CN109344640A - A kind of subgraph match method based on homomorphic cryptography and polynomial computation - Google Patents
A kind of subgraph match method based on homomorphic cryptography and polynomial computation Download PDFInfo
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Abstract
The present invention provides a kind of subgraph match method based on homomorphic cryptography and polynomial computation, is related to technical field at data mining and image.This method includes two roles, is the figure that verifier and certifier and each role hold respectively；The multinomial of the public key of generation and construction is obtained ciphertext using the polynomial coefficient of Paillier cryptographic system homomorphic cryptography and is sent to certifier by verifier；Certifier uses the homomorphism property of Paillier cryptographic system, seeks polynomial value, and be encrypted as single ciphertext, ciphertext is then sent to verifier；Verifier decrypts ciphertext and is interacted according to decrypted result and certifier, and last verifier draws a conclusion；During verifying, both sides will not obtain the useful information in relation to another party's figure, at the end of verifying, only verifier's knowledge of result, it was demonstrated that person does not know verification result always；The privacy and the safety during interaction that the present invention effectively improves both sides.
Description
Technical field
The present invention relates to data minings and technical field of image processing, more particularly to one kind to be based on homomorphic cryptography and multinomial
The subgraph match method of calculating.
Background technique
Figure can depict to pithiness the connection between common thing, therefore the number based on figure as a kind of data structure
According to excavating and no matter administrative skill in academic research or industrial application all enjoys consequence.Most basic times among these
Business is that given query graph, that is, subgraph match problem how are focused to find out in diagram data.For the figure to flourish
For the fields such as database, bioinformatics and social network analysis, the importance of an efficient subgraph match algorithm is not sayed
And it explains.The Fundamentals of Mathematics of subgraph match are Subgraph Isomorphism problems classical in graph theory, a famous np problem.As one can imagine
It designs efficient subgraph match algorithm and is faced with and quite huge greatly challenge.Currently, the research work of subgraph match algorithm is main
There are two problems.One is how effectively to be filtered for the more figure of a number of edges, the second is how vertex to be selected to search
Suo Shunxu come accelerate Subgraph Isomorphism search speed.Especially the latter is the focus that subgraph match is studied in recent years.
Subgraph Isomorphism is that the matched one kind of accurate model is important and very general form.Subgraph Isomorphism is many significance maps
The common popularization of shape problem, including find Hamilton path, group, matching, perimeter and shortest path.The variation of Subgraph Isomorphism
It is used to simulation such as molecular structure to compare, integrated circuit testing, microprogram control unit optimization, robot motion planning is semantic
Network retrieval, the various practical problems such as polytopic plants identification.
In graph theory, Subgraph Isomorphism problem definition is to give two figure G and H, it is determined whether there are subgraph G ' ∈ G, so that
G ' and H isomorphism.Subgraph Isomorphism problem has been widely studied.Since graphic data structure is widely used to each neck of industry
Domain, therefore the problem can be used in many application programs, graphic data structure storage and management information can be used, and have one
Group pattern algorithm abundant can be used for solving different problems.It can be used for solving many calculating tasks in different application field,
Such as Chemoinformatics, computer vision field and the field of data mining.
In pattern match research, in data integration (data integration) and service interoperability (service
Interoperability) in research, pattern match (schema matching) plays very important effect.It is mainly used
To identify the corresponding relationship of metadata (metadata) or model.For example, the comparative shopping website of lot of domestic and international large size
(comparison shopping website), such as Yahoo, Shopping, BizRate, a naughty net and ratio purchase net, Ke Yicong
Merchandise news is integrated in multiple independent online shops (online store), price is provided for user and compares and evaluation analysis function
Energy.The goods catalogue and hierarchical relationship of each independent online shop can indicate with graph structure, and figure matching algorithm can be with
For solving the pattern matching problem for carrying out occurring when information is integrated to different online shops.In medical domain, EEG signal
The active procedure of neuron (neuron) is had recorded, for describing quick brain activity, graph structure can also be converted into.We
From energy pulse is extracted in the time-frequency figure (time-frequency map) of brain wave, it is denoted as the vertex of figure.If some
Pulse and previous or next pulse time interval in a certain range, are just connected them with side.To such
Two figures are matched, and can compare EEG signal in retardance (latency), frequency (fre-quency), energy
(energy) and the difference of active regions (activated areas) etc., and then compare two corticocerebral activities.
In image and video field, each frame (frame) in each image or video can be indicated with graph structure.In image
In, the interested object of user can be indicated with bounding box (bounding box).There are many spatial relationships between object
(spatial relation), such as be overlapped (overlap), include (contain) and connect (meet).On two-dimensional space,
This spatial relationship is up to 169 kinds.For each image, we can construct a Region adjacency graph (region
Adjacency graph, RAG), each point indicates an object in figure, and side indicates the spatial relationship between object.To two regions
Adjacent map is matched, us can be helped to extract a series of analogical object in multiple pictures or video lens set.
Summary of the invention
It is a kind of for secret protection the technical problem to be solved by the present invention is in view of the above shortcomings of the prior art, provide
Subgraph match method, for solving the problems, such as the subgraph match problem in Subgraph Isomorphism.
In order to solve the above technical problems, the technical solution used in the present invention is: a kind of be based on homomorphic cryptography and multinomial
The subgraph match method of calculating, including two roles, verifier PAWith certifier PBAnd verifier PAFigure GAWith certifier PB
Figure GB, specifically includes the following steps:
Step 1, verifier PARun key schedule (pk, sk) ← KeyGen (1k) generate key, the key packet of generation
Include public key and private key, verifier PAPublic key is sent to certifier PB, verifier PAIt is domain by each apex marker of the figure of oneself
<vIn value；Verifier PAThe public key of Paillier cryptographic system include number N one big, it is desirable that N can satisfy so that from bright
The element that literary domain uniformly generates is in domain <vThe middle probability for indicating element is negligible；
Step 2, verifier PAIt constructs multinomial P (x), and is obtained using the polynomial coefficient of Paillier cryptosystem encryption
Ciphertext is obtained, ciphertext is then sent to certifier PB, method particularly includes:
Step 2.1, verifier PAIt constructs multinomial P (x), polynomial is Wherein, ai∈VA, VAIndicate verifier PAThe vertex set for the figure held, m are verifier PAThe vertex for the figure held
Number；The property of multinomial P (x): and if only if x ∈ VAWhen, P (x)=0；With C={ α0..., αmIndicate that P's (x) is all
Coefficient；
Step 2.2, verifier PAUsing all elements in Paillier cryptosystem encryption C, and obtain ciphertext Wherein, Enc () is Paillier system encryption function, then verifier PAIt willHair
Give certifier PB；
Step 3, certifier PBUsing the homomorphism property of Paillier cryptographic system, seek the value of multinomial P (x), and by its
It is encrypted as single ciphertext, ciphertext is then sent to verifier PA, method particularly includes:
Step 3.1 is receivingLater, it was demonstrated that person PBUsing the homomorphism property of Paillier cryptographic system, ask multinomial
The value of formula P (x)；By all bl∈VBAs the parameter for executing polynomial solving function, VBIndicate certifier PBThe figure held
Vertex set, then, it was demonstrated that person PBBy each result of evaluation homomorphism multiplied by different non-zero random number γ,Under the conditions of, it usesIndicate result set；
Step 3.2, certifier PBHomomorphism by all ciphertextsIt is added together to obtain single ciphertextWherein Later, it was demonstrated that person PBBy ciphertextIt is sent to verifier PA；
Step 4, verifier PARun the decryption function of Paillier cryptographic systemDecryption institute is received close
Text, and the value r after being decrypted；If decrypted result r is zero,Then step 5 is executed, if decrypted result r is not
It is zero, thenExecute step 6；
Step 5, verifier PAThe degree for constructing the figure oneself held is all vertex set V ' of non-zeroA, and construct more than one group
Item formula pair, passes through the V ' under Paillier cryptosystem encryption specified requirements laterAIn vertex and polynomial coefficient, finally
Ciphertext is sent to certifier PB, method particularly includes:
Step 5.1, verifier PAConstruction set V 'A, V 'AMeet vertex aiNeighborhoodCondition,
In, ai∈VA, V 'A={ a '1..., a 'g, g is V 'AIn include VAIn there is degree to be the quantity on all vertex of non-zero, and it is each
a′j∈V′AIt is mapped to unique ai∈VA；
Step 5.2, for each vertex a 'j∈V′A, j=1,2 ..., g, verifier PAOne group of multinomial is constructed to { (F1
(x), G1(y)) ..., (Fg(x), Gg(y)) }, Fj(x) it is defined as Fj(x)=(x-a 'j), Gj(y) it is defined asFj(x) there are a properties, and if only if x=a 'jWhen, Fj(x)=0；Gj(y) there are one
A property, and if only if y ∈ N (a 'j) when, Gj(y)=0；Verifier PABy Gj(y) it is rewritten asShape
Formula, wherein βI, jIt is Gj(y) coefficient,
Step 5.3, verifier PAUnder Paillier cryptographic system, a ' under the conditions of 1≤i '≤g is encryptedi′And βi′, encryption
After obtainVerifier PAIt willIt is sent to proof
Person PB, then execute step 7；
Step 6, verifier PAConstruction is comprising meetingAll vertex ai∈VASet V 'A, wherein V 'A=
{a′1..., a 'g, then verifier PAFor each aj∈V′AG set of construction, wherein g is V 'AThe quantity on middle vertex, Mei Geji
Conjunction is defined asLast verifier PABy constructionIt is sent to certifier PB；
Step 7, certifier PBConstruction set V 'B, and evaluator Fi(b′j) and Gi(bk), then pass through homomorphic cryptography
Single ciphertext is obtained, ciphertext is integrated into set and generates V 'BThe ciphertext set of number of elements in set, finally by ciphertext set
It is sent to verifier PA, method particularly includes:
Step 7.1 is receivingLater, it was demonstrated that person PBWith with construction V 'AIdentical mode construction set V 'B,
It is denoted as V 'B={ b '1... b 'h}；
Step 7.2, for all i ' ∈ [1, g] and all k ∈ [1, h], it was demonstrated that person PBHomomorphism ground evaluator Fi′
(b′k), and by result homomorphism multiplied by non-zero random number γ；Then, it was demonstrated that person PBIt chooses and all meets bk′∈N(b′k) top
Point is as input, homomorphism ground evaluator Gi′(bk′), and by each result homomorphism multiplied by non-zero random number γ；Then, it demonstrate,proves
Bright person PBAll previous result homomorphisms are added together and obtain single ciphertext Wherein, 1≤i ' of i ' satisfaction≤g, k satisfaction 1≤
K≤h, γ are non-zero random numbers；
Step 7.3, certifier PBIt will be allIt is integrated into h set, and every group of set includes g ciphertext, it is raw
At ciphertext Ji TaiThen certifier PBAll ciphertext collection are sent to verifier PA；
If the r in step 8, step 4 is not 0, certifier PBFigure be not verifier PASubgraph, i.e.,
Conversely, verifier PAAll ciphertexts received are decrypted, and check zero number in every group；If definitely there is one in every group
Zero, then certifier PBFigure be verifier PAFigure subgraph, i.e.,Otherwise, it was demonstrated that person PBFigure be not verifier PA's
The subgraph of figure, i.e.,
The beneficial effects of adopting the technical scheme are that provided by the invention a kind of based on homomorphic cryptography and more
The subgraph match method that item formula calculates, the both sides of participatory approaches are verifier PAWith certifier PB, both sides are owned by the figure knot of privacy
Structure data, after joint execution method, verifier PAIt only will appreciate that certifier PBFigure whether be verifier PAThe subgraph of figure.
This method is based on Paillier cryptographic system and casual polynomial computation, ensure that data safety, and ensure that data
Privacy.During subgraph match, either side will not all obtain the useful information in relation to another party's diagram data.
Detailed description of the invention
Fig. 1 is two role's schematic diagrames provided in an embodiment of the present invention for carrying out subgraph match；
Fig. 2 is a kind of stream of the subgraph match method based on homomorphic cryptography and polynomial computation provided in an embodiment of the present invention
Cheng Tu；
Fig. 3 is the flow chart that Paillier encryption system provided in an embodiment of the present invention generates public key and private key method.
Specific embodiment
With reference to the accompanying drawings and examples, specific embodiments of the present invention will be described in further detail.Implement below
Example is not intended to limit the scope of the invention for illustrating the present invention.
The present embodiment is by taking verifier shown in FIG. 1 and certifier as an example, using of the invention based on homomorphic cryptography and multinomial
Formula calculate subgraph match method validation certifier figure whether be verifier subgraph；
A kind of subgraph match method based on homomorphic cryptography and polynomial computation is tested as shown in Figure 1, including two roles
Card person PAWith certifier PBAnd verifier PAFigure GAWith certifier PBFigure GB, as shown in Fig. 2, specifically includes the following steps:
Step 1, verifier PARun key schedule (pk, sk) ← KeyGen (1k) key is generated, generate the stream of key
Journey is as shown in figure 3, the key generated includes public key and private key, verifier PAPublic key is sent to certifier PB, verifier PAIt will be certainly
Each apex marker of oneself figure be domain <vIn value；Verifier PAThe public key of Paillier cryptographic system include one big number
N, it is desirable that N can satisfy so that the element uniformly generated from plaintext domain domain <vThe middle probability for indicating element is negligible；
Step 2, verifier PAIt constructs multinomial P (x), and is obtained using the polynomial coefficient of Paillier cryptosystem encryption
Ciphertext is obtained, ciphertext is then sent to certifier PB, method particularly includes:
Step 2.1, verifier PAIt constructs multinomial P (x), polynomial is Wherein, ai∈VA, VAIndicate verifier PAThe vertex set for the figure held, m are verifier PAThe vertex for the figure held
Number；The property of multinomial P (x): and if only if x ∈ VAWhen, P (x)=0；With C={ α0..., αmIndicate that P's (x) is all
Coefficient；
Step 2.2, verifier PAUsing all elements in Paillier cryptosystem encryption C, and obtain ciphertext Wherein, Enc () is Paillier system encryption function, then verifier PAIt willHair
Give certifier PB；
Step 3, certifier PBUsing the homomorphism property of Paillier cryptographic system, seek the value of multinomial P (x), and by its
It is encrypted as single ciphertext, ciphertext is then sent to verifier PA, method particularly includes:
Step 3.1 is receivingLater, it was demonstrated that person PBUsing the homomorphism property of Paillier cryptographic system, ask multinomial
The value of formula P (x)；By all bl∈VBAs the parameter for executing polynomial solving function, VBIndicate certifier PBThe figure held
Vertex set, then, it was demonstrated that person PBBy each result of evaluation homomorphism multiplied by different non-zero random number γ,Under the conditions of, it usesSurely show result set；
Step 3.2, certifier PBHomomorphism by all ciphertextsIt is added together to obtain single ciphertextWherein Later, it was demonstrated that person PBBy ciphertextIt is sent to verifier PA；
Step 4, verifier PARun the decryption function of Paillier cryptographic systemDecryption institute is received close
Text, and the value r after being decrypted；If decrypted result r is zero,Then step 5 is executed, if decrypted result r is not
It is zero, thenExecute step 6；
Step 5, verifier PAThe degree for constructing the figure oneself held is all vertex set V ' of non-zeroA, and construct more than one group
Item formula pair, passes through the V ' under Paillier cryptosystem encryption specified requirements laterAIn vertex and polynomial coefficient, finally
Ciphertext is sent to certifier PB, method particularly includes:
Step 5.1, verifier PAConstruction set V 'A, V 'AMeet vertex aiNeighbours Ji TaiCondition,
In, ai∈VA, V 'A={ a '1..., a 'g, g is V 'AIn include VAIn there is degree to be the quantity on all vertex of non-zero, and it is each
a′j∈V′AIt is mapped to unique ai∈VA；
Step 5.2, for each vertex a 'j∈V′A, j=1,2 ..., g, verifier PAOne group of multinomial is constructed to { (F1
(x), G1(y)) ..., (Fg(x), Gg(y)) }, Fj(x) it is defined as Fj(x)=(x-a 'j), Gj(y) it is defined asFj(x) there are a properties, and if only if x=a 'jWhen, Fj(x)=0；Gj(y) there are one
A property, and if only if y ∈ N (a 'j) when, Gj(y)=0；Verifier PABy Gj(y) it is rewritten asShape
Formula, wherein βI, jIt is Gj(y) coefficient,
Step 5.3, verifier PAUnder Paillier cryptographic system, a ' under the conditions of 1≤i '≤g is encryptedi′And βi′, encryption
After obtainVerifier PAIt willIt is sent to proof
Person PB, then execute step 7；
Step 6, verifier PAConstruction is comprising meetingAll vertex ai∈VASet V 'A, wherein V 'A=
{a′1..., a 'g, then verifier PAFor each aj∈V′AG set of construction, wherein g is V 'AThe quantity on middle vertex, Mei Geji
Conjunction is defined asLast verifier PABy constructionIt is sent to certifier PB；
Step 7, certifier PBConstruction set V 'B, and evaluator Fi(b′j) and Gi(bk), then pass through homomorphic cryptography
Single ciphertext is obtained, ciphertext is integrated into set and generates V 'BThe ciphertext set of number of elements in set, finally by ciphertext set
It is sent to verifier PA, method particularly includes:
Step 7.1 is receivingLater, it was demonstrated that person PBWith with construction V 'AIdentical mode construction set V 'B,
It is denoted as V 'B={ b '1... b 'h}；
Step 7.2, for all i ' ∈ [1, g] and all k ∈ [1, h], it was demonstrated that person PBHomomorphism ground evaluator Fi′
(b′k), and by result homomorphism multiplied by non-zero random number γ；Then, it was demonstrated that person PBIt chooses and all meets bk′∈N(b′k) top
Point is as input, homomorphism ground evaluator Gi′(bk′), and by each result homomorphism multiplied by non-zero random number γ；Then, it demonstrate,proves
Bright person PBAll previous result homomorphisms are added together and obtain single ciphertext Wherein, 1≤i ' of i ' satisfaction≤g, k satisfaction 1≤
K≤h, γ are non-zero random numbers；
Step 7.3, certifier PBIt will be allIt is integrated into h set, and every group of set includes g ciphertext, it is raw
At ciphertext Ji TaiThen certifier PBAll ciphertext collection are sent to verifier PA；
If the r in step 8, step 4 is not 0, certifier PBFigure be not verifier PASubgraph, i.e.,
Conversely, verifier PAAll ciphertexts received are decrypted, and check zero number in every group；If definitely there is one in every group
Zero, then certifier PBFigure be verifier PAFigure subgraph, i.e.,Otherwise, it was demonstrated that person PBFigure be not verifier PA
Figure subgraph, i.e.,
Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although
Present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: it still may be used
To modify to technical solution documented by previous embodiment, or some or all of the technical features are equal
Replacement；And these are modified or replaceed, model defined by the claims in the present invention that it does not separate the essence of the corresponding technical solution
It encloses.
Claims (5)
1. a kind of subgraph match method based on homomorphic cryptography and polynomial computation, including two roles, verifier PAAnd certifier
PBAnd verifier PAFigure GAWith certifier PBFigure GB, it is characterised in that: specifically includes the following steps:
Step 1, verifier PARun key schedule (pk, sk) ← KeyGen (1k) key is generated, the key of generation includes public affairs
Key and private key, verifier PAPublic key is sent to certifier PB, verifier PABy each apex marker of the figure of oneself be domain <vIn
Value；Verifier PAThe public key of Paillier cryptographic system include number N one big, it is desirable that N can satisfy so that from plaintext domain
The element uniformly generated domain <vThe middle probability for indicating element is negligible；
Step 2, verifier PAIt constructs multinomial P (x), and close using the polynomial coefficient acquisition of Paillier cryptosystem encryption
Then ciphertext is sent to certifier P by textB；
Step 3, certifier PBUsing the homomorphism property of Paillier cryptographic system, the value of multinomial P (x) is sought, and is encrypted as
Then ciphertext is sent to verifier P by single ciphertextA；
The decryption function of step 4, verifier PA operation Paillier cryptographic systemThe received ciphertext of decryption institute,
And the value r after being decrypted；If decrypted result r is zero,Then step 5 is executed, if decrypted result r is not
Zero, thenExecute step 6；
Step 5, verifier PAThe degree for constructing the figure oneself held is all vertex set V ' of non-zeroA, and construct one group of multinomial
It is right, pass through the V ' under Paillier cryptosystem encryption specified requirements laterAIn vertex and polynomial coefficient, finally will be close
Text is sent to certifier PB, then execute step 7；
Step 6, verifier PAConstruction is comprising meetingAll vertex ai∈VASet V 'A, wherein V 'A=
{a′1..., a 'g, then verifier PAFor each aj∈V′AG set of construction, wherein g is V 'AThe quantity on middle vertex, Mei Geji
Conjunction is defined asLast verifier PABy constructionIt is sent to certifier PB；
Step 7, certifier PBConstruction set V 'B, and evaluator Fi(b′j) and Gi(bk), then obtained by homomorphic cryptography
Ciphertext is integrated into set and generates V ' by single ciphertextBThe ciphertext set of number of elements, finally sends ciphertext set in set
Give verifier PA；
If the r in step 8, step 4 is not 0, certifier PBFigure be not verifier PA subgraph, i.e.,Conversely,
Verifier PA decrypts all ciphertexts received, and checks zero number in every group；If definitely there is one zero in every group, demonstrate,prove
Bright person PBFigure be verifier PA figure subgraph, i.e.,Otherwise, it was demonstrated that person PBFigure be not verifier PA figure son
Figure, i.e.,
2. a kind of subgraph match method based on homomorphic cryptography and polynomial computation according to claim 1, feature exist
In: the step 2 method particularly includes:
Step 2.1, verifier PA construction multinomial P (x), polynomial are Wherein, ai∈VA, VAIndicate that the vertex set for the figure that verifier PA holds, m are verifier PAThe top for the figure held
Point number；The property of multinomial P (x): and if only if x ∈ VAWhen, P (x)=0；With C={ α0..., αmIndicate the institute of P (x)
Some coefficients；
Step 2.2, verifier PAUsing all elements in Paillier cryptosystem encryption C, and obtain ciphertext Wherein, Enc () is Paillier system encryption function, then verifier PAIt willHair
Give certifier PB。
3. a kind of subgraph match method based on homomorphic cryptography and polynomial computation according to claim 2, feature exist
In: the step 3 method particularly includes:
Step 3.1 is receivingLater, it was demonstrated that person PBUsing the homomorphism property of Paillier cryptographic system, multinomial P is sought
(x) value；By all bl∈VBAs the parameter for executing polynomial solving function, VBIndicate certifier PBThe top for the figure held
Point set, then, it was demonstrated that person PBBy each result of evaluation homomorphism multiplied by different non-zero random number γ,Under the conditions of, it usesIndicate result set；
Step 3.2, certifier PBHomomorphism by all ciphertextsIt is added together to obtain single ciphertextWherein Later, it was demonstrated that person PBBy ciphertextIt is sent to verifier PA。
4. a kind of subgraph match method based on homomorphic cryptography and polynomial computation according to claim 3, feature exist
In: the step 5 method particularly includes:
Step 5.1, verifier PAConstruction set V 'A, V 'AMeet vertex aiNeighborhoodCondition, wherein ai
∈VA, V 'A={ a '1..., a 'g, g is V 'AIn include VAIn there is degree to be the quantity on all vertex of non-zero, and each a 'j∈
V′AIt is mapped to unique ai∈VA；
Step 5.2, for each vertex a 'j∈V′A, j=1,2 ..., g, verifier PAOne group of multinomial is constructed to { (F1(x), G1
(y)) ..., (Fg(x), Gg(y)) }, Fj(x) it is defined as Fj(x)=(x-a 'j), Gj(y) it is defined asFj(x) there are a properties, and if only if x=a 'jWhen, Fj(x)=0；Gj(y) there are one
A property, and if only if y ∈ N (a 'j) when, Gj(y)=0；Verifier PABy Gj(y) it is rewritten asShape
Formula, wherein βI, jIt is Gj(y) coefficient,
Step 5.3, verifier PAUnder Paillier cryptographic system, a ' under the conditions of 1≤i '≤g is encryptediAnd βi′, after encryption
It arrivesVerifier PAIt willIt is sent to certifier PB,
Then step 7 is executed.
5. a kind of subgraph match method based on homomorphic cryptography and polynomial computation according to claim 4, feature exist
In: the step 7 method particularly includes:
Step 7.1 is receivingLater, it was demonstrated that person PBWith with construction V 'AIdentical mode construction set V 'B, it is denoted as
V′B={ b '1... b 'h}；
Step 7.2, for all i ' ∈ [1, g] and all k ∈ [1, h], it was demonstrated that person PBHomomorphism ground evaluator Fi′(b′k), and
And by result homomorphism multiplied by non-zero random number γ；Then, it was demonstrated that person PBIt chooses and all meets bk′∈N(b′k) vertex conduct
Input, homomorphism ground evaluator Gi′(bk′), and by each result homomorphism multiplied by non-zero random number γ；Then, it was demonstrated that person PB
All previous result homomorphisms are added together and obtain single ciphertext Wherein, 1≤i ' of i ' satisfaction≤g, k satisfaction 1≤
K≤h, γ are non-zero random numbers；
Step 7.3, certifier PBIt will be allIt is integrated into h set, and every group of set includes g ciphertext, is generated close
Collected works closeThen certifier PBAll ciphertext collection are sent to verifier PA。
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN110011784A (en) * | 2019-04-04 | 2019-07-12 | 东北大学 | Support the KNN classified service system and method for secret protection |
| CN112865958A (en) * | 2020-12-31 | 2021-05-28 | 北方工业大学 | Privacy protection system and method for searching target through Internet of things camera |
| CN114422220A (en) * | 2022-01-06 | 2022-04-29 | 浙江数秦科技有限公司 | Data encryption transmission method with non-unique ciphertext |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109818752A (en) * | 2019-02-27 | 2019-05-28 | 矩阵元技术（深圳）有限公司 | Credit scoring generation method, device, computer equipment and storage medium |
| CN109818752B (en) * | 2019-02-27 | 2022-09-30 | 矩阵元技术（深圳）有限公司 | Credit score generation method and device, computer equipment and storage medium |
| CN110011784A (en) * | 2019-04-04 | 2019-07-12 | 东北大学 | Support the KNN classified service system and method for secret protection |
| CN110011784B (en) * | 2019-04-04 | 2021-06-08 | 东北大学 | KNN classification service system and method supporting privacy protection |
| CN112865958A (en) * | 2020-12-31 | 2021-05-28 | 北方工业大学 | Privacy protection system and method for searching target through Internet of things camera |
| CN112865958B (en) * | 2020-12-31 | 2023-04-18 | 北方工业大学 | Privacy protection system and method for searching target through Internet of things camera |
| CN114422220A (en) * | 2022-01-06 | 2022-04-29 | 浙江数秦科技有限公司 | Data encryption transmission method with non-unique ciphertext |
| CN114422220B (en) * | 2022-01-06 | 2024-02-27 | 浙江数秦科技有限公司 | Ciphertext non-unique data encryption transmission method |
| WO2024001558A1 (en) * | 2022-06-29 | 2024-01-04 | 中兴通讯股份有限公司 | Data processing method and device, and computer device and readable storage medium |
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