CN106788962B - Vector similarity judgment method under privacy protection - Google Patents

Abstract

The invention relates to a vector similarity judgment method under privacy protection, wherein the vector similarity judgment method under privacy protection based on vector scaling transformation comprises the following steps: A. receiving two standard vectors x1, x2 and a vector to be queried x 3; B. stretching x1, x2 and x3 to obtain two standard output vectors L1 and L2 and an output vector L3 to be queried; C. after an error threshold d is set, respectively calculating L1-L3 and L2-L3; D. comparing the size relationship between L1-L3-L2-L3 and d, determining that x3 is similar to x1 or x 2. The invention can efficiently judge the similarity between vectors by comparing the modular length of the vectors on the premise of not disclosing the value of each dimension of the vector, and the performance is hardly reduced by comparing the efficiency of ciphertext comparison with that of plaintext comparison.

Description

Vector similarity judgment method under privacy protection

Technical Field

The invention relates to a vector similarity judgment method under privacy protection.

Background

In the big data era, data is often outsourced to third party agent clouds. However, in this process the user's data may imply some sensitive information, which directly makes the private data potentially compromised. The most direct way to solve the problem is to encrypt the data and send the encrypted data to the server, and then the server realizes machine learning under the ciphertext to complete the related data mining algorithm. But it is difficult to do this, such as to implement the comparison in the ciphertext. The existing schemes are low in efficiency. In a practical application scenario, the features of some things can be often characterized by feature vectors. In this process, some attributes of the vectors, such as included angle, mode length, inner product, etc., are often compared. Such as biometric-based authentication, is to identify the identity of a user through the user's biometric features, such as a fingerprint, iris, DNA, etc. Firstly, a user inputs the biological characteristics of the user as a template, when the user logs in the system, the biological characteristics of the user and the template need to be provided for comparison, and if the biological characteristics and the template are similar enough, the user passes the authentication of the system. On the other hand, the user's biometric features are related to the user's privacy and need to be protected.

When characterizing the similarity between two vectors, the euclidean distance can be used to measure the similarity between the two vectors. In the existing template feature vector V ═ V (V)₁,…,V_l) And (W) a feature vector W at the time of user authentication₁,…,W_l) As many matches as possible to return the similarity of the two vectors. One of the most common methods is to calculate the Euclidean distance between two vectors<V,W>＝∑_i(V_i-W_i)²The smaller the distance, the more similar. To protect the privacy of the user, both vector V and vector W should be encrypted. However, encryption limits the use of data, and it is difficult for the server to compare which two vectors have smaller euclidean distances using conventional encryption methods. Whereas Fully Homomorphic Encryption (FHE) can be computed directly on the basis of the ciphertext without decryption. One possible solution is then to use the homomorphic encryption of vectors to securely compute the two ciphertext euclidean distances:<V',W'>and X' represents the encryption of X. However, the traditional fully homomorphic encryption is based on integers, and the operation of the traditional fully homomorphic encryption on vectors is performed on a single dimension of the vectors, so that the efficiency is extremely low.

In addition, the inner product can be used to characterize the similarity between two vectors. By the existing template feature vector V ═ V₁,…,V_l) And (W) a feature vector W at the time of user authentication₁,…,W_l) To return two vectorsA similarity score. We can compute the inner product of two vectors<V,W>＝∑_iV_i*W_iThe greater the distance, the more similar. Also to protect the privacy of the user, both vector V and vector W should be encrypted. It is also difficult to compare the inner products of the vectors in the ciphertext.

From experimental results, current encryption schemes are fast when encrypting single-dimensional data, but require multiple interactions of both parties for homomorphic operation of multiplication. And when the Euclidean distance or the inner product of the vector is calculated, multiple times of multiplication operations are involved, so that the efficiency of the existing method is low. Secondly, the processing for comparing the ciphertext involves very complicated calculation, and the efficiency is far lower than the calculation speed in the plaintext from the existing experimental result.

Disclosure of Invention

According to the vector similarity judging method under privacy protection, provided by the invention, on the premise that the value of each dimension of the vector is not disclosed, the similarity between the vectors can still be judged by comparing the modular length of the vectors.

The invention discloses or partially discloses the modular length of the vector to meet the comparison requirement on the premise of ensuring the self safety of the number vector. Since the privacy of the vector modulo length is not as strong with respect to the value of each dimension of the vector, which is important for comparison of the vectors, the privacy of the vector modulo length can be sacrificed in exchange for reducing the complexity of comparison under the vector cipher text.

The vector similarity judgment method under the privacy protection based on the vector scaling transformation comprises the following steps:

A. receiving two standard vectors x1 and x2, and receiving a vector to be queried x 3;

B. by L ═ λ x + e_xThe two standard vectors x1 and x2 and the vector to be queried x3 are expanded to obtain two standard output vectors L1 and L2 corresponding to the two standard vectors x1 and x2 and a vector to be queried L3 of the vector to be queried x3, wherein L is an output vector, lambda is a received large integer, x is a received vector, e is a received vector_xFor a gaussian distribution corresponding to the vector x, subject to the desired μ ═ 0A noise vector;

C. setting an error threshold d, wherein d is subject to a Gaussian distribution of expected mu-2 lambda, and calculating L1-L3L and L2-L3L respectively;

D. and calculating the size relation between (| L1-L3 | - | | L2-L3 |) and the error threshold value d, and determining that the vector x3 to be queried is similar to the standard vector x1 or the standard vector x 2.

For two vectors, the same multiple is simultaneously stretched, the relative size of the modular length is unchanged, and a noise vector e is added in consideration of safety_xBy L ═ λ x + e_xAnd (5) scaling each received vector, wherein x is a plaintext vector. The modulo length of λ x is expressed in terms of the modulo length of L at the time of comparison. Since the vector x is after the normalization process, the modulo length error of x is expressed by the vector L as approximately 2/λ, and when λ is large enough, the error is small enough.

Further, since there is an error in the above method, after setting the error threshold D according to the gaussian distribution, a specific manner of step D is:

if (| | L1-L3 | - | | L2-L3 |) > d, the vector x3 to be queried is similar to the standard vector x 2;

if (| | L1-L3 | - | | L2-L3 |) < -d, the vector x3 to be queried is similar to the standard vector x 1;

if-d is less than or equal to (L1-L3-L2-L3) less than or equal to d, the similarity of the vector x3 to be queried and the standard vector x1 and the standard vector x2 is the same.

The invention also provides a vector similarity judgment method under privacy protection based on vector orthogonal transformation, which comprises the following steps:

A. receiving two standard vectors x1 and x2, an orthogonal matrix P and a vector to be queried x 3;

B. performing orthogonal transformation on the two standard vectors x1 and x2 and the vector to be queried x3 through L-Px to obtain two standard output vectors L1 and L2 corresponding to the two standard vectors x1 and x2 and a vector to be queried L3 of the vector to be queried x3, wherein L is an output vector, and x is a received vector;

C. respectively calculating L1-L3 and L2-L3;

D. and calculating the size relation between (| L1-L3 | - | | L2-L3 |) and 0, and determining that the vector x3 to be queried is similar to the standard vector x1 or the standard vector x 2.

Orthogonal transformation can not change the modular length of the vector, and can ensure the homomorphism of the modular length, the inner product and the like. The orthogonal matrix definition is: if A^TA ═ I or AA^TI, then a or AT is called an orthogonal matrix. Thus, an orthogonal transformation L ═ Px can be performed, and P is an orthogonal matrix. Since this method is error-free, the accuracy of the determination can reach 100%, which is not available in the existing determination methods.

Further, one of the modes of the step D is:

if (| | L1-L3 | - | | L2-L3 |) > 0, the vector x3 to be queried is similar to the standard vector x 2;

if (| | L1-L3 | - | | L2-L3 |) < 0, the vector x3 to be queried is similar to the standard vector x 1;

if (| | L1-L3 | - | | L2-L3 |) -0, the similarity of the vector x3 to be queried and the standard vector x1 and the standard vector x2 is the same.

The invention also provides a vector similarity judgment method under privacy protection based on vector homomorphic encryption, which comprises the following steps:

A. receiving two standard vectors x1 and x2 and receiving a vector to be queried x 3;

B. obtaining a key conversion matrix M through vector homomorphic encryption, and obtaining a classification vector c3 of a vector x3 to be queried by the vector x3 to be queried through the key conversion matrix M;

C. obtaining a ciphertext c1 corresponding to the standard vector x1, a ciphertext c2 corresponding to the standard vector x2 and a matrix H corresponding to the ciphertext c1, the ciphertext c2 and the classification vector c3 through vector homomorphic encryption;

D. calculation ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) and 0, determining that the vector x3 to be queried is similar to the standard vector x1 or the standard vector x2, wherein (c1-c3)^TIs a transposed vector of (c1-c3), (c2-c3)^TIs the transposed vector of (c2-c 3).

The vector homomorphic encryption method applied in the invention is proposed by Zhou and WornellThe method can ensure the privacy of the operation function when the encrypted data is operated, and supports homomorphic operation of vector addition, linear transformation and weighted inner product. Key transformation is an important concept in the calculation process. For a given plaintext

And its corresponding cipher text

And corresponding key

The linear transformation Gx can be calculated. For arbitrary matrices

They satisfy (GS) c ═ w (gx) + Ge. Gx may be treated as plain text under the key GS in this process. In the process, a key conversion matrix can be calculated

Transforming the key GS into any feasible key by a key transformation method

And satisfies the new ciphertext c ═ Mc^*. Wherein c is^*A bit representation representing the original ciphertext c. The original encryption process is to convert the unit matrix I into the key S output from vhe.kg (λ), and then there is the relation c ═ m (wx)^*And c is the generated ciphertext.

Further, one of the modes of the step D is:

if ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) > 0, the vector to be queried x3 is similar to the standard vector x 2;

if ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) < 0, the vector to be queried x3 is similar to the standard vector x 1;

if ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) -0, the similarity of the vector x3 to be queried and the standard vector x1 and the standard vector x2 are the same.

The method of the present invention can be applied in a plurality of fields, for example, if it is required to predict whether a suspected lung cancer patient has lung cancer, the diagnostic feature vector x3 of the suspected lung cancer patient can be extracted: (number of leukocytes, number of platelets, …, t3(t3 is the label to be classified)), i.e. the category of the vector x3 to be queried, received in the method of the invention. Two existing past patient records x1 are entered simultaneously: (leukocyte count, platelet count, … t1 (with lung cancer)), x 2: (number of leukocytes, number of platelets, … t2 (no lung cancer)), i.e., the respective categories of the standard vectors x1 and x2 received in the methods of the invention. Through calculation of the method, whether the vector x3 to be queried is similar to the standard vector x1 or similar to the standard vector x2 is obtained, and the category of the vector x3 to be queried is defined as the category of the standard vector expected to be similar, namely t3 is defined as lung cancer or no lung cancer.

In the existing method for determining similarity of vectors, a method based on secure multi-party computation is used in 2015, which is published by Bharath k. One of the biggest drawbacks of secure multiparty protocols is the need for both parties to interact many times to achieve a comparison of sizes. This comparison is too costly to communicate with the method of the present invention, which only needs to be transmitted once and does not require any interaction in subsequent calculations.

Another existing method is that in 2015, Jianwei Yuan et al use a vector splitting mode in the SEISA paper, Secure and efficient Encrypted Image Search With Access Control, and a random number is added into the vector to realize comparison of Euclidean distance of the vector on the premise of protecting the privacy of the vector. Although the comparison of Euclidean distances is realized by the comparison method, compared with the method of the invention, the operation is more complicated, and the expansibility of the schemes is poorer, so that the method is only suitable for comparing the Euclidean distances. The method of the present invention may support comparison of a variety of metrics including, but not limited to, euclidean distance metrics, manhattan distance metrics, chebyshev distance metrics, minkowski distance metrics, vector inner product metrics, and the like.

Compared with the prior art, the three methods have the following advantages by experimental comparison:

table 1:

using range comparisons

As can be seen from table 1, the vector similarity determination method under privacy protection based on vector scaling transformation and the vector similarity determination method under privacy protection based on vector orthogonal transformation both can be applied to the determination of the real number range, and no existing method can achieve real number domain comparison at present.

The method of the invention also has the advantages of low communication and calculation, and the comparison data is shown in tables 2 and 3:

table 2:

comparison of computational complexity

As can be seen from table 2, the comparison of the plain text by the vector similarity determination method under privacy protection based on vector scaling transform and the vector similarity determination method under privacy protection based on vector orthogonal transform of the present invention hardly increases complexity compared with the conventional method, and the vector similarity determination method under privacy protection based on vector homomorphic encryption only increases one norm matrix H during plain text comparison, and hardly causes performance loss in the case of a large data amount.

Table 3:

comparison of traffic

Therefore, the method for judging the similarity of the vectors under the privacy protection can judge the similarity between the vectors by comparing the modular length of the vectors on the premise of not disclosing the value of each dimension of the vectors, and experiments show that the performance of the method is hardly reduced when the efficiency of ciphertext comparison is compared with that of plaintext comparison. The calculation method of the vector inner product is similar to the judgment method of the modular length of the present invention, and such a characteristic can be satisfied.

The present invention will be described in further detail with reference to the following examples. This should not be understood as limiting the scope of the above-described subject matter of the present invention to the following examples. Various substitutions and alterations according to the general knowledge and conventional practice in the art are intended to be included within the scope of the present invention without departing from the technical spirit of the present invention as described above.

Drawings

Fig. 1 is a flowchart of a vector similarity determination method under privacy protection based on vector scaling.

Fig. 2 is a flowchart of a vector similarity determination method under privacy protection based on vector orthogonal transformation according to the present invention.

Fig. 3 is a flowchart of a method for determining vector similarity under privacy protection of vector homomorphic encryption according to the present invention.

Detailed Description

Example 1:

as shown in fig. 1, the method for determining vector similarity under privacy protection based on vector scaling transform of the present invention includes:

A. receiving two standard vectors x1 and x2, and receiving a vector to be queried x 3;

B. by L ═ λ x + e_xThe two standard vectors x1 and x2 and the vector to be queried x3 are expanded to obtain two standard output vectors L1 and L2 corresponding to the two standard vectors x1 and x2 and a vector to be queried L3 of the vector to be queried x3, wherein L is an output vector, lambda is a received large integer, x is a received vector, e is a received vector_xIs a noise vector corresponding to vector x that follows a gaussian distribution with the desired μ ═ 0;

C. setting an error threshold d, wherein d is subject to a Gaussian distribution of expected mu-2 lambda, and calculating L1-L3L and L2-L3L respectively;

D. if (| | L1-L3 | - | | L2-L3 |) > d, the vector x3 to be queried is similar to the standard vector x 2;

if (| | L1-L3 | - | | L2-L3 |) < -d, the vector x3 to be queried is similar to the standard vector x 1;

if-d is less than or equal to (L1-L3-L2-L3) less than or equal to d, the similarity of the vector x3 to be queried and the standard vector x1 and the standard vector x2 is the same.

Example 2:

as shown in fig. 2, the method for determining vector similarity under privacy protection based on vector orthogonal transformation of the present invention includes:

A. receiving two standard vectors x1 and x2, an orthogonal matrix P and a vector to be queried x 3;

B. performing orthogonal transformation on the two standard vectors x1 and x2 and the vector to be queried x3 through L-Px to obtain two standard output vectors L1 and L2 corresponding to the two standard vectors x1 and x2 and a vector to be queried L3 of the vector to be queried x3, wherein L is an output vector, and x is a received vector;

C. respectively calculating L1-L3 and L2-L3;

D. if (| | L1-L3 | - | | L2-L3 |) > 0, the vector x3 to be queried is similar to the standard vector x 2;

if (| | L1-L3 | - | | L2-L3 |) < 0, the vector x3 to be queried is similar to the standard vector x 1;

if (| | L1-L3 | - | | L2-L3 |) -0, the similarity of the vector x3 to be queried and the standard vector x1 and the standard vector x2 is the same.

Example 3:

as shown in fig. 3, the method for determining vector similarity under privacy protection based on vector homomorphic encryption of the present invention includes:

A. receiving two standard vectors x1 and x2 and receiving a vector to be queried x 3;

B. obtaining a key conversion matrix M through vector homomorphic encryption, and obtaining a classification vector c3 of a vector x3 to be queried by the vector x3 to be queried through the key conversion matrix M;

the basic encryption process of vector homomorphic encryption is as follows:

KG (lambda) inputting a safety parameter lambda, selecting the parameter

And satisfy

m<n, q > p and w (p-1)<q, the construction matrix S satisfies

And is

Is an identity matrix, the output key S and the public parameter Param ═ (l, m, n, p, q, w, χ).

Input plaintext vector (S) — VHE.E (x, S)

And a key matrix

Outputting the ciphertext

And Sc-wx + e where w is a large integer, e is a noise vector w/2, and | S | < w. Writing the cryptographic process VHE.E (x, S) to E_s(x)。

VHE.D (c, S) inputting a ciphertext vector

And a key matrix

Outputting the plaintext

Wherein the decryption process is

The key conversion process in the vector homomorphic encryption process is as follows:

-for a given plaintext

And its corresponding cipher text

And corresponding key

Capable of computing linear transformation Gx for arbitrary matrices

They satisfy (GS) c ═ w (Gx) + Ge. in this process Gx can be treated as plaintext under the key GS. In the process, a key transformation matrix is calculated

Transforming the key GS into any feasible key by a key transformation method

And satisfies the new ciphertext c ═ Mc^*In which c is^*A bit representation representing the original ciphertext c. The original encryption process is to convert the unit matrix I into the key S output from vhe.kg (λ), and then there is the relation c ═ m (wx)^*And c is the generated ciphertext.

C. Obtaining a ciphertext c1 corresponding to the standard vector x1, a ciphertext c2 corresponding to the standard vector x2 and a matrix H corresponding to the ciphertext c1, the ciphertext c2 and the classification vector c3 through vector homomorphic encryption;

since the present embodiment is based on the vector homomorphic encryption scheme (VHE). In VHE there is the formula:

where x is a plaintext vector, so it can be simplified as:

wx＝W(wx)^*

then the following results are obtained:

(wx)^T(wx)＝((wx)^*)^TW^TW(wx)^*

and then through the formula: c ═ M (wx)^*The matrix a is constructed such that AM ═ W. Let H be A^TA, obtaining

c^THc＝H((wx)^*)^TM^TA^TAM(wx)^T

c^THc＝H((wx)^*)^TM^TA^TAM(wx)^T＝(wx)^T(wx)＝w²x^Tx

From AM ═ W, the calculation is exactly the square of W in plaintext modulo length.

D. Calculation ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) and 0,

if ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) > 0, the vector to be queried x3 is similar to the standard vector x 2;

if ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) < 0, the vector to be queried x3 is similar to the standard vector x 1;

if ((c1-c3)^TH(c1-c3)－(c2-c3)^TH (c2-c3)) -0, the similarity of the vector x3 to be queried and the standard vector x1 and the standard vector x2 are the same.

Claims (2)

1. The vector similarity judgment method under privacy protection based on vector scaling transformation is characterized by comprising the following steps:

A. receiving two standard vectors x1 and x2, and receiving a vector to be queried x 3;

B. by L ═ λ x + e_xThe two standard vectors x1 and x2 and the vector to be queried x3 are expanded to obtain two standard output vectors L1 and L2 corresponding to the two standard vectors x1 and x2 and a vector to be queried L3 of the vector to be queried x3, wherein L is an output vector, lambda is a received large integer, x is a received vector, e is a received vector_xIs a noise vector corresponding to vector x that follows a gaussian distribution with the desired μ ═ 0;

C. setting an error threshold d, wherein d is subject to a Gaussian distribution of expected mu-2 lambda, and calculating L1-L3L and L2-L3L respectively;

D. and calculating the size relation between (| L1-L3 | - | | L2-L3 |) and the error threshold value d, and determining that the vector x3 to be queried is similar to the standard vector x1 or the standard vector x 2.

2. The vector similarity determination method under privacy protection based on vector scaling transformation as claimed in claim 1, characterized by: in the step D, the step of the method is carried out,

if (| | L1-L3 | - | | L2-L3 |) > d, the vector x3 to be queried is similar to the standard vector x 2;

if (| | L1-L3 | - | | L2-L3 |) < -d, the vector x3 to be queried is similar to the standard vector x 1;

if-d is less than or equal to (L1-L3-L2-L3) less than or equal to d, the similarity of the vector x3 to be queried and the standard vector x1 and the standard vector x2 is the same.

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