PPG Secure Biometric Authentication Method and System Based on Homomorphic Random Forest

Abstract

The present invention discloses a PPG security biometric authentication method based on homomorphic random forests, comprising the following steps: S1, collecting PPG signals from logged-in users; S2, preprocessing the collected PPG signals, specifically separating the denoised PPG signals into single cycles, eliminating signals with pulse frequencies outside a preset frequency range, signals with a maximum value of a single signal cycle less than a preset number, and signals where the difference between the PPG signal after dynamic time warping and the time series of a standard waveform is less than a preset value; S3, extracting statistical features, curve width features, spectral features, and reference point features from each filtered cycle as a PPG feature set; S4, homomorphically encrypting the PPG feature set; and S5, inputting the homomorphically encrypted PPG feature set into a pre-trained neural random forest model for recognition. If the feature set meets the criteria, authentication is passed. The present invention can achieve accurate and continuous authentication while protecting the privacy of the PPG features.

Description

Technical Field

[0001] The present invention relates to the field of secure and efficient authentication of PPG signals (pulse wave signals), and in particular to a PPG secure biometric authentication method and system based on homomorphic random forests. Background Art

[0002] Current identity authentication methods typically use passwords, fingerprints, and facial recognition. Photoplethysmography (PPG) measures the human pulse wave signal. Similar to biometric information such as fingerprints and irises, pulse wave signals are also biometric features that can be used for unique identification. However, compared to biometric features such as fingerprints, passwords, and irises, pulse wave signals are more difficult to forge and can be continuously collected in real time using sensor devices, making them more suitable for identity authentication.

[0003] Existing PPG authentication methods include discrete decomposition template matching, Fourier transform analysis, and pattern recognition. The information extracted by discrete decomposition template matching and Fourier transform analysis is relatively coarse, and the authentication accuracy is far from meeting practical application requirements. Pattern recognition methods, particularly machine learning and deep learning methods based on support vector machines (SVM), random forests (RF), and k-nearest neighbors (K-NN), can achieve high authentication accuracy, but they do not fully consider the security of PPG signal authentication and pose security issues such as privacy leakage. Once a user's PPG features are lost, they become permanent, requiring effective protection during transmission and storage to prevent the leakage of user privacy. Furthermore, deep learning models must be trained on separate servers or resources before they can be implemented on local devices, making them difficult to widely promote and apply at this stage.

[0004] Research has found that the technical defects of the existing PPG identity authentication method and the possible causes are:

[0005] (1) The data used in the research and experiments of existing methods are mostly high-quality data collected in competition environments or professional medical environments. However, the PPG signals collected in actual applications are often interfered with and the signal quality is low;

[0006] (2) At different times, due to changes in a person's mood, stress, health, diet, and other conditions, the features extracted by the original model will have distribution differences, resulting in a decrease in the performance of the authentication model;

[0007] (3) Using deep learning to train the authentication model can more accurately identify known users participating in the training. However, in real applications, it is often necessary to identify unknown users, which causes the authentication model to fail.

[0008] (4) The PPG feature template has the characteristics of immutability and permanence. Once lost, it will lead to various difficult security issues. Therefore, it is necessary to provide security protection for the PPG feature template during the PPG feature matching process. Existing research has not been able to achieve efficient authentication while securely storing the PPG template;

[0009] (5) The traditional manual feature extraction method requires a lot of calculations in the process of PPG signal preprocessing and feature extraction. Compared with multiple feature vectors and classifiers, the complexity of the algorithm limits the scenarios in which the model can be applied.

[0010] Therefore, the existing PPG identity authentication method cannot take into account both authentication accuracy and security. Summary of the Invention

[0011] The main purpose of the present invention is to provide a PPG security biometric authentication method and system based on homomorphic random forest, which can achieve accurate continuous authentication while protecting feature privacy.

[0012] The technical solution adopted in the present invention is:

[0013] A PPG security biometric authentication method based on homomorphic random forest is provided, comprising the following steps:

[0014] S1. Collect PPG signals from logged-in users;

[0015] S2. Preprocess the collected PPG signal, specifically separating the denoised PPG signal into individual cycles, and removing signals with pulse frequencies outside a preset frequency range, signals with a maximum value of a single signal cycle less than a preset number, and signals with a time series difference between the PPG signal after dynamic time warping and the standard waveform less than a preset value;

[0016] S3. Extract statistical features, curve width features, spectrum features, and reference point features from each filtered cycle as a PPG feature set, where the statistical features include the minimum value, maximum value, maximum-minimum difference, and cycle length of the signal; the line width feature is the width of the cycle curve at a predetermined height set; and the reference point features include the diastolic peak, systolic peak, and descending mid-wave notch.

[0017] S4, homomorphically encrypt the PPG feature set;

[0018] S5. Input the homomorphically encrypted PPG feature set into the pre-trained neural random forest model for recognition. If it meets the requirements, it passes the authentication.

[0019] According to the above technical solution, the pulse beat frequency is within a preset frequency range of 30 to 120 beats per minute.

[0020] Following the above technical solution, the preset number of maximum values of a single signal cycle is at least 3.

[0021] Following the above technical solution, the preset value of the difference between the time series of the PPG signal after dynamic time warping and the standard waveform is at most 2. Specifically, the average value of the PPG signal of the public dataset and the real-time collected PPG signal is used as the standard waveform.

[0022] Following the above technical solution, step S3 further includes the step of performing dimensionality reduction processing on the PPG feature set, specifically including:

[0023] Principal component analysis (PCA) is used on frequency domain features and curve width features to reduce the number of features;

[0024] Combine the filtered frequency domain features and curve width features with the statistical features and reference point features, and compare the features in the combination two by two. If the correlation coefficient is greater than the threshold, only one of the features is retained and the features of the outliers are proposed;

[0025] The top 60% features are selected based on the minimum redundancy and maximum relevance (mRMR);

[0026] The features ranked in the top 60% are selected by relative mutual information (RMI) to generate the final biometric features.

[0027] Following the above technical solution, after feature dimensionality reduction processing, the number of PPG features in a single cycle is no less than 18.

[0028] Following the above technical solution, step S4 specifically performs homomorphic encryption on the PPG feature set through the CKKS method.

[0029] Following the above technical solution, in step S1, a remote photogrammetry (rPPG) algorithm is used to collect PPG signals via a camera. The camera captures a person's face or other body part, extracts the average heart rate and pulse duration from the skin surface, and detects the user's pulse wave signal based on physiological fluctuations, ultimately acquiring the PPG signal.

[0030] The present invention also provides a PPG security biometric authentication system based on homomorphic random forest, comprising:

[0031] Signal acquisition module, used to collect PPG signals from logged-in users;

[0032] The signal preprocessing module is used to preprocess the collected PPG signals. Specifically, it separates the denoised PPG signals into single cycles and removes signals with pulse frequencies outside a preset frequency range, signals with a maximum value of a single signal cycle less than a preset number, and signals where the difference between the time series of the PPG signal after dynamic time warping and the standard waveform is less than a preset value;

[0033] A feature extraction module is used to extract statistical features, curve width features, spectral features, and reference point features from each filtered cycle as a PPG feature set. Statistical features include the minimum value, maximum value, maximum-minimum difference, and cycle length of the signal; line width features are the width of the cycle curve at a predetermined height set; and reference point features include diastolic peak, systolic peak, and descending mid-wave notch.

[0034] Homomorphic encryption module, used to perform homomorphic encryption on the PPG feature set;

[0035] The authentication module is used to input the homomorphically encrypted PPG feature set into the pre-trained neural random forest model for recognition. If it meets the requirements, it passes the authentication.

[0036] The present invention also provides a computer storage medium storing a computer program executable by a processor, which executes the PPG security biometric authentication method based on homomorphic random forest described in the above technical solution.

[0037] The beneficial effects of the present invention are as follows: the present invention separates the PPG signal into single periodic signals to extract signals that do not meet the requirements, retains only the signals that best reflect the PPG morphological characteristics, then homomorphically encrypts the extracted PPG feature set, and finally performs neural random forest model authentication, thereby achieving safe, efficient and accurate continuous authentication while protecting feature privacy.

[0038] Furthermore, by collecting human PPG signals through a remote photogrammetry (rPPG) algorithm, liveness detection of the human face is achieved. This can effectively prevent some counterfeit attacks that use photos of people or other objects to impersonate legitimate users, further improving the security of the proposed authentication system.

[0039] Furthermore, the present invention addresses the problem of PPG signals having few morphological features and being susceptible to interference by proposing a new feature extraction method. This method comprehensively extracts signal features in the time domain, frequency domain, morphology, and other aspects, and selects the most representative biometric features through methods such as principal component analysis (PCA) and maximum correlation and minimum redundancy (mRMR). Furthermore, the present invention incorporates a signal quality screening step to avoid interference from high-noise signals on authentication accuracy, thus ensuring high authentication accuracy.

[0040] Compared with traditional face recognition and fingerprint detection, the present invention is more reliable, fast and practical, and can be further expanded to fields such as mobile phones, smart wearable devices and cloud networks to improve the user experience; moreover, the present invention can ensure the security of user feature data during the transmission process, and can also ensure that it is invisible to third-party servers, providing data security protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0042] Figure 1 is a flow chart of a PPG secure biometric authentication method based on homomorphic random forests according to an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the homomorphic encryption CKKS mode structure according to an embodiment of the present invention;

[0044] FIG3( a ) is a schematic diagram of a decision tree according to an embodiment of the present invention;

[0045] FIG3( b ) is a schematic diagram of a neural network corresponding to the decision tree in FIG3( a );

[0046] Figure 4 This is the PPG signal acquisition process and some features of the embodiment of the present invention;

[0047] Figure 5 This is a flowchart of the PPG signal authentication process according to an embodiment of the present invention;

[0048] Figure 6 This is a schematic diagram of the PPG authentication system according to an embodiment of the present invention. Figure 1 ;

[0049] Figure 7 This is a schematic diagram of a PPG secure biometric authentication system based on homomorphic random forests according to an embodiment of the present invention. Figure 2 ;

[0050] Figure 8 Schematic diagram of the reference points and related features of the PPG signal according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0052] Example 1

[0053] like Figure 1 、 6 As shown, the PPG security biometric authentication method based on homomorphic random forest in an embodiment of the present invention includes the following steps:

[0054] S1. Collect PPG signals from logged-in users;

[0055] S2. Preprocess the collected PPG signal, specifically separating the denoised PPG signal into individual cycles, and removing signals with pulse frequencies outside a preset frequency range, signals with a maximum value of a single signal cycle less than a preset number, and signals with a time series difference between the PPG signal after dynamic time warping and the standard waveform less than a preset value;

[0056] S3. Extract statistical features, curve width features, spectrum features, and reference point features from each filtered cycle as a PPG feature set, where the statistical features include the minimum value, maximum value, maximum-minimum difference, and cycle length of the signal; the line width feature is the width of the cycle curve at a predetermined height set; and the reference point features include the diastolic peak, systolic peak, and descending mid-wave notch.

[0057] S4, homomorphically encrypt the PPG feature set;

[0058] S5. Input the homomorphically encrypted PPG feature set into the pre-trained neural random forest model for recognition. If it meets the requirements, it passes the authentication.

[0059] The present invention separates the PPG signal into single periodic signals, extracts signals that do not meet the requirements, and only retains the signals that best reflect the PPG morphological characteristics. It then homomorphically encrypts the extracted PPG feature set and finally performs neural random forest model authentication, thereby achieving safe, efficient and accurate continuous authentication while protecting feature privacy.

[0060] Example 2

[0061] The basic steps are the same as those in Example 1 above, except that the PPG acquisition in step S1 is specifically as follows:

[0062] In addition to collecting PPG signals through professional sensors, the remote photogrammetry (rPPG) algorithm is innovatively used to collect PPG signals through consumer-grade cameras. This method uses a camera to shoot a person's face or other body parts, and can extract the average heart rate and heart pulse time from the skin surface, eliminating the need to purchase professional equipment. The skin surface and the light it reflects often change rhythmically with the heartbeat. Each heartbeat causes the blood vessels to widen, resulting in physical and color changes in the texture of the skin surface. These changes are undetectable to the human eye, but digital cameras (such as webcams) can capture tiny fluctuations in texture. These physiological fluctuations can be used to estimate and detect the user's pulse wave signal, and then obtain the PPG signal, such as Figure 4 shown.

[0063] After extracting the PPG signal from the face, combined with Figure 5 As shown, the main process is as follows:

[0064] (1) Body part tracking

[0065] The camera captures a face and detects its surface to determine the range of the face. However, if the target object moves, the pulse signal will be distorted, so when recording, try to avoid violent movements and keep the face facing the center of the camera.

[0066] (2) Pulse detection

[0067] The camera detects the current human body's pulse signal through subtle texture changes on the surface of the face and based on relevant estimation algorithms, and then obtains the PPG signal.

[0068] Example 3

[0069] The basic steps are the same as those in Example 1 above, except that the pre-processing of the collected PPG signal in step S2 is specifically as follows:

[0070] Although PPG-based authentication offers the convenience of continuous authentication and signal acquisition, compared to other physiological features, PPG signals have fewer morphological features. Furthermore, due to the low signal-to-noise ratio (SNR) of captured PPGs, signal quality is poor, which poses a challenge to accurate authentication based on PPG signals. Therefore, in order to obtain the most accurate PPG features and improve authentication accuracy, the collected PPG signals need to be preprocessed as follows:

[0071] (1) Signal denoising

[0072] First, the extracted signal is subjected to a rolling average method to remove the trend, and then a low-pass filter is used to remove high-frequency noise.

[0073] (2) Cycle division

[0074] Because PPG signals are periodic, each feature set is extracted within each cycle. Therefore, it is necessary to first separate the continuous PPG signal into individual cycles. First, estimate the minimum interval between cycles for initial signal segmentation. Then, apply a moving average algorithm to the denoised signal to remove random perturbations. Next, use the arg_rel_min function to find the index of the relative minimum of the signal. Finally, use this index to complete beat separation.

[0075] (3) Quality screening

[0076] PPG signals acquired by devices like biosensors or cameras can be of poor quality due to movement, friction, poor contact, and other factors, affecting authentication accuracy. Therefore, a screening step is added to eliminate unqualified signal cycles. The following three criteria can be used to determine signal eligibility.

[0077] 1) The number of heartbeats per minute is between 30 and 120. After the cycle segmentation step, the length of a single cycle can be obtained. Combined with the sampling frequency of the acquisition device, the number of signal cycles per minute can be obtained, that is, the number of heartbeats per minute.

[0078] 2) The number of maximum values in a single signal cycle is 3 or more. Based on the morphological characteristics of the PPG signal, a signal cycle with fewer than 3 maximum values is considered unqualified. The sampling amplitude method and slope method can be used to detect the peak and trough (maximum) locations in the PPG signal.

[0079] 3) The difference between the dynamic time warping (DTW) and the standard waveform is less than 2. DTW can assess the similarity between two time series and is particularly suitable for time series of different lengths and rhythms. DTW automatically warps the time series (i.e., performs local scaling on the time axis) to make the two series' shapes as consistent as possible, achieving the greatest possible similarity. The standard waveform is the average of the PPG data from the public dataset and our own collected data.

[0080] Only signals that meet all three criteria can pass the screening, which ensures the quality of the extracted signal features and thus improves the accuracy of authentication.

[0081] Example 3

[0082] The basic steps are the same as those in Example 1 above, except that the feature extraction of the pre-processed PPG signal in step S3 is specifically as follows:

[0083] In the PPG-based biometric system, four sets of features, namely statistical features, curve width features, frequency domain features and reference points, are used as the user's unique biometric features. We resample all beats to a sampling rate of 1000 Hz and normalize them so that the amplitude is within a fixed range. The statistical features used in this biometric system include minimum value, maximum value, maximum-minimum difference and cycle length. The curve width feature is the width of the beat curve at a predetermined height set. The frequency domain feature uses discrete Fourier transform as a feature. Reference point detection is that after separating the individual cycles, the system detects the reference points in each beat, and these reference points are selected as part of the final feature. Figure 8 As shown in Figure 1, three reference points are generated by the extreme values of the first and second derivatives of the PPG signal: the diastolic peak, the systolic peak, and the descending mid-wave notch. These three reference points have unique physiological characteristics, from which more features can be derived.

[0084] In one embodiment of the present invention, reference point features (such as Figure 8As shown in Figure 2, a total of approximately 541 features can be extracted from a beat (i.e., a single cycle of PPG signals of approximately 0.5 to 2 seconds), including 4 statistical features, 18 curve width features, 500 frequency domain features, and 19 reference point features. These features can accurately and comprehensively represent an individual.

[0085] Example 3

[0086] The basic steps are the same as those in the above embodiment 1, except that step S3 further includes performing dimensionality reduction processing on the PPG feature set, i.e., feature dimensionality reduction.

[0087] Because too many features can lead to poor performance, feature selection is used to reduce feature dimensionality and eliminate redundancy. This selection process involves the following steps: Principal component analysis is performed on both the frequency domain and the curve width features to reduce the number of features. The top 60% of the most important features are selected by maximizing correlation and minimizing redundancy. Finally, the final biometric signature is generated by selecting the top 60% of features ranked by relative mutual information.

[0088] Specifically:

[0089] (1) Use principal component analysis (PCA) to reduce the number of features in the frequency domain and curve width. For the frequency features, we first fit a PCA model with 100 components, using 0.99 as the number of components parameter, which means returning n principal components that satisfy the cumulative contribution rate of the principal component variance to reach 99%. For the curve width features, we do the same thing, but only need to fit a PCA model with 15 components. We found that after performing PCA on the frequency features, approximately 5 features are retained, while the curve width features retain 9.

[0090] (2) Combine the features obtained in (1) with the statistical features and the benchmark features. First, we calculate the Pearson correlation coefficient between each of these features. For a pair of features (f1, f2), if the absolute value of the correlation coefficient between them is greater than 0.95, then we retain only one of the features. Then, to avoid the influence of outliers, we use a logarithmic transformation to transform the feature distribution to a normal distribution and delete features that fall outside the 1% to 99% percentile of the feature distribution. (Features between the 1% and 99% percentile of the feature distribution are retained).

[0091] (3) Select the top 60% features based on minimum redundancy maximum relevance (mRMR). This step maximizes the correlation between features and categorical variables, minimizes the correlation between features, and greatly reduces redundancy.

[0092] (4) Using relative mutual information (RMI), we select the top 60% of features to generate the final biometric features. The number of features obtained on different datasets varies, and the number of features obtained for each user in one beat is more than 18.

[0093] At this point, after a series of signal processing, feature extraction, and redundancy removal methods, the final PPG feature set used for authentication was obtained, as shown in Table 1 below. This feature set is comprehensive, stable, and has low redundancy, and is an important basis for achieving high-precision authentication.

[0094] Table 1 Feature set

[0095]

[0096] Example 4

[0097] The basic steps are the same as those in Example 1 above, except that the PPG feature set is homomorphically encrypted in step S4.

[0098] Homomorphic encryption is used because it focuses on data processing security. Homomorphic encryption enables the processing of encrypted data. This means that anyone can perform operations on encrypted data without leaking any of the original content.

[0099] Figure 2 The structural diagram of the CKKS mode is provided. In our scheme, let N be a power of 2, M=2N, and the Mth cyclic polynomial of N rounds ΦM(X)=x N +1. For efficiency and safety reasons, we will use R = Z[X] / (x N +1) as the ring integer of the Mth cyclic polynomial. We can see that the message m is encoded as a plaintext polynomial p(X), which is then encrypted using the public key. The message is encrypted as c, a pair of polynomials. CKKS provides several operations that can be performed on them, such as addition, multiplication, and rotation.

[0100] We use the homomorphic encryption library SEAL for encryption. The TenSEAL context is the core part of the library. It generates and stores keys for encryption and decryption calculations, Galois keys for rotation, and relinearization keys for ciphertext relinearization. This object will also handle the thread pool, which is responsible for deciding and controlling the amount of work that should be run in parallel when executing parallelizable operations. The context can also be configured to automatically relinearize and rescale the ciphertext during the calculation process. In the present invention, relevant configuration and key initialization are performed on the client, and then the PPG feature vector is encrypted.

[0101] Furthermore, given the need for efficiency, we used a method for calculating the power of the encrypted vector to improve runtime speed. The batching feature of the CKKS scheme allows an N×N matrix to be encrypted into N ciphertexts, with each row or column being a ciphertext. Our goal is to use the minimum number of ciphertexts and have the maximum depth with the minimum runtime, thereby optimizing memory and computation. To pursue this ideal goal, we use a single ciphertext to encrypt an input and evaluate it on a convolutional neural network. This requires a preprocessing step on the client side, encoding the signal into a matrix consisting of convolution windows as rows, which is then flattened into a vector via vertical scanning.

[0102] In addition, considering the need for efficiency, we used a method to calculate the power of encrypted vectors to improve the running speed of homomorphic encryption matrix multiplication. The main implementation ideas are as follows:

[0103] We use the real number field R of the same size d×d as the ciphertext matrix d×d In the example, first customize four useful arrangements:

[0104] ·σ(A) i,j =A i,i+j

[0105] ·τ(A) i,j =A i,i+j

[0106] ·φ(A) i,j =A i,i+j

[0107] ·ψ(A) i,j =A i,i+j

[0108] Where σ and φ represent column shift functions, τ and ψ represent row shift functions, i and j represent rows and columns. Then for two square matrices A and B of order d, we can express their matrix product AB as:

[0109]

[0110] Where ⊙ represents the component-wise multiplication between vectors. d×d Any permutation operation on can be understood as a linear transformation, R n →R n (n=d 2 ), in general, such a matrix can be expressed as Where U has n non-zero diagonal vectors. However, according to the above formula, O(d 2 ) homomorphic operations, combined with multiplication operations, the total complexity of matrix multiplication is O(d 3). This time complexity is too large for practical calculations, so we propose the following method for calculating the power of the encryption vector:

[0111] Step 1: For the ciphertext matrix A and ciphertext matrix B, both of size d×d, when k∈Z∩(-d,d), the matrix Is a sparse matrix with (2d-1) non-zero diagonal vectors, which are linearly transformed by the following formula:

[0112]

[0113] where a = ι -1 (A)∈R n , represents the vector representation of the ciphertext matrix A or B, ι(·) is the isomorphism between the additive groups of homomorphic encryption, ρ(a; k) represents the rotation of the ciphertext vector a, and a=(a0,…,a n-1 ) is converted to ρ(a;k)=(a k ,...,a n-1 ,a0,...,a k-1 ).

[0114] Step 2: Then get the ciphertext vector A 0 With B 0 Safely calculate σ(A 0 ) and τ(B 0 ) is performed on the columns and rows, and then the obtained A and B are subjected to a Hadamard multiplication. All ciphertexts are aggregated to obtain the product of the encrypted ciphertext matrix A and B.

[0115] In this way, the cipher matrix operation performed by this method involves 5d additions, 5d constant multiplications, 6d rotations, and d multiplications, with a time complexity of O(d), which is much faster than the previous O(d). 3 ), greatly improving efficiency.

[0116] Example 4

[0117] The basic steps are the same as those in Example 1 above, except for the construction of the neural random forest tree model in step S5.

[0118] To achieve the authentication of PPG ciphertext features, we modified the random forest.

[0119] First, we conduct neural modeling of random forest. Figure 3(a) 、 3(b)This article demonstrates how to simulate a decision tree using a DNN. Suppose an observation belongs to leaf 4. According to the decision tree, this means starting at the root node O, then moving left, right from node 1, and finally left from node 3. The idea behind a neural random forest is to first perform all comparisons simultaneously in the first layer and then determine which leaf the observation belongs to. Each neuron in the second layer represents a leaf, and only one neuron in the second layer will be activated. The activated neuron will represent the leaf where the observation belongs, using the comparisons calculated in the first layer to determine the observation's exact location. Finally, once the observation's location is determined, the final output layer simply outputs the mean of that leaf for regression or the distribution of that leaf for classification. To generalize from a single tree to a random forest with L trees, we can compute all predictions in parallel and, given weights, take the weighted sum of the outputs of each tree to obtain the neural random forest's prediction.

[0120] The neural transformation of random forest is as follows:

[0121] set up Regularized input space is X=[0,1] d , the output space of regression is Assume that T is a binary decision tree, given a data set D n =((X1,Y i ),…,(X n ,Y n )), n ≥ 2. We use K to represent the number of leaf nodes, i.e., the terminal nodes in the tree. If a binary decision tree has K leaf nodes, it must have K-1 internal nodes. Let x∈X be an observation, H=(H1,...,H k-1 ) is the set of hyperplanes used in constructing T. For k∈[1...k-1], we have H k ={x∈X∶h k (x) = 0}, where h k (x) = x τ (k)-t k ,τ∶[1..K-1]→[1..D], where τ(k) is the variable index used to compare k, t k ∈[0,1] is the threshold used for comparison k. Therefore, the first linear layer simply applies the comparison and applies a nonlinear If the variable is above the threshold, it is sent to +1, otherwise -1. Therefore, the K-1 outputs of the first layer are:

[0122]

[0123] The second hidden layer will take K-1 output bits ±1 and output K bits with 1 bit +1 at the index of the leaf to which the observation belongs and -1 elsewhere. To do this, let us denote the index of a given leaf by k′∈[1..K] and define v k′ (x) is an output of the second layer. If and only if comparison k is used to reach leaf k′, we will k (x) uses a non-zero weight. If in this path, H k If the split node is from one node to a right child node, the weight of the connection is +1, otherwise it is -1. Then we get:

[0124]

[0125] The symbol k→k′ represents the connection between k and k′, V k,k′ = ±1 is the corresponding weight. Here l(k′) is the path length from the root to the leaf k′. When implementing this in CKKS, it is important to note that:

[0126]

[0127] More specifically, if and only if x belongs to a leaf k′, ∑ k→k′ V k,k′ u k (x)+b k′ is positive. Therefore, the output of the second layer is +1 if the observation is on the leaf, and -1 otherwise. Finally, the output of the tree is denoted as T(x):

[0128]

[0129] in, Y i and L k′ is the index of the observation value of leaf k′. In the authentication scenario, the authentication result is obtained by classification, so we will output the category distribution in this leaf. In order to generalize from a single tree to a forest with L ≥ 1 trees (T (1) …T (L) ), we compute all predictions in parallel and give them weights α l , the output of each tree is weighted summed to obtain the prediction of the neural random forest

[0130]

[0131] In summary, we have effectively modeled random forests using a DNN with two hidden layers and one output layer.

[0132] Next, we show how neural random forests can be adapted to CKKS. As can be seen, the neural random forest described above is evaluated using three equations: (1), (2), and (5). Observe that the first layer is a special sparse matrix multiplication where only one variable is selected per row. The last layer can be thought of as performing some dot multiplications. Therefore, to adapt the neural random forest to the homomorphic encryption scheme, we only need to perform a parallel matrix multiplication for each tree in the second layer.

[0133] For the first-level formula (1), linear operations are performed instead of matrix multiplications in our system because linear operations are more advantageous in terms of performance and do not compromise the confidentiality of the model. Then, for the second-level formula (2), we use the Packed Matrix Multiplication algorithm to perform all matrix multiplications. This algorithm is particularly suitable for our scenario because we can evaluate all L trees simultaneously without any additional cost, regardless of the number of inputs d or the number of trees L, because the complexity of the algorithm depends only on the number of leaves K.

[0134] In the last layer, formula (5), we will calculate the score of each class c, which can be viewed as v and vector W c The dot product between Where W c Each W (l) The concatenation of the weighted c-th row in . Plus β c , which is the weighted sum of the deviations of class c on L trees. Therefore, we can use the Dot Product method to calculate it homomorphically. Assuming there are K leaf nodes, the probability simplex of the classification is In this case, only addition is required in the first linear layer, and the complexity of the homomorphic operation is 1. The second linear layer needs to perform addition, multiplication, and rotation operations, and the complexity of each operation is K. The complexity of addition and rotation in the third linear layer is The complexity of multiplication is C.

[0135] The following Algorithm 1 describes the process of homomorphic random forest evaluation. In this algorithm, the homomorphic random forest consists of a tree T1 with input x∈X and a polynomial activation function On the client side, the user first needs to prepare the data, copy the inputs of each tree, and concatenate all the inputs. The client then encrypts the data using the homomorphic encryption method mentioned above. The client sends the encrypted data to the server for evaluation. Similar to the input, the server first sets the threshold and fills the gap. It then performs matrix multiplication and comparison. The leaf scores are then calculated in parallel, and the probability of each classification is finally determined by calculating the weights of the dot product.

[0136]

[0137]

[0138] Example 5

[0139] The embodiment of the present invention is based on the PPG security biometric authentication system of homomorphic random forest, such as Figure 6 、 7 Shown, including:

[0140] Signal acquisition module, used to collect PPG signals from logged-in users;

[0141] The signal preprocessing module is used to preprocess the collected PPG signals. Specifically, it separates the denoised PPG signals into single cycles and removes signals with pulse frequencies outside a preset frequency range, signals with a maximum value of a single signal cycle less than a preset number, and signals where the difference between the time series of the PPG signal after dynamic time warping and the standard waveform is less than a preset value;

[0142] A feature extraction module is used to extract statistical features, curve width features, spectral features, and reference point features from each filtered cycle as a PPG feature set. Statistical features include the minimum value, maximum value, maximum-minimum difference, and cycle length of the signal; line width features are the width of the cycle curve at a predetermined height set; and reference point features include diastolic peak, systolic peak, and descending mid-wave notch.

[0143] Homomorphic encryption module, used to perform homomorphic encryption on the PPG feature set;

[0144] The authentication module is used to input the homomorphically encrypted PPG feature set into the pre-trained neural random forest model for recognition. If it meets the requirements, it passes the authentication.

[0145] The functions of each module correspond to the above method embodiments and are mainly used to implement the above method embodiments, which will not be described in detail here.

[0146] Example 6

[0147] The present invention also provides a computer-readable storage medium, such as a flash memory, a hard disk, a multimedia card, a card-type memory (e.g., an SD or DX memory), a random access memory (RAM), a static random access memory (SRAM), a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a programmable read-only memory (PROM), a magnetic memory, a disk, an optical disk, a server, an App store, etc., on which a computer program is stored, and when the program is executed by a processor, a corresponding function is implemented. The computer-readable storage medium of this embodiment is used to implement the PPG secure biometric authentication method based on homomorphic random forests of the method embodiment when executed by the processor.

[0148] In summary, the PPG-based system proposed in the present invention achieves secure, efficient and accurate authentication by using homomorphic random forest and CKKS scheme.

[0149] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A PPG secure biometric authentication method based on homomorphic random forest, characterized in that: The following steps are involved: S1. Collect PPG signals from logged-in users; S2. Preprocess the collected PPG signal, specifically separating the denoised PPG signal into individual cycles, and removing signals with pulse frequencies outside a preset frequency range, signals with a maximum value of a single signal cycle less than a preset number, and signals with a time series difference between the PPG signal after dynamic time warping and the standard waveform less than a preset value; S3. Extract statistical features, curve width features, spectrum features, and reference point features from each filtered cycle as a PPG feature set, where the statistical features include the minimum value, maximum value, maximum-minimum difference, and cycle length of the signal; the line width feature is the width of the cycle curve at a predetermined height set; and the reference point features include the diastolic peak, systolic peak, and descending mid-wave notch. S4, homomorphically encrypt the PPG feature set; S5. Input the homomorphically encrypted PPG feature set into the pre-trained neural random forest model for recognition. If it meets the requirements, it passes the authentication. Among them, step S3 also includes the step of performing dimensionality reduction processing on the PPG feature set, specifically including: Principal component analysis (PCA) is used on frequency domain features and curve width features to reduce the number of features; Combine the filtered frequency domain features and curve width features with the statistical features and reference point features, and compare the features in the combination two by two. If the correlation coefficient is greater than the threshold, only one of the features is retained and the features of the outliers are proposed; The top 60% features are selected based on the minimum redundancy and maximum relevance mRMR; The features ranked in the top 60% are selected by relative mutual information (RMI) to generate the final biometric features.

2. The PPG secure biometric authentication method based on homomorphic random forest according to claim 1, characterized in that: The pulse beat frequency is within a preset frequency range of 30 to 120 beats per minute.

3. The PPG secure biometric authentication method based on homomorphic random forest according to claim 1, characterized in that: The maximum preset number of a single signal cycle is at least 3.

4. The PPG secure biometric authentication method based on homomorphic random forest according to claim 1, characterized in that: The preset value of the difference between the time series of the PPG signal after dynamic time warping and the standard waveform is at most 2. Specifically, the average value of the PPG signal of the public dataset and the real-time collected PPG signal is used as the standard waveform.

5. The PPG secure biometric authentication method based on homomorphic random forest according to claim 1, characterized in that: After feature dimensionality reduction, the number of PPG features in a single cycle is no less than 18.

6. The PPG secure biometric authentication method based on homomorphic random forest according to claim 1, characterized in that: Step S4 specifically performs homomorphic encryption on the PPG feature set through the CKKS method.

7. The PPG secure biometric authentication method based on homomorphic random forest according to claim 1, characterized in that: In step S1, the remote photogrammetry (rPPG) algorithm is used to collect PPG signals through a camera. The camera captures the face or other body parts, extracts the average heart rate and heart pulse time from the skin surface, and estimates the pulse wave signal of the logged-in user through physiological fluctuations to collect the PPG signal.

8. A PPG security biometric authentication system based on homomorphic random forest, characterized in that: include: Signal acquisition module, used to collect PPG signals from logged-in users; The signal preprocessing module is used to preprocess the collected PPG signals. Specifically, it separates the denoised PPG signals into single cycles and removes signals with pulse frequencies outside a preset frequency range, signals with a maximum value of a single signal cycle less than a preset number, and signals where the difference between the time series of the PPG signal after dynamic time warping and the standard waveform is less than a preset value; A feature extraction module is used to extract statistical features, curve width features, spectral features, and reference point features from each filtered cycle as a PPG feature set. Statistical features include the minimum value, maximum value, maximum-minimum difference, and cycle length of the signal; line width features are the width of the cycle curve at a predetermined height set; and reference point features include diastolic peak, systolic peak, and descending mid-wave notch. Homomorphic encryption module, used to perform homomorphic encryption on the PPG feature set; The authentication module is used to input the homomorphically encrypted PPG feature set into the pre-trained neural random forest model for recognition. If it meets the requirements, it passes the authentication; Among them, the feature extraction module is also used to perform dimensionality reduction processing on the PPG feature set separately, specifically: using principal component analysis (PCA) on the frequency domain features and curve width features to reduce the number of features; combining the filtered frequency domain features and curve width features with statistical features and reference point features, and comparing the features in the combination two by two. If the correlation coefficient is greater than the threshold, only one of the features is retained, and the features of the outliers are proposed; the features in the top 60% of the ranking are selected based on the minimum redundancy maximum correlation (mRMR); and the features in the top 60% of the ranking are selected through relative mutual information (RMI) to generate the final biometric features.

9. A computer storage medium, characterized in that A computer program executable by a processor is stored therein, and the computer program executes the PPG security biometric authentication method based on homomorphic random forest according to any one of claims 1 to 7.

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