A method and system for side-channel analysis of a class of matrix restricted regularized adaptive optimization

Abstract

The application discloses a side channel analysis method and system of a matrix restriction regularization adaptive optimization, wherein the method steps comprise: obtaining a plurality of side channel trace data and recombining and dividing; pre-processing the divided side channel trace data to obtain processed data; constructing a side channel analysis model, classifying and identifying the processed data to obtain the probability of a predicted label value of each side channel trace data; optimizing the side channel analysis model based on the obtained probability of the predicted label value of the side channel trace data to obtain a final model; and completing side channel analysis by using the final model. The application improves the model training stability and generalization ability by adaptive learning rate and regularization term, avoids overfitting, and accelerates the convergence speed, especially when the data is limited or the model is complex.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of side channel analysis, in particular to a kind of side channel analysis method and system of matrix restriction regularization adaptive optimization. BACKGROUND

[0002] The application of deep learning in the field of side channel analysis has promoted the research in this field into a new stage.Compared with traditional statistical analysis methods, deep learning-based side channel analysis rarely needs to preprocess data, because neural networks can implicitly extract features. Since deep learning-based side channel analysis is considered as a supervised classification problem, classification models are a natural choice in this regard.

[0003] Most scholars who focus on side channel analysis research focus on the construction of neural networks for classification models, and there is little involvement in the selection of optimizers. Recent studies have shown that choosing the right optimizer can indeed greatly improve the predictive ability of the model. The study also found that Adam and RMSprop perform better than other optimizers in short training time and small-scale neural networks. In fact, without large-scale neural networks and long training time, short training time and small-scale neural networks can also achieve excellent results. Therefore, Adam and RMSprop, two types of optimizers, can be the first choice for side channel analysis models.

[0004] The choice of learning rate is crucial to the use of the optimizer and is an indispensable part of hyperparameter tuning. Studies have shown that the adaptive optimization algorithm Adam has a new problem, which is that without preheating (warm up), it can cause the learning rate to change too much, thereby affecting the training of the model.

[0005] The generalization ability of adaptive algorithms such as Adam is another important factor that affects model training. In particular, in deep neural networks, it is easy to cause the model to overfit. These shortcomings indicate that there is still much room for improvement in optimization algorithms in terms of improving the training efficiency and stability of side channel analysis models.

[0006] A significant drawback of existing optimization algorithms is that they can easily lead to overfitting of the side-channel analysis model. Since optimizers mainly focus on quickly reducing the loss function value, their constraint ability on model parameters is limited, which can make the model perform well on the training set but have poor generalization ability on the test set. This phenomenon is particularly evident in deep neural networks, especially when the network parameter quantity is large but the training data is insufficient. In addition, optimization algorithms without regularization can lead to excessive weight updates, especially adaptive learning rate algorithms such as Adam and RMSprop. This drastic parameter fluctuation can further amplify the risk of overfitting. Therefore, optimization algorithms lacking regularization methods are difficult to balance the training performance and generalization ability of the model when faced with complex data distribution and limited data quantity. SUMMARY

[0007] To address the problem of existing optimization algorithms easily leading to overfitting, the present application proposes a class of side-channel analysis methods of moment restriction regularization adaptive optimization. The purpose of the application is to suppress the excessive update of model parameters by explicitly introducing regularization constraints during optimization, thereby improving the generalization ability of the model. The core goal of this optimization algorithm is to balance optimization efficiency and model generalization ability. During optimization, the regularization strength is dynamically adjusted to seamlessly integrate the regularization effect into the gradient update process, so that the regularization constraint on model complexity is automatically considered during weight update. This not only reduces the decline in test performance caused by the optimizer overfitting the training data, but also improves the robustness to noise during training.

[0008] To achieve the above purpose, the present application provides a class of side-channel analysis methods of moment restriction regularization adaptive optimization, comprising the following steps:

[0009] Obtain a plurality of side-channel trace data and reorganize and divide them;

[0010] Preprocess the divided side-channel trace data to obtain processed data;

[0011] Construct a side-channel analysis model, classify and identify the processed data to obtain the probability of the predicted label value of each side-channel trace data;

[0012] Based on the probability of the predicted label value of the obtained side-channel trace data, optimize the side-channel analysis model to obtain a final model;

[0013] Complete side-channel analysis using the final model.

[0014] Preferably, the method for performing the recombination division comprises: obtaining a plurality of side channel trace data and corresponding labels, and randomly shuffling the obtained side channel trace data while keeping the corresponding labels, and then dividing the shuffled side channel trace data into a plurality of batches of side channel trace data and corresponding labels; wherein the expression of the side channel trace data comprises:

[0015] Batch k = ((sample k1 , label k1 ), …, (sample kn , label kn ))

[0016] sample ki = t ki1 , …, t kij , …, t kim )

[0017] label ki = (y ki )

[0018] wherein Batch k represents the trace data and corresponding labels of the kth batch; sample ki represents the ith trace data of the kth batch; t kij represents the jth power consumption data in the ith trace data of the kth batch; and label ki represents the label corresponding to the ith trace data of the kth batch.

[0019] Preferably, the method for performing the preprocessing comprises: preprocessing each t ki in sample kij by normalization, and scaling each t kij to between 0 and 1:

[0020]

[0021] wherein t max represents the maximum value in sample ki ; and t min represents the minimum value in sample ki .

[0022] Preferably, the side channel analysis model comprises:

[0023] a first convolutional layer, a first batch normalization layer, a first pooling layer, and a flattening layer,

[0024] a first full connection layer, a second full connection layer, a third full connection layer, and a softmax layer;

[0025] The first convolution layer, the first batch normalization layer, the first pooling layer, the flattening layer, the first full connection layer, the second full connection layer, the third full connection layer, and the softmax layer are sequentially connected.

[0026] Preferably, the method for optimizing the side channel analysis model comprises: predicting the probability of a label value by using the obtained side channel trace data, and constructing a cross-entropy loss function model by using the true label value of each piece of side channel trace data; and training the loss function model by using a matrix restriction regularization adaptive optimization algorithm to obtain the final model.

[0027] Preferably, the constructed cross-entropy loss function model has the following expression:

[0028]

[0029] wherein C represents the total number of categories; y i represents a true label value; represents the predicted probability output by the softmax layer in the side channel analysis model.

[0030] The application also provides a side channel analysis system based on matrix restriction regularization adaptive optimization, which is used to implement the method according to any one of claims 1-6 and comprises a collection module, a processing module, a construction module, an optimization module and an analysis module.

[0031] The collection module is used to obtain and recombine and divide a plurality of pieces of side channel trace data.

[0032] The processing module is used to pre-process the divided side channel trace data to obtain processed data.

[0033] The construction module is used to construct a side channel analysis model, classify and identify the processed data, and obtain the probability of the predicted label value of each piece of side channel trace data.

[0034] The optimization module is used to optimize the side channel analysis model based on the probability of the predicted label value of the obtained side channel trace data to obtain a final model.

[0035] The analysis module is used to complete side channel analysis by using the final model.

[0036] Compared with the prior art, the application has the following beneficial effects:

[0037] 1. Enhancing model training stability: The adaptive learning rate of the proposed algorithm is based on the exponentially weighted average of gradients, with a memory effect that makes the learning rate smoother during training. The smoothed learning rate improves the stability of the model training process, avoiding premature or late learning rate adjustments, making the optimization process more efficient, especially when the model is deep or the training data is small, preventing overfitting caused by unstable learning rate.

[0038] 2. Accelerating convergence speed: The proposed algorithm adjusts the learning rate by weighting the gradient square, while adding an additional penalty term to control the model complexity during optimization. By using the square norm of the second moment instead of the second moment itself, the proposed algorithm can make the optimization process more stable. Especially in the case of non-convex optimization and multiple local minima, it can effectively avoid falling into local optimum, thereby accelerating the convergence speed of the algorithm and improving the model optimization effect.

[0039] 3. Improving generalization ability: The introduction of the regularization term in the proposed algorithm ensures the performance of the side-channel analysis model outside the training data. Regularization helps the algorithm to automatically control the model complexity during training, ensuring that the parameters will not change too much due to the noise of the training data, thereby improving the generalization ability of the model. Especially in the case of limited data, the introduction of the regularization term can effectively improve the robustness of the model and prevent overfitting. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed in the embodiments of the present application. Obviously, the drawings described in the following embodiments are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of these drawings.

[0041] Figure 1 The method flowchart of the embodiments of the present application. DETAILED DESCRIPTION

[0042] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0043] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the following will further describe the present application in detail with reference to the drawings and specific embodiments.

[0044] As Figure 1As shown, the method flowchart of the embodiment is shown, and the steps include:

[0045] S1. Obtain several side channel trace data and recombine and divide.

[0046] Obtain several side channel trace data and corresponding labels, and randomly shuffle the obtained side channel trace data while keeping the corresponding labels, and then uniformly divide the side channel trace data and the corresponding labels into several batches; wherein the expression of the several batches of side channel trace data includes:

[0047] Batch k = ((sample k1 , label k1 ), …, (sample kn , label kn ))

[0048] sample ki = (t ki1 , …, t kij , …, t kim )

[0049] labe ki = (y ki )

[0050] Wherein Batch k represents the trace data and the corresponding label of the kth batch; sample ki represents the ith trace data of the kth batch; t kij represents the jth power consumption data in the ith trace data of the kth batch; label ki represents the label corresponding to the ith trace data of the kth batch.

[0051] S2. Preprocess the divided side channel trace data to obtain processed data.

[0052] The divided side channel trace data is normalized, that is, each t kij in sample ki is preprocessed, and each t kij is scaled to (0, 1):

[0053]

[0054] Wherein t max represents the maximum value in sample ki ; t min represents the minimum value in sample ki .

[0055] S3. Constructing a side channel analysis model, classifying and identifying the processed data, and obtaining the probability of the predicted label value of each side channel trace data.

[0056] A convolutional neural network is used to construct a side channel analysis model, and the structure thereof comprises:

[0057] a first convolutional layer, a first batch normalization layer, a first pooling layer, a flattening layer,

[0058] a first fully connected layer, a second fully connected layer, a third fully connected layer, and a softmax layer.

[0059] The first convolutional layer, the first batch normalization layer, the first pooling layer, the flattening layer, the first fully connected layer, the second fully connected layer, the third fully connected layer, and the softmax layer are sequentially connected.

[0060] The first convolutional layer is used to input each batch of ASCAD trace data, extract first convolutional features through one-dimensional convolution, and output to the first batch normalization layer. The specific parameters are in_channels=1, out_channels=4, kernel_size=3, kernel_initializer=he_uniform, activation=selu, padding=same. Wherein in_channels represents the dimension of the input, out_channels represents the dimension of the output, kernel_size represents the size of the convolution kernel, kernel_initializer represents the way of initializing the neural network, activation represents the selection of the activation function, and padding represents adding zero padding on the edge of the input data.

[0061] The first batch normalization layer is used to input the first convolutional features extracted through one-dimensional convolution, and after normalizing the features, the normalized features of the first batch normalization layer are obtained and output to the first pooling layer. The specific parameters are in_channels=4, out_channels=4.

[0062] The first pooling layer is used to input the normalized features of the first batch normalization layer, downsample the input to obtain first pooling features, and output to the flattening layer. The specific parameters are pool_size=2, stride=2. Wherein pool_size represents the size of the pooling window, and stride represents the downsampling factor.

[0063] The flattening layer is used to input the first pooling features, flatten the two-dimensional features into a one-dimensional vector, and output to the first fully connected layer.

[0064] The first full connection layer is configured to input the flattened features of the flattened layer, extract nonlinear features through a full connection operation, obtain first full connection layer features, and output to a second full connection layer. The specific parameters are units = 10 and activation = selu, where units represents the number of neurons in the full connection layer.

[0065] The second full connection layer is configured to input the first full connection layer features, extract nonlinear features through a full connection operation, obtain second full connection layer features, and output to a third full connection layer. The specific parameters are units = 10 and activation = selu.

[0066] The third full connection layer is configured to input the second full connection layer features, extract nonlinear features through a full connection operation, obtain third full connection layer features, and output to a softmax layer. The specific parameters are units = 256.

[0067] The softmax layer is configured to input the third full connection layer features, calculate the probability of the predicted label value of each batch of trace data through a softmax function.

[0068] The processed data is input into the side channel analysis model for classification and recognition to obtain the probability of the predicted label value of each batch of trace data.

[0069] S4. Based on the obtained probability of the predicted label value of the side channel trace data, the side channel analysis model is optimized to obtain a final model.

[0070] S401. A cross-entropy loss function model is constructed using the probability of the predicted label value of each batch of trace data and the true label value of each batch of trace data.

[0071] The constructed cross-entropy loss function model is defined as follows:

[0072]

[0073] where C represents the total number of categories, y i represents the true label value, represents the predicted probability output by the softmax layer in the side channel analysis model.

[0074] S402. The loss function model is trained by a matrix restriction regularization adaptive optimization algorithm to obtain a final model.

[0075] The matrix restriction regularization adaptive optimization algorithm is defined as follows:

[0076] Algorithm: AdamodW;

[0077] Input: the parameters x0 of the model x0 ∈ Rd the gradient of the loss function L with respect to the model parameters algorithm first moment coefficient β1=0.9, algorithm second moment coefficient β2=0.999, algorithm learning rate α=1e-3, algorithm learning rate momentum coefficient β3=0.9, algorithm regularization parameter λ=1e-3, constant ∈=1e-8;

[0078] Output: optimized model parameters x n+1

[0079]

[0080]

[0081] wherein g n , m n , v n , η n , s n , all represent intermediate variables.

[0082] S5. Utilize the final model to complete side channel analysis.

[0083] The contrast experiment is conducted on the side channel analysis models optimized by different optimizers, and the side channel analysis model optimized by the moment restriction regularization adaptive optimization algorithm AdamodW has a significantly improved recognition accuracy rate of the label compared with the models optimized by the existing optimization algorithms (NAdam, Adam, RMSProp, and SGD).

[0084] Embodiment Two

[0085] The embodiment also provides a kind of moment restriction regularization adaptive optimization side channel analysis system, comprising: acquisition module, processing module, construction module, optimization module and analysis module;Acquisition module is used to obtain a plurality of side channel trace data and reorganization division;Processing module is used to pre-process the side channel trace data after division, and obtain processed data;Construction module is used to construct side channel analysis model, and the processed data is classified and identified, to obtain the probability of the predicted label value of each side channel trace data;Optimization module is used to optimize side channel analysis model based on the probability of the predicted label value of the obtained side channel trace data, to obtain final model;Analysis module is used to utilize final model, and complete side channel analysis.

[0086] The technical problems in practical work will be explained in detail in combination with the embodiment.

[0087] Firstly, acquisition module is used to obtain a plurality of side channel trace data and reorganization division.

[0088] Acquire several side channel traces and their corresponding labels. Randomly shuffle the acquired side channel trace data while maintaining the corresponding labels, and then evenly divide it into several batches of side channel trace data and their corresponding labels. The expressions for these several batches of side channel trace data include:

[0089] Batch k =((sample) k1 label k1 ),…,(sample kn label kn )

[0090] sample ki =t ki1 , ..., t kij ,…,t kim )

[0091] labe ki =(y ki )

[0092] Among them, Batch k This represents the trace data and corresponding label for the k-th batch; sample ki This represents the i-th trace data in the k-th batch; t kij This represents the j-th power consumption data in the i-th trace of the k-th batch; label ki This represents the label corresponding to the i-th trace data in the k-th batch.

[0093] The processing module preprocesses the divided side channel trace data to obtain the processed data.

[0094] The divided side channel trace data is then normalized, i.e., the sample... ki Each t in kij Preprocessing is performed on each t kij Scale to between (0,1):

[0095]

[0096] Among them, t max Indicates sample ki The maximum value in t; min Indicates sample ki The minimum value in.

[0097] A side-channel analysis model is built using building modules to classify and identify the processed data, and to obtain the probability of the predicted label value for each side-channel trace data.

[0098] The side channel analysis model is constructed by using a convolutional neural network, and the structure comprises:

[0099] a first convolutional layer, a first batch normalization layer, a first pooling layer, a flattening layer,

[0100] a first full connection layer, a second full connection layer, a third full connection layer, and a softmax layer.

[0101] a first convolutional layer, a first batch normalization layer, a first pooling layer, a flattening layer, a first full connection layer, a second full connection layer, a third full connection layer, and a softmax layer are sequentially connected.

[0102] The first convolutional layer is used for inputting ASCAD trace data of each batch, extracting first convolutional features through one-dimensional convolution, and outputting to the first batch normalization layer. The specific parameters are in_channels=1, out_channels=4, kernel_size=3, kernel_initializer=he_uniform, activation=selu, and padding=same. Wherein in_channels represents the dimension of the input, out_channels represents the dimension of the output, kernel_size represents the size of the convolution kernel, kernel_initializer represents the way of initializing the neural network, activation represents the selection of the activation function, and padding represents adding zero padding on the edge of the input data.

[0103] The first batch normalization layer is used for inputting the first convolutional features extracted through one-dimensional convolution, and obtaining normalized features of the first batch normalization layer after normalizing the features, and outputting to the first pooling layer. The specific parameters are in_channels=4 and out_channels=4.

[0104] The first pooling layer is used for inputting the normalized features of the first batch normalization layer, downsampling the input to obtain first pooling features, and outputting to the flattening layer. The specific parameters are pool_size=2 and stride=2. Wherein pool_size represents the size of the pooling window, and stride represents the downsampling factor.

[0105] The flattening layer is used for inputting the first pooling features, flattening the two-dimensional features into a one-dimensional vector, and outputting to the first full connection layer.

[0106] The first full connection layer is used for inputting the flattened features of the flattening layer, extracting nonlinear features through full connection operation to obtain first full connection layer features, and outputting to the second full connection layer. The specific parameters are units=10 and activation=selu, wherein units represents the number of neurons in the full connection layer.

[0107] The second fully connected layer is configured to input the first fully connected layer feature, extract nonlinear features through a fully connected operation, obtain a second fully connected layer feature, and output to a third fully connected layer. The specific parameters are units = 10 and activation = selu.

[0108] The third fully connected layer is configured to input the second fully connected layer feature, extract nonlinear features through a fully connected operation, obtain a third fully connected layer feature, and output to a softmax layer. The specific parameters are units = 256.

[0109] The softmax layer is configured to input the third fully connected layer feature, calculate the probability of the predicted label value of each batch of trace data through a softmax function.

[0110] The processed data is input into the side channel analysis model for classification and recognition to obtain the probability of the predicted label value of each batch of trace data.

[0111] The optimization module optimizes the side channel analysis model based on the obtained probability of the predicted label value of the side channel trace data to obtain a final model.

[0112] S401. A cross-entropy loss function model is constructed using the probability of the predicted label value of each batch of trace data and the true label value of each batch of trace data.

[0113] The constructed cross-entropy loss function model is defined as follows:

[0114]

[0115] where C represents the total number of categories, y i represents the true label value, represents the predicted probability output by the softmax layer in the side channel analysis model.

[0116] S402. The loss function model is trained by a matrix limit regularization adaptive optimization algorithm to obtain a final model.

[0117] The matrix limit regularization adaptive optimization algorithm is defined as follows:

[0118] Algorithm: AdamodW;

[0119] Input: the parameter x0 of the model x0 ∈ R d , the gradient of the loss function L with respect to the model parameter The algorithm first moment coefficient is beta1=0.9, the algorithm second moment coefficient is beta2=0.999, the algorithm learning rate is alpha=1e-3, the algorithm learning rate momentum coefficient is beta3=0.9, the algorithm regularization parameter is lambda=1e-3, and the constant is epsilon=1e-8.

[0120] Output: optimized model parameters x n+1 ;

[0121]

[0122] Wherein, g n , m n , v n , eta n , s n , All represent intermediate variables.

[0123] The final analysis module utilizes the final model to complete side channel analysis.

[0124] The contrast experiment is carried out on the side channel analysis models optimized by different optimizers, the side channel analysis model optimized by the matrix constraint regularization adaptive optimization algorithm AdamodW has a significant improvement on the recognition accuracy rate of the label compared with the models optimized by the existing optimization algorithms (NAdam, Adam, RMSProp, SGD).

[0125] The above-described embodiments are only descriptions of the preferred modes of the present application, and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those skilled in the art shall fall within the protection scope determined by the claims of the present application.

Claims

1. A side-channel analysis method of matrix restricted regularized adaptive optimization, characterized by the steps of The method comprises the following steps: acquiring a plurality of side channel trace data and reorganizing and dividing the side channel trace data; preprocessing the divided side channel trace data to obtain processed data; constructing a side channel analysis model, classifying and identifying the processed data, and obtaining the probability of the predicted label value of each side channel trace data; the constructed side channel analysis model comprises: a first convolutional layer, a first batch normalization layer, a first pooling layer, a flattening layer, a first full connection layer, a second full connection layer, a third full connection layer, and a softmax layer; the first convolutional layer, the first batch normalization layer, the first pooling layer, the flattening layer, the first full connection layer, the second full connection layer, the third full connection layer, and the softmax layer are connected in sequence; the first convolutional layer is used to input each batch of ASCAD trace data, extract first convolutional features through one-dimensional convolution, and output to the first batch normalization layer; the first batch normalization layer is used to input the first convolutional features extracted through one-dimensional convolution, normalize the features, obtain the normalized features of the first batch normalization layer, and output to the first pooling layer; the first pooling layer is used to input the normalized features of the first batch normalization layer, downsample the input, obtain first pooling features, and output to the flattening layer; the flattening layer is used to input the first pooling features, flatten the two-dimensional features into a one-dimensional vector, and output to the first full connection layer; the first full connection layer is used to input the flattened features of the flattening layer, extract nonlinear features through full connection operation, obtain first full connection layer features, and output to the second full connection layer; based on the probability of the predicted label value of the acquired side channel trace data, the side channel analysis model is optimized to obtain a final model; the method for optimizing the side channel analysis model comprises: constructing a cross-entropy loss function model using the probability of the predicted label value of the acquired side channel trace data and the true label value of each side channel trace data; training the loss function model through a matrix restriction regularization adaptive optimization algorithm to obtain the final model; the constructed cross-entropy loss function model has the following expression: wherein, represents the total number of classes; represents the true label value; represents the predicted probability of the softmax layer output in the side-channel analysis model; the final model is used to complete side channel analysis.

2. The method of claim 1, wherein the method is a method of matrix restriction regularized adaptive optimization of side-channel analysis. The method for reorganizing and dividing comprises the following steps: acquiring a plurality of side channel trace data and corresponding labels, randomly rearranging the obtained side channel trace data while keeping the corresponding labels, and then uniformly dividing the side channel trace data and corresponding labels into a plurality of batches; wherein, the expression of the side channel trace data comprises: in, Indicates the first Each batch of trace data and corresponding labels; Indicates the first The first batch Strip data; Indicates the first The first batch The first in the trace data Power consumption data; Indicates the first The first batch The labels corresponding to the stripe data.

3. The method of claim 2, wherein the method is characterized by, The method of performing the preprocessing includes normalizing the divided side channel trace data by each of performing preprocessing, scaling each to between (0, 1): wherein denotes the maximum value in denotes the minimum value in .​ 4. A side-channel analysis system of matrix restriction regularized adaptive optimization, the system being configured to implement the method of any one of claims 1 to 3, characterized in that, The method comprises the following steps: The method comprises the following steps: an acquisition module, a processing module, a construction module, an optimization module, and an analysis module.

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