Fingerprint activity detection method based on CKKS homomorphic encryption

Abstract

The invention provides a fingerprint activity detection method based on CKKS homomorphic encryption. The fingerprint activity detection method based on CKKS homomorphic encryption comprises the following steps: step 1, establishing a three-party interaction system model composed of a user side, a key distribution center and a cloud server; step 2, after identity verification is completed, the user side encrypts an image by using a public key, and transmits a ciphertext image to the cloud server through a public channel; 3, after the ciphertext image is received, the cloud server uses a second deep learning model to identify the secret state image, and a secret state result is obtained; and the cloud server transmits the secret state result to the user side through a public channel, and the user side decrypts the secret state result by using the held private key to finally obtain a fingerprint activity detection result. According to the method, the activity of the fingerprint can be accurately and effectively judged on the premise that the input fingerprint image information is not exposed. The core goal of adding the homomorphic encryption technology is to ensure the privacy of fingerprint data and effectively distinguish spoofing attacks initiated by living fingerprints and forged fingerprints at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of information security, and in particular relates to a fingerprint liveness detection method based on CKKS homomorphic encryption. Background Art

[0002] With the widespread adoption of smart devices, privacy and data security are receiving increasing attention. Currently, most identity authentication technologies still rely on a "identity information + password" model, but this model carries the widespread risk of password forgetting, leakage, and even theft. To address these issues, biometric recognition technology has emerged. Fingerprints, due to their uniqueness and convenience, have found widespread application in fields such as payment verification, access control systems, and attendance management. However, fingerprint authentication is not without risk. Recent advances in high-resolution simulation technology, 3D printing, and generative adversarial networks have enabled criminals to forge fingerprints using materials such as silicone and gelatin, thereby deceiving authentication systems. Consequently, fingerprint liveness detection technologies have been developed to distinguish genuine fingerprint images from fake ones and effectively defend against spoofing attacks using forged fingerprints.

[0003] Fingerprints, as crucial user biometric information, pose significant security risks if uploaded directly to a server. They are easily sniffed by hackers and can lead to privacy leaks. For ease of explanation, the holder of the fingerprint image is referred to as the client, and the third-party server provider is referred to as the server. Directly uploading raw fingerprints to a server presents significant security risks and can potentially lead to data leakage. Therefore, it is imperative to design a fingerprint liveness detection technology with privacy protection to effectively mitigate the risk of privacy leaks on the server side. Homomorphic encryption technology offers an effective solution. It not only encrypts fingerprint data but also allows third-party servers to perform inference without decrypting it. Furthermore, leveraging the homomorphic properties of homomorphic encryption, the server performs computations on the encrypted data, and the decrypted result is consistent with the result obtained by performing the same computation on the plaintext data. This mechanism ensures that the fingerprint remains encrypted throughout the inference process, and only the data owner can decrypt the computation results, effectively protecting user privacy.

[0004] The CKKS homomorphic encryption architecture is built on the BGV scheme. Unlike previous homomorphic encryption algorithms, which strive for exact correspondence between the decrypted result and the plaintext, the CKKS algorithm focuses on approximate computation. This algorithm allows for a certain degree of computational error, moderately relaxing the stringent accuracy requirement. This feature simplifies the CKKS scheme's design details and significantly improves computational efficiency compared to other homomorphic encryption schemes based on the LWE / RLWE problem. The CKKS scheme consists of seven parts: initialization, key generation, encryption, decryption, addition, multiplication, and rescaling. The CKKS scheme supports homomorphic operations such as addition, scalar multiplication, non-scalar multiplication, and circular left shift. Compared to BGV and BFV, CKKS offers advantages in privacy-preserving deep learning applications. However, there is still room for further improvement and optimization. The most basic operations supported are addition and multiplication, which can be combined to calculate polynomial values ​​of ciphertext. However, the traditional computational approach of multiplying and adding items one by one is inefficient and computationally expensive. Furthermore, homomorphic encryption introduces additional noise, and during the decryption phase, errors can be amplified as computational depth increases.

[0005] In 2022, Joon-Woo Lee et al. designed a residual network Resnet20 model that supports the CKKS homomorphic encryption scheme (Reference: Brakerski, Zvika, Gentry, Craig, and Vaikuntanathan, Vinod. FullyHomomorphic Encryption from Ring-LWE and Security for Key Dependent Messages[J]. Cryptology ePrint Archive, 2012, 2012: 220). As the first work to combine complex deep learning networks with homomorphic encryption, this method mainly improved in two aspects: 1. It used the latest approximate methods to evaluate non-arithmetic functions such as ReLU and normalized exponential function softmax to ensure sufficient accuracy. 2. The bootstrapping technology of the RNS-CKKS scheme was used in this model, which enables the method to evaluate deep learning models on encrypted data. The plaintext accuracy verified on the CIFAR-10 dataset reached , and the ciphertext accuracy is . It demonstrates the potential of applying FHE to advanced deep learning models. However, this method generally exposes some problems in practical applications: First, the CKKS scheme uses floating-point approximation calculations, which causes rounding errors to accumulate after each operation. As the reasoning process progresses, the accuracy of the calculation results will continue to decline, which will eventually have an adverse effect on the classification accuracy of the Resnet20 model. In addition, the CKKS scheme does not support the ReLU function, and usually uses quadratic or cubic polynomials to approximate it. But the gradient of the ReLU function is only 0 or 1, while the polynomial function The gradient of the ciphertext changes continuously, and this difference can interfere with the model's training convergence speed and generalization ability. Secondly, in actual application scenarios, the data volume of high-resolution fingerprint datasets is often at least an order of magnitude higher than the datasets used in homomorphic encryption experiments. This type of high-resolution data not only consumes a large amount of memory space but can also cause memory overflow issues. In particular, under the CKKS scheme, each floating-point number is encoded into a high-dimensional ciphertext vector. Model parameters (such as convolution kernels, weights, feature maps, etc.) will expand rapidly after encryption, resulting in a significant increase in memory overhead. Summary of the Invention

[0006] Purpose of the invention: The technical problem to be solved by the present invention is to address the deficiencies of the existing technology and provide a fingerprint liveness detection method based on CKKS homomorphic encryption, aiming to design a customized protocol to ensure the privacy and security of fingerprint data and realize the fingerprint liveness detection function under confidential data.

[0007] The method comprises the following steps: Step 1: Establish a three-party interactive system model consisting of the user terminal, key distribution center, and cloud server; The client initiates a service request, encrypts the fingerprint image using the public key distributed by the key distribution center (KDC), sends the encrypted image to the cloud server, receives and decrypts the encrypted result returned by the cloud server, and finally obtains the plaintext liveness detection result; The key distribution center generates a public-private key pair for the user terminal and the cloud server, and securely distributes the generated public-private key pair to the user terminal and the cloud server respectively through a secure channel; The cloud server performs reasoning on the input encrypted image under confidential conditions to determine the authenticity; The user terminal and cloud server register with the key distribution center, which generates a public and private key pair and transmits it to the user through a secure channel. It also generates an authentication certificate so that the user and cloud server can verify each other's identities. Step 2: After completing identity authentication, the user end encrypts the image using the public key and transmits the encrypted image to the cloud server through a public channel; Step 3: Deploy the first deep learning model trained with the plaintext image and the second deep learning model that supports the homomorphic encryption scheme on the cloud server; the parameters of the second deep learning model are the same as those of the first deep learning model (generally including the degree of the ciphertext polynomial, the scale setting, and the bit lengths of the basic modulus, special modulus, and default modulus); After receiving the encrypted image, the cloud server uses the second deep learning model to identify the encrypted image and obtain the encrypted result; Subsequently, the cloud server transmits the encrypted result to the user through a public channel. The user then decrypts it using the private key it holds, ultimately obtaining the fingerprint liveness detection result. In step 3, the second deep learning model is a Resnet20 model that supports the CKKS scheme (named after the initials of the four authors Cheon, Kim, Kim, and Song), and optimizes the ReLU and Sigmoid activation function protocols and the maximum pooling protocol of the original Resnet20 model.

[0008] In step 3, the second deep learning model uses the minimum maximum polynomial approximation method to solve the gap problem between linear and nonlinear operations, specifically including: According to the following formula: , in is a real variable, the nonlinear part ,right The polynomial approximation is performed using the minimum maximum polynomial generation algorithm, which uses a concavity discrimination operator. : , in is the objective function, is a polynomial; The minimum maximum polynomial generation algorithm includes: input: domain , a continuous function f in every interval on D, an approximation parameter , the degree n of the fitting polynomial; where represents the real number space; is the union operator, is a real closed interval; represents the lower bound, Indicates the upper bound; Output: Minimax approximation The polynomial p of Perform the following steps: Step a1, randomly select the initial sampling point sequence Strictly increasing; Indicates the n+1th sampling point; Step a2: For the extreme error parameter E, find the polynomial , making ; i ranges from 1 to n+1; Step a3, find all points that meet the following conditions: , group the points into a set B; Step a4, select from set B points ,in Represents the n+1th point, and makes the selected The sum of the absolute values ​​of the points is the largest; the maximum single point error and minimum single point error The calculation formula is: , , in It means taking the maximum value of all values ​​traversed by index i. Indicates taking the minimum value of all values ​​traversed by index i; Step a5, when the convergence condition is met: , the relative error volatility is less than the threshold When the approximation effect is determined to be stable, the iteration is terminated and returned Otherwise, all Replace with , return to step a2.

[0009] In step 3, the second deep learning model uses a polynomial algorithm to generate an approximate sign function. Perform a polynomial approximation: Input: Parameters , a set of polynomial degree sequences ; s is the number of iterations, Every polynomial A set of preset times; Output: a set of polynomial sequences satisfy ;in represents p(x) when j=0; For each j , do the following: When j is satisfied When the condition is ; Otherwise: Domain is a polynomial In the interval The value range of ; Generator polynomial Z ; Where Z represents the minimum maximum polynomial generation algorithm; End the loop; output the polynomial sequence .

[0010] In step 3, the following improvements are made to the ReLU activation function in the second deep learning model: The polynomial sequence input to the ReLU activation function is a polynomial sequence generated by the polynomial algorithm that approximates the sign function; Input: ciphertext tensor , a list of polynomials fitting the sign function ; Represents the ciphertext data of the kth channel in the tensor, Represents height and width respectively, is the number of slots configured, is the number of channels; Output: activated ciphertext tensor ; For each channel index implement: Temporary ciphertext variable ; For j implement: EvalPoly ; Where EvalPoly means calculating a polynomial on the ciphertext; ReLU activation implementation , where @ represents the element-by-element multiplication of the ciphertext, and 1 represents the all-1 ciphertext constant; Returns the output tensor .

[0011] In step 3, to address the problem of scarce sample data in fingerprint liveness detection, a class feature center representation model is constructed, and a high-discriminative metric space is constructed using the bulldozer distance algorithm; The class feature center representation model embeds the true and false fingerprint class features into the metric space to establish a classification decision mechanism based on feature similarity, specifically including: Calculate the class center feature: For category m, let the sample set of m be , the features extracted from each sample are , then the category center feature for: , , in represents the qth sample of category m; is the total number of samples of category m; Indicates the calculation of the push distance function, which is a measure of sample characteristics. and class center features distance.

[0012] In step 3, to improve the generalization performance of the second deep learning model in cross-sensor scenarios, an incremental feature optimization learning mechanism is designed. In the first stage, 1 / k (generally 3) parts of the network are trained, and in the second stage, 2 / k parts are trained. The training is iterated step by step until the entire network is finally trained. Through the feature decoupling and reconstruction strategy (the feature decoupling strategy explicitly separates the sensor-specific features and the common features of forgeries in the fingerprint image by introducing a domain discrimination module and orthogonal constraints; while the feature reconstruction strategy introduces an autoencoder structure, so that the model can maintain the ability to reconstruct the original image structure while extracting discriminative features, thereby enhancing the integrity and stability of feature expression), the sensor-specific features and the common features of forgeries are separated (the sensor-specific features and the common features of forgeries are automatically learned by a deep neural network through feature space division. The multi-task structure and domain discrimination module are adopted to guide the network to explicitly separate the feature differences generated by different sensors and the deceptive features shared by forged fingerprints during the training phase. On this basis, the separability of the features is further enhanced by the feature decoupling regularization term, thereby improving the accuracy of cross-device liveness detection), and the effective extraction of invariant features across sensor domains is achieved.

[0013] In step 3, an improved loss function fusion strategy is proposed to address the forgetting problem in the incremental learning process: based on the gated recurrent unit (GRU) model, the training data of each round of the Resnet20 model is recorded to determine whether forgetting occurs. By combining the dual constraints of cross-entropy classification loss and knowledge distillation loss, a dynamic balance optimization objective function is constructed to achieve the absorption of new knowledge and the stable retention of old knowledge.

[0014] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the method.

[0015] The present invention also provides a storage medium storing a computer program or instruction, which executes the steps of the method when the computer program or instruction is run on a computer.

[0016] Beneficial effects: The present invention first improves the activation function layer based on the original Resnet20 model using the minimum maximum polynomial approximation method to improve the classification ability of the neural network. It then processes the spatial dimension of the input through layer-by-layer rotation operations, continuously sums and aggregates spatial information, and then multiplies each pooled tensor with the weight matrix of the fully connected layer, and adds a bias to obtain a one-dimensional output vector. It also realizes the functions of the average pooling layer and the fully connected layer, and finally designs a Resnet20 deep learning model that supports the CKKS homomorphic encryption scheme to ensure security during fingerprint detection and effectively improve the accuracy of detection. At the same time, the defects of the current model in training and application are taken into account, the problem of excessive memory usage during training is optimized, and the generalization of the model is improved to cope with diverse detection environments in reality. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a model diagram of the method of the present invention.

[0018] Figure 2 This is a schematic diagram of the Resnet20 model supporting the CKKS solution proposed in the present invention.

[0019] Figure 3 It is a few-shot incremental learning framework.

[0020] Figure 4 It is a GRU model detection framework.

[0021] Figure 5 This is a comparison chart of the fingerprint liveness detection accuracy of different sensors. DETAILED DESCRIPTION

[0022] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more apparent.

[0023] The embodiment of the present invention provides a fingerprint liveness detection method based on CKKS homomorphic encryption, comprising: Step 1: Establish a three-party interactive system model consisting of the user terminal, key distribution center, and cloud server; The client initiates a service request, encrypts the fingerprint image using the public key distributed by the Key Distribution Center (KDC), sends the encrypted image to the cloud server, receives and decrypts the encrypted result returned by the cloud server, and finally obtains the plaintext liveness detection result. The key distribution center generates a public-private key pair for the user terminal and the cloud server, and securely distributes the generated public-private key pair to the user terminal and the cloud server respectively through a secure channel; The cloud server performs reasoning on the input encrypted image under confidential conditions to determine the authenticity; The user terminal and cloud server register with the key distribution center, which generates a public and private key pair and transmits it to the user through a secure channel. It also generates an authentication certificate so that the user and cloud server can verify each other's identities. Step 2: After completing identity authentication, the user end encrypts the image using the public key and transmits the encrypted image to the cloud server through a public channel; Step 3: Deploy a first deep learning model trained with plaintext images and a second deep learning model supporting a homomorphic encryption scheme with parameters of the first deep learning model as parameters on a cloud server; After receiving the encrypted image, the cloud server uses the second deep learning model to identify the encrypted image and obtain the encrypted result; Subsequently, the cloud server transmits the encrypted result to the user through a public channel. The user then decrypts it using the private key it holds, ultimately obtaining the fingerprint liveness detection result. In step 3, this method designs a Resnet20 model that supports the CKKS scheme based on the original Resnet20, and optimizes the ReLU and Sigmoid activation function protocols and the maximum pooling protocol, such as Figure 2 As shown in the figure, this method designs a Resnet20 model that supports the CKKS scheme. This model consists of convolutional layers (Conv) for extracting local spatial features of the image; batch normalization layers (BN) for accelerating training and improving stability; ReLU activation layers (ReLU) for introducing nonlinearity and improving model expressiveness; bootstrap layers (Boot), unique to the CKKS encryption scheme, for refreshing ciphertext noise when the encryption depth is too deep to ensure continued computation; average pooling layers (AP) for dimensionality reduction and parameter reduction; fully connected layers (FC) for mapping high-dimensional features to the output space; and sigmoid activation layers for binary classification, outputting a live or non-live result. This model can be used to identify live fingerprint images.

[0024] Figure 2 In the figure, Conv1 represents the first convolutional layer module, Conv2, Conv3, and so on. Conv2_1 represents the first submodule in the second convolutional layer module. These submodules together form the second convolutional layer. Stacking Conv modules can better extract fingerprint features.

[0025] The second deep learning model uses the minimum maximum polynomial approximation method to address the gap between linear and nonlinear operations, specifically including: According to the following formula: , in is a real variable, the nonlinear part ,right The polynomial approximation is performed using the minimum maximum polynomial generation algorithm, which uses a concavity discrimination operator. : , in is the objective function, is a polynomial; The minimum maximum polynomial generation algorithm includes: input: domain , a continuous function f in every interval on D, an approximation parameter , the degree n of the fitting polynomial; where represents the real number space; is the union operator, is a real closed interval; represents the lower bound, Indicates the upper bound; Output: Minimax approximation The polynomial p of Perform the following steps: Step a1, randomly select the initial sampling point sequence Strictly increasing; Indicates the n+1th sampling point; Step a2: For the extreme error parameter E, find the polynomial , making ; i ranges from 1 to n+1; Step a3, find all points that meet the following conditions: , group the points into a set B; Step a4, select from set B points ,in Represents the n+1th point, and makes the selected The sum of the absolute values ​​of the points is the largest; the maximum single point error and minimum single point error The calculation formula is: ; ; It means taking the maximum value of all values ​​traversed by index i. Indicates taking the minimum value of all values ​​traversed by index i; Step a5, when the convergence condition is met: , the relative error volatility is less than the threshold When the approximation effect is determined to be stable, the iteration is terminated and returned Otherwise, all Replace with , return to step a2.

[0026] The second deep learning model uses a polynomial algorithm to generate an approximate sign function Perform a polynomial approximation: Input: Parameters In this method , the polynomial degree sequence is 7, 15, 27. A set of polynomial degree sequences ; s is the number of iterations, Every polynomial A set of preset times; Output: a set of polynomial sequences satisfy ;in represents p(x) when j=0; For each j , do the following: When j is satisfied When the condition is ; Otherwise: Domain is a polynomial In the interval The value range of ; Generator polynomial Z ; Where Z represents the minimum maximum polynomial generation algorithm; End the loop; output the polynomial sequence .

[0027] In the second deep learning model, the following improvements were made to the ReLU activation function: The polynomial sequence input to the ReLU activation function is a polynomial sequence generated by the polynomial algorithm that approximates the sign function; Input: ciphertext tensor , a list of polynomials fitting the sign function ; Represents the ciphertext data of the kth channel in the tensor, Represents height and width respectively, is the number of slots configured, is the number of channels; Output: activated ciphertext tensor ; For each channel index implement: Temporary ciphertext variable ; For j implement: EvalPoly ; Where EvalPoly means calculating a polynomial on the ciphertext; ReLU activation implementation , where @ represents the element-by-element multiplication of the ciphertext, and 1 represents the all-1 ciphertext constant; Returns the output tensor .

[0028] In step 3, first, to address the problem of scarce sample data in fingerprint liveness detection, a class feature center representation model is constructed, and a high-discriminative metric space is constructed using the bulldozer distance algorithm.

[0029] The class feature center representation model embeds the true and false fingerprint class features into this space and establishes a classification decision mechanism based on feature similarity, which effectively reduces the model's dependence on the scale of training data and achieves high-precision liveness detection under small sample conditions. Class center feature calculation: For category m, let the sample set of m be , the features extracted from each sample are , then the category center feature for: , , in represents the qth sample of category m; is the total number of samples of category m; Indicates the calculation of the push distance function, which is a measure of sample characteristics. and class center features distance.

[0030] In order to improve the generalization performance of the model in cross-sensor scenarios, the present invention designs an incremental feature optimization learning mechanism such as Figure 3 As shown, in the initial stage, only 1 / 3 of the network parameters are activated, maintaining a simple model structure and learning only basic live fingerprint features. In the incremental expansion stage, a residual structure is gradually introduced, activating 2 / 3 of the parameters. Finally, all connections are fully trained, and the task loss is combined to determine whether to optimize the model. This learning mechanism replaces the original ReLu function with the minimum maximum polynomial approximation method mentioned above, and replaces the maximum pooling layer with an average pooling layer to achieve model training that supports the CKKS homomorphic encryption algorithm. Through feature decoupling and reconstruction strategies, sensor-specific features are separated from forged common features, achieving effective extraction of invariant features across sensor domains. This method can adaptively eliminate feature distribution differences between different sensors, significantly improving the model's detection generalization in unknown sensor environments.

[0031] Finally, to address the catastrophic forgetting problem in the incremental learning process, an improved loss function fusion strategy is proposed. Figure 4 The gated recurrent unit (GRU) model shown first segments the collected fingerprint training data, using 80% as a training set and 20% as a test set for batch incremental training. During this process, the GRU extracts temporal features and records the training data of each round of the Resnet20 model. After the incremental training is completed, the Resnet20 model is tested using the test set to monitor whether the Resnet20 model has forgotten the original knowledge.

[0032] By combining the dual constraints of cross-entropy classification loss and knowledge distillation loss, a dynamic balanced optimization objective function is constructed to achieve efficient absorption of new knowledge and stable retention of old knowledge. This mechanism ensures that the model continuously optimizes detection performance during incremental updates while maintaining the integrity of the memory of learned sensor features.

[0033] The technical solution of the present invention, through the collaborative innovation of the few-sample learning framework and the incremental optimization mechanism, effectively solves the problem of model overfitting in small sample scenarios while ensuring the accuracy of model detection, improves the generalization performance of cross-sensor detection, and provides a reliable solution for the practical application of fingerprint liveness detection technology.

[0034] The analytical results of this embodiment are as follows Figure 5 As shown, the liveness detection accuracy of fingerprints collected by the Orcathus sensor in plaintext mode is significantly higher than that of fingerprints collected by the GreenBit and DigitalPersona sensors. This is likely due to the higher clarity and quality of the texture details of the Orcathus sensor, resulting in more accurate liveness classification results. The plaintext classification results of the GreenBit and DigitalPersona sensors are similar, both achieving an accuracy rate exceeding 96%, which is practically significant. The overall liveness detection accuracy of fingerprints collected in ciphertext mode is roughly the same as that of plaintext. Due to errors caused by homomorphic encryption and decryption, as well as homomorphic operations, the accuracy is slightly lower than that of plaintext detection, with an average decrease of 2.24%, which is within an acceptable range. Combining the liveness detection accuracy of plaintext and ciphertext fingerprints from the three sensors, we calculated that the average liveness detection accuracy for plaintext is 97.39%, while the average liveness detection accuracy for ciphertext is 95.15%, both of which are relatively high.

[0035] It can be clearly seen that the accuracy of the model proposed in the present invention has been significantly improved in both plaintext and ciphertext, which can further promote the field of fingerprint liveness detection, has privacy protection characteristics, and has great practical value.

[0036] In a specific embodiment of the present invention, the fingerprint image is first compressed proportionally to reduce memory consumption and then input into the model. The following steps are followed: 1. Extract image features in the convolution layer, add slot structure parameters to the ciphertext tensor, and count the number of strided convolutions.

[0037] 2. Call the model parameters after plain text training, represents the kth eigenvalue, Represents the normalized eigenvalue, Var is the variance calculation operation, and performs normalization on the tensor data: , 3. Yes The function performs a polynomial approximation, where the parameters are chosen as follows: , the polynomial degree sequence is 7, 15, 27. The minimum maximum polynomial approximation method is used to replace the original ReLU function to obtain the activated ciphertext tensor.

[0038] 4. In the process of alternating convolutional layers and activation function layers, bootstrapping operations are automatically performed based on the noise growth.

[0039] 5. The average pooling layer performs an average pooling operation on the input tensor data to retain the key information of the image. The fully connected layer multiplies the input tensor by the weight of the fully connected layer and adds a bias. As shown in Table 1, after passing the last convolutional layer, the proposed network enters the last average pooling layer and the fully connected layer. The number of input channels and output channels of the average pooling layer are all assigned to 64, while the number of output channels of the fully connected layer is assigned to 1, which corresponds to a one-bit output of the binary classification problem. Therefore, the output of the fully connected layer in this method is a ciphertext, that is, .

[0040] 6. The input shape of the sigmoid activation function layer is 1 ciphertext. As the last layer of the proposed network, the sigmoid activation function layer can map the input value to The closer the value is to 1, the higher the confidence level that the fingerprint is judged to be alive.

[0041] Table 1 Network convolutional layer and channel number parameters

[0042]

[0043] Table 2 Experimental results

[0044]

[0045] The Resnet20 residual neural network constructed by the present invention is used to train a fingerprint dataset, and its classification accuracy is tested. The experiment is tested on the sensors used to collect fingerprints. The three sensors DigitalPersona, Greenbit, and Orcathus in the LivDet2019 dataset are trained and tested respectively. The experimental results are shown in Table 2. The plaintext test accuracy of the DigitalPersona sensor reaches 96.21%, and the ciphertext test accuracy reaches 94.07%; the plaintext test accuracy of the GreenBit sensor reaches 96.44%, and the ciphertext test accuracy reaches 94.04%; the test accuracy of the Orcathus sensor reaches 99.52%, and the ciphertext test accuracy reaches 97.35%.

[0046] During the experiments, this example used the LivDet 2019 dataset, the MINST dataset, and the CIFAR-10 dataset. Three different sensors, DigitalPersona, Greenbit, and Orcathus, were used in the LivDet 2019 dataset. This method was also compared with the work of Lee et al. The comparative analysis of these experimental results demonstrates that the proposed method can effectively perform fingerprint liveness detection and classification tasks while ensuring data security, demonstrating its efficiency and practicality.

[0047] This invention provides a fingerprint liveness detection method based on CKKS homomorphic encryption. There are many methods and approaches to implement this technical solution. The above is only a preferred embodiment of the invention. It should be noted that those skilled in the art may make various improvements and modifications without departing from the principles of the invention, and such improvements and modifications should also be considered within the scope of protection of the invention. Any components not specified in this embodiment may be implemented using existing technologies.

Claims

1. A fingerprint liveness detection method based on CKKS homomorphic encryption, characterized in that: The following steps are involved: Step 1: Establish a three-party interactive system model consisting of the user terminal, key distribution center, and cloud server; The client initiates a service request, encrypts the fingerprint image using the public key distributed by the key distribution center (KDC), sends the encrypted image to the cloud server, receives and decrypts the encrypted result returned by the cloud server, and finally obtains the plaintext liveness detection result; The key distribution center generates a public-private key pair for the user terminal and the cloud server, and securely distributes the generated public-private key pair to the user terminal and the cloud server respectively through a secure channel; The cloud server performs reasoning on the input encrypted image under confidential conditions to determine the authenticity; The user terminal and cloud server register with the key distribution center, which generates a public and private key pair and transmits it to the user through a secure channel. It also generates an authentication certificate so that the user and cloud server can verify each other's identities. Step 2: After completing identity authentication, the user end encrypts the image using the public key and transmits the encrypted image to the cloud server through a public channel; Step 3: Deploy a first deep learning model trained with plaintext images and a second deep learning model that supports a homomorphic encryption scheme on a cloud server; the parameters of the second deep learning model are the same as those of the first deep learning model; After receiving the encrypted image, the cloud server uses the second deep learning model to identify the encrypted image and obtain the encrypted result; Subsequently, the cloud server transmits the encrypted results to the user end through a public channel. The user end then decrypts it using the private key it holds and finally obtains the fingerprint activity detection result.

2. The method according to claim 1, characterized in that In step 3, the second deep learning model is a Resnet20 model that supports the CKKS scheme, and the ReLU and Sigmoid activation function protocols and the maximum pooling protocol of the original Resnet20 model are optimized.

3. The method according to claim 2, characterized in that In step 3, the second deep learning model uses the minimum maximum polynomial approximation method to solve the gap problem between linear and nonlinear operations, specifically including: According to the following formula: ， in is a real variable, the nonlinear part ,right The polynomial approximation is performed using the minimum maximum polynomial generation algorithm, which uses a concavity discrimination operator. : ， in is the objective function, is a polynomial; The minimum maximum polynomial generation algorithm includes: input: domain , a continuous function f in every interval on D, an approximation parameter , the degree n of the fitting polynomial; where represents the real number space; is the union operator, is a real closed interval; represents the lower bound, Indicates the upper bound; Output: Minimax approximation The polynomial p of Perform the following steps: Step a1, randomly select the initial sampling point sequence Strictly increasing; Indicates the n+1th sampling point; Step a2: For the extreme error parameter E, find the polynomial , making ; i ranges from 1 to n+1; Step a3, find all points that meet the following conditions: , group the points into a set B; Step a4, select from set B points ,in Represents the n+1th point, and makes the selected The sum of the absolute values ​​of the points is the largest; the maximum single point error and minimum single point error The calculation formula is: ， ， in It means taking the maximum value of all values ​​traversed by index i. Indicates taking the minimum value of all values ​​traversed by index i; Step a5, when the convergence condition is met: , the relative error volatility is less than the threshold When the approximation effect is determined to be stable, the iteration is terminated and returned Otherwise, all Replace with , return to step a2.

4. The method according to claim 3, characterized in that In step 3, the second deep learning model uses a polynomial algorithm to generate an approximate sign function. Perform a polynomial approximation: Input: Parameters , a set of polynomial degree sequences ; s is the number of iterations, Every polynomial A set of preset times; Output: a set of polynomial sequences satisfy ;in represents p(x) when j=0; For each j , do the following: When j is satisfied When the condition is ; Otherwise: Domain is a polynomial In the interval The value range of ; Generator polynomial Z ; Where Z represents the minimum maximum polynomial generation algorithm; End the loop; output the polynomial sequence .

5. The method according to claim 4, characterized in that In step 3, the following improvements are made to the ReLU activation function in the second deep learning model: The polynomial sequence input to the ReLU activation function is a polynomial sequence generated by the polynomial algorithm that approximates the sign function; Input: ciphertext tensor , a list of polynomials fitting the sign function ; Represents the ciphertext data of the kth channel in the tensor, Represents height and width respectively, is the number of slots configured, is the number of channels; Output: activated ciphertext tensor ; For each channel index implement: Temporary ciphertext variable ; For j implement: EvalPoly ; in EvalPoly means computing a polynomial on the ciphertext; ReLU activation implementation , where @ represents the element-by-element multiplication of the ciphertext, and 1 represents the all-1 ciphertext constant; Returns the output tensor .

6. The method according to claim 5, characterized in that In step 3, to address the problem of scarce sample data in fingerprint liveness detection, a class feature center representation model is constructed, and a high-discriminative metric space is constructed using the bulldozer distance algorithm; The class feature center representation model embeds the true and false fingerprint class features into the metric space to establish a classification decision mechanism based on feature similarity, specifically including: Calculate the class center feature: For category m, let the sample set of m be , the features extracted from each sample are , then the category center feature for: ， ， in represents the qth sample of category m; is the total number of samples of category m; Indicates the calculation of the push distance function, which is a measure of sample characteristics. and class center features distance.

7. The method according to claim 6, characterized in that In step 3, an incremental feature optimization learning mechanism is designed. In the first stage, 1 / k parts of the network are trained, and in the second stage, 2 / k parts are trained. This process is repeated step by step until the entire network is trained. Through feature decoupling and reconstruction strategies, sensor-specific features and forgery common features are separated to achieve effective extraction of invariant features across sensor domains.

8. The method according to claim 7, characterized in that In step 3, an improved loss function fusion strategy is proposed to address the forgetting problem in the incremental learning process: based on the gated recurrent unit (GRU) model, the training data of each round of the Resnet20 model is recorded to determine whether forgetting occurs. By combining the dual constraints of cross-entropy classification loss and knowledge distillation loss, a dynamic balance optimization objective function is constructed to achieve the absorption of new knowledge and the stable retention of old knowledge.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 8 are executed.

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