CN106790069A - Secret protection K NN sorting techniques based on vectorial homomorphic cryptography - Google Patents
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Abstract
Secret protection K NN sorting techniques the present invention relates to be based on vectorial homomorphic cryptography, including：A. query vector group and standard vector group are received；B. by query vector group generator matrix G, standard vector group passes through vectorial homomorphic cryptography and generates ciphertext group and new key GS using key S；C. key is carried out to new key GS and is converted to transition key S', obtain transition matrix M now and conversion ciphertext group；D. conversion ciphertext group is decrypted using transition key S', obtains descrambled vector group；E. according to the K component of the descrambled vector of minimum value for corresponding each query vector encloses tag along sort.The present invention can be good to privacy of user data protection; and in the case where private data is protected; efficient, accurate classification is carried out to the query vector of user by K NN algorithms, the efficiency judged vector type is improve, the range of application of vector type judgement is expanded.
Description
Technical field
The present invention relates to vector sorting method of the K-NN algorithms under secret protection, added based on vectorial homomorphism
Close secret protection K-NN sorting techniques.
Background technology
K closes on algorithm (K-NN) and is widely used in pattern-recognition, also has good performance in data classification.Counting greatly
According to the epoch, complicated calculating is often contracted out to third party cloud.But in this process, the data of outsourcing may include quick user
Some sensitive data, the information of user be directly contracted out to third party cloud likely result in some privacy informations of user and let out
Expose, caused damage to user.A kind of direct settling mode exactly will again upload to high in the clouds after data encryption, but this
Also the efficiency to K-NN algorithms brings some new challenges.Homomorphic cryptography technology can be operated under ciphertext, and decrypt it
Result afterwards is correct.In can be by running K-NN side after homomorphic cryptography technology secrecy under ciphertext again by data
Method.Traditional encipherment scheme is encrypted mainly for integer, and the integrated operation for vector is inefficient, for efficiency aspect
Consider can carry out encryption data using vectorial homomorphic cryptography technology, can so greatly improve operational efficiency.
K-NN methods are number of samples K (n) that fixation is fallen into neighborhood in a neighborhood centered on characteristic vector x.
Generally realize in the following way：Under a suitable distance scale (conventional Euclidean (Euclidean) distance), little by little
The volume in the region of x points is surrounded in increase, until there is the individual sample points of K (n) to fall into the region.Need to carry out probability during this
Density estimation, its density estimation form is：
Wherein, n is number of samples, and V (n) is the volume in the region.If the sample around x points
This number is less, then corresponding region will become very big, i.e. the value of V (n) is very big,Value become very little.Phase
Instead, if the sample point number around x points is more, then corresponding region will become smaller, i.e. the value of V (n) is smaller,Value become very big.And K (n) can also increase with the increase of n.Because k nearest neighbor rule carries out probability Estimation density
When, there are two shortcomings, one is that the integration for estimating density must diffuse into infinity, and two is there is white elephant on calculating.
Therefore, some researchers are directly classified with K-NN algorithms, and the principle of classification is：Under a certain distance yardstick, it is considered to
The individual nearest samples of K (n) around sample x to be identified, and x is included into most that of a certain class sample in the individual arest neighbors of K (n)
In individual classification.Algorithm steps：
(1) data object y to be sorted to, the distance of each data object in calculating it with training set R；
(2) the closest k of the data object treated in divided data object y and training set R is found out individual；
(3) generic of this k according to object is counted successively, finds out the class comprising most numbers；
(4) will treat divided data y be divided into it is such in；
(5) above step is repeated, until the classification of needed divided data terminates；
K-NN algorithms can be not only used for classification, can be also used for returning.By finding out a K arest neighbors of sample
Occupy, the average value of the attribute of these neighbours is assigned to the sample, it is possible to obtain the attribute of the sample.
The content of the invention
The secret protection K-NN sorting techniques based on vectorial homomorphic cryptography that the present invention is provided, can be to privacy of user data
In the case of protection, efficient, accurate classification is carried out to the query vector of user by K-NN algorithms.
Secret protection K-NN sorting technique of the present invention based on vectorial homomorphic cryptography, step includes：
A. query vector group (x is received1, x2... xn) and standard vector group (p1, p2... pm), wherein standard vector group (p1,
p2... pm) to that should have criteria classification label (t1, t2... tm)；
B. it is key due to having formula S c=ω x+e, S, c is ciphertext, and ω is big integer, and x is query vector, and e is error
, and the value of each element of e is not more thanMake | S | ＜ ＜ ω simultaneously.So pass through arbitrary matrixThen may be used
To obtain：(GS) c=ω Gx+Ge, can regard Gx as and ciphertext c is encrypted under key GS.Therefore query vector group is passed through
(x1, x2... xn) obtain inquiring about matrix G, inquire about matrixN represents the line number of inquiry matrix G, is query vector group
Vectorial number, w represents the columns of inquiry matrix G, is the dimension of each query vector, standard vector group (p1, p2... pm) in
Each standard vector using key S pass through vectorial homomorphic cryptography generate key transition matrix M and with standard vector group (p1, p2...
pm) corresponding ciphertext group (c1, c2... cm), obtain new key GS by inquiring about matrix G and key S；
C. key conversion is carried out to described new key GS：Transition key S', wherein S'=[I, T] are set, andWherein I is unit matrix, and T is random matrix, and n is the dimension of query vector, and m is the dimension for changing ciphertext group；So
New key GS is converted into transition key S' afterwards, now corresponding key transition matrix M is obtained, is turned by the key now
Change matrix M and obtain ciphertext group (c1, c2... cm) corresponding conversion ciphertext group (c1', c2' ... cm'), whereinWherein h
It is each conversion ciphertext ci' dimension, w is the dimension of each query vector, and λ meets | ci' | ＜ 2λ, i≤m；
D. using described transition key S' to described conversion ciphertext group (c1', c2' ... cm') decryption, obtain decrypting to
Amount group (D1, D2... Dm), wherein each descrambled vector DiComponent be (di1, di2... din), i≤m；
E. it is query vector group (x1, x2... xn) in each query vector xyEnclose tag along sort, y≤n：Compare decryption to
Amount group (D1, D2... Dm) in each descrambled vector y-th component (d1y, d2y... dmy) size, find wherein minimum K point
Amount；The most tag along sort of occurrence number in the corresponding tag along sort of the K component is assigned to vector x againy, wherein component
(d1y, d2y... dmy) corresponding tag along sort is respectively criteria classification label (t1, t2... tm), K values are determined in itself by K-NN algorithms
It is fixed.
Further, the key conversion described in step C, can be realized, by the method for vectorial homomorphic cryptography wherein wrapping
Include：
C1, first by ciphertext group (c1, c2... cm) in each ciphertext and new key GS be converted into the ratio that corresponding bit is represented
Special ciphertext group (c1 *, c2 *... cm *) and bit keys (GS)*；
C2, setting transition key S', wherein S'=[I, T], andWherein I is unit matrix, and T is random square
Battle array, n is the dimension of query vector, and m is the dimension for changing ciphertext group；Then pass throughNow corresponded to
Key transition matrix M, wherein A is random matrix, and E is random noise matrix；
C3, by the now corresponding key transition matrix M and c '=Μ c*, obtain described conversion ciphertext group
(c1', c2' ... cm')。
Ciphertext group c and new key GS are converted into the process that bit represents can be realized by vectorial homomorphic cryptography.Institute
C is represented so that they are first converted into corresponding bit*And S*Because | c*|=max | ci|=1, can so prevent from missing
Difference item increases excessive, so as to ensure the correctness of decryption.Its transfer process is：
Selection λ and satisfaction | c | ＜ 2λ, each component c of ciBit represent bi=[bi(λ-1),...,bi1,bi0]Τ, bik
∈ { -1,0,1 }, then：
S is constructed by initial key S*：Its formula is, by each component S of key SijIt is substituted for Bij=[2λ- 1Sij,...,2Sij,Sij], wherein：I is the line number of key S components, and j is the columns of key S components, and meets S*c*=Sc.Will
All SijReplace with BijAfterwards, will key S conversion for S*.According to above-mentioned formula by new key GS switch bits key (GS)*。
Above-mentioned steps can be realized by the method for vectorial homomorphic cryptography, no longer described in detail in the present invention.Vectorial homomorphism
The method of encryption is proposed by Zhou and Wornell, and the method can ensure operation function when computing is carried out to encryption data
Privacy.The homomorphism computing that the addition of program supporting vector, linear transformation and weighting Inner are accumulated.The present invention changes to the method for putting
On the basis entered so that the method for the present invention in the case where being maintained secrecy to third party cloud, can realize the classification of efficiently and accurately.
It, for the determination methods in K-NN algorithms, and is that two vectors are characterized by Euclidean distance to be due to the present invention
Between similarity degree, the Euclidean distance between query vector x and standard vector p is：||x-p||2=xTx+pTp-2xTP,
Therefore can in stepb, by standard vector group (p1, p2... pm) in each standard vector be converted to pi'=(pi Tpi,1,-
2pi T)T, i≤m, by the standard vector group (p after conversion1', p2' ... pm') right by vectorial homomorphic cryptography generation using key S
Ciphertext group (the c for answering1, c2... cm)。
Likewise, can also be by query vector group (x in step B1, x2... xn) in each query vector be converted to xj'=
(1,xj Txj,xj T)T, j≤n, and inquiry matrix is setSo just cause | | x-p | |2=p'TX', thus calculates
Each query vector xjWith standard vector piBetween Euclidean distance, and now the supplier of standard vector is to query vector plaintext
Content do not know, has reached the purpose of protection data-privacy.
In actual implementation process, data are all contracted out to third party high in the clouds to be calculated.And in this process
In, third party high in the clouds is generally all incredible, therefore the privacy for ensureing data to incredible high in the clouds in this process is
It is necessary.
Actual implementation process is as follows：
1) the key S transmission that standard vector supplier is encrypted to standard vector using the method for the present invention and will encrypted
Give query vector owner.
2) the corresponding ciphertext group c of standard vector group after encryption is uploaded to high in the clouds by standard vector supplier.
3) then query vector owner selectes transition key S' using the key S for obtaining, and key is carried out to query vector
Conversion, obtains key transition matrix M, and corresponding transition matrix M then is sent into high in the clouds.
4) high in the clouds receives the ciphertext group from standard vector supplier and the key conversion from query vector owner
After matrix M, new ciphertext group c' is calculated.
5) after high in the clouds calculates new ciphertext group c', new ciphertext group c' is returned into query vector owner, inquire about to
Amount owner obtains the tag along sort of each query vector using the step of the invention.
In whole process, data are all secrecy for high in the clouds, therefore have reached the purpose of secret protection.
Secret protection K-NN sorting technique of the present invention based on vectorial homomorphic cryptography, can be good to privacy of user data
Protection, and in the case where private data is protected, the query vector of user is carried out by K-NN algorithms efficient, accurate
Classification, improve to vector type judge efficiency, expand vector type judgement range of application.
Specific embodiment with reference to embodiments, is described in further detail again to the above of the invention.
But this scope for being interpreted as above-mentioned theme of the invention should not be only limitted to following example.Think above-mentioned technology of the invention is not departed from
In the case of thinking, according to various replacements or change that ordinary skill knowledge and customary means are made, this hair all should be included in
In bright scope.
Brief description of the drawings
Fig. 1 is the flow chart of secret protection K-NN sorting technique of the present invention based on vectorial homomorphic cryptography.
Specific embodiment
Secret protection K-NN sorting technique of the present invention based on vectorial homomorphic cryptography, including step as shown in Figure 1：
A. query vector group (x is received1, x2... xn) and standard vector group (p1, p2... pm), wherein standard vector group (p1,
p2... pm) to that should have criteria classification label (t1, t2... tm)；
B. it is key due to having formula S c=ω x+e, S, c is ciphertext, and ω is big integer, and x is query vector, and e is error
, and the value of each element of e is not more than| S | simultaneously<<ω.So pass through arbitrary matrix(n is represented and looked into
The line number of matrix G is ask, is the vectorial number of query vector group, w represents the columns of inquiry matrix G, is the dimension of each query vector
Degree), then can obtain：(GS) c=ω Gx+Ge, can regard Gx as and ciphertext c is encrypted under key GS.Therefore by looking into
Ask Vector Groups (x1, x2... xn) obtain inquiry matrix G.Characterized by Euclidean distance in K-NN algorithms between two vectors
Similarity degree, represent that the distance between query vector x and standard vector p are with Euclidean distance：||x-p||2=xTx+pTp-
2xTP, therefore by standard vector group (p1, p2... pm) in each standard vector be converted to pi'=(pi Tpi,1,-2pi T)T, i≤m,
Standard vector group (p after conversion1', p2' ... pm') using key S pass through vectorial homomorphic cryptography generate key transition matrix M with
And with standard vector group (p1, p2... pm) corresponding ciphertext group (c1, c2... cm).By query vector group (x1, x2... xn) in
Each query vector is converted to xj'=(1, xj Txj,xj T)T, j≤n, and inquiry matrix is setSo just cause | | x-p
||2=p'TX', new key GS is obtained by inquiring about matrix G and key S；
The method of described vectorial homomorphic cryptography is proposed by Zhou and Wornell, and the method is carried out to encryption data
The privacy of operation function can be ensured during computing.The homomorphism of the addition, linear transformation and weighting Inner products of program supporting vector
Computing.
C. key conversion is carried out to described new key GS：Transition key S', wherein S'=[I, T] are set, andWherein I is unit matrix, and T is random matrix, and n is the dimension of query vector, and m is the dimension for changing ciphertext group；So
New key GS is converted into transition key S' afterwards, now corresponding key transition matrix M is obtained, is turned by the key now
Change matrix M and obtain ciphertext group (c1, c2... cm) corresponding conversion ciphertext group (c1', c2' ... cm'), whereinWherein h
It is each conversion ciphertext ci' dimension, w is the dimension of each query vector, and λ meets | ci' | ＜ 2λ, i≤m.Specially：
C1, first by ciphertext group (c1, c2... cm) in each ciphertext and new key GS be converted into the ratio that corresponding bit is represented
Special ciphertext group (c1 *, c2 *... cm *) and bit keys (GS)*；
C2, setting transition key S', wherein S'=[I, T], andWherein I is unit matrix, and T is random square
Battle array, n is the dimension of query vector, and m is the dimension for changing ciphertext group；Then pass throughNow corresponded to
Key transition matrix M, wherein A is random matrix, and E is random noise matrix；
C3, by the now corresponding key transition matrix M and c '=Μ c*, obtain described conversion ciphertext group
(c1', c2' ... cm')。
All random vectors or the equal Gaussian distributed of matrix in the present embodiment.Because above-mentioned steps can pass through
The method of vectorial homomorphic cryptography is realized, no longer described in detail in the present embodiment.
D. using described transition key S' to described conversion ciphertext group (c1', c2' ... cm') decryption, obtain decrypting to
Amount group (D1, D2... Dm), wherein each descrambled vector DiComponent be (di1, di2... din), i≤m；
E. it is query vector group (x1, x2... xn) in each query vector xyEnclose tag along sort, y≤n：Compare decryption to
Amount group (D1, D2... Dm) in each descrambled vector y-th component (d1y, d2y... dmy) size, find wherein minimum K point
Amount；The most tag along sort of occurrence number in the corresponding tag along sort of the K component is assigned to vector x againy, wherein component
(d1y, d2y... dmy) corresponding tag along sort is respectively criteria classification label (t1, t2... tm), K values are determined in itself by K-NN algorithms
It is fixed.
Claims (4)
1. the secret protection K-NN sorting techniques of vectorial homomorphic cryptography are based on, it is characterized by：
A. query vector group (x is received1, x2... xn) and standard vector group (p1, p2... pm), wherein standard vector group (p1, p2...
pm) to that should have criteria classification label (t1, t2... tm)；
B. query vector group (x is passed through1, x2... xn) obtain inquiring about matrix G, inquire about matrixN represents inquiry matrix G's
Line number, is the vectorial number of query vector group, and w represents the columns of inquiry matrix G, is the dimension of each query vector, standard to
Amount group (p1, p2... pm) in each standard vector using key S pass through vectorial homomorphic cryptography generate key transition matrix M and with
Standard vector group (p1, p2... pm) corresponding ciphertext group (c1, c2... cm), obtain new key by inquiring about matrix G and key S
GS；
C. key conversion is carried out to described new key GS：Transition key S', wherein S'=[I, T] are set, andIts
Middle I is unit matrix, and T is random matrix, and n is the dimension of query vector, and m is the dimension for changing ciphertext group；Then by new key
GS is converted to transition key S', obtains now corresponding key transition matrix M, is obtained by the key transition matrix M now
To ciphertext group (c1, c2... cm) corresponding conversion ciphertext group (c1', c2' ... cm'), whereinWherein h is each turn
Change ciphertext ci' dimension, w is the dimension of each query vector, and λ meets | ci' | ＜ 2λ, i≤m；
D. using described transition key S' to described conversion ciphertext group (c1', c2' ... cm') decryption, obtain descrambled vector group
(D1, D2... Dm), wherein each descrambled vector DiComponent be (di1, di2... din), i≤m；
E. it is query vector group (x1, x2... xn) in each query vector xyEnclose tag along sort, y≤n：Compare descrambled vector group
(D1, D2... Dm) in each descrambled vector y-th component (d1y, d2y... dmy) size, find K wherein minimum component；
The most tag along sort of occurrence number in the corresponding tag along sort of the K component is assigned to vector x againy, wherein component
(d1y, d2y... dmy) corresponding tag along sort is respectively criteria classification label (t1, t2... tm)。
2. the secret protection K-NN sorting techniques of vectorial homomorphic cryptography are based on as claimed in claim 1, it is characterized by：Step C
Described in key conversion, including：
C1, first by ciphertext group (c1, c2... cm) in each ciphertext and new key GS to be converted into the bit that corresponding bit represents close
Literary group of (c1 *, c2 *... cm *) and bit keys (GS)*；
C2, setting transition key S', wherein S'=[I, T], andWherein I is unit matrix, and T is random matrix, and n is
The dimension of query vector, m is the dimension for changing ciphertext group；Then pass throughObtain now corresponding key
Transition matrix M, wherein A are random matrix, and E is random noise matrix；
C3, by the now corresponding key transition matrix M and c '=Μ c*, obtain described conversion ciphertext group (c1',
c2' ... cm')。
3. the secret protection K-NN sorting techniques of vectorial homomorphic cryptography are based on as claimed in claim 1 or 2, it is characterized by：Step
In rapid B, by standard vector group (p1, p2... pm) in each standard vector be converted to pi'=(pi Tpi,1,-2pi T)T, i≤m will
Standard vector group (p after conversion1', p2' ... pm') pass through the corresponding ciphertext group (c of vectorial homomorphic cryptography generation using key S1,
c2... cm)。
4. the secret protection K-NN sorting techniques of vectorial homomorphic cryptography are based on as claimed in claim 1 or 2, it is characterized by：Step
In rapid B, by query vector group (x1, x2... xn) in each query vector be converted to xj'=(1, xj Txj,xj T)T, j≤n, and set
Put inquiry matrix
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| CN112152777A (en) * | 2020-08-18 | 2020-12-29 | 西安交通大学 | Homomorphic cryptographic operation-oriented key conversion method, system, equipment and readable storage medium |
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| CN114817999A (en) * | 2022-06-28 | 2022-07-29 | 北京金睛云华科技有限公司 | Outsourcing privacy protection method and device based on multi-key homomorphic encryption |
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