CN112215165B - Face recognition method based on wavelet dimensionality reduction under homomorphic encryption - Google Patents

Face recognition method based on wavelet dimensionality reduction under homomorphic encryption Download PDF

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CN112215165B
CN112215165B CN202011093672.3A CN202011093672A CN112215165B CN 112215165 B CN112215165 B CN 112215165B CN 202011093672 A CN202011093672 A CN 202011093672A CN 112215165 B CN112215165 B CN 112215165B
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彭冬毡
郑培嘉
骆伟祺
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Sun Yat Sen University
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Abstract

The invention provides a face recognition method based on wavelet dimension reduction under homomorphic encryption, which is designed in the technical field of face recognition and solves the problems of large occupied space, long face recognition time and poor real-time property in the face recognition process of the conventional face recognition method based on homomorphic encryption.

Description

Face recognition method based on wavelet dimensionality reduction under homomorphic encryption
Technical Field
The invention relates to the technical field of face recognition, in particular to a face recognition method based on wavelet dimension reduction under homomorphic encryption.
Background
With the rapid development of social economy, the application scenes of face recognition in our lives are more and more, the face is an important mode for identity recognition, and the face recognition method can be applied to the fields of public security, transportation, hospitals and the like, improves efficiency for public safety, information management and the like, has more accurate recognition, and can also be applied to the aspects of mobile phone unlocking, software login, payment verification, transaction verification and the like on line. By forming a face library and identifying whether the user operates by face recognition, the privacy, property and personal account safety of the client can be fully protected.
The face recognition comprises face detection, face image processing, face image feature extraction and face image recognition. For the human face image processing, human face image feature extraction and human face image recognition part, in order to protect privacy, in the past, how to encrypt a human face image and recognize and match the human face under the encryption condition is the subject of research, one method is to perform pattern matching by extracting human face image features and then encrypt through feature conversion, the conversion can be a random function or a confusion matrix, and the like, the human face recognition result is to match through the similarity of the converted value of the image in a checking library and the converted value of an input image, but the confidentiality of a secret key needs to be ensured, otherwise, if the conversion matrix is leaked, the privacy is further leaked; another method does not depend on a transformation matrix, and directly encrypts an image by using the property of homomorphic encryption, for example, a safe and efficient face recognition method based on deep learning and homomorphic encryption is disclosed in a Chinese patent (publication number: CN 109145829A) with publication number of 2019, 1, month and 4.
Disclosure of Invention
In order to solve the problems of large occupied space, long face recognition time and poor real-time performance in the face recognition process of the conventional face recognition method based on homomorphic encryption, the invention provides a face recognition method based on wavelet dimension reduction under homomorphic encryption, so that the time and space complexity in the face recognition process is reduced and the recognition speed is increased while the privacy requirement is met.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
a face recognition method based on wavelet dimension reduction under homomorphic encryption at least comprises the following steps:
s1, preprocessing a face picture input by a client and a face picture in a face database;
s2, encrypting the face picture preprocessed by the client and sending the face picture to a cloud server;
s3, the cloud server performs discrete wavelet transformation under a homomorphic encryption domain on the encrypted face picture Y transmitted by the client;
s4, picture X in face database is aligned to cloud server i (i = 1.. Multidot.N) performing discrete wavelet transform in a plaintext state to obtain X i ' (i = 1., N) and obtaining a feature vector through dimension reduction transformation, wherein N represents the total number of face pictures in the face database;
s5, processing the face database and the face picture vector group in the client through the feature vector to obtain a final dimensionality-reduced client low-dimensional ciphertext face picture vector group and a final dimensionality-reduced client low-dimensional plaintext face picture vector group in the face database;
s6, according to the property of homomorphic encryption, the cloud server calculates the Euclidean distance between the low-dimensional ciphertext face picture vector group of the client and each face picture vector in the low-dimensional plaintext face picture vector group in the face database;
s7, comparing Euclidean distances in a ciphertext state based on heap sorting;
s8, judging whether the Euclidean distance is within a threshold epsilon, if so, successfully identifying the face, returning a ciphertext result, and sending the ciphertext result to the client for decryption to obtain a decryption result; otherwise, face recognition fails.
In the technical scheme, a face picture input by a client and a face picture in a face database are preprocessed, then an encrypted face picture Y transmitted by the client is subjected to discrete wavelet transformation (namely wavelet transformation is carried out in a face picture plaintext state in the face database) and dimension reduction processing transformation in a homomorphic encryption domain, and a face picture vector group in the face database and the client is processed through a characteristic vector, namely dimension reduction for the second time.
Preferably, the preprocessing of step S1 includes: the method has the advantages that the face pictures input by the client and the face pictures in the face database are converted into pixel texts, the sizes of the pixel texts are compressed in a mean value filtering template and compression mode, two-dimensional images are converted into one-dimensional images, the picture dimensionality is reduced, and the subsequent processing difficulty is reduced.
Preferably, in step S3, the encrypted face picture transmitted by the client is decomposed into a CD of a high frequency part and a CA of a low frequency part after performing discrete wavelet transform in a homomorphic encryption domain, and the process includes:
s31, setting a face picture vector encrypted by the client as [ Y ], wherein the length of Y is M;
s32, performing primary wavelet transformation under the ciphertext domain to obtain a primary transformation high-frequency part CD1 and a primary transformation low-frequency part CA1, wherein the requirements are respectively met:
[CD1[k]]＝[Y[2k]]·[Y[2k+1]] -1 mod paillier.n 2
[CA1[k]]＝[Y[2k]]·[Y[2k+1]]mod paillier.n 2
wherein k = 1., M/2; n is 2 Representing a given number, paillier representing paillier encryption;
s33, performing secondary wavelet transformation on the primary transformation low-frequency part CA1 to obtain a secondary transformation high-frequency part CD2 and a secondary transformation low-frequency part CA2, wherein the requirements are respectively met:
[CD2[k]]＝[CA1[2k]]·[CA1[2k+1]] -1 mod paillier.n 2
[CA2[k]]＝[CA1[2k]]·[CA1[2k+1]]mod paillier.n 2
s34, performing three-level wavelet transformation on the second-level transformation low-frequency part CA2 to obtain a third-level transformation high-frequency part CD3 and a third-level transformation low-frequency part CA3, wherein the three-level transformation high-frequency part CD3 and the three-level transformation low-frequency part CA3 respectively meet the following requirements:
[CD3[k]]＝[CA2[2k]]·[CA2[2k+1]] -1 modpaillier.n 2
[CA3[k]]＝[CA2[2k]]·[CA2[2k+1]]mod paillier.n 2
s35, obtaining four coefficient sub-bands CA3, CD2 and CD1 after three-level wavelet transformation, enabling the coefficient sub-band CA3 to be a wavelet coefficient [ Y' ] of a client side after three-level wavelet transformation in a homomorphic encryption domain, obtaining main energy of a picture to realize dimension reduction while keeping main characteristics of the picture, reducing the coefficient to 1/8 after three-level wavelet transformation, further compressing the picture size and reducing the space occupation degree.
Preferably, the dimension reduction conversion in the step S4 is implemented by using Principal Component Analysis (PCA) or local linear discriminant analysis (LFDA), and the feature vector W ∈ R is obtained m*K M represents the number of eigenvalues when Principal Component Analysis (PCA) or local linear discriminant analysis (LFDA) is used, R represents a real number, K represents the length of an eigenvector, and W = [ W ] 1 w 2 ...w i ...w K ]，w i ∈R m*K ，i＝1，...K。
After wavelet transformation, feature vectors are obtained by Principal Component Analysis (PCA) or local linear discriminant analysis (LFDA), and the feature vectors are K × m dimensional matrixes w 1 ，w 2 ....w K And (K & lt N), so that the dimension reduction is performed for the second time, and the space occupation rate in the face recognition process is reduced.
Preferably, the processing of the face picture vector group in the face database by the feature vector in step S5 includes:
s51, calculating an average value of the face picture vectors in the face database after wavelet transformation:
Figure BDA0002722106720000041
therein, Ψ X Representing the average value of the face pictures in the face database after wavelet transformation; n represents the total number of face pictures, X' i Is small in representationThe ith class face picture vector after the wave transformation;
s52, calculating each face picture vector in the face database after dimension reduction through features
Figure BDA0002722106720000042
Figure BDA0002722106720000043
Wherein i, j respectively represent the category of the face picture vector, psi m Mean value, W, representing the m-th class of face picture vectors mj Represents a feature vector, j = 1.., K;
s53, passing each face picture vector subjected to dimension reduction
Figure BDA0002722106720000044
And forming a low-dimensional plaintext face picture vector group in the face database.
Preferably, it is assumed that, in step S5, each face picture vector after the face picture vector group in the client is processed by the feature vector is
Figure BDA0002722106720000045
The expression is as follows:
Figure BDA0002722106720000046
wherein, Y' m Representing wavelet coefficients after the m-th face picture vector dimension reduction in the client; Ψ Ym Representing the mean value of the m-th class face picture vector in the client; w mj Represents the feature vector, j = 1.
After the face image vector groups in the face database and the client are processed through the feature vectors, the secondary dimension reduction of the face image is realized, the space occupation degree of the face image is reduced, and the face recognition speed is improved.
Preferably, the face picture vector of the client after dimension reduction is set
Figure BDA0002722106720000047
With each vector in the face database
Figure BDA0002722106720000048
Has a Euclidean distance of
Figure BDA0002722106720000049
The calculation formula is as follows:
Figure BDA0002722106720000051
wherein i = 1.
Figure BDA0002722106720000052
S 1 Part of the data is directly transmitted by each vector in the face database
Figure BDA0002722106720000053
Calculating and encrypting; depending on the nature of the homomorphic encryption,
Figure BDA0002722106720000054
S 2 partially meets the following requirements:
Figure BDA0002722106720000055
S 3 and part is obtained by the client interacting with the server.
Preferably, S 3 The specific process partially obtained by the interaction of the client and the server comprises the following steps:
s61, the cloud server generates a plaintext random number r j And calculating a ciphertext:
Figure BDA0002722106720000056
sending the data to a client;
s62, the client decrypts the ciphertext and calculates
Figure BDA0002722106720000057
Post-encrypted to [ S' 3 ]Returns to the cloud server；
S63, the cloud server is composed of S' 3 ]To obtain [ S ] 3 ]The formula is as follows:
Figure BDA0002722106720000058
wherein i = 1.
Preferably, the face picture vector of the client
Figure BDA0002722106720000059
With each vector in the face database
Figure BDA00027221067200000510
European distance of
Figure BDA00027221067200000511
After the two are calculated, the process of comparing the euclidean distances in step S7 is based on one euclidean distance and another euclidean distance, and two pairwise comparisons are performed, and the process of comparing the euclidean distances in the ciphertext state based on the heap sorting is as follows:
s71, setting one Euclidean distance as a and the other Euclidean distance as b, wherein a is more than or equal to 0, and b is less than 2 l L represents a length parameter;
s72. There is a positive number [ z ] of one (l + 1) bit]And satisfies the following conditions: [ z ] is]＝[2 l +a-b]＝[2 l ]·[a]·[b] -1 The value of the highest order is z l ，z l ＝2 -l ·(z-(z mod 2 l ) Calculate [ z mod2 ] l ]；
S73, the cloud server generates a random number r with (k + l + 1) bits, calculates [ d ] = [ z + r ] = [ z ] · [ r ], and sends the calculated [ d ] = [ z ] · [ r ] to the client;
s74, the client decrypts after receiving the data to calculate [ d mod2 ] l ]Sending to a cloud server, and calculating by the cloud server: (z mod2 l )＝((d mod 2 l )-(r mod 2 l )mod 2 l ，
Figure BDA0002722106720000066
S75. Order
Figure BDA0002722106720000061
Existence of S epsilon R {1, -1}, so that the cloud server can calculate an intermediate parameter ciphertext [ c i ]]And satisfies the following conditions:
Figure BDA0002722106720000062
wherein the content of the first and second substances,
Figure BDA0002722106720000063
s76, the intermediate parameter ciphertext [ c ] i ]]Set of constituent vectors [ [ c ]]]Sent to the client, which decrypts it and encrypts it
Figure BDA0002722106720000064
Sent to the cloud server according to
Figure BDA0002722106720000065
And S calculates [ lambda ]]Then [ z mod2 ] is calculated l ]And obtaining a comparison result and returning the comparison result to the client.
Here, the number of comparison times of images is reduced by the heap sorting, the recognition speed is increased, and if λ =1 before step S75 is executed, it indicates that r mod2 is present l Greater than d mod2 l Since there may be data overflow, the calculation in and after step S75 is required.
Preferably, step S76 further includes: and the client checks whether the received vector group [ c ] is 0 or not, and the vector group is used as the identification of the ciphertext identification result, so that the identification speed is increased.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention provides a face recognition method based on wavelet dimension reduction under homomorphic encryption, which reduces the occupation rate of resource space and the time consumed in the face recognition process by preprocessing a face picture input by a client and a face picture in a face database, then performing discrete wavelet transform under a homomorphic encryption domain on an encrypted face picture Y transmitted by the client, performing wavelet transform on the face picture in the face database under a plaintext state, and then performing dimension reduction processing transform, and ensures the requirements of a cloud server and the client on privacy by only an image owner according to the property of homomorphic encryption.
Drawings
FIG. 1 is a schematic flow chart of a face recognition method based on wavelet dimension reduction under homomorphic encryption according to the present invention;
fig. 2 is a diagram illustrating energy transfer of a face picture input by a client in a discrete wavelet transform process according to an embodiment of the present invention;
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for better illustration of the present embodiment, certain parts of the drawings may be omitted, enlarged or reduced, and do not represent actual dimensions;
it will be understood by those skilled in the art that certain well-known descriptions of the figures may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
Fig. 1 is a schematic flow chart of a face recognition method based on wavelet dimension reduction under homomorphic encryption, which, referring to fig. 1, includes:
s1, preprocessing a face picture input by a client and a face picture in a face database;
s2, encrypting the face picture preprocessed by the client and sending the face picture to a cloud server; the encryption is encrypted by a paillier encryption algorithm;
s3, the cloud server performs discrete wavelet transformation under a homomorphic encryption domain on the encrypted face picture Y transmitted by the client;
s4, picture X in face database is matched by cloud server i (i = 1.., N) performing discrete wavelet transform in a plaintext state to obtain X i ' (i = 1.. Once, N) and obtaining a feature vector through dimension reduction transformation, wherein N represents the total number of face pictures in a face database;
s5, processing the face database and the face picture vector group in the client through the feature vector to obtain a final dimensionality-reduced client low-dimensional ciphertext face picture vector group and a final dimensionality-reduced client low-dimensional plaintext face picture vector group in the face database;
s6, according to the property of homomorphic encryption, the cloud server calculates the Euclidean distance between the low-dimensional ciphertext face picture vector group of the client and each face picture vector in the low-dimensional plaintext face picture vector group in the face database;
s7, comparing Euclidean distances in a ciphertext state based on the heap sorting;
s8, judging whether the Euclidean distance is within a threshold epsilon, if so, successfully identifying the face, returning a ciphertext result, and sending the ciphertext result to the client for decryption to obtain a decryption result; otherwise, face recognition fails. The threshold value epsilon is defined to define the top T names closest to the euclidean distance as the same recognized face, for example, epsilon =1, i.e. only the closest face is the face picture of the user input client, and when epsilon =2, i.e. the top two closest faces are the face pictures of the user input client.
In this embodiment, the preprocessing described in step S1 includes: the method comprises the steps of converting a face picture input by a client and a face picture in a face database into a pixel text, compressing the size of the pixel text in a mean filtering template and a compression mode, wherein in the specific implementation, an ORL standard database is used, firstly, averaging every 2 points of the face picture from 112 x 90, cutting the face picture into 46 x 56, and converting the face picture into a one-dimensional vector of 1 x 2576. After all pictures are preprocessed, the length of each picture is N (N = 2576), the length of each picture represents the length of a vector, and a vector Y and a Bob vector group X of a client are obtained at this time i (i = 1.. N), so that the two-dimensional image is converted into a one-dimensional image, the image dimension is reduced, and the subsequent processing difficulty is reduced.
In this embodiment, the process of decomposing the encrypted face picture transmitted by the client in step S3 into a CD of a high frequency part and a CA of a low frequency part after performing discrete wavelet transform in a homomorphic encryption domain includes:
s31, setting a face picture vector encrypted by the client as [ Y ], wherein the length of Y is M;
s32, performing primary wavelet transformation under the ciphertext domain to obtain a primary transformation high-frequency part CD1 and a primary transformation low-frequency part CA1, wherein the requirements are respectively met:
[CD1[k]]＝[Y[2k]]·[Y[2k+1]] -1 mod paillier.n 2
[CA1[k]]＝[Y[2k]]·[Y[2k+1]]mod paillier.n 2
wherein k = 1.., M/2; n is 2 Representing a given number, paillier representing paillier encryption;
s33, performing secondary wavelet transformation on the primary transformation low-frequency part CA1 to obtain a secondary transformation high-frequency part CD2 and a secondary transformation low-frequency part CA2, wherein the requirements are respectively met:
[CD2[k]]＝[CA1[2k]]·[CA1[2k+1]] -1 mod paillier.n 2
[CA2[k]]＝[CA1[2k]]·[CA1[2k+1]]mod paillier.n 2
s34, performing three-level wavelet transformation on the second-level transformation low-frequency part CA2 to obtain a third-level transformation high-frequency part CD3 and a third-level transformation low-frequency part CA3, wherein the three-level transformation high-frequency part CD3 and the three-level transformation low-frequency part CA3 respectively meet the following requirements:
[CD3[k]]＝[CA2[2k]]·[CA2[2k+1]] -1 mod paillier.n 2
[CA3[k]]＝[CA2[2k]]·[CA2[2k+1]]mod paillier.n 2
s35, obtaining four coefficient sub-bands CA3, CD2 and CD1 after three-level wavelet transformation, and enabling the coefficient sub-band CA3 to be a wavelet coefficient | Y' of a client side subjected to three-level wavelet transformation in a homomorphic encryption domain, wherein an energy transfer diagram of the wavelet transformation expressed in the steps S32 to S34 is shown in FIG 2, a low-frequency part of each level is used as a basis, the main characteristic of the image is kept, meanwhile, the main energy of the image is obtained to achieve dimension reduction, after three-level wavelet transformation, the coefficient is reduced to 1/8, the size of the image is further compressed, and the space occupation degree is reduced.
In this embodiment, the dimension reduction transformation described in step S4 is implemented by Principal Component Analysis (PCA) or local linear discriminant analysis (LFDA), and the obtained feature vector W ∈ R m*K M represents the number of eigenvalues when Principal Component Analysis (PCA) or local linear discriminant analysis (LFDA) is used, R represents a real number, K represents the length of an eigenvector, and W = [ W = 1 w 2 ...w i ...w K ]，w i ∈R m*K K, where PCA finds a set of mutually orthogonal coordinate axes from the original space. The first axis is selected in the direction of the largest variance in the original data, the second axis is selected in the plane orthogonal to the first axis, so that the variance is the largest, and the third axis is the largest one of the planes in which the variance is sequentially orthogonal to the two axes. And by analogy, the rest axes are ignored, only the first k axes are left, and most of variance is reserved to realize the dimensionality reduction of the data features. Thus, defining P as implementing a dimensionality reduction of w:
Figure BDA0002722106720000091
the feature vector W ∈ R m*K Is the eigenvector W = [ W ] corresponding to the m eigenvalues with Pmax 1 w 2 ...w k ]Composition of, wherein w i ∈R m*K K. PCA is not suitable for distinguishing different sample classes since it is an unsupervised algorithm. LFDA solves this problem by finding a feature vector W that maximizes the local inter-class scatter matrix P B While minimizing local intra-class scatter P W . Meanwhile, the method can overcome the problem of multiple peaks of the image caused by the locality of the FLDA, and the calculation process is as follows:
Figure BDA0002722106720000092
Figure BDA0002722106720000093
wherein the content of the first and second substances,
Figure BDA0002722106720000094
Figure BDA0002722106720000095
wherein the content of the first and second substances,
Figure BDA0002722106720000096
similarly, the feature vector W is belonged to R m*K Is formed by P B /P W Eigenvector W = [ W ] corresponding to maximum m eigenvalues 1 w 2 ...w k ]Composition of w wherein i ∈R m*K ，i＝1，...K。
In this embodiment, the processing the face image vector group in the face database by using the feature vector in step S5 includes:
s51, calculating the average value of the face picture vectors in the face database after wavelet transformation:
Figure BDA0002722106720000101
therein, Ψ X Representing the average value of the face pictures in the face database after wavelet transformation; n represents the total number of face pictures, X' i Representing the i-th class face picture vector after wavelet transformation;
s52, calculating each face picture vector in the face database after dimension reduction through features
Figure BDA0002722106720000102
Figure BDA0002722106720000103
Wherein, i and j respectively represent the category of the face picture vector, psi m Mean value, W, representing the m-th class of face picture vectors mj Represents a feature vector, j = 1.., K;
s53, passing each face picture vector after dimension reduction
Figure BDA0002722106720000104
And forming a low-dimensional plaintext face picture vector group in the face database.
Setting each face picture vector as
Figure BDA0002722106720000105
The expression is as follows:
Figure BDA0002722106720000106
wherein, Y' m Representing wavelet coefficients of m-th class face picture vectors in the client after dimension reduction; Ψ Ym Representing the mean value of the m-th class face picture vector in the client; w mj Represents the feature vector, j = 1.
Setting face picture vector of client after dimension reduction
Figure BDA0002722106720000107
With each vector in the face database
Figure BDA0002722106720000108
Has a Euclidean distance of
Figure BDA0002722106720000109
The calculation formula is as follows:
Figure BDA00027221067200001010
wherein i = 1.
Figure BDA00027221067200001011
The S1 part directly uses each vector in the face database
Figure BDA0002722106720000111
Calculating and encrypting; depending on the nature of the homomorphic encryption,
Figure BDA0002722106720000112
S 2 partially satisfies the following conditions:
Figure BDA0002722106720000113
S 3 and part is obtained by the client interacting with the server.
S 3 The specific process partially obtained by the interaction of the client and the server comprises the following steps:
s61, the cloud server generates a plaintext random number r j And calculating a ciphertext:
Figure BDA0002722106720000114
sending the data to a client;
s62, the client decrypts the ciphertext and calculates
Figure BDA0002722106720000115
Is encrypted to [ S' 3 ]Returning to the cloud server;
s63, the cloud server is composed of S' 3 ]To obtain [ S ] 3 ]The formula is as follows:
Figure BDA0002722106720000116
wherein i = 1.
Face picture vector of client
Figure BDA0002722106720000117
With each vector in the face database
Figure BDA0002722106720000118
European distance ofSeparation device
Figure BDA0002722106720000119
After the two are calculated, the process of comparing the euclidean distances in step S7 is based on one euclidean distance and another euclidean distance, and two pairwise comparisons are performed, and the process of comparing the euclidean distances in the ciphertext state based on the heap sorting is as follows:
s71, setting one of the Euclidean distances as a and the other as b, wherein a is more than or equal to 0, and b is less than 2 l L represents a length parameter;
s72. There is a positive number [ z ] of one (l + 1) bit]And satisfies the following conditions: [ z ] A]＝[2 l +a-b]＝[2 l ]·[a]·[b] -1 Let the value of the highest bit be z l ，z l ＝2 -l ·(z-(z mod 2 l ) Calculate [ z mod 2l ]]；
S73, the cloud server generates a random number r with (kappa + l + 1) bits, calculates [ d ] = [ z + r ] = [ z ] · r ], and sends the [ d ] = [ z ] · r ] to the client;
s74, the client side decrypts after receiving the data to calculate [ d mod2 ] l ]Sending to a cloud server, and calculating by the cloud server: (z mod2 l )＝((d mod 2 l )-(r mod 2 l )mod2 l ，
Figure BDA00027221067200001111
S75. Order
Figure BDA00027221067200001110
Existence of S epsilon R {1, -1}, so that the cloud server can calculate an intermediate parameter ciphertext [ c i ]]And satisfies the following conditions:
Figure BDA0002722106720000121
wherein the content of the first and second substances,
Figure BDA0002722106720000122
s76, the intermediate parameter ciphertext [ c ] i ]]Set of constituent vectors [ [ c ]]]Sent to the client, which willIt decrypts and encrypts one
Figure BDA0002722106720000123
Sent to the cloud server according to
Figure BDA0002722106720000124
And S calculates [ lambda ]]Then [ z mod2 ] is calculated l ]And obtaining a comparison result and returning the comparison result to the client. The number of comparison times of images is reduced by the heap sorting, the recognition speed is increased, and if λ =1, r mod2 is represented before step S75 is executed l Greater than d mod2 l Since there may be data overflow, the calculation in and after step S75 is required. In addition, step S76 further includes: the client checks the received vector set [ c [ [ c ]]]If the value is 0, the recognition speed is increased.
The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. This need not be, nor should it be exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (8)

1. A face recognition method based on wavelet dimension reduction under homomorphic encryption is characterized by at least comprising the following steps:
s1, preprocessing a face picture input by a client and a face picture in a face database;
the pretreatment of the step S1 comprises the following steps: converting a face picture input by a client and a face picture in a face database into a pixel text, compressing the size of the pixel text by using a mean filtering template and a compression mode, and converting a two-dimensional image into a one-dimensional image;
s2, encrypting the face picture preprocessed by the client and sending the face picture to a cloud server;
s3, the cloud server performs discrete wavelet transformation under a homomorphic encryption domain on the encrypted face picture Y transmitted by the client;
s3, decomposing the encrypted face picture transmitted by the client into a CD of a high-frequency part and a CA of a low-frequency part after performing discrete wavelet transform under a homomorphic encryption domain, wherein the process comprises the following steps:
s31, setting a face picture vector encrypted by the client as [ Y ], wherein the length of Y is M;
s32, performing primary wavelet transformation under the ciphertext domain to obtain a primary transformation high-frequency part CD1 and a primary transformation low-frequency part CA1, wherein the requirements are respectively met:
[CD1[k]]＝[Y[2k]]·[Y[2k+1]] -1 modpaillier.n 2
[CA1[k]]＝[Y[2k]]·[Y[2k+1]]modpaillier.n 2
wherein k = 1.., M/2; n is 2 Representing a given number, paillier representing paillier encryption;
s33, performing secondary wavelet transformation on the primary transformation low-frequency part CA1 to obtain a secondary transformation high-frequency part CD2 and a secondary transformation low-frequency part CA2, wherein the requirements are respectively met:
[CD2[k]]＝[CA1[2k]]·[CA1[2k+1]] -1 modpaillier.n 2
[CA2[k]]＝[CA1[2k]]·[CA1[2k+1]]modpaillier.n 2
s34, performing three-level wavelet transformation on the second-level transformation low-frequency part CA2 to obtain a three-level transformation high-frequency part CD3 and a three-level transformation low-frequency part CA3, wherein the three-level transformation high-frequency part CD3 and the three-level transformation low-frequency part CA3 respectively meet the following requirements:
[CD3[k]]＝[CA2[2k]]·[CA2[2k+1]] -1 modpaillier.n 2
[CA3[k]]＝[CA2[2k]]·[CA2[2k+1]]modpaillier.n 2
s35, obtaining four coefficient sub-bands CA3, CD2 and CD1 after three-level wavelet transformation, wherein the coefficient sub-band CA3 is a wavelet coefficient [ Y' ] of the client side which is subjected to three-level wavelet transformation in a homomorphic encryption domain;
s4, counting the number of the human faces by the cloud serverPicture X in database i (i = 1.. Multidot.N) performing discrete wavelet transform in a plaintext state to obtain X i ' (i = 1.. An, N), and obtaining a feature vector through dimension reduction transformation, wherein N represents the total number of face pictures in the face database;
s5, processing the face database and the face picture vector group in the client through the feature vector to obtain a final dimensionality-reduced client low-dimensional ciphertext face picture vector group and a final dimensionality-reduced client low-dimensional plaintext face picture vector group in the face database;
s6, according to the property of homomorphic encryption, the cloud server calculates the Euclidean distance between the low-dimensional ciphertext face picture vector group of the client and each face picture vector in the low-dimensional plaintext face picture vector group in the face database;
s7, comparing Euclidean distances in a ciphertext state based on heap sorting;
s8, judging whether the Euclidean distance is within a threshold epsilon, if so, successfully identifying the face, returning a ciphertext result, and sending the ciphertext result to the client for decryption to obtain a decryption result; otherwise, face recognition fails.
2. The face recognition method based on wavelet dimension reduction under homomorphic encryption according to claim 1, characterized in that the dimension reduction transformation in step S4 is realized by Principal Component Analysis (PCA) or local linear discriminant analysis (LFDA) to obtain a feature vector W e R m*K M represents the number of eigenvalues when Principal Component Analysis (PCA) or local linear discriminant analysis (LFDA) is used, R represents a real number, K represents the length of an eigenvector, and W = [ W = 1 w 2 ...w i ...w K ]，w i ∈R m*K ，i＝1,...K。
3. The wavelet dimension reduction-based face recognition method under homomorphic encryption according to claim 2, wherein the step S5 of processing the face image vector group in the face database through the feature vectors comprises:
s51, calculating an average value of the face picture vectors in the face database after wavelet transformation:
Figure FDA0003708148930000021
therein, Ψ X Representing the average value of the face pictures in the face database after wavelet transformation; n represents the total number of face pictures, X' i The ith personal face picture vector after wavelet transformation is represented;
s52, calculating each face picture vector in the face database after dimension reduction through features
Figure FDA0003708148930000022
Figure FDA0003708148930000023
Therein, Ψ m Mean value, W, representing the m-th class of face picture vectors mj Represents the eigenvector, j =1, \8230;, K;
s53, passing each face picture vector subjected to dimension reduction
Figure FDA0003708148930000024
And forming a low-dimensional plaintext face picture vector group in the face database.
4. The face recognition method based on wavelet dimension reduction under homomorphic encryption according to claim 3, wherein it is assumed that, in step S5, each face picture vector is after processing the face picture vector group in the client by the feature vector
Figure FDA0003708148930000031
The expression is as follows:
Figure FDA0003708148930000032
wherein, Y' m Representing wavelet coefficients of m-th class face picture vectors in the client after dimension reduction;Ψ Ym representing the mean value of the m-th class face picture vector in the client; w is a group of mj Representing the feature vector, j =1, \8230;, K.
5. The face recognition method based on wavelet dimension reduction under homomorphic encryption according to claim 4, characterized in that the face picture vector of the client after dimension reduction is set
Figure FDA0003708148930000033
With each vector in the face database
Figure FDA0003708148930000034
Has a Euclidean distance of
Figure FDA0003708148930000035
The calculation formula is as follows:
Figure FDA0003708148930000036
wherein i = 1.
Figure FDA0003708148930000037
S 1 Part of the data is directly transmitted by each vector in the face database
Figure FDA0003708148930000038
Calculating and encrypting; depending on the nature of the homomorphic encryption,
Figure FDA0003708148930000039
S 2 partially satisfies the following conditions:
Figure FDA00037081489300000310
S 3 and part is obtained by the client interacting with the server.
6. Homomorphic encryption based on according to claim 5The wavelet dimension reduction face recognition method is characterized in that S 3 The specific process partially obtained by the interaction of the client and the server comprises the following steps:
s61, the cloud server generates a plaintext random number r j And calculating a ciphertext:
Figure FDA00037081489300000311
sending the data to a client;
s62, the client decrypts the ciphertext and calculates
Figure FDA00037081489300000312
Is encrypted to [ S' 3 ]Returning to the cloud server;
s63, the cloud server is composed of S' 3 ]Obtaining [ S ] 3 ]The formula is as follows:
Figure FDA0003708148930000041
wherein i = 1.
7. The face recognition method based on wavelet dimension reduction under homomorphic encryption according to claim 6, characterized in that the face picture vector of the client
Figure FDA0003708148930000042
With each vector in the face database
Figure FDA0003708148930000043
European distance of
Figure FDA0003708148930000044
After the two Euclidean distances are calculated, the process of comparing the Euclidean distances in the step S7 is based on one Euclidean distance and the other Euclidean distance, pairwise comparison is carried out, and the process of comparing the Euclidean distances in the ciphertext state based on the heap sorting is as follows:
s71, setting one Euclidean distance as a and the other Euclidean distance as b, wherein 0≤a,b＜2 l L represents a length parameter;
s72. There is a positive number [ z ] of one (l + 1) bit]Satisfies the following conditions: [ z ] is]＝[2 l +a-b]＝[2 l ]·[a]·[b] -1 Let the value of the highest bit be z l ，z l ＝2 -l ·(z-(zmod2 l ) Calculate [ zmod2 ] l ]；
S73, the cloud server generates a random number r with (kappa + l + 1) bits, calculates [ d ] = [ z + r ] = [ z ] · r ], and sends the [ d ] = [ z ] · r ] to the client;
s74, the client decrypts the received data to calculate [ dmod2 ] l ]Sending to a cloud server, and calculating by the cloud server: (zmod 2) l )＝((dmod2 l )-(rmod2 l )mod2 l ，
Figure FDA0003708148930000045
S75. Order
Figure FDA0003708148930000046
The existence of S epsilon R {1, -1} enables the cloud server to calculate the intermediate parameter ciphertext [ c [ [ C ] i ]]And satisfies the following conditions:
Figure FDA0003708148930000047
wherein the content of the first and second substances,
Figure FDA0003708148930000048
s76, the intermediate parameter ciphertext [ c ] i ]]Set of vectors of composition [ [ c ]]]Sent to the client, which decrypts it and encrypts it
Figure FDA0003708148930000049
Sent to the cloud server according to
Figure FDA00037081489300000410
And S calculates [ lambda ]]Then [ zmod2 ] is calculated l ]And obtaining a comparison result and returning the comparison result to the client.
8. The face recognition method based on wavelet dimension reduction under homomorphic encryption according to claim 7, wherein step S76 further comprises: the client checks whether the received vector set [ c ] is 0.
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