Fingerprint image global protection publishing method and device based on differential privacy protection

Abstract

The application discloses a fingerprint image global protection publishing method and device based on differential privacy protection, and relates to the technical field of biological information security. The method comprises the following steps: preprocessing a fingerprint image, converting the fingerprint image into a two-dimensional gray matrix, performing wavelet transform on the two-dimensional gray matrix, extracting a low-frequency region, performing singular value decomposition on the low-frequency region, extracting non-zero singular values, adding Laplace noise to the non-zero singular values, reconstructing the low-frequency region according to the non-zero singular values to which the Laplace noise is added, reconstructing the low-frequency region and other regions of the wavelet transform based on the reconstructed low-frequency region, obtaining a protected fingerprint image, and publishing the protected fingerprint image. The method adopts singular value decomposition technology to reduce the amount of data added with disturbance, and through wavelet transform and reconstruction, the privacy protection acting on the low-frequency region is applied to the privacy protection of the global fingerprint image, so that the global privacy protection effect of the fingerprint image is achieved.

Description

Technical Field

[0001] This invention relates to the field of bio-information security technology. Background Technology

[0002] In this era of rapid information technology development, internet communication has become the most important means of information exchange. Simultaneously, with the continuous development of internet technology and the constant dissemination of information, the security and privacy of a large amount of information are not well protected. Biometric images are the easiest way to expose sensitive private information, yet they are also an unavoidable form of information exchange. Therefore, ensuring that biometric images are both private and usable when published is a crucial method for protecting privacy.

[0003] The core of differential privacy technology lies in balancing data privacy and usability. By adjusting the privacy budget variable, the interconversion between privacy and usability can be achieved. According to the nature and definition of differential privacy, the protection of a fingerprint image is related to the amount of noise added. The greater the added noise, the greater the data perturbation, the higher the data privacy, and the lower the usability; conversely, the smaller the added noise, the smaller the data perturbation, the lower the data privacy, and the higher the usability.

[0004] Based on the privacy protection strategy for fingerprint images during publication, it is necessary to ensure that fingerprint images possess both privacy and usability during publication, achieving the desired function while protecting sensitive privacy information. Therefore, this paper employs differential privacy technology to protect fingerprint images. Differential privacy is a technique that can protect privacy content regardless of the attacker's background knowledge. Furthermore, the definition of differential privacy includes a parameter variable ε, which can be adjusted to control the degree of privacy protection. This allows for reasonable planning and adjustment of the privacy and usability of fingerprint images, preventing excessive privacy from severely compromising usability. The amount of noise added to the fingerprint image is adjusted based on the amount of sensitive information, independent of the overall data in the dataset. This prevents excessive noise from corrupting useful data, thus achieving the highest level of privacy protection. Singular value decomposition (SVD) is a generalization of eigenvalue decomposition. Since eigenvalue decomposition can only decompose square matrices, when decomposing non-square matrices, the relationship between square matrices and ordinary matrices is considered for generalization, resulting in a SVD applicable to all matrices. Singular value decomposition has wide applications in dimensionality reduction, data compression, and recommender systems. Any matrix can be decomposed into three parts through singular value decomposition.

[0005] Existing differential privacy technologies and image privacy protection only apply to the privacy protection of facial images. Compared to facial images, which have relatively fixed feature locations, fingerprint images have discrete recognition features and random feature point distributions. Therefore, it is difficult to directly apply differential privacy protection technologies for facial images to fingerprint image protection.

[0006] Therefore, how to solve the problem of fingerprint privacy leakage that may occur during the publication of fingerprint images, and provide a fingerprint image privacy protection method and device that combines privacy and usability, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a method and apparatus for global protection and publishing of fingerprint images based on differential privacy protection. This method and apparatus employ singular value decomposition technology to reduce the amount of data with added perturbations, and through wavelet transform and reconstruction, apply the privacy protection effect applied to the low-frequency region to the global fingerprint image, thereby achieving the effect of global privacy protection of the fingerprint image.

[0008] Based on the same inventive concept, this invention has four independent technical solutions:

[0009] 1. A method for globally protecting and publishing fingerprint images based on differential privacy, comprising:

[0010] The fingerprint image is preprocessed and converted into a two-dimensional grayscale matrix;

[0011] Perform wavelet transform on the two-dimensional grayscale matrix and extract the low-frequency region;

[0012] Singular value decomposition is performed on the low-frequency region to extract non-zero singular values;

[0013] Laplace noise is added to the non-zero singular values;

[0014] The low-frequency region is reconstructed based on the non-zero singular values ​​of the added Laplace noise;

[0015] The reconstructed low-frequency region is combined with other regions of the wavelet transform to obtain a protected fingerprint image.

[0016] The protected fingerprint image is published.

[0017] Furthermore, wavelet transform is performed on the two-dimensional grayscale matrix to obtain four regions, including: a low-frequency region, a high-frequency region, a high-frequency region in the row direction and a low-frequency region in the column direction, and a low-frequency region in the row direction and a high-frequency region in the column direction.

[0018] The four region matrices each have 0.5m columns and 0.5n rows, where m is the number of columns in the two-dimensional grayscale matrix and n is the number of rows in the two-dimensional grayscale matrix.

[0019] Furthermore, the low-frequency region is represented by singular value decomposition as follows:

[0020]

[0021] Where LL is the low-frequency region matrix, U is the first unitary matrix of (0.5×m)×(0.5×m), and V is the second unitary matrix of (0.5×n)×(0.5×n), i.e., U T U = I, V T V = I, It is an m×n matrix, ∑=diag(δ1,δ2,δ3,...,δ s Let be a diagonal matrix, and δ1≥δ2≥δ3≥...≥δ s , where represents all non-zero singular values ​​of matrix LL.

[0022] Furthermore, the non-zero singular values ​​are represented by Laplace noise as follows:

[0023]

[0024] ΔQ SDP =0.25×m×n;

[0025] Where, ∑′ r×r For a non-zero singular value diagonal matrix with added Laplace noise, δ i This represents the singular values ​​for which Laplace noise needs to be added, where r represents the number of non-zero singular values, and ΔQ SDP ε represents global sensitivity, and ε represents the size of the privacy budget. Noise error conforming to the Laplace distribution.

[0026] Furthermore, the feature is that, after adding Laplace noise to the non-zero singular values, the pairs of non-zero singular values ​​with added Laplace noise are sorted, and the sorted pairs satisfy the following relationship:

[0027] ∑′ r×r =diag(δ′1, δ′2, δ′3,..., δ′ r );

[0028] δ′1≥δ′2≥δ′3≥...≥δ′ r ;

[0029] Among them, δ′1, δ′2, δ′3,..., δ′ rNon-zero singular values ​​for adding Laplace noise.

[0030] Furthermore, the low-frequency region is reconstructed based on the non-zero singular values ​​of the added Laplace noise, as follows:

[0031]

[0032] Among them, LL′ 0.5m×0.5n To reconstruct the low-frequency region matrix, U 0.5m×r U is the first unitary matrix 0.5m×0.5m A matrix consisting of the first r columns of data, V is the second unitary matrix 0.5m×0.5m The transpose of the matrix consisting of the first r rows of data.

[0033] Furthermore, the probability density function of the Laplace noise is expressed as follows:

[0034]

[0035]

[0036] Where x is the disturbed noise data, b is the scaling factor, ε is the privacy budget, and ΔQ is the sensitivity level.

[0037] 2. A fingerprint image global protection and publishing device based on differential privacy protection, comprising:

[0038] The preprocessing module is used to preprocess the fingerprint image and convert the fingerprint image into a two-dimensional grayscale matrix;

[0039] The wavelet transform module is used to perform wavelet transform on the two-dimensional grayscale matrix and extract the low-frequency region;

[0040] The singular value decomposition module is used to perform singular value decomposition on the low-frequency region and extract non-zero singular values.

[0041] A noise addition module is used to add Laplace noise to the non-zero singular values;

[0042] The singular value reconstruction module is used to reconstruct the low-frequency region based on the non-zero singular values ​​with added Laplace noise;

[0043] The wavelet reconstruction module is used to reconstruct the fingerprint image based on the reconstructed low-frequency region and other regions of the wavelet transform, thereby obtaining a protected fingerprint image.

[0044] The publishing module is used to publish the protected fingerprint image.

[0045] 3. A computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0046] 4. An electronic device, comprising a processor and a storage device, wherein the storage device stores a plurality of instructions, and the processor is configured to read the plurality of instructions from the storage device and execute the method described above.

[0047] The fingerprint image global protection and publishing method and apparatus based on differential privacy protection provided by this invention includes at least the following:

[0048] Beneficial effects:

[0049] (1) Based on the Laplace mechanism of differential privacy, the amount of noise is proportional to the magnitude of global sensitivity. Starting from the definition of differential privacy, this invention uses wavelet transform to decompose the image in order to reduce the magnitude of global sensitivity. By adding perturbation noise to the low-frequency region, the magnitude of global sensitivity is reduced. In order to reduce the amount of data with added perturbation, singular value decomposition is used to extract singular values ​​from the two-dimensional image matrix and add perturbation noise to the non-zero singular values, thereby reducing the amount of data with added perturbation. In the reconstruction process, by adding perturbation singular values ​​to reconstruct singular value decomposition, the sensitive data protection acting on singular values ​​can be transformed into a privacy protection effect acting on the whole. By adding perturbation to the low-frequency region and reconstructing the wavelet transform, the privacy protection acting on the low-frequency region can be applied to the privacy protection of the global fingerprint image, thus achieving the global privacy protection effect of the fingerprint image.

[0050] (2) Based on the algebraic decomposition of the two-dimensional matrix, under the condition that the wavelet transform reduces the global sensitivity, the singular value decomposition is then applied to the transformed data to extract the singular values ​​of the matrix and add perturbation noise, which can effectively reduce the perturbation of pixel values, reduce the error size, and improve the usability of fingerprint images, thus taking into account both the privacy and usability of fingerprint images. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A flowchart of one embodiment of the fingerprint image global protection and publishing method based on differential privacy provided by the present invention;

[0053] Figure 2The flowcharts for the fingerprint image global protection and publishing (SVP), DWP, and SDP algorithms based on differential privacy protection provided by this invention are shown below.

[0054] Figure 3 This is a published image of fingerprint images with different privacy budgets obtained under the LAP algorithm provided in Example 1;

[0055] Figure 4 This is a publishing diagram of fingerprint images with different privacy budgets obtained under the SVP algorithm provided in Example 2;

[0056] Figure 5 This is a publishing diagram of fingerprint images with different privacy budgets obtained under the DWP algorithm provided in Example 3;

[0057] Figure 6 This is a publishing diagram of fingerprint images with different privacy budgets obtained under the SDP algorithm provided in Example 4;

[0058] Figure 7 This is a schematic diagram comparing the pixel value distribution of the privacy-preserving image published using the SDP algorithm provided in Example 4 with that of the original image;

[0059] Figure 8 This is a schematic diagram comparing the feature point recognition rates of different algorithms provided in Examples 1 to 4 under different privacy budget conditions. Detailed Implementation

[0060] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0061] This invention provides a global protection and publishing method for fingerprint images based on differential privacy. First, the fingerprint image is preprocessed. Based on the definition of differential privacy and the analysis of perturbation noise generated by the Laplace mechanism, the protection effect of the fingerprint image is related to the global sensitivity, which determines the magnitude of the perturbation noise, and the amount of data to which the perturbation is added. Analysis shows that wavelet transform is used to reduce the global sensitivity, and singular value decomposition is used to reduce the amount of data to which the perturbation is added. The experimental effects are analyzed by using each method individually, and finally, the optimal protection effect is achieved by combining the results. Following a progressive improvement order, this section provides four method embodiments. Embodiment four is the final optimal global protection and publishing method for fingerprint images, and its flowchart is shown below. Figure 1 As shown, Examples 1 to 3 are improvements on Example 4.

[0062] Example 1 involves directly adding Laplace perturbation noise to all pixel values ​​in the fingerprint image, known as the LAP algorithm. Example 2 is the SVP algorithm, whose specific steps include: performing singular value decomposition on the two-dimensional matrix of the fingerprint image, adding Laplace perturbation noise to the singular values, eliminating outliers and sorting them according to the characteristics of the singular values, and finally performing singular value reconstruction. Example 3 is the DWP algorithm, whose specific steps include: performing wavelet transform on the fingerprint image, adding Laplace perturbation noise to the low-frequency region of the wavelet transform, and performing wavelet reconstruction based on the perturbated low-frequency region. Example 4 is the SDP algorithm, whose specific steps include: first performing wavelet transform on the fingerprint image, then performing singular value decomposition on the low-frequency region of the wavelet transform, adding Laplace perturbation noise to the singular values, eliminating outliers and sorting them according to the characteristics of the singular values, and finally performing singular value reconstruction and wavelet reconstruction. The flowcharts for Examples 2 to 4 are as follows: Figure 2 As shown.

[0063] Example 1:

[0064] The LAP algorithm is implemented by treating the fingerprint image as a two-dimensional matrix based on the two-dimensional characteristics of the grayscale fingerprint image. Laplace perturbation noise is added directly to each element of the matrix to change the pixel values ​​in the image, thereby achieving simple protection of the fingerprint image.

[0065] Before fingerprint image recognition, the image is first preprocessed. Fingerprint image recognition is mainly a process of recognizing two-dimensional grayscale fingerprint images. Converting the fingerprint image into a two-dimensional grayscale matrix is ​​a preprocessing step in fingerprint image processing.

[0066] LAP algorithm flow:

[0067] Input: Raw fingerprint image X

[0068] Output: A globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy.

[0069] Parameters: Image size m×n, privacy budget ε

[0070] 1) Read the original image X

[0071] 2) Calculate the global sensitivity ΔQ LAP ΔQ LAP =m×n

[0072] 3) Add Laplace noise:

[0073] for p in range(m):

[0074] for q in range(n):

[0075] X′ (p，q) =X (p，q) +lap(ΔQ LAP / ε)

[0076] 4) Output a globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy.

[0077] Based on the calculation process of adding perturbation noise using differential privacy technology, the total noise level in the protected image is related to the amount of data with added noise. Therefore, the image size needs to be considered when adding the privacy budget. Furthermore, since the noise distribution follows a Laplace distribution, the privacy budget value needs to account for pixel distortion. Therefore, in the experiment, the privacy budget values ​​were set as follows:

[0078] like Figure 3 As shown, with the continuous increase of the privacy budget (gradually increasing from left to right), the fingerprint images released by the LAP algorithm have clearer ridge contours and gradually reduced noise points, which conforms to the definition of differential privacy.

[0079] Example 2:

[0080] In the implementation of the SVP algorithm, for the two-dimensional image matrix of the fingerprint image, singular value decomposition is first performed to extract the singular values ​​during the decomposition process. Then, perturbation noise is added to the singular values ​​according to the Laplace mechanism of differential privacy. Finally, the fingerprint image is reconstructed using the perturbated singular values. By adding perturbation noise to a small number of singular values, global perturbation is achieved during the reconstruction process, which can significantly reduce the amount of noise added. Analysis of the SVP algorithm reveals the impact of the amount of added perturbation noise on the overall image protection effect.

[0081] The specific steps for singular value decomposition of a two-dimensional image matrix are as follows:

[0082] Singular value decomposition of an m×n matrix A is as follows:

[0083] Where U is an m×m unitary matrix; V is an n×n unitary matrix, i.e., U T U = I, V T V = I. It is an m×n matrix, ∑=diag(δ1,δ2,δ3,...,δ s Let be a diagonal matrix, and δ1≥δ2≥δ3≥...≥δ s , where is all the non-zero singular values ​​of matrix A.

[0084] The specific representation of adding Laplace perturbation noise to singular values ​​is as follows:

[0085]

[0086] Where, δ i This represents the singular values ​​for which Laplace noise needs to be added. According to the definition of the differential privacy Laplace mechanism, noise errors conforming to the Laplace distribution are added to each singular value. ε is the privacy budget. For Laplace mechanisms that satisfy ε-differential privacy protection, each non-zero singular value receives a perturbation noise with a privacy budget of ε. ΔQ SVP The global sensitivity of the SVP algorithm, according to the definition of differential privacy global sensitivity, is related to the changed data set. Therefore, the global sensitivity is related to the image size, which is determined by ΔQ. SVP It can be represented as m×n.

[0087] The specific representation of singular value removal and sorting is as follows:

[0088] According to the definition of singular value decomposition, ∑=diag(δ1,δ2,δ3,...,δ s Let be a diagonal matrix, and δ1≥δ2≥δ3≥...≥δ s Let be all the non-zero singular values ​​of matrix A. After adding the Laplace perturbation, ∑′ is processed accordingly, retaining only the non-zero singular values ​​and sorting them. ∑′ = diag(δ′1, δ′2, δ′3, ..., δ′) r ), and δ′1≥δ′2≥δ′3≥...≥δ′ r .

[0089] Based on the computational process of singular value decomposition, the reconstruction process of singular value decomposition can be achieved through... Reconstruction is performed. During the reconstruction process, due to the occurrence of zero singular values, some data in the m×m unitary matrix U and some data in the n×n unitary matrix V are discarded, which will produce some noise error.

[0090] In summary, the SVP algorithm flow is as follows:

[0091] Input: Raw fingerprint image X;

[0092] Output: A globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy;

[0093] Parameters: Image size m×n, privacy budget ε;

[0094] 1. Read the original image X;

[0095] 2. Calculate the global sensitivity ΔQ SVP ΔQ SVP =m×n;

[0096] 3. Convert the fingerprint image X into a two-dimensional matrix X. m×n ;

[0097] 4. For a two-dimensional matrix X m×n Perform singular value decomposition

[0098] 5. Extract non-zero singular values ​​∑ r×r =diag(δ1, δ2, δ3,..., δ r );

[0099] 6. Add Laplace noise to non-zero singular values.

[0100] 7. Remove outliers and sort the perturbed singular values: ∑′=diag(δ′1,δ′2,δ′3,...,δ′ r ), δ′1≥δ′2≥δ′3≥...≥δ′ r ;

[0101] 8. Reconstruct the image matrix based on the data with added perturbations.

[0102] 9. Output a globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy;

[0103] During the experiment, the privacy budget was set to the following values: like Figure 4 As shown, with the continuous increase of the privacy budget (gradually increasing from left to right), the fingerprint image released by the SVP algorithm has clearer ridge contours and gradually reduced noise points, which conforms to the definition of differential privacy.

[0104] Example 3:

[0105] In the implementation of the DWP algorithm, the fingerprint image is first decomposed using wavelet transform X→LL+HL+LH+HH. Based on the characteristics of wavelet transform, most features of the original image are preserved in the low-frequency region. Therefore, Laplace perturbation noise LL→LL′ is added to the low-frequency region. By combining the perturbated low-frequency region with the high-frequency region, the wavelet transform reconstruction process LL′+HL+LH+HH→X′ is achieved. During reconstruction, the perturbated low-frequency region is combined with the high-frequency region, which acts on the privacy protection of the low-frequency region, achieving a global protection effect. Adding perturbation noise reduces the size of the protected dataset, thereby reducing the global sensitivity and thus reducing the magnitude of Laplace noise, thereby improving the protection effect of the fingerprint image.

[0106] Wavelet transform decomposes fingerprint images through row and column transformations. Different levels of wavelet transform decomposition yield different degrees of decomposition coefficients. As the decomposition level increases, the range of the wavelet transform expands, indicating that higher-level wavelet coefficients are more important. Except for the low-frequency region, the variance and energy in other regions decrease significantly, demonstrating the crucial role of low-frequency wavelet transform coefficients in image encoding.

[0107] The second-order wavelet transform process decomposes the original fingerprint image into four regions, which can be represented by the equation X→LL+HL+LH+HH. LL represents the low-frequency region; HL and LH represent the high frequency in the row direction and the low frequency in the column direction, respectively; HH represents the high frequency in the diagonal direction. In wavelet transform, since the low-frequency region plays a crucial role, and most of the original image data is preserved in the low-frequency region, directly adding Laplace perturbation noise to the low-frequency region can effectively protect the fingerprint image.

[0108] Meanwhile, based on the perturbation noise generation process of the Laplace mechanism of differential privacy, the magnitude of the perturbation noise is proportional to the magnitude of global sensitivity. Adding noise to the low-frequency region of wavelet transform can effectively reduce the magnitude of global sensitivity, thereby effectively reducing the magnitude of perturbation noise under the same privacy budget.

[0109] Applying wavelet transform to a two-dimensional image matrix of size m×n yields a low-frequency region LL of size (0.5×m)×(0.5×n). The process of adding perturbation noise to the low-frequency region LL can be represented as follows:

[0110] This indicates that the low-frequency matrix LL has the same size and structure. According to the Laplace mechanism of differential privacy, the protected data should also satisfy the Laplace distribution. This is represented by adding a matrix of perturbed data conforming to the Laplace distribution to the LL matrix, thereby changing all data in the LL matrix to achieve privacy protection. ε is the privacy budget. For Laplace mechanism protection that satisfies ε-differential privacy, each data point in the low-frequency matrix LL receives a perturbation noise with a privacy budget of ε. ΔQ DWP The global sensitivity is denoted as ΔQ. According to the definition of global sensitivity in differential privacy, the magnitude of global sensitivity is related to the size of the protected dataset. Therefore, the global sensitivity is calculated as ΔQ. DWP =0.25×m×n.

[0111] The reconstruction process of wavelet transform corresponds to the decomposition process. It reconstructs the decomposition matrix both directionally and column-wise, resulting in an image matrix with the same size and structure as the original image. The process of reconstructing the low-frequency and high-frequency regions after adding noise can be represented as LL′+HL+LH+HH→X′. The wavelet transform process involves changes in the frequency domain, thus introducing a certain amount of reconstruction error. Additionally, the noise added to the low-frequency region also introduces noise error.

[0112] In summary, the DWP algorithm process is as follows:

[0113] Input: Raw fingerprint image X;

[0114] Output: A globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy;

[0115] Parameters: Image size m×n, privacy budget ε;

[0116] 1. Read the original image X;

[0117] 2. Convert the fingerprint image X into a two-dimensional matrix X. m×n ;

[0118] 3. For the two-dimensional matrix X m×n Perform wavelet transform X→LL+HL+LH+HH;

[0119] 4. Extract the low-frequency region image LL 0.5m×0.5n ;

[0120] 5. Calculate the global sensitivity ΔQ DWP ΔQ DWP =0.5m × 0.5n;

[0121] 6. Add Laplace noise;

[0122] for p in range(m):

[0123] for q in range(n):

[0124] LL′ (p，q) =LL (p，q) +lap(ΔQ DWP / ε);

[0125] 7. Reconstruct the fingerprint image based on the perturbated low-frequency image: LL′+HL+LH+HH→X′;

[0126] 8. Output a globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy;

[0127] During the experiment, the privacy budget was set to the following values: like Figure 5 As shown, with the continuous increase of the privacy budget (gradually increasing from left to right), the fingerprint image published by the DWP algorithm has clearer ridge contours and gradually reduced noise points, which meets the definition of differential privacy.

[0128] Example 4:

[0129] In the implementation of the SDP algorithm, the image is first decomposed using wavelet transform to reduce global sensitivity. Based on the properties of wavelet transform, wavelet coefficients in the low-frequency region contain the most energy; therefore, adding perturbation noise to the low-frequency region can reduce global sensitivity. To reduce the amount of data with added perturbation, singular value decomposition (SVD) is used to extract singular values ​​from the two-dimensional image matrix and add perturbation noise to the non-zero singular values, thus reducing the amount of data with added perturbation. During reconstruction, reconstructing using the perturbated singular values ​​transforms the sensitive data protection applied to singular values ​​into a global privacy protection effect. Reconstructing using wavelet transform in the perturbated low-frequency region extends the privacy protection applied to the low-frequency region to the global fingerprint image, achieving global privacy protection for the fingerprint image.

[0130] First, based on the two-dimensional characteristics of grayscale fingerprint images, the fingerprint image is processed as a two-dimensional matrix, and Laplace noise is directly added to each element of the matrix, changing the pixel values ​​in the image and thus protecting the fingerprint image. The implementation does not involve image transformation or restoration, therefore there is no reconstruction error; only the noise error caused by the Laplace noise added due to differential privacy needs to be considered. Subsequently, the two-dimensional image matrix is ​​transformed using linear algebraic decomposition, primarily employing singular value decomposition (SVD). According to the definition of SVD, the image matrix is ​​decomposed, singular values ​​are extracted, noise is added to these singular values, and the image matrix is ​​reconstructed based on the data after adding singular values, following the SVD reconstruction process. According to the definition of the differential privacy Laplace mechanism, the Laplace mechanism of differential privacy technology mainly controls the noise level through the definition of global sensitivity and the privacy budget. Therefore, wavelet transform is used to reduce the global sensitivity. Based on the form of wavelet transform, the image after each wavelet transform is one-quarter of the original image, meaning the global sensitivity is reduced to one-quarter. Meanwhile, for the low-frequency region of wavelet transform, singular value decomposition can also be used to extract singular values ​​and add Laplace noise to the singular values.

[0131] In Embodiment 4, a method for globally protecting and publishing fingerprint images based on differential privacy is provided, including:

[0132] S1. Preprocess the fingerprint image to convert it into a two-dimensional grayscale matrix;

[0133] S2. Perform wavelet transform on the two-dimensional grayscale matrix and extract the low-frequency region;

[0134] S3. Perform singular value decomposition on the low-frequency region and extract non-zero singular values;

[0135] S4. Add Laplace noise to the non-zero singular values;

[0136] S5. Reconstruct the low-frequency region based on the non-zero singular values ​​of the added Laplace noise;

[0137] S6. Based on the reconstructed low-frequency region and other regions of the wavelet transform, a protected fingerprint image is obtained.

[0138] S7. Publish the protected fingerprint image.

[0139] In step S2, wavelet transform is performed on the two-dimensional gray matrix to obtain four regions, including: a low-frequency region, a high-frequency region, a high-frequency region in the row direction and a low-frequency region in the column direction, and a low-frequency region in the row direction and a high-frequency region in the column direction.

[0140] The four region matrices each have 0.5m columns and 0.5n rows, where m is the number of columns in the two-dimensional grayscale matrix and n is the number of rows in the two-dimensional grayscale matrix.

[0141] The original fingerprint image is decomposed into four regions, which can be represented by the equation X→LL+HL+LH+HH. LL represents the low-frequency region; HL and LH represent the high frequency in the row direction and the low frequency in the column direction, respectively; HH represents the high frequency in the diagonal direction. Analysis of the results from the DWP algorithm shows that adding protection to the low-frequency region through wavelet transform reduces the size of the protection dataset, thereby reducing the global sensitivity and thus decreasing the magnitude of Laplace noise.

[0142] In step S3, singular value decomposition is a generalization of eigenvalue decomposition. Eigenvalue decomposition can only be performed on square matrices. Therefore, when decomposing non-square matrices, the relationship between square matrices and ordinary matrices is considered for generalization, thus generating singular value decomposition applicable to all matrices.

[0143] The singular value decomposition of the low-frequency region is represented as follows:

[0144]

[0145] Where LL is the low-frequency region matrix, U is the first unitary matrix of (0.5×m)×(0.5×m), and V is the second unitary matrix of (0.5×n)×(0.5×n), i.e., U T U = I, V T V = I, It is an m×n matrix, ∑=diag(δ1,δ2,δ3,...,δ s Let be a diagonal matrix, and δ1≥δ2≥δ3≥...≥δ s , where represents all non-zero singular values ​​of matrix LL.

[0146] Analysis of the results from the SVP algorithm shows that by extracting singular values ​​from the two-dimensional image matrix through singular value decomposition and adding perturbation noise to the singular values, the amount of data with added perturbation can be reduced, thereby reducing the total amount of noise in the image and improving the protection effect of the fingerprint image.

[0147] In step S4, Laplace noise is added to the non-zero singular values ​​as follows:

[0148]

[0149] ΔQ SDP =0.25×m×n;

[0150] Where, ∑′ r×r For a non-zero singular value diagonal matrix with added Laplace noise, δ i This represents the singular values ​​for which Laplace noise needs to be added, where r represents the number of non-zero singular values, and ΔQ SDP ε represents global sensitivity, and ε represents the size of the privacy budget. Noise error conforming to the Laplace distribution.

[0151] The global sensitivity of differential privacy is defined as follows: Let Q be any query function, and Q: X→R n Then the global sensitivity of Q can be expressed as ΔQ = max X，X′ ||Q(X)-Q(X′)|| p express.

[0152] Global sensitivity can be applied to all protection methods that satisfy differential privacy. However, when the global sensitivity is large for certain data volumes, privacy queries using global sensitivity can introduce excessive noise into the data, compromising its usability. For the same publication function, compared to calculating global sensitivity, the data distribution characteristics in a subset x (x∈X) are predictable, and the prediction results may lead to a relatively small local sensitivity.

[0153] According to the definition of the differential privacy Laplace mechanism, noise errors conforming to the Laplace distribution are added to each singular value. ε is the privacy budget. For a Laplace mechanism that satisfies ε-differential privacy protection, each non-zero singular value receives a perturbation noise with a privacy budget of ε. ΔQ SDP For global sensitivity, according to the definition of global sensitivity in differential privacy, the magnitude of global sensitivity is related to the changed data set. Therefore, the magnitude of global sensitivity is related to the size of the low-frequency region, which is determined by ΔQ. SDP =0.25×m×n is used to represent this.

[0154] The differential privacy Laplace mechanism is defined as follows: Let X be an m×n fingerprint image, and let M be a random algorithm. Take the image X as the data input and X′ as the output, and satisfy X′=X+(Lap(ΔQ / ε)). n If so, then the Laplace mechanism of algorithm M is said to satisfy ε-differential privacy. (Lap(ΔQ / ε)) n The noise matrix is ​​the same size as the image X structure. The magnitude of the noise is proportional to the sensitivity ΔQ and inversely proportional to the privacy budget ε.

[0155] The Laplace mechanism is the most commonly used noise perturbation mechanism in differential privacy. It perturbs the data that needs to be protected by adding Laplace noise, thereby achieving a distortion effect. The noise follows the Laplace distribution.

[0156] The probability density function of the Laplace noise is expressed as follows:

[0157]

[0158]

[0159] Where x is the disturbed noise data, b is the scaling factor, ε is the privacy budget, and ΔQ is the sensitivity level.

[0160] After adding Laplace noise to the non-zero singular values, the pairs of non-zero singular values ​​with added Laplace noise are sorted. The ∑′ after adding Laplace perturbation is then processed accordingly, retaining only the non-zero singular values, and these non-zero singular values ​​are then sorted. The sorted pairs satisfy the following relationship:

[0161] ∑′ r×r =diag(δ′1, δ′2, δ′3,..., δ′ r );

[0162] δ′1≥δ′2≥δ′3≥...≥δ′r ;

[0163] Among them, δ′1, δ′2, δ′3,..., δ′ r Non-zero singular values ​​for adding Laplace noise.

[0164] In step S5, the low-frequency region is reconstructed based on the non-zero singular values ​​of the added Laplace noise, as shown below:

[0165]

[0166] Among them, LL′ 0.5m×0.5n To reconstruct the low-frequency region matrix, the original matrix is ​​decomposed into three parts according to the singular value decomposition process: the unitary matrix U, the eigenvalue matrix, and the eigenvalue matrix. The unitary matrix V. During the reconstruction process of singular value decomposition, the zero part of the eigenvalue matrix is ​​discarded, and only the non-zero part ∑ of the eigenvalue matrix is ​​retained. r×r And add protection, for ∑′ r×r Similarly, during the reconstruction process, the unitary matrix also only takes the portion corresponding to the non-zero part of the eigenvalue matrix, U. 0.5m×r U is the first unitary matrix 0.5m×0.5m A matrix consisting of the first r columns of data, V is the second unitary matrix 0.5m×0.5m The transpose of the matrix consisting of the first r rows of data.

[0167] During the reconstruction process, due to the occurrence of zero singular values, some data in the (0.5×m)×(0.5×m) unitary matrix U and some data in the (0.5×n)×(0.5×n) unitary matrix V are discarded, which will produce certain noise errors.

[0168] The reconstruction process of Singular Value Decomposition (SVD) generally follows the characteristic that the sequence of singular values ​​decreases rapidly. SVD utilizes this property, using the r largest singular values ​​and their corresponding left and right singular vectors to approximate the reconstruction of the matrix.

[0169] In step S6, the process of reconstructing the low-frequency region and the high-frequency region after adding perturbation noise can be represented as LL′+HL+LH+HH→X′. The wavelet transform process involves changes in the frequency domain, so a certain amount of reconstruction error will be generated during the reconstruction process. At the same time, due to the influence of the noise added to the low-frequency region, a certain amount of noise error will also be generated.

[0170] In summary, the specific process of the SDP algorithm is as follows:

[0171] Input: Raw fingerprint image X;

[0172] Output: A globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy;

[0173] Parameters: Image size m×n, privacy budget ε;

[0174] 1. Read the original image X;

[0175] 2. Convert the fingerprint image X into a two-dimensional matrix X. m×n ;

[0176] 3. For the two-dimensional matrix X m×n Perform wavelet transform X→LL+HL+LH+HH;

[0177] 4. Extract the low-frequency region image LL 0.5m×0.5n ;

[0178] 5. Calculate the global sensitivity ΔQ DWP ΔQ DWP =0.5m × 0.5n;

[0179] 6. For low-frequency region images LL 0.5m×0.5n Perform singular value decomposition;

[0180]

[0181] 7. Extract non-zero singular values ​​∑ r×r =diag(δ1, δ2, δ3,..., δ r );

[0182] 8. Add Laplace noise to non-zero singular values.

[0183] 9. Reconstruct the low-frequency region image based on the data with added perturbations.

[0184] 10. Reconstruct the fingerprint image using wavelet LL′+HL+LH+HH→X′ based on the low-frequency region image after perturbation;

[0185] 11. Output a globally privacy-preserving fingerprint image X′ that satisfies ε-differential privacy;

[0186] During the experiment, the privacy budget was set to the following values: like Figure 6 As shown, with the continuous increase of the privacy budget (gradually increasing from left to right), the fingerprint image released by the SDP algorithm has clearer ridge contours and gradually reduced noise points, which conforms to the definition of differential privacy.

[0187] Figure 7The paper demonstrates a comparison of pixel values ​​between the fingerprint image protected by the algorithm of this invention and the original fingerprint image. Through image comparison, the protected fingerprint image and the original image show the same pixel value distribution, therefore, it can be determined that the protected fingerprint image has high usability.

[0188] See Figure 8 This section compares the feature point recognition rates of different algorithms in Examples 1 to 4 under different privacy budget conditions. Protected images published under different protection methods of this invention are compared, and different privacy budgets are used for comparison. During the experiment, the privacy budget values ​​were as follows: Figure 8 This paper presents a comparative analysis of the recognition rates of protected images and original images at different protection stages under varying privacy budgets. Under the same privacy budget, the LAP algorithm has a very low feature point recognition rate; the DWP algorithm has a higher recognition rate than LAP but still cannot achieve accurate fingerprint recognition; the SVP algorithm has a higher recognition rate than the previous two algorithms, showing a significant improvement in feature recognition; and the SDP algorithm has a very high feature point recognition rate, enabling fingerprint image recognition. The comparative experiments conclude that the algorithms studied in this paper meet the research requirements and significantly improve the usability of protected fingerprint images.

[0189] Under the same algorithmic conditions, comparing the feature point recognition rates for different privacy budgets reveals that as the privacy budget increases, the feature point recognition rate continuously improves, resulting in better usability of the fingerprint images published using the protected algorithm. Conversely, as the privacy budget decreases, the feature point recognition rate continuously decreases, leading to higher privacy for the fingerprint images published using the protected algorithm. Adjusting the privacy budget effectively controls the balance between usability and privacy in the fingerprint images published by the protected algorithm, conforming to the definition of differential privacy.

[0190] Example 5:

[0191] A fingerprint image global protection and publishing device based on differential privacy protection is provided, comprising:

[0192] The preprocessing module is used to preprocess the fingerprint image and convert the fingerprint image into a two-dimensional grayscale matrix;

[0193] The wavelet transform module is used to perform wavelet transform on the two-dimensional grayscale matrix and extract the low-frequency region;

[0194] The singular value decomposition module is used to perform singular value decomposition on the low-frequency region and extract non-zero singular values.

[0195] A noise addition module is used to add Laplace noise to the non-zero singular values;

[0196] The singular value reconstruction module is used to reconstruct the low-frequency region based on the non-zero singular values ​​with added Laplace noise;

[0197] The wavelet reconstruction module is used to reconstruct the fingerprint image based on the reconstructed low-frequency region and other regions of the wavelet transform, thereby obtaining a protected fingerprint image.

[0198] The publishing module is used to publish the protected fingerprint image.

[0199] Example 6:

[0200] A computer-readable storage medium is provided, the computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0201] Example 7:

[0202] An electronic device is provided, including a processor and a storage device, wherein the storage device stores a plurality of instructions, and the processor is configured to read the plurality of instructions from the storage device and execute the method described above.

[0203] This embodiment provides a fingerprint image global protection and publishing method and apparatus based on differential privacy protection. To address the potential fingerprint privacy leakage problem during fingerprint image publishing, this invention designs a method for protecting fingerprint images during the publishing process. Since the fingerprint image publishing process is for application purposes, it is necessary to ensure both privacy and usability during fingerprint image protection. Research on fingerprint image protection based on differential privacy technology can well meet this requirement. According to the definition of differential privacy, by adjusting the privacy budget, as the privacy budget decreases, the magnitude of perturbation noise continuously increases during differential privacy protection, thereby enhancing the privacy of the fingerprint image and decreasing its usability. When the privacy budget is close to zero, the fingerprint image has the strongest privacy. Conversely, as the privacy budget increases, the magnitude of perturbation noise continuously decreases during differential privacy protection, thereby decreasing the privacy of the fingerprint image and enhancing its usability. When the privacy budget approaches infinity, the fingerprint image has the strongest usability.

[0204] In differential privacy-based fingerprint image protection, the lower bound of the privacy budget is zero, thus maximizing privacy. The upper bound of the privacy budget is a fixed value; when the privacy budget reaches its upper bound, optimal usability of fingerprint image protection is achieved, but a difference still exists from the highest usability. Therefore, research on differential privacy-based fingerprint image protection primarily focuses on achieving better usability of fingerprint images when the privacy budget is set to a specific value.

[0205] This invention starts with the definition of differential privacy. Analysis of this definition reveals that the protection process based on differential privacy mainly involves the total amount of perturbation data added to the dataset. Reducing the total amount of perturbation data added to the dataset can effectively reduce the protection effect of differential privacy. The total amount of perturbation data added to the dataset is related to the size of individual perturbation data and the amount of perturbation data added. The size of individual perturbation data is related to the global sensitivity and privacy budget, while the amount of perturbation data added is related to the sensitivity of the data.

[0206] Based on the definition of global sensitivity, to reduce its magnitude, wavelet transform is used to decompose the image. According to the properties of wavelet transform, wavelet coefficients in the low-frequency region contain the most energy; therefore, adding perturbation noise to the low-frequency region can reduce the magnitude of global sensitivity. To reduce the amount of data with added perturbation, singular value decomposition (SVD) is used to extract singular values ​​from the two-dimensional image matrix, and perturbation noise is added to the non-zero singular values, thereby reducing the amount of data with added perturbation. During reconstruction, reconstructing using the perturbated singular values ​​transforms the sensitive data protection applied to singular values ​​into a global privacy protection effect. Reconstructing using wavelet transform in the perturbated low-frequency region extends the privacy protection applied to the low-frequency region to the global fingerprint image, achieving a global privacy protection effect for the fingerprint image.

[0207] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.

Claims

1. A method for globally protecting and publishing fingerprint images based on differential privacy protection, characterized in that, include: The fingerprint image is preprocessed and converted into a two-dimensional grayscale matrix; Perform wavelet transform on the two-dimensional grayscale matrix and extract the low-frequency region; Singular value decomposition is performed on the low-frequency region to extract non-zero singular values; Laplace noise is added to the non-zero singular values; The low-frequency region is reconstructed based on the non-zero singular values ​​of the added Laplace noise; The reconstructed low-frequency region is combined with other regions of the wavelet transform to obtain a protected fingerprint image. The protected fingerprint image is published.

2. The method according to claim 1, characterized in that, Wavelet transform is performed on the two-dimensional grayscale matrix to obtain four regions, including: a low-frequency region, a high-frequency region, a high-frequency region in the row direction and a low-frequency region in the column direction, and a low-frequency region in the row direction and a high-frequency region in the column direction. The four region matrices each have 0.5m columns and 0.5n rows; where m is the number of columns in the two-dimensional grayscale matrix and n is the number of rows in the two-dimensional grayscale matrix.

3. The method according to claim 1, characterized in that, The singular value decomposition of the low-frequency region is represented as follows: ； in, For the low-frequency region matrix, U is The first unitary matrix, V is The second unitary matrix, i.e. , , yes The matrix, It is a diagonal matrix, and , where represents all non-zero singular values ​​of matrix LL.

4. The method according to claim 1, characterized in that, Adding Laplace noise to the non-zero singular values ​​is represented as follows: ； ； in, For a non-zero singular value diagonal matrix with added Laplace noise, This represents the singular values ​​for which Laplace noise needs to be added, where r represents the number of non-zero singular values. For global sensitivity, For the size of the privacy budget, Noise error conforming to the Laplace distribution.

5. The method according to claim 4, characterized in that, After adding Laplace noise to the non-zero singular values, the pairs of non-zero singular values ​​with added Laplace noise are sorted, and the sorted pairs satisfy the following relationship: ； ； in, Non-zero singular values ​​for adding Laplace noise.

6. The method according to claim 3, characterized in that, The low-frequency region is reconstructed based on the non-zero singular values ​​of added Laplace noise, as follows: ； in, For a non-zero singular value diagonal matrix with added Laplace noise, To reconstruct the low-frequency region matrix, The first unitary matrix A matrix consisting of the first r columns of data, The second unitary matrix The transpose of the matrix consisting of the first r rows of data.

7. The method according to claim 1, characterized in that, The probability density function of the Laplace noise is expressed as follows: ； in, For disturbed noise data, This is the scaling factor. For the size of the privacy budget, This represents the sensitivity level.

8. A fingerprint image global protection and publishing device based on differential privacy protection, characterized in that, include: The preprocessing module is used to preprocess the fingerprint image and convert the fingerprint image into a two-dimensional grayscale matrix; The wavelet transform module is used to perform wavelet transform on the two-dimensional grayscale matrix and extract the low-frequency region; The singular value decomposition module is used to perform singular value decomposition on the low-frequency region and extract non-zero singular values. A noise addition module is used to add Laplace noise to the non-zero singular values; The singular value reconstruction module is used to reconstruct the low-frequency region based on the non-zero singular values ​​with added Laplace noise; The wavelet reconstruction module is used to reconstruct the fingerprint image based on the reconstructed low-frequency region and other regions of the wavelet transform, thereby obtaining a protected fingerprint image. The publishing module is used to publish the protected fingerprint image.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-7.

10. An electronic device comprising a processor and a storage device, characterized in that, The storage device contains multiple instructions, and the processor is used to read the multiple instructions in the storage device and execute the method as described in any one of claims 1-7.

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