, I unitary transformations
Obtain | β+>,|β+>,|α+>.Unequal by measuring and being found with original record comparison, then Bob announces two side's secret informations
Comparing result is unequal.
The content that this specification is not described in detail belongs to the prior art well known to those skilled in the art.
Embodiment described above is only to absolutely prove preferred embodiment that is of the invention and being lifted, protection model of the invention
It encloses without being limited thereto.Those skilled in the art on the basis of the present invention made by equivalent substitute or transformation, in the present invention
Protection domain within.Protection scope of the present invention is subject to claims.
Claims (2)
1. a kind of two side's quantum information control methods based on bell bases, characterized in that include the following steps:
A, there is Alice secret information x, Bob to have secret information y;Both Alice and Bob arrange a hash function H, and
The cryptographic Hash for calculating separately respective secret information, obtainsWith
B, the cryptographic Hash of respective secret information is divided by Alice and BobIt is a group, precedingEvery group of m element in group, most
K element in later group, m≤n, k≤m;
C, according to the cryptographic Hash in first group, the secret information of Alice and Bob is compared;
According to m cryptographic Hash in first group, the secret information of Alice and Bob is compared, is specifically comprised the following steps:
C1, Alice (Bob) prepare m Bell state, and each Bell state isOrAlice
(Bob) it is S to record m Bell state prepared by itA(SB);By SA(SB) in each Bell state the molecular sequence of first grain
It is denoted asBy SA(SB) in the sequence of residual particles composition of each Bell state be denoted as
C2, Alice (Bob) prepare single-photon state and are inserted into as trick stateIt is middle to form new sequence
And by new sequenceIt is sent to Bob (Alice);
C3, when confirm Bob (Alice) receive sequenceAfterwards, Alice (Bob) inform other side inveigle state position and
Measurement base;Bob (Alice) is from sequenceMiddle extraction inveigles state and measurement result is sent to Alice (Bob),
Alice (Bob) compares measurement result and original state, and calculates error rate;If error rate is executed less than the threshold value of setting
Step c4;Otherwise, step c1 is executed;
The particle sequence that c4, Bob (Alice) will be receivedIn trick state removal, obtain sequence
And according to m cryptographic Hash in its first group, to particle sequenceIn m particle execute unitary transformation respectively;IfTransform then is executed to corresponding particle, Z=| 1><0|+|0><1|;IfIt is then right
Corresponding particle executes I transformation, I=| and 0><0|+|1><1|;It is i-th of Hash in first group of Bob secret informations cryptographic Hash
Value,I-th of cryptographic Hash in first group of Alice secret informations cryptographic Hash, i=1,2 ..., m;Unitary transformation is executed
After obtain sequence
C5, Bob (Alice) prepare single-photon state and are inserted into sequence as trick stateIt is middle to form new sequence And by sequenceIt is sent to Alice (Bob);
C6, when confirm Alice (Bob) receive sequenceAfterwards, Bob (Alice) informs that other side inveigles the position of state
And measurement base;Alice (Bob) is from sequenceMiddle extraction inveigles state and measurement result is sent to Bob (Alice),
Bob (Alice) compares measurement result and original state, and calculates error rate;If error rate is executed less than the threshold value of setting
Step c7;Otherwise, step c1 is executed;
The particle sequence that c7, Alice (Bob) will be receivedIn trick state removal, obtain sequenceAnd according to m cryptographic Hash in its first group, to sequenceIn m particle execute unitary respectively
Transformation;IfTransform then is executed to corresponding particle, Z=| 1><0|+|0><1|;IfI transformation then is executed to corresponding particle, I=| 0><0|+|1><1|;It is Alice secret information Hash
I-th of cryptographic Hash in first group of value,It is i-th of cryptographic Hash in first group of Bob secret informations cryptographic Hash, i=1,
2、……、m;Sequence is obtained after having executed unitary transformation
C8, Alice (Bob) are according to sequenceAnd sequenceObtain state SA′(SB′);Alice (Bob) will
State SA′(SB') and state SA(SB) be compared, if SA'=SA(SB'=SB), then it is assumed that knot is compared according to the cryptographic Hash in first group
Fruit is equal, executes step d;Otherwise then think unequal according to the cryptographic Hash comparison result in first group, execute step e;
D, according to method in step c, sequentially according to second group, third group ...,Cryptographic Hash in group, compares respectively
The secret information of Alice and Bob;If when according to cryptographic Hash comparison result is unequal in any group, step e is directly executed;If
According to when cryptographic Hash comparison result is equal in all groups, then the secret information for obtaining both Alice and Bob is equal;
E, the secret information of both Alice and Bob is unequal.
2. two side's quantum information control methods according to claim 1 based on bell bases, characterized in that in step c2
Single-photon state is | 0>、Or
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CN109462473A (en) * | 2018-10-30 | 2019-03-12 | 成都华安永信信息技术有限公司 | A kind of quantum secret information equality exchange method and system |
CN109660329A (en) * | 2018-12-27 | 2019-04-19 | 安徽继远软件有限公司 | A kind of more equal agreement of two side's quantum secures for resisting external attack |
CN110572259A (en) * | 2019-08-06 | 2019-12-13 | 河北大学 | Third-party-free quantum information equality comparison method based on permutation operation |
CN110572259B (en) * | 2019-08-06 | 2022-03-25 | 河北大学 | Third-party-free quantum information equality comparison method based on permutation operation |
CN110730069A (en) * | 2019-09-27 | 2020-01-24 | 浙江工商大学 | Bell entanglement state-based semi-quantum conversation method |
CN110730069B (en) * | 2019-09-27 | 2022-04-15 | 浙江工商大学 | Bell entanglement state-based semi-quantum conversation method |
CN111431712A (en) * | 2020-03-26 | 2020-07-17 | 浙江工商大学 | Multi-user quantum private query method |
CN111431712B (en) * | 2020-03-26 | 2022-04-15 | 浙江工商大学 | Multi-user quantum private query method |
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