Electromagnetic fingerprint identification method based on frequency domain constellation diagram characteristics

Abstract

The invention discloses an electromagnetic fingerprint identification method based on frequency domain constellation diagram characteristics, and the method comprises the following steps: obtaining a near-field electromagnetic radiation signal of a to-be-identified chip, and extracting an electromagnetic radiation signal segment from the starting moment to the ending moment when the chip is executing a function; carrying out fast Fourier transform on the electromagnetic radiation signal segments, carrying out frequency domain amplitude normalization, and constructing a frequency domain constellation diagram by using normalized spectrum characteristics of the electromagnetic radiation signal segments; and inputting the frequency domain constellation diagram into the trained convolutional neural network, and identifying the execution function of the chip. The method is applied to the field of signal identification, the electromagnetic leakage characteristics of the chip are displayed in a frequency domain constellation diagram mode, unique characteristics of electromagnetic leakage of different functions are highlighted, and the method has the advantages of being high in identification precision and low in complexity and has unique advantages in the aspect of Gaussian white noise interference resistance.

Description

Technical Field

[0001] The invention relates to the technical field of signal recognition, and in particular to an electromagnetic fingerprint recognition method based on frequency domain constellation diagram features. Background Art

[0002] Side channel attacks based on chip electromagnetic leakage are an emerging physical layer attack method in recent years. They are used to identify chips or integrated circuits, determine their functions, and estimate their remaining life. Due to defects in the chip processing process, there are slight differences between internal components and bonding wires. When multifunctional chips perform different functions, there are also differences in internal conduction circuits and operating frequencies. These differences are collectively referred to as chip electromagnetic fingerprints. The fingerprint features of a chip are unique and persistent and can be regarded as the "DNA" of the chip. Chip fingerprints are presented in the form of unintentional electromagnetic leakage. Through advanced electromagnetic measurement technology and feature extraction methods, it is possible to identify individual chips, their functions, and their aging status.

[0003] Existing theories have proven that unintentional radiation from the near field of the MCU chip surface carries information about the function being executed. By analyzing and comparing the near-field radiation of the IC, different functions can be distinguished and the IC function can be identified. Initially, some studies collected the radiation field on the surface of the MCU through a near-field test antenna, and applied a convolutional neural network to perform functional identification on the time-frequency diagrams of the radiation fields of different functions. The final function recognition accuracy can reach 30% without grouping. Thereafter, by converting the time domain data into transform domain data and improving the classification method, the recognition accuracy of a single function was increased to 37.78%. The recognition rate of the radiation field on the surface of the integrated circuit of these research results is not high. The main reason can be attributed to the fact that no suitable feature extraction method has been found, resulting in insufficient ability of the algorithm to extract functional features from near-field data.

[0004] In order to extract more functional features, subsequent research optimized the test scheme, improving the previous near-field single-point acquisition to multi-point data acquisition controlled by a robotic arm, and increasing the sampling rate from the previous 100MSa / s to 1.428GSa / s. Ultimately, the function recognition rate for MCUs was increased to 39.24%, and the function recognition rate for FPGAs was 98.71%. The function recognition rate for FPGAs is satisfactory, but improving feature extraction capabilities is not the best choice from a testing perspective, because it not only requires more testing time and increases test complexity, but also requires more data to be processed, and the computational complexity increases accordingly. How to pre-process the data of a single test to highlight more feature information for the classification and recognition algorithm to extract features is a problem that needs to be solved at present.

[0005] In the field of radio frequency fingerprint recognition, differential constellation diagrams are widely used for signal feature extraction. Researchers receive and demodulate the IQ signals emitted by radio frequency transmitting devices and present them on CTF to distinguish different device individuals. Inspired by CTF, we consider displaying the electromagnetic leakage characteristics of chips in the form of frequency domain constellation diagrams (FCTF) to highlight the unique characteristics of electromagnetic leakage of different functions. CNN has many successful applications in image recognition and classification tasks. Inspired by this, the present invention applies CNN to FCTF classification of electromagnetic leakage data of different chip functions to improve the recognition rate. At the same time, we compared the recognition accuracy under different signal-to-noise ratios to demonstrate the advantages of the proposed method in resisting Gaussian white noise. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the present invention provides an electromagnetic fingerprint recognition method based on frequency domain constellation diagram features, which displays the electromagnetic leakage characteristics of the chip in the form of a frequency domain constellation diagram to highlight the unique characteristics of electromagnetic leakage of different functions. It not only has high recognition accuracy and low complexity, but also has unique advantages in resisting Gaussian white noise interference.

[0007] To achieve the above object, the present invention provides an electromagnetic fingerprint recognition method based on frequency domain constellation diagram features, comprising the following steps: Step 1, obtaining the near-field electromagnetic radiation signal of the chip to be identified, and extracting the electromagnetic radiation signal segment from the start to the end time when the chip is executing the function; Step 2, performing fast Fourier transform on the electromagnetic radiation signal segment, and performing frequency domain amplitude normalization, and constructing a frequency domain constellation diagram using the normalized frequency spectrum characteristics of the electromagnetic radiation signal segment; Step 3: Input the frequency domain constellation diagram into the trained convolutional neural network to identify the execution function of the chip.

[0008] In one embodiment, step 1 specifically includes: Record the near-field electromagnetic radiation signal of the chip to be identified by using an oscilloscope; Use IO-Mark technology to mark the start and end time of the chip's function execution; According to the start and end time of the function being executed by the chip, the near-field electromagnetic radiation signal recorded by the oscilloscope is extracted to obtain the electromagnetic radiation signal segment from the start to the end time of the function being executed by the chip.

[0009] In one embodiment, in step 2, constructing a frequency domain constellation diagram using the normalized frequency spectrum characteristics of the electromagnetic radiation signal fragments is specifically: The frequency domain constellation diagram is constructed with the normalized imaginary part of the spectrum in the electromagnetic radiation signal segment as the horizontal axis and the normalized real part of the spectrum in the electromagnetic radiation signal segment as the vertical axis.

[0010] In one embodiment, in step 2, the convolutional neural network has three convolutional layers and one fully connected layer; The kernel size of the convolutional layer is 5×5 and the stride is 1 to capture the chip fingerprint details in the frequency domain constellation diagram; The number of channels of the three convolutional layers are 16, 32, and 64 respectively to obtain higher dimensional features; The convolution layer uses a rectified linear unit as an activation function to reduce the possibility of gradient disappearance and speed up training; The fully connected layer performs feature classification via a Softmax activation function In one of the embodiments, the output ends of the first two convolutional layers in the convolutional neural network are respectively connected to 2×2 maximum pooling layers to downsample data features and limit the size of the neural network.

[0011] In one of the embodiments, in the process of the convolutional neural network, the loss function adopts Softmaxloss and the training algorithm adopts the gradient descent algorithm.

[0012] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention displays the electromagnetic leakage characteristics of the chip in the form of a frequency domain constellation diagram to highlight the unique characteristics of electromagnetic leakage of different functions. The accuracy of functional recognition of the MCU chip can reach more than 99%. It not only has high recognition accuracy and low complexity, but also has unique advantages in resisting Gaussian white noise interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0014] Figure 1 It is a flow chart of an electromagnetic fingerprint recognition method based on frequency domain constellation diagram features in an embodiment of the present invention; Figure 2 Schematic diagram of the time domain test waveform and amplitude-frequency characteristics of the surface radiation field of the MCU when performing the ADC and DAC functions in an embodiment of the present invention, where: Figure 2 (a) is a schematic diagram of the time domain test waveform when executing the ADC function. Figure 2 (b) is a schematic diagram of the amplitude-frequency characteristics when performing the ADC function. Figure 2 (c) is a schematic diagram of the time domain test waveform when executing the DAC function. Figure 2 (d) is a schematic diagram of the amplitude-frequency characteristics when performing the DAC function; Figure 3 The frequency domain constellation diagram corresponding to the ADC and DAC executed by the MCU in the embodiment of the present invention, wherein: Figure 3 (a) is the frequency domain constellation diagram when performing the ADC function. Figure 3 (b) is the frequency domain constellation diagram when performing the DAC function; Figure 4 Schematic diagram of the result of a convolutional neural network in an embodiment of the present invention; Figure 5 Schematic diagram of the variation range of signal points in an embodiment of the present invention; Figure 6 This is a schematic diagram of near-field radiation data of the MCU within an instruction cycle in an embodiment of the present invention; Figure 7 Schematic diagram of the training results of the convolutional neural network in an embodiment of the present invention, wherein: Figure 7 (a) is a schematic diagram of training and testing results. Figure 7 (b) is a schematic diagram of recognition accuracy of different image qualities; Figure 8 The following is a schematic diagram of the training results of the convolutional neural network using different learning rates in an embodiment of the present invention, where: Figure 8 (a) is a diagram showing the training results at a learning rate of 0.001. Figure 8 (b) is a diagram of the training results at a learning rate of 0.01. Figure 8 (c) is a schematic diagram of the training results under a learning rate of 0.1; Fig. 9 A schematic diagram showing comparison of recognition accuracy in an embodiment of the present invention; Fig.10 A schematic diagram of a confusion matrix in an embodiment of the present invention, wherein: Fig.10 (b) is a schematic diagram of the confusion matrix under a -10db signal-to-noise ratio. Fig.10 (b) is a schematic diagram of the confusion matrix under a -15db signal-to-noise ratio.

[0015] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0016] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0018] This embodiment discloses an electromagnetic fingerprint recognition method based on frequency domain constellation features, which processes the data of a single test of a chip (integrated circuit) and displays the features in the form of a frequency domain constellation diagram. At the same time, it combines the convolutional neural network classification method to effectively improve the accuracy of functional recognition of the chip surface radiation field. Figure 1 The electromagnetic fingerprint recognition method based on frequency domain constellation diagram features in this embodiment specifically includes the following steps: Step 1: obtain the near-field electromagnetic radiation signal of the chip to be identified, and extract the electromagnetic radiation signal fragment from the start to the end time when the chip is executing the function. The specific process is as follows: Record the near-field electromagnetic radiation signal of the chip to be identified by using an oscilloscope; Use IO-Mark technology to mark the start and end time of the chip's function execution; According to the start and end time of the function being executed by the chip, the near-field electromagnetic radiation signal recorded by the oscilloscope is extracted to obtain the electromagnetic radiation signal fragment from the start to the end time of the function being executed by the chip; Step 2, perform fast Fourier transform on the electromagnetic radiation signal fragment, and perform frequency domain amplitude normalization, and construct a frequency domain constellation diagram using the normalized spectrum characteristics of the electromagnetic radiation signal fragment, specifically: A frequency domain constellation diagram is constructed by taking the normalized imaginary part of the spectrum in the electromagnetic radiation signal segment as the horizontal axis and taking the normalized real part of the spectrum in the electromagnetic radiation signal segment as the vertical axis; Step 3: Input the frequency domain constellation diagram into the trained convolutional neural network to identify the execution function of the chip.

[0019] When the MCU (Microcontroller Unit) chip is working, the internal CPU will control the operating frequency by frequency division or frequency combination, and control the on and off of different functional peripheral circuits through instructions. Some functions of the MCU will run at different main frequencies. At this time, the frequency domain of the near-field receiving signal will have significantly different amplitude-frequency characteristics, which can be easily distinguished using common data classification algorithms. However, in more general cases, some functions of the MCU are executed at the same main frequency, and it is not easy to distinguish them from the perspective of the frequency domain alone. At this time, the coupling path of the signal can be used as a basis for distinction. Although the main frequency is the same when the chip performs different functions, the internal signal path must be different. Due to the different routing positions, lengths, and delays of different connection paths, the radiated electromagnetic waves coupled to the near-field receiving end will present different amplitude and phase characteristics. These characteristics can be used as a basis for distinguishing different functions.

[0020] For example Figure 2 It is the time domain test waveform and amplitude-frequency characteristics of the surface radiation field when the MCU performs ADC and DAC functions. Figure 2 (b) Figure 2 From the amplitude-frequency characteristic distribution in (d), it can be seen that the bottom noise distribution of the two signals is almost the same, and a few frequency points with large amplitudes are the operating frequency of the chip and its higher harmonics. The main difference between the two signal frequency domains is reflected in these frequency points with large amplitudes. The accuracy of directly using the test signal frequency domain data for classification and recognition is not high, because a large amount of bottom spurious "dilutes" the characteristic information carried by the main frequency and its harmonics. When the conventional recognition algorithm performs the classification task, a large amount of computing power is allocated to the processing of spurious data, so the algorithm execution efficiency is very low and the recognition rate is not high. It is also not advisable to use filtering to filter out the redundancy and then perform classification and recognition, because although the main functional features are hidden in a few main frequencies and their harmonics, other frequency components will also contain a small amount of features. Although these frequencies contain few characteristic components, their number occupies the vast majority of the frequency points in the passband, so the sum of the characteristic content cannot be ignored and cannot be simply filtered out. Therefore, the best solution to improve the feature extraction capability is to highlight the characteristics carried by the frequency points with large amplitudes and weaken the characteristics of the bottom redundant frequency points by processing the original data before classification.

[0021] The constellation trajectory diagram has a wide range of applications in the field of radio frequency fingerprint recognition. Its principle is to demodulate the received signal, perform differential operations on the baseband signal, convert the IQ signal into a stable graph, and present the amplitude and phase information of the signals transmitted by different devices on one graph. Due to the slight differences between different individual devices, different distribution patterns will be presented on the constellation trajectory diagram. Different individuals can be distinguished by using the classification and recognition methods in the field of image recognition. The IC near-field radiation wave is an unmodulated broadband electromagnetic wave, which is significantly different from the intentionally emitted radio frequency signal. Its broadband characteristics make it impossible to extract the amplitude and phase information from the time domain perspective to draw a constellation trajectory diagram. Based on this, this embodiment adopts a feature enhancement scheme based on the frequency domain constellation diagram. Analogously to the method of drawing the time domain constellation trajectory diagram, the horizontal axis is the normalized imaginary part of the spectrum, and the vertical axis is the normalized real part of the spectrum. The single-cycle spectrum amplitude and phase data of the radiated electromagnetic wave are extracted and plotted on the frequency domain constellation diagram. A constellation diagram can be drawn for a single-cycle radiation signal of each function, for example Figure 3 This is the frequency domain constellation diagram corresponding to the ADC and DAC executed by the MCU.

[0022] In this embodiment, by converting the radiation data into a frequency domain constellation diagram, the frequency points with larger amplitudes are scattered around the periphery, and the features of these points are easier to extract from the perspective of image recognition. The frequency points with smaller amplitudes are concentrated near the origin, and the feature information carried by a single frequency point is difficult to extract. In this way, the purpose of highlighting the features of large-value frequency points and weakening the features of small-value frequency points is achieved.

[0023] Since the frequency domain constellation diagram is a two-dimensional image, a mature CNN model can be used for classification and recognition. This embodiment designs a convolutional neural network with three convolutional layers and one fully connected layer, namely Figure 4 As shown. Among them, the size of the convolutional neural network input image is limited to 227×227×3, the kernel size of the convolutional layer is 5×5, and the step size is 1 to capture the chip fingerprint details in the frequency domain constellation diagram. The number of channels of the three convolutional layers are 16, 32, and 64, respectively, to obtain higher-dimensional features. At the same time, the convolutional layer uses the rectified linear unit as the activation function to reduce the possibility of gradient vanishing and speed up training. In addition, the output ends of the first two convolutional layers in the convolutional neural network are respectively connected to 2×2 maximum pooling layers to downsample the data features and limit the size of the neural network. At the end of the convolutional neural network, a fully connected layer and a Softmax activation function are used to perform functional classification. In the process of the convolutional neural network, the loss function uses Softmax loss, and the training algorithm uses the gradient descent algorithm. Specifically, the specific parameters of each layer of the convolutional neural network are as follows: The first convolutional layer has: 5×5×1×16 weights and 16 biases, the number of parameters to be trained is 416, and the output is 112×112 after the 2×2 maximum pooling layer; The second convolutional layer has: 5×5×16×32 weights and 32 biases, the number of parameters to be trained is 12832, and the output is 54×54 after the 2×2 maximum pooling layer; The third convolutional layer has: 5×5×32×64 weights and 64 biases, the number of parameters to be trained is 51264, and the output is 25×25 after the 2×2 maximum pooling layer; The fully connected layer has: Since the final image size is 25×25 and the number of channels is 64, there are 25×25×64 weight parameters and 1 bias; when there are L classification targets, the number of trainable parameters is L×40001; That is, the total weight and bias parameters of the network are: 416+12832+51264+L×40001=64512+L×40001.

[0024] In this embodiment, the electromagnetic leakage characteristics of the chip are displayed in the form of a frequency domain constellation diagram to highlight the unique characteristics of electromagnetic leakage of different functions, and it also has unique advantages in resisting Gaussian white noise interference. Since the near-field radiation field signal has a limited bandwidth, the Gaussian white noise is band-limited, and its power spectrum density is It is expressed as:

[0025] in, is a constant, which represents the power density per unit frequency within the band limit. is the frequency, and is the start frequency and the cut-off frequency According to the calculation formula of signal-to-noise ratio SNR, we have:

[0026] in, is the noise power, is the signal power is the time domain signal, and are the start and stop times of the signal respectively; According to the Bashevar equation, the signal power It can also be expressed as:

[0027] Among them, is the spectrum of the signal; Substituting the signal power of equation (3) and the noise power of equation (1) into equation (2) and transforming them, the power spectral density of the band-limited noise can be obtained as follows:

[0028] The power spectral density of the signal It can also be expressed as:

[0029] Substituting the signal power spectrum density of formula (5) into formula (4) yields:

[0030] in, It can be regarded as the average power density of the signal.

[0031] From the SNR perspective, when SNR is taken, is a constant, and the noise is evenly distributed in the entire passband. Since the energy of the signal in the passband is relatively concentrated, the presence of noise has a smaller impact on the frequency points with large amplitudes and a greater impact on the frequency points with small amplitudes. In order to accurately quantify the impact of noise on signals with different amplitudes, this embodiment defines the power density ratio as:

[0032] in, express The power density at The logarithm of the ratio of the power density at to the average power density of the signal; When the SNR is given, the frequency The ratio of signal power density to noise power density at is

[0033] Frequency The actual signal-to-noise ratio of the signal interfered by noise is Since the energy of electromagnetic leakage of the chip is mainly concentrated on the operating frequency and its harmonics, the M value of these energy-concentrated frequency points is generally greater than 40dB, while the M value of the spurious frequency points at the bottom of the spectrum is generally less than -10dB. Therefore, the actual signal-to-noise ratio of these large-amplitude frequency points to Gaussian white noise is greater than , and the signal-to-noise ratio of the spurious frequency point to Gaussian white noise is less than .

[0034] From the perspective of the frequency domain constellation diagram, let the distance from the signal point to the origin be F (i.e., the frequency domain amplitude). When the SNR is given, the signal point may change to Figure 5 At any position within the circle shown, the radius of the circle can be calculated based on the signal-to-noise ratio:

[0035] Table 1 lists the variation radius of different signal amplitudes under different signal-to-noise ratio conditions.

[0036] Table 1

[0037] As can be seen from Table 1, in the case of low signal-to-noise ratio, large-amplitude signals carrying more characteristic information are less disturbed by noise, while small-amplitude spurious waves are more disturbed by noise. There are many small-amplitude spurious waves and a clustering effect appears on the frequency domain constellation diagram. Although the position of a single point in the constellation diagram changes significantly after adding noise, the statistical characteristics are still concentrated in large numbers near the origin, so it will not have a significant impact on the feature classification of the frequency domain constellation diagram. Large-amplitude frequency points are scattered around the periphery of the frequency domain constellation diagram, and there are often large blank areas around a single point. Even if they are subject to a certain degree of interference, their range of variation still has unique characteristics without overlapping with surrounding points, and can be used as feature points to distinguish different classes.

[0038] From the perspective of classification and recognition methods, the position change of feature points far away from the central area on the frequency domain constellation diagram is equivalent to the image pixels being disrupted, and convolutional neural networks have unique advantages in identifying images with disrupted pixels: 1. The convolutional layer of the convolutional neural network extracts local features of the image through the local receptive field. Even if the pixels are disrupted, feature structures such as corners can still be detected; 2. The pooling layer further enhances the robustness of the convolutional neural network to pixel position changes by reducing the dimension of the feature map. The pooling operation ignores the precise position of the pixel to a certain extent, but focuses on the statistical characteristics of the feature, so that the convolutional neural network can identify important features when the pixels are shuffled; 3. The fully connected layer combines and abstracts the previously extracted features to form a higher-level feature representation. These high-level features are usually not sensitive to the specific location of the pixels, but focus on the overall structure and semantic information of the image; therefore, even if the pixels are shuffled, the fully connected layer can still classify based on these abstract features; 4. Convolutional neural networks represent pixel features in a distributed form through multiple layers of convolution and pooling operations, which means that the feature information is distributed across multiple neurons and multiple levels instead of being concentrated in a specific location. Therefore, even if the pixels are shuffled, the distributed representation of the features can still retain enough information for classification.

[0039] In summary, Gaussian white noise has little disturbance on the main features of the frequency domain constellation diagram. At the same time, the convolutional neural network classification method can also reduce the impact of disturbance on the recognition accuracy. Therefore, the electromagnetic fingerprint recognition method based on the frequency domain constellation diagram feature in this embodiment has a unique advantage in the ability to resist Gaussian white noise.

[0040] The following is a collection of specific experimental examples to further illustrate the electromagnetic fingerprint recognition method based on the frequency domain constellation diagram features in this embodiment.

[0041] The experimental system uses a stripline chamber as the core equipment for chip radiation emission testing. The stripline chamber can effectively shield external interference, making the measurement results more accurate, and the core board is closer to the object to be tested, which is conducive to capturing the subtle characteristics of near-field radiation. The microcontroller is controlled by instructions to perform different functions. The stripline chamber is used to receive the MCU surface radiation wave and read and record the radiation data through an oscilloscope. The oscilloscope sampling rate is 1GSa / s, and the input is dual-channel, one channel is the surface radiation data received by the stripline chamber, and the other channel is the execution mark output by the microcontroller pin.

[0042] During the experiment, the microcontroller used was STM32F103ZET6, which was designed on one side of the PCB board, and the other peripheral devices were placed on the other side of the PCB board. 14 functions of the MCU were selected, and the surface radiation field when each function was executed was tested separately. The function information executed by the MCU is shown in Table 2.

[0043] Table 2

[0044] In Table 2: ADC means analog-to-digital conversion, LED means pin output signal on / off, DAC means digital-to-analog conversion, PWM means pulse width modulation, DMA means direct memory access data, IWDG means independent watchdog, WWDG means window watchdog, MALLOC means memory management experiment, USART serial communication, TIMER means timer, TSENSOR means internal temperature sensor, PWM+DAC means pulse width modulation and digital-to-analog conversion, PWM+ADC means pulse width modulation and analog-to-digital conversion, PWM+DAC+ADC means pulse width modulation, digital-to-analog conversion and analog-to-digital conversion.

[0045] During the experiment, all measurements were performed in accordance with IEC61967-8. The electromagnetic field radiated by the MCU to be tested was received by the stripline chamber and transmitted to the oscilloscope. At the same time, the instructions were marked using IOMARK technology. Figure 6 As shown in the figure, when the instruction starts to execute, the designated IO port of the MCU starts to output a high level, and after the instruction is executed, the IO port outputs a low level. Each execution of an instruction is called an instruction cycle, and the oscilloscope records the near-field radiation data within the cycle.

[0046] In addition, in order to reduce the impact of peripheral devices on functional classification, five PCB boards were made in the experiment. Each PCB board tested 14 functions. Each test saved 19-22 functional cycles, and a total of 1,385 cycle data of different instructions were obtained. In order to increase the data set and evaluate the anti-noise ability at the same time, 9 groups of Gaussian white noise with different levels were added to the test data, with a signal-to-noise ratio of 0~32dB and a level of 4dB. After adding Gaussian white noise, a total of 13,850 groups of instruction cycle data were formed with the original test data, and 13,850 frequency domain constellation diagrams were drawn.

[0047] The prepared data is used to train and test the convolutional neural network. During the initial training, the batch size is set to 64, the maximum epoch is set to 30, and the initial learning rate is set to 0.001. Figure 7 (a) is the training and testing results. It can be seen that after about 20 epochs of training and testing, the accuracy reaches 99.9%, and there is no overfitting phenomenon.

[0048] The pixel size of the frequency domain constellation map affects the recognition accuracy and training time. The higher the pixel size of the frequency domain constellation map, the lower the probability that different frequency points fall into the same pixel, and more frequency domain feature details can be displayed, but the increase in pixels will extend the network training time. On the other hand, smaller pixels will reduce the complexity of calculation and reduce the training time, but it will also blur the frequency domain features. Figure 7 (b) is the recognition accuracy of different image qualities. It can be seen that the recognition accuracy of 227×227 pixels is the highest (99.99%), and the recognition accuracy of 57×57 and 113×113 also reaches more than 99%. When the pixel is less than 29×29, the recognition accuracy will drop below 90%. Table 3 shows the training time to achieve the highest recognition accuracy with different image qualities. It can be seen that the overall complexity of the network is not high. When the sample image is 227×227 pixels, the training time for 13,850 samples is only 82 minutes. The smaller the image pixels, the shorter the training time, but the more difficult it is to distinguish the features, and more epochs are required to achieve the best training accuracy.

[0049] Table 3

[0050] The efficiency and accuracy of convolutional neural networks are affected by batch size, maximum epoch, and initial learning rate. Larger batch sizes can speed up the training process, but may lead to increased memory usage; smaller batches can reduce memory usage but prolong training time. Increasing the number of epochs can improve the training accuracy of the network, but may also lead to overfitting. A larger learning rate can speed up training but may cause the network to oscillate around the optimal solution. When further optimizing the method of this embodiment, 13,850 frequency domain constellation maps of size 57×57 were used for training. The performance of different batch sizes (from 32 to 1024) and different maximum epochs (from 5 to 40) were evaluated when the initial learning rates were 0.001, 0.01, and 0.1. The results obtained are shown in the figure. Figure 8 shown.

[0051] from Figure 8 It can be seen that the lower the learning rate, the more stable the training process. When the initial learning rate is 0.001, the network is trained faster and more accurately. When the batch size is 64 or 128, the system performs better. Larger batches require more epochs to obtain high accuracy, and smaller batches require longer computation time. In addition, when the initial learning rate is 0.01 and 0.1, small batches will lead to a decrease in accuracy even if it takes longer computation time.

[0052] In addition, the classification accuracy of the method of this embodiment under different signal-to-noise ratios is evaluated in the signal-to-noise ratio range of {-20, -15, -10, -5, 0} dB. The pixel size of the frequency domain constellation map is 227×227, the learning rate is 0.001, the batch size is 32, and the maximum epoch is 40.

[0053] Fig. 9 The electromagnetic fingerprint recognition method based on frequency domain constellation diagram features (PCTF-CNN) in this embodiment is compared with the existing one-dimensional CNN classification method based on time domain data (TIME-CNN), the one-dimensional CNN method based on frequency domain data (PREO-CNN), and the time domain data classification method based on the nearest neighbor algorithm (KNN). All evaluations used the same data set. Among them, the one-dimensional convolutional neural network adopts a three-layer convolution structure, the convolution kernel size is 5×1, and the number of channels is 16, 32, and 64 respectively. The confusion matrix obtained by the method of this embodiment for 14 MCU function recognition problems at -10db and -15db signal-to-noise ratios is as follows Fig.10 When the signal-to-noise ratio is greater than -5dB, the accuracy of the method in this embodiment is greater than 95%, and when it is above 0dB, the accuracy is greater than 99.9%.

[0054] Due to the feature representation of the frequency domain constellation diagram and the classification ability of the convolutional neural network, the method in this embodiment achieves significant performance improvement in low signal-to-noise ratio scenarios. When the signal-to-noise ratio is -20dB, the recognition accuracy of 14 functions can be 64.98%, while the accuracy of the one-dimensional CNN based on time domain data is 26.6%, the accuracy of the one-dimensional CNN based on frequency domain data is 29.9%, and the KNN recognition accuracy is only 7.8%. In the case of high signal-to-noise ratio, the recognition accuracy of the electromagnetic fingerprint recognition method based on the frequency domain constellation diagram features in this embodiment is slightly higher than the recognition accuracy of the one-dimensional CNN based on time domain data and frequency domain data.

[0055] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. An electromagnetic fingerprint recognition method based on frequency domain constellation features, characterized in that: The steps include: Step 1, obtaining the near-field electromagnetic radiation signal of the chip to be identified, and extracting the electromagnetic radiation signal segment from the start to the end time when the chip is executing the function; Step 2, performing fast Fourier transform on the electromagnetic radiation signal segment, and performing frequency domain amplitude normalization, and constructing a frequency domain constellation diagram using the normalized frequency spectrum characteristics of the electromagnetic radiation signal segment; Step 3: Input the frequency domain constellation diagram into the trained convolutional neural network to identify the execution function of the chip.

2. The electromagnetic fingerprint recognition method based on frequency domain constellation features according to claim 1 is characterized in that: Step 1 specifically includes: Record the near-field electromagnetic radiation signal of the chip to be identified by using an oscilloscope; Use IO-Mark technology to mark the start and end time of the chip's function execution; According to the start and end time of the function being executed by the chip, the near-field electromagnetic radiation signal recorded by the oscilloscope is extracted to obtain the electromagnetic radiation signal segment from the start to the end time of the function being executed by the chip.

3. The electromagnetic fingerprint recognition method based on frequency domain constellation features according to claim 1 is characterized in that: In step 2, the frequency domain constellation diagram is constructed by using the normalized frequency spectrum characteristics of the electromagnetic radiation signal fragments, specifically: The frequency domain constellation diagram is constructed with the normalized imaginary part of the spectrum in the electromagnetic radiation signal segment as the horizontal axis and the normalized real part of the spectrum in the electromagnetic radiation signal segment as the vertical axis.

4. The electromagnetic fingerprint recognition method based on frequency domain constellation features according to claim 1, 2 or 3, characterized in that: In step 2, the convolutional neural network has three convolutional layers and one fully connected layer; The kernel size of the convolutional layer is 5×5 and the stride is 1 to capture the chip fingerprint details in the frequency domain constellation diagram; The number of channels of the three convolutional layers are 16, 32, and 64 respectively to obtain higher dimensional features; The convolution layer uses a rectified linear unit as an activation function to reduce the possibility of gradient disappearance and speed up training; The fully connected layer performs feature classification via a Softmax activation function.

5. The electromagnetic fingerprint recognition method based on frequency domain constellation features according to claim 4 is characterized in that: The output ends of the first two convolutional layers in the convolutional neural network are respectively connected to 2×2 maximum pooling layers to downsample the data features and limit the size of the neural network.

6. The electromagnetic fingerprint recognition method based on frequency domain constellation features according to claim 4 is characterized in that: In the process of the convolutional neural network, the loss function adopts Softmax loss and the training algorithm adopts the gradient descent algorithm.

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