CN107145792A - Multi-user's secret protection data clustering method and system based on ciphertext data - Google Patents
Multi-user's secret protection data clustering method and system based on ciphertext data Download PDFInfo
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Abstract
The present invention provides a kind of multi-user's secret protection data clustering method and system based on ciphertext data, belongs to data mining technology field.The inventive method includes step：Two or more user sends data and cluster centre point, trap door information after each encryption to server；Server calculates ciphertext data point and the distance of cluster centre point, and partition clustering；The data point of user different in each cluster is added by server respectively, and the summation and number of data are sent respectively into user；User by the data summation received and is sent to server after number re-encrypted；Server calculates new cluster centre point, and new cluster centre point is sent into each user；Each user calculates data point in each cluster of the common calculating of agreement by outsourcing secret protection average and, apart from the average value of cluster centre point, is then sent to server, carries out iteration next time.The present invention substantially increases cluster efficiency；The safety calculating under semi-honesty model is realized, while conspiracy attack to a certain extent can be resisted.
Description
Technical field
The present invention relates to data mining technology field, more particularly to a kind of multi-user's secret protection number based on ciphertext data
According to clustering method, additionally provide multi-user's secret protection data clustering method based on ciphertext data described in a kind of realize is
System.
Background technology
Secret protection data mining (Privacy Preserving Data Mining, PPDM), which is mainly solution, two
Or the data mining that multiple partners participate in, but oneself private data one kind side compromised in calculating process is not desired to again
Method.The data mining of secret protection ensure that data mining can be carried out on both sides or even multi-party joint data, protect simultaneously
Card data-privacy is not stolen by other people.
The technology of secret protection data mining is broadly divided into the technical method based on data perturbation and the technology based on password
Method.Technology based on data perturbation is mainly protected by adding interference on the basis of source data so as to realize to the privacy of source data
Shield, but certain loss of significance can be brought.In technology based on password it is main using homomorphic cryptography and multi-party computations be main
Method, cryptographic technique is compared to data interference, and data intervene low, and precision is high, but its time complexity is often higher, calculates
Cost is larger.
Technical method based on password is broadly divided into the distributed computing method predominantly participated in without high in the clouds early stage, this method
The agreement or half homomorphism encryption that the main safety circuit by using Andrew Chi-Chih Yao is assessed realize the secret protection of data, but bring
Problem is mainly less efficient, and the amount of calculation that each participant undertakes is larger, it is difficult to practical.Later, after 2012,
Peter et al. proposes the outsourcing multi-party computations based on cloud computing based on BCP encryption methods so that reduce ginseng using high in the clouds
It is possibly realized with the amount of calculation of side.The same year, Asharov proposes the door calculated in many ways and falls into homomorphic cryptography method, further lifting
The efficiency that high in the clouds is calculated, but such a method can not protect privacy of user, user content easily stolen by other users.
As for clustering method, relatively more classical is exactly traditional K-means clustering algorithms, and substantially process of its realization is,
K point is randomly selected as cluster centre point from data in first round iteration, then calculates other each points into cluster
The Euclidean distance of heart point, comparing will go apart from the most short corresponding cluster centre that is divided into, after the completion of clustering, each
Each component in point in cluster recalculates average value, recalculates cluster centre, and after the completion of calculating, first round iteration is complete
Finish, into next round iteration.The cluster centre for being recycled to iterative calculation is not changing, and stops iteration, and cluster is completed.
K-means should be fairly simple one kind in clustering algorithm, and K-means is calculated by algorithm, and sample is pressed
It is K cluster according to certain rule confidence, but traditional clustering algorithm can not realize that privacy of user is protected, data participant holds very much
Easily obtain the data of other users, therefore the Shortcomings in terms of security.
The content of the invention
To solve the problems of the prior art, the present invention provides a kind of multi-user's secret protection data based on ciphertext data
Clustering method, also provides a kind of system for realizing methods described.
Multi-user's secret protection data clustering method of the invention based on ciphertext data comprises the following steps：
S1：Two or more user sends data and cluster centre point, trap door information after each encryption to server；
S2：Server calculates ciphertext data point and the distance of cluster centre point, and divides poly- according to distance and trap door information
Class；
S3：The data point of user different in each cluster is added by server respectively, and by the summation of data and
Number is sent respectively to respective user；
S4：Each user is according to the data summation and number received, by being sent to service after BCP enciphered method re-encrypteds
Device；
S5：Server calculates new cluster centre point, and new cluster centre point is sent into each user；
S6：Each user calculates data point in each cluster and, apart from the average value of cluster centre point, is then sent to jointly
Server, returns and performs step S1, until the average value is less than threshold value, classification terminates, and server is by classification results according to number
Each user is sent respectively to according to source.
The present invention is further improved, in step sl, and the server is outsourcing service device, and user passes through homomorphism respectively
Encryption and BCP encryptions are encrypted twice to data, data set D={ d1,d2,...,dnInclude n data, each data point
di=(xi,1,...,xi,m), m represents that each data point is m dimensional vectors, each data point diIn component xi,jIt will be added
It is close to be uploaded to outsourcing service device Enc (x twicei,j)=(ce(i,j),cp(i,j)), wherein, 1≤i≤n, 1≤j≤m, ce(i,j)Represent
Using the ciphertext after Liu homomorphic encryption scheme encryption, cp(i,j)Represent with the ciphertext after the encryption of BCP encipherment schemes.
The present invention is further improved, and step S2 processing method includes：
S21：Server is according to ciphertext ce(i,j)Calculate ciphertext data point diWith t-th of cluster centre point EtApart from ED2
(di,Et), wherein, k is the number of cluster centre point, 1≤t≤k；
S22：Trapdoor functions in the trap door information provided according to user, outsourcing service device calculates ED2(di,Et)+
Trapdoor compares each data point to the distance of each cluster centre, nearest one of chosen distance, by this dot-dash
Assign in corresponding cluster.
The present invention is further improved, in the step s 21, each data point di=(xi,1,...,xi,m) and each
Cluster centre point Et=(et,1,...,et,m) all it is m dimensional vectors, and the encryption data of each data point is ce(i,j)=
(ce(i,1),...,ce(i,m)), it is described apart from ED2(di,Et) calculation formula be：
The present invention is further improved, in step S22, and the Trapdoor functions, which are used for generation, can compare two numbers
According to the order-preserving encrypted indexes of size.
The present invention is further improved, in step s3, and server end uses ciphertext cp(i,j)To calculate each cluster
In, how many data point, and data point respective components plus and, and according to data distribution respectively will plus and result be sent to
Each user Pi.
The present invention is further improved, in step S4- steps S6, due to the re-computation of each cluster centre be will be every
In the cluster of one division, the corresponding component of discrete point for belonging to the center is mutually added in and averaged, it is assumed that in one clusters
There is a n point, t user, each user Pi,For Pi value,Each the value after user encryption isOften
One cpiIt is the vector of a m dimension, high in the clouds calculates each cluster centre Pi discrete point c respectivelypiThe value phase adduction of respective components
And calculate number.SoAddition result is Xi=(xi1,xi2,...,xim), and the number for belonging to Pi points in cluster is
aiai, server is the X calculatedi,aiEach user Pi is sent respectively to, each user Pi is encrypted with BCP encipherment schemes
Afterwards, calculate then with server combination OPPWAP agreementsValue, last result is the average value of calculating.
The present invention is further improved, and server and processing procedure of each user based on OPPWAP agreements include following step
Suddenly：A1：Outsourcing service device S initialized by Setup and generate common parameter PP=(N, K, g), and by common parameter PP
It is sent to each user Pi；
A2：Each user Pi is obtained after common parameter, and generating machine by key generates the public key and private key (pk of oneselfi,
ski), and by public key pkiIt is sent to server；
A3：All are combined the unified public key of calculating by server, and unified public key Prod.pk is sent into each use
Family Pi；
A4：The data of oneself are obtained result (A with being encrypted by user Pii,Bi) and (Ai′,Bi′)；
A5：User Pi generates two random number ρiAnd ρi', re-computation is carried out to encryption data and obtained：
And send these data to server；
A6：Server is obtained after data, is calculated according to formulaAnd
WillWithReturn to each user Pi；
A7：User Pi is calculated and obtainedWithAnd it is sent to server；
A8：Server obtains data XiWith X 'iAfterwards, then new data are calculatedWithThen generate
Random number τ, then by K, K ',It is sent to each user Pi；
A9：Each user Pi is obtained after data, is finally calculatedIt is every so as to obtain
Average value of the data point apart from cluster centre point in individual cluster.
Present invention also offers a kind of system for realizing the above method, including server and two or more user, the use
Family is used for the data after encryption and cluster centre point, trap door information to server, according to the data summation and number received, leads to
Cross and server be sent to after BCP enciphered method re-encrypteds, calculate the average value of data point in each cluster apart from cluster centre point,
It is then sent to server；The server is used to calculating the distance of ciphertext data point and cluster centre point, and according to distance and
Trap door information partition clustering, the data point of user different in each cluster is added respectively, and by the summation of data and
Number is sent respectively to respective user, calculates new cluster centre point, and new cluster centre point is sent into each user,
After classification terminates, classification results are sent respectively to each user according to data source.
The present invention is further improved, and the server is the cloud server of outsourcing.
Compared with prior art, the beneficial effects of the invention are as follows：Cryptological technique is selected, is added by the way that selection is relatively more efficient
Close algorithm and the mode of data outsourcing improve efficiency；The algorithm that improved door falls into encryption is mutually tied with the data mining of secret protection
Close, raising efficiency；The safety calculating under semi-honesty model is realized, while conspiracy attack to a certain extent can be resisted.
Brief description of the drawings
Fig. 1 is the inventive method flow chart；
Fig. 2 is that an iteration structure of the present invention and data processing flow to schematic diagram；
Fig. 3 is part cluster data；
Fig. 4 is the cluster result of Fig. 3 data ciphertexts；
Fig. 5 is the cluster result of Fig. 3 data clear texts；
Fig. 6 is the time contrast that server and user consume during an iteration；
Fig. 7 is data clear text and ciphertext in last time data and an iteration time contrast histogram；
Fig. 8 is data clear text and the ciphertext time in whole iteration to contrast histogram.
Embodiment
The present invention is described in further details with reference to the accompanying drawings and examples.
Secret protection data clusters are calculated present invention is generally directed to multi-user or multi-data source, to ensure that multiple data possess
The private data of person is revealed not in calculating process, it is necessary to the private data for taking scheme to protect data owner.While data
Secret protection substantial amounts of calculate, it is necessary to which calculating is contracted out into server reduces data owner can be brought to data owner
Amount of calculation.The present invention combines two aspect demands above, by the K-means clustering algorithms and outsourcing meter of multiparty data secret protection
It is combined, secret protection is realized by encryption, multi-party computations realize cryptogram computation.Multiple data owners add data
It is close, outsourcing service device is uploaded to, server is calculated under ciphertext, returns to data owner's cluster result.It is most
Outsourcing service device is given in calculating, and data owner is calculated on a small quantity, while cluster is realized, it is ensured that data in cluster process
The private data of owner is not compromised.The present invention needs to overcome two main difficult points, and one is the K- for realizing secret protection
The outsourcing of means clustering algorithms is calculated；Another is the various calculating problem brought of data distribution of multiparty data collection.The present invention is main
To be broken through for two above difficult point.
As shown in figure 1, multi-user's secret protection data clustering method of the invention based on ciphertext data comprises the following steps：
Two or more user sends data and cluster centre point, trap door information after each encryption to server；
S2：Server calculates ciphertext data point and the distance of cluster centre point, and divides poly- according to distance and trap door information
Class；
S3：The data point of user different in each cluster is added by server respectively, and by the summation of data and
Number is sent respectively to respective user；
S4：Each user is according to the data summation and number received, by being sent to service after BCP enciphered method re-encrypteds
Device；
S5：Server calculates new cluster centre point, and new cluster centre point is sent into each user；
S6：Each user calculates data point in each cluster and, apart from the average value of cluster centre point, is then sent to jointly
Server, returns and performs step S1, until the average value is constant, classification terminates, and server comes classification results according to data
Source is sent respectively to each user.
Wherein, in step sl, the present invention is using two kinds of encipherment scheme encryption datas, and Liu homomorphic cryptography and BCP add
It is close.Data set D={ d1,d2,...,dnInclude n data, each data point di=(xi,1,...,xi,m), m represents every number
Strong point is all m dimensional vectors, each data point diIn component xi,jEncrypted outsourcing service device Enc will be uploaded to twice
(xi,j)=(ce(i,j),cp(i,j)), wherein, 1≤i≤n, 1≤j≤m, ce(i,j)Represent to encrypt using Liu homomorphic encryption scheme
Ciphertext afterwards, cp(i,j)Represent with the ciphertext after the encryption of BCP encipherment schemes.
The server of this example is the cloud server of outsourcing, and most of computing is calculated by the cloud server of outsourcing,
Effectively improve cluster efficiency.
As shown in Fig. 2 once complete iterative process mainly comprises the following steps the present invention：Assuming that each user Pi is
Outsourcing service device will be uploaded to after the completion of respective data encryption, the data set D of synthesis is the equal of a bivariate table, encrypted
Journey is that each data completes to encrypt twice in generated data collection D, is uploaded to cloud server.The cloud server of outsourcing is main
What is completed is the distance for calculating data point to cluster centre, and Trapdoor (trapdoor) information is received from data owner there, than
Compared with chosen distance most short cluster centre, partition clustering.Then according to the cluster result of division, the data during each is clustered
Each component of point is added, different according to the distribution of data, and the data addition result and number of belonging to P1 are issued into P1, belonged to
P2's is sent to P2, and belong to Pn is sent to Pn.Each user Pi (1<=i<=n) it will be sent out again after the information re-encrypted of oneself
High in the clouds is given, high in the clouds calculates new cluster centre point, finally wait high in the clouds to calculate and complete, be sent to each user, user's decryption
New cluster centre is sent to high in the clouds afterwards, into next round iteration.
From the perspective of user, an iteration process is that each user Pi each provides the Trapdoor trapdoors of oneself
Information (according to the difference of data distribution), waiting for server send each cluster centre the summation for belonging to various data and
Number, Pi is taken after data, and data are encrypted with BCP encipherment schemes, is completed in conjunction with high in the clouds using OPPWAP agreements
The re-computation of cluster centre, wherein, because being distributed as horizontal distribution in the data of users more than two sides, then in data set
Each data point distribution belongs to each user, owns, and this example is in both sides or multi-party re-computation cluster centre, both sides or multi-party
Consult one group of common r of generation1v,r2v,...rmvTo encrypt the value of cluster centre, then it will be returned to after cluster centre re-encrypted
High in the clouds outsourcing service device, so ensures the uniformity that database is calculated.It is emphasized that in the re-encrypted of cluster centre
When, it is without using BCP encipherment schemes to new cluster centre, that is to say, that cluster centre point is only needed to by Liu encryption
Scheme is encrypted once.
Specifically, step S2 processing method includes：
S21：Server is according to ciphertext ce(i,j)Calculate ciphertext data point diWith t-th of cluster centre point EtApart from ED2
(di,Et), wherein, k is the number of cluster centre point, 1≤t≤k；
Assuming that there is n data point D={ d in data set D1,d2,...,dn, the cluster centre set in advance has K, di(1
≤ i≤n) represent i-th of data point, Et(1≤t≤k) represents t-th of cluster centre.Each data point di=(xi,1,...,
xi,m) and each cluster centre point Et=(et,1,...,et,m) all it is m dimensional vectors.Under plaintext, the calculating such as public affairs of Euclidean distance
Formula isJ represents j-th of vector.
But, this example is due to using two kinds of cryptographic calculations, so each xi,jIt can be encrypted upload Enc (x twicei,j)=
(ce(i,j),cp(i,j))。ce(i,j)For calculating discrete point to the distance of central point, partition clustering center；cp(i,j)For re-computation
Cluster centre.In order to represent convenient, in distance of the discrete point to central point, partition clustering central process is calculated, this example ci,j
Instead of ce(i,j).Comparing and calculating data point to cluster centre apart from this part, using Liu homomorphic encryption scheme.
Encryption key in the AES is a list K (v), because only one of which t in cipher key listi≠ 0, so data possess
Person only need to be by ti≠ 0 ciIt is uploaded to outsourcing service device, that assume to upload in the present invention is c1。
, it is necessary to calculate each point to the distance of central point, this example is with d during partition clusteringi=(xi,1,xi,2,
...xi,m) arrive Et=(et,1,et,2,...et,m) exemplified by, because only uploading c1, so using ci,jRepresent, Enc (K (v), xi,j)
=(c1(i,j),...,cv(i,j)), ci,j=k1*t1*xi,j+s1 *rv(i,j)+k1 *(r1-rv-1), similarly, with c 't,jRepresent after encryption
et,j, then c 't,j=k1*t1*et,j+s1*r′v(t,j)+k1*(r1-rv-1).Then ED2(di,Et) represent the data point d after encryptioniArrive
Cluster centre EtDistance.Following equation is calculating process of the data point to the distance of cluster centre under the conditions of ciphertext：
But, the distance under this ciphertext is calculated, it is impossible to is directly used in distance and is compared, because original apart from D2(di,
Et) add afterwards and rvRelated suffix.Therefore, size is compared under the conditions of ciphertext, in addition it is also necessary to data in encryption are fallen into by door and possessed
Person that is to say that user provides Trapdoor sunken information to balance out the part that influence distance compares.
S22：Trapdoor functions in the trap door information provided according to user, outsourcing service device calculates ED2(di,Et)+
Trapdoor compares each data point to the distance of each cluster centre, nearest one of chosen distance, by this dot-dash
Assign in corresponding cluster.
The threshold information of this example is a kind of encrypted indexes of order-preserving, the encrypted indexes (Order- of order-preserving
PreservingIndexing, OPI) introduced in Liu outsourcing computations in 2014.Give a key k and plaintext
X, expression formula OPI (k, x) can produce an index on x.If two clear data x1And x2If, x1＞ x2, then
The encrypted indexes of order-preserving can ensure OPI (k, x1) ＞ OPI (k, x2).This scheme can not recover x1And x2, but can compare
Their size.
Such as, the scale of a plaintext is numeral that decimal representation of place of rightmost after plaintext decimal point,
The form of such as one numeral in plain text is XXX.XX, generally can the scale of expository writing be 2, susceptibility is 10-2, so such as
Really the scale of a plaintext array is s, then its susceptibility is 10-s.The key k for the index that this example is used is a pair of numerals
(a, b) and a ＞ 0.This example represents the susceptibility of plaintext with Sens, while OPI (k, x)=a*x+r, wherein r are in data field
Between [0, a*sens) Uniformly distributed.That is, r size has no effect on the comparison of x value.If x1＞ x2, then OPI
(k,x1)-OPI(k,x2)=a* (x1-x2)+r1-r2.Due to a* (x1-x2) ＞ a*Sens ＞ r1-r2, then, OPI (k, x1) ＞
OPI(k,x2)。
Therefore, ciphertext size is compared in this example, it is necessary to set up the index form of order-preserving for a*f (X)+g (X, R), here a tables
Show the key of encryption, X is the clear data collection for needing to compare, and R is the set of random number, and f and g are two functions, are represented respectively
Definition in addition and multiplying.The susceptibility for stating f (X) simultaneously is f (x1) and f (x2) between lowest difference away from.Assuming that f
(x1) scale be s1, f (x2) scale be s2, then f (x1)+f(x2) scale be s1And s2It is middle than larger that；f
(x1)*f(x2) scale be s1+s2。
Assuming that f (X) susceptibility is Senf, the form of ciphertext is a*f (X)+g (X, R), if this form changed
To OPI (k, x)=a*x+r.So a*f (X)+g (X, R) ciphertext form is converted into form a*f if necessary to outsourcing service device
(X)+r order-preserving index, data owner needs to construct trap door information-g (X, R)+r.Firstly the need of by ED2(di,Et) write as a*
F (X)+g (X, R) form, specific formula for calculation is as follows：
Wherein, a, f (X) and g (X, R) are as follows respectively：
A=(k1*t1)2
It is assumed here that D (di,Et) scale be s, then D2(di,Et) scale be exactly s+s=2*s, so D2(di,Et)
Susceptibility be 10-2*s, because data owner needs to provide trap door information (Trapdoor), different data distributions can cause
The form of trap door information (Trapdoor) is different.
Calculating D2(di,Et) when, outsourcing service device need not be made for data source in different data owners
Different calculating.But it is to come from which user that outsourcing service device, which needs to record each record,.Calculating distance, partition clustering
User is needed to provide trap door information (Trapdoor) during center, because outsourcing service device knows each diIt is to come from P1 or P2
Deng, so which side data owner is the data point to be calculated belong to, it is exactly that corresponding data owner provides trap door information
(Trapdoor)。
This example is in horizontal data distribution, it is assumed that diFrom P1, then just provide trap door information by P1.The lattice of trap door information
Formula is-g (X, R)+r.The trapdoor function designed in this example is made up of two parts：
Trapit(di,Et)+Trapt(Et)
Part I Trap in this two partsit(di,Et) it is trapdoor function of each data point to cluster centre point distance,
This part is the part that data owner can calculate in advance, Trapt(Et) be each cluster centre point trapdoor function, this
Part is that iteration changes as different cluster centres changes each time, and calculation formula is as follows：
Wherein, NBtjMagnitude range is [0, (k1*t1)2* sens], equivalent to one of the random number r in-g (X, R)+r
Point, the result after two parts addition is as shown in following equation.
Wherein-g (X, R) equivalent toAnd with
Machine number
In re-computation cluster centre, this example will utilize the ciphertext c encrypted in second of BCP encipherment schemep(i,j)To enter
Row is calculated, and server end uses ciphertext cp(i,j)To calculate in each cluster, how many data point, and data point correspondence
Component plus and, and according to data distribution respectively will plus and result be sent to each user Pi.It is every in order to calculate between parties
The average value of data point in individual cluster centre, this example devises OPPWAP agreements (outsourcing secret protection average calculates agreement),
The data to be calculated are attributed in the case of ciphertext and calculatedThe problem of.
Specifically, in step S4- steps S6, because the re-computation of each cluster centre is by the poly- of each division
In class, the corresponding component of discrete point for belonging to the center is mutually added in and averaged, it is assumed that have n point in being clustered at one, and t is used
Family, each user Pi,For Pi value,Each the value after user encryption isEach cpiIt is a m
The vector of dimension, high in the clouds calculates each cluster centre Pi discrete point c respectivelypiThe value of respective components is added and calculates number.That
Addition result is Xi=(xi1,xi2,...,xim), and the number for belonging to Pi points in cluster is ai, server is calculating
Good Xi,aiEach user Pi is sent respectively to, after each user Pi is encrypted with BCP encipherment schemes, then is combined with server
OPPWAP agreements are calculatedValue, last result is the average value of calculating.
Concrete methods of realizing comprises the following steps：
A1：Outsourcing service device S initialized by Setup and generate common parameter PP=(N, K, g), and by public ginseng
Number PP is sent to each user Pi；
A2：Each user Pi is obtained after common parameter, and generating machine by key generates the public key and private key (pk of oneselfi,
ski), and by public key pkiIt is sent to server；
A3：All are combined the unified public key of calculating by server, and unified public key Prod.pk is sent into each use
Family Pi；
A4：The data of oneself are obtained result (A with being encrypted by user Pii,Bi) and (Ai′,Bi′)；
A5：User Pi generates two random number ρiAnd ρi', re-computation is carried out to encryption data and obtained：
And send these data to server；
A6：Server is obtained after data, is calculated according to formula
And willWithReturn to each user Pi；
A7：User Pi is calculated and obtainedWithAnd it is sent to server；
A8：Server obtains data XiWith X 'iAfterwards, then new data are calculatedWithThen generate
Random number τ, then by K, K ',It is sent to each user Pi；
A9：Each user Pi is obtained after data, is finally calculatedIt is every so as to obtain
Average value of the data point apart from cluster centre point in individual cluster.
The present invention is from more typical K-means algorithms in cluster, in even multi-party case of the data source for two sides
Under, the secret protection of data owner's personal data is realized with cryptological technique, safe calculating is carried out with multi-party computations.
In addition, each iteration of K-means algorithms is required for calculating each data point to the distance of each central point, cycle calculations
Time cost it is very big, this problem by this part calculating be contracted out to server, improve efficiency.
The effect of the present invention is further illustrated with reference to experimental data：
The experiment of the present invention is carried out on unit, and system development environment is as follows：
(1) system of operation is windows7, and processor is that Intel (R) Core (TM) i5-4570CPU speed is
3.2GHz, the memory size of system is 8G；
(2) be 512 from the BCP encryption keys encrypted, in the operation phase, can because key than larger speed ratio compared with
Slowly；
(3) programming language is Java, and running environment is eclipse, and system database is Mysql.
Experimental data of the present invention is the data for the data mining downloaded from common data sets UCI, and former data are decimals, by
It is the encipherment scheme based on group in BCP encryptions, does not support fractional arithmetic, the later stage is processed data into as integer.Number after processing
According to for 7 attributes, 10000 datas.Partial data is as shown in Figure 3.
As shown in Figure 4 and Figure 5, in order to verify the correctness of the invention calculated under ciphertext, in an experiment, carried out in plain text
Under K-means cluster, by contrast as can be seen that identical data under ciphertext and plaintext cluster result it is completely the same, with reality
Test the theoretical correctness of result verification this paper.
Fig. 3 and Fig. 4 are the parts for having intercepted cluster result, cluster centre initial point be set to three 15,14,2,6,
4,4,6 }, { 1,1,1,1,1,1,1 }, { 15,13,2,6,4,4,6 }, wherein the first data is test data, can therefrom be seen
To data it is identical in the case of, cluster result is completely the same.The time of data encryption, ciphering process was two kinds as shown in table 1
Homomorphic cryptography is carried out simultaneously.
Encrypt the spent time within the acceptable range as can be seen from Table 1, the time that Trapdoor is spent
With it is more less slightly than encryption times because in Trapdoor calculating be directed to each diNeed to calculate the cumulative of each component, plus
Close number of times is few, but formula is more complex for relatively encrypting, with encryption diThe time contrast of cost is less slightly, but gap is little.
The encryption times of table 1 are consumed
During an iteration, the time spent required for data owner mainly includes trap door information (Trapdoor)
Calculating, and OPPWAP agreements calculate spend time.Contrast is made respectively in the case where data point number is different, as a result
As shown in table 2.
An iteration elapsed time of table 2
As shown in fig. 6, carrying out the line chart of the time loss contrast of an iteration for server and a user.Abscissa
The central point number of cluster is represented, ordinate represents the time of cluster, with millisecond (ms) for unit.It can be seen that data owner
Time loss is much smaller than server.Table 3 is during an iteration, the time of user Alice and Bob consumption, mainly to include
The time of OPPWAP and Trapdoor consumption.
Data owner needs the time consumed in an iteration of table 3
What table 2 and table 3 were shown is all it can be seen that with data in the time cost that an iteration is consumed, table 3 and table 2
The number of point increases, and the time cost of server end can increase, because increasing relevant with iterations, is not linear increase
It is long.But time cost consumption and the number of data point between Alice and Bob and uncorrelated, as can be seen from Table 3
The time cost that Trapdoor is consumed is relatively small, and time cost is largely all accounted for by the OPPWAP time loss calculated
With.But the number of times that OPPWAP is calculated is related to the dimension m of data point to cluster number k, so in an iteration,
The time that the time that OPPWAP is calculated is consumed in Alice and Bob is basicly stable, because k and m do not have in calculating process
There is change.As can be seen from Table 2 when the number increase of data point, server end can undertake more calculation costs, and
The cost that data owner is calculated tends towards stability substantially, and the time cost that Trapdoor is calculated is far smaller than server.
Because the iterations of K-means cluster calculations is less controllable, iterations and data point number, the number of cluster
And each selected initial point correlation.In K-means algorithms in use, K (cluster number) is often the number of a determination,
Cluster in the case that number K values determine, this, which is tested, is set as 3, data point number and iterations substantially degree of correlation such as table 4
It is shown.
The reference of the data point number of table 4 and iterations
Communication consumption in whole cluster, it is main to include uploading ciphertext data, OPPWAP agreements and upload in new cluster
The heart and Trapdoor functions, cluster centre and Trapdoor are uploaded together here, so communication cost is calculated together.
Whole communication cost as shown in table 5, it is necessary to explanation be OPPWAP agreements and cluster centre and Trapdoor functions are with one
Exemplified by secondary iteration, because K-means iterationses are uncontrollable, total communication consumption after successive ignition is provided, it is too late once to change
For more meaningful.
The communication consumption of table 5
From table 5, it is close with the time for uploading cluster centre point to upload data, because being to upload one in an experiment
Three-dimensional array, thus upload data time be substantially it is consistent.Whole OPPWAP time because calculate and communication when
Between substantially carry out simultaneously, so entirely OPPWAP time is that Alice and Bob is calculated respectively in an iteration in table 2
The result that OPPWAP time is added, because how much indefinite each computing computer unlatching process is, so the time taken is many
Average value after secondary operation program.
Finally, this example is calculated under the ciphertext according to the progress of this programme by Experimental comparison time efficiency and plaintext
The time efficiency of lower calculating.It is broadly divided into three parts：The difference for uploading clear data and ciphertext data respectively, in plain text and
The time-consuming contrast of ciphertext next iteration, and the contrast that the whole cluster process time is time-consuming.In order to make experimental data contrast bright
It is aobvious, select to carry out in the case of 2000 data points, 7 property values.
The calculating time contrast of the plaintext of table 6 and ciphertext
Table 6 represents to calculate in plain text in data, an iteration time and time for entirely clustering is uploaded and cryptogram computation
Overall contrast.Because data are uploaded in experiment to be uploaded in 7 dimension group forms, the time for uploading array is substantially one
The fixed time is 79ms.In an iteration, due to needing to carry out OPPWAP calculating and communication consumption in cryptogram computation,
So cryptogram computation is relatively in plain text, it can have more the time by about one time.In whole cluster calculation, because experiment is using reading document
Form, reading data time can be than very fast, and cryptogram computation is relatively calculated in plain text can also have more the time of encryption.If reading number
According to storehouse, the time can relatively read document and have more 2-3s, and this example is in order to calculate the accurate of time, so in experiment with computing efficiency process
In, using the form for reading document.In figures 7 and 8, the difference of plaintext and ciphertext is represented using histogrammic form.Nogata
Ordinate represents the time in figure, and Fig. 7 unit is millisecond (ms), and Fig. 8 unit is the second (s).
The outsourcing experiment with computing that the present invention is carried out, the K-means outsourcings compared with secret protection are calculated, and are simply had more
The time that OPPWAP agreements are calculated.From table 5, it can be seen that OPPWAP time loss is about 412ms in an iteration, due to repeatedly
Generation number is uncontrollable, so this experiment is on the basis of providing an iteration time.Whether it is multi-party, or folk prescription, transmission
The consumption of Trapdoor versus times is essentially identical.
In summary, the data mining and outsourcing of secret protection are calculated and are combined by the present invention, and have carried out experimental analysis.
The main achievement of the present invention has following several respects：
(1) advantage and disadvantage of different technologies of the analysis and summary in terms of the data mining of secret protection, data perturbation technology
Data are often damaged, and are a kind of a kind of methods compromised in secret protection and data mining precision.Cryptological technique is not
Data mining results can be influenceed, data encryption is also with than larger time cost.Present invention selection cryptological technique, passes through choosing
The mode for selecting the efficient AES of comparison and data outsourcing improves efficiency；
(2) conventional method application Andrew Chi-Chih Yao calculates the safety circuit appraisal procedure proposed for safety, and this method passes through
The step-by-step of 01 string encrypts to realize, time cost is very big；And only with secret protection weighted average problem data point away from
From comparison on again processing it is not perfect enough.The present invention falls into algorithm and the secret protection of encryption by using a kind of improved door
Data mining is combined, and relatively good solves the above problems, and also has lifting in efficiency；
(3) outsourcing for devising a kind of K-means clustering algorithms of secret protection calculates agreement, by K-means algorithms
The calculating of the point distance of cycle calculations two is contracted out to server, comes real by using the multi-party computations of two kinds of encryption technology designs
It is existing.Improved Liu encipherment scheme is used to compare data point to the distance of cluster centre, partition clustering；BCP is encrypted for clustering
The re-computation at center；
(4) time complexity analysis, space complexity and safety analysis have been carried out for the present invention, and finally carried out
Experimental verification.The present invention realizes the safety calculating under semi-honesty model, while the conspiracy that can be resisted to a certain extent is attacked
Hit.
Embodiment described above is the better embodiment of the present invention, not limits the specific of the present invention with this
Practical range, the scope of the present invention includes being not limited to present embodiment, all equal according to the equivalence changes of the invention made
Within the scope of the present invention.
Claims (10)
1. multi-user's secret protection data clustering method based on ciphertext data, it is characterised in that comprise the following steps：
S1：Two or more user sends data and cluster centre point, trap door information after each encryption to server；
S2：Server calculates ciphertext data point and the distance of cluster centre point, and according to distance and trap door information partition clustering；
S3：The data point of user different in each cluster is added by server respectively, and by the summation and number of data
It is sent respectively to respective user；
S4：Each user is according to the data summation and number received, by being sent to server after BCP enciphered method re-encrypteds；
S5：Server calculates new cluster centre point, and new cluster centre point is sent into each user；
S6：Each user calculates data point distance cluster in each cluster of the common calculating of agreement by outsourcing secret protection average
The average value of central point, is then sent to server, returns and performs step S1, until the average value is less than threshold value, classification knot
Classification results are sent respectively to each user by beam, server according to data source.
2. multi-user's secret protection data clustering method according to claim 1, it is characterised in that：In step sl, institute
Server is stated for outsourcing service device, user is encrypted twice by homomorphic cryptography and BCP encryptions to data respectively, data set D
={ d1,d2,...,dnInclude n data, each data point di=(xi,1,...,xi,m), m represents that each data point is m dimensions
Vector, each data point diIn component xi,jEncrypted outsourcing service device Enc (x will be uploaded to twicei,j)=(ce(i,j),
cp(i,j)), wherein, 1≤i≤n, 1≤j≤m, ce(i,j)Represent the ciphertext after the homomorphic encryption scheme encryption using Liu, cp(i,j)
Represent with the ciphertext after the encryption of BCP encipherment schemes.
3. multi-user's secret protection data clustering method according to claim 2, it is characterised in that：Step S2 processing side
Method includes：
S21：Server is according to ciphertext ce(i,j)Calculate ciphertext data point diWith t-th of cluster centre point EtApart from ED2(di,Et),
Wherein, k is the number of cluster centre point, 1≤t≤k；
S22：Trapdoor functions in the trap door information provided according to user, outsourcing service device calculates ED2(di,Et)+
Trapdoor compares each data point to the distance of each cluster centre, nearest one of chosen distance, by this dot-dash
Assign in corresponding cluster.
4. multi-user's secret protection data clustering method according to claim 3, it is characterised in that：In the step s 21, often
One data point di=(xi,1,...,xi,m) and each cluster centre point Et=(et,1,...,et,m) all it is m dimensional vectors, and it is every
The encryption data of individual data point is ce(i,j)=(ce(i,1),...,ce(i,m)), it is described apart from ED2(di,Et) calculation formula be：
5. multi-user's secret protection data clustering method according to claim 4, it is characterised in that：In step S22, institute
State Trapdoor functions be used for produce can compare the order-preserving encrypted indexes of two size of data.
6. multi-user's secret protection data clustering method according to claim 3, it is characterised in that：In step s3, take
Device end be engaged in using ciphertext cp(i,j)Come calculate each cluster in, how many data point, and data point respective components add
With, and it is sent to each user Pi by plus with result respectively according to data distribution.
7. multi-user's secret protection data clustering method according to claim 6, it is characterised in that：In step S4- steps
In S6, due to the re-computation of each cluster centre be will each divide cluster in, belong to the center discrete point correspondence
Component be mutually added in and average, it is assumed that have n point in being clustered at one, t user, each user Pi,For Pi value,Each the value after user encryption isEach cpiIt is the vector of a m dimension, high in the clouds calculates each poly- respectively
Class center Pi discrete point cpiThe value of respective components is added and calculates number.SoAddition result is Xi=(xi1,
xi2,...,xim), and the number for belonging to Pi points in cluster is ai, server is the X calculatedi,aiIt is sent respectively to each use
Family Pi, after each user Pi is encrypted with BCP encipherment schemes, then is calculated with server combination OPPWAP agreementsValue, last result is the average value of calculating.
8. multi-user's secret protection data clustering method according to claim 7, it is characterised in that：Server and each use
Processing procedures of the family Pi based on OPPWAP agreements comprises the following steps：
A1：Outsourcing service device S initialized by Setup and generate common parameter PP=(N, K, g), and by common parameter PP
It is sent to each user Pi；
A2：Each user Pi is obtained after common parameter, and generating machine by key generates the public key and private key (pk of oneselfi,ski), and
By public key pkiIt is sent to server；
A3：All are combined the unified public key of calculating by server, and unified public key Prod.pk is sent into each user
Pi；
A4：The data of oneself are obtained result (A with being encrypted by user Pii,Bi) and (Ai′,Bi′)；
A5：User Pi generates two random number ρiWith ρ 'i, re-computation is carried out to encryption data and obtained：
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And send these data to server；
A6：Server is obtained after data, is calculated according to formulaAnd
WillWithReturn to each user Pi；
A7：User Pi is calculated and obtainedWithAnd it is sent to server；
A8：Server obtains data XiAnd Xi' after, then calculate new dataWithThen generate random
Number τ, then by K, K ',It is sent to each user Pi；
A9：Each user Pi is obtained after data, is finally calculatedSo as to obtain each cluster
Average value of the middle data point apart from cluster centre point.
9. a kind of system realized according to any one of claim 1-8 multi-user's secret protection data clustering methods, it is special
Levy and be：Including server and two or more user, the user is used to believe the data after encryption and cluster centre point, trapdoor
Cease to server, according to the data summation and number received, by being sent to server after BCP enciphered method re-encrypteds, calculate
Data point is then sent to server apart from the average value of cluster centre point in each cluster；The server is used to calculate close
The distance of literary data point and cluster centre point, and according to distance and trap door information partition clustering, by use different in each cluster
The data point at family is added respectively, and the summation and number of data are sent respectively into respective user, calculates new cluster
Central point, and new cluster centre point is sent to each user, after classification terminates, classification results are distinguished according to data source
It is sent to each user.
10. system according to claim 9, it is characterised in that：The server is the cloud server of outsourcing.
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