Side channel attack method, device and medium

Abstract

The present invention discloses a side channel attack method, device, and medium, relating to the technical field of side channel cryptographic analysis. Multiple sample plaintexts are encrypted using each hypothetical key in a hypothetical key space to obtain a hypothetical intermediate value matrix; each element of the hypothetical intermediate value matrix is ​​input into a leakage model, and the hypothetical intermediate value matrix is ​​modeled using Hamming weight and unevenly weighted bit sums using the leakage model to generate a hypothetical energy consumption matrix; each element of the hypothetical energy consumption matrix is ​​subjected to correlation analysis with energy traces corresponding to multiple sample plaintexts to determine a joint decision matrix; the hypothetical key space is updated based on the correlation ranking in the joint decision matrix, and the joint decision matrix is ​​obtained through iteration of the updated hypothetical key space; the hypothetical key with the highest correlation ranking in the joint decision matrix that meets preset conditions is determined as the key of the encryption device. This method can obtain a relatively accurate key using a relatively small number of samples.

Description

Technical Field

[0001] The present invention relates to the technical field of side channel cryptanalysis, and in particular to a side channel attack method, device and medium. Background Art

[0002] In cryptography or cryptanalysis, a chosen-plaintext attack refers to a type of attack. An attacker with access to an encryption machine can construct the ciphertext corresponding to any plaintext. This cryptanalysis method uses a specific plaintext and its corresponding ciphertext to determine the key or the corresponding plaintext from the intercepted ciphertext. In a chosen-plaintext attack, the cryptanalyst has the ability to select or control the plaintext, allowing them to choose any plaintext and its corresponding ciphertext they deem advantageous. This attack is more powerful than a known-plaintext attack. If a cryptosystem is resistant to chosen-plaintext attacks, it must also be resistant to ciphertext-only attacks and known-plaintext attacks. Chosen-plaintext attacks are more difficult to implement.

[0003] In the prior art, one attack method is to assume that a cryptanalyst temporarily obtains access to the encryption machine, but the encryption key is securely embedded in the encryption device and the analyst cannot obtain the key. In this case, the key can be inferred by encrypting a large amount of selected plaintext and then using the generated ciphertext.

[0004] However, the attack methods in the prior art require a large number of samples to obtain the key. Summary of the Invention

[0005] Based on this, it is necessary to provide a side channel attack method, device and medium to address the above technical problems. This method can obtain a more accurate key with a smaller sample size.

[0006] The present invention adopts the following technical solutions:

[0007] The present invention provides a side channel attack method, comprising:

[0008] Encrypting multiple sample plaintexts using each hypothetical key in the hypothetical key space to obtain a hypothetical intermediate value matrix; the hypothetical key space includes multiple hypothetical keys of the encryption device;

[0009] Inputting each element of the hypothetical intermediate value matrix into a leakage model, performing Hamming weight and unevenly weighted bit sum modeling on the hypothetical intermediate value matrix using the leakage model to generate a hypothetical energy consumption matrix; each element in the hypothetical energy consumption matrix represents a correlation between a sample plaintext and a hypothetical key;

[0010] Correlation analysis is performed on each element of the hypothetical energy consumption matrix and the energy traces corresponding to multiple sample plaintexts to determine a joint decision matrix; the elements in the joint decision matrix represent the correlation ranking of each hypothetical key and the encryption device;

[0011] According to the correlation ranking in the joint decision matrix, the hypothesis key space is updated, and the joint decision matrix is ​​obtained by iteratively obtaining the updated hypothesis key space;

[0012] The hypothetical key with the highest correlation ranking in the joint decision matrix that meets the preset conditions is determined as the key of the encryption device.

[0013] Preferably, multiple sample plaintexts are encrypted using each hypothetical key in the hypothetical key space to obtain a hypothetical intermediate value matrix, including:

[0014] For each sample plaintext, perform round key addition and byte replacement operations on the first byte of the sample plaintext with each hypothetical key to obtain multiple encrypted sample plaintexts;

[0015] According to each encrypted sample plaintext, a hypothetical intermediate value matrix is ​​determined.

[0016] Preferably, the leakage model includes a Hamming weight energy consumption model and an unevenly weighted bit sum model; the assumed energy consumption matrix includes a Hamming weight energy consumption matrix and an unevenly weighted bit sum energy consumption matrix; the assumed intermediate value matrix is ​​input into the leakage model, and the assumed intermediate value matrix is ​​subjected to Hamming weight and unevenly weighted bit sum modeling by the leakage model to generate the assumed energy consumption matrix, including:

[0017] Substitute the Hamming weight, proportionality coefficient, uncorrelated leakage and noise of each element of the assumed intermediate value matrix into the Hamming weight energy consumption model to obtain the Hamming weight energy consumption matrix;

[0018] Each element value of the assumed intermediate value matrix, the corresponding weight, and the constant component and noise component in the real leakage are substituted into the unevenly weighted bit sum model to obtain the unevenly weighted bit sum energy consumption matrix.

[0019] Preferably, correlation analysis is performed on each element of the hypothetical energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to determine a joint decision matrix, including:

[0020] Using the Pearson correlation coefficient as a discriminator, the correlation analysis is performed on the Hamming weight energy consumption matrix and the energy traces corresponding to multiple sample plaintexts to obtain the first correlation matrix;

[0021] Using the Pearson correlation coefficient as a discriminator, the unevenly weighted bit and energy consumption matrix and the energy traces corresponding to multiple sample plaintexts are subjected to correlation analysis to obtain a second correlation matrix;

[0022] The first correlation matrix and the second correlation matrix are added together to obtain a joint decision matrix.

[0023] Preferably, updating the hypothetical key space according to the correlation ranking in the joint decision matrix includes:

[0024] According to the correlation ranking in the joint decision matrix, the hypothetical keys with correlation rankings after a preset number of bits are deleted from the hypothetical key space.

[0025] Preferably, the method for obtaining the sample plaintext includes:

[0026] Encrypting multiple original plaintexts in the plaintext training set through an encryption device to obtain multiple original energy traces generated by the multiple original plaintexts during the encryption process;

[0027] Dividing the plurality of original plaintexts into a plurality of groups according to Hamming weights to obtain a plurality of groups of plaintext data, each group of plaintext data including at least one original plaintext and a corresponding original energy trace;

[0028] Perform a chosen plaintext attack on each group separately to obtain multiple groups of hypothetical key correlations; each group of hypothetical key correlations is the correlation under each hypothetical key;

[0029] Based on the assumed key correlation of each group, a preset number of groups of plaintext data with the greatest correlation are selected from multiple groups of data;

[0030] From the multiple groups of screened plaintext data, the original plaintext of each group of plaintext data corresponding to the original energy trace that conforms to the normal distribution is determined as the sample plaintext.

[0031] Preferably, the energy trace of the sample plaintext is obtained by:

[0032] For any sample plaintext, perform outlier detection on multiple raw energy traces of the sample plaintext to determine the raw energy traces with abnormalities;

[0033] The average of multiple original energy traces is used to replace the original energy trace corresponding to the anomaly to obtain the original energy trace after anomaly detection;

[0034] Performing singular value decomposition denoising on the original energy trace after anomaly detection to obtain the original energy trace after singular value decomposition denoising;

[0035] The original energy trace after singular value decomposition and denoising is subjected to Gaussian mean filtering to obtain the original energy trace after Gaussian mean filtering;

[0036] The original energy trace after Gaussian mean filtering is determined as the energy trace of the corresponding sample plaintext.

[0037] Preferably, performing singular value decomposition denoising processing on the original energy trace after anomaly detection to obtain the original energy trace after singular value decomposition denoising includes:

[0038] Embed all original energy traces after anomaly detection into Hankel matrix point by point;

[0039] The Hankel matrix is ​​decomposed into a low-rank signal matrix and a noise sparse matrix by truncated singular value decomposition;

[0040] The low-rank signal matrix is ​​attenuated by damping attenuation to obtain the original energy trace after singular value decomposition and denoising.

[0041] The present invention provides a side channel attack device, comprising:

[0042] An encryption module is used to perform encryption operations on multiple sample plaintexts using each hypothetical key in a hypothetical key space to obtain a hypothetical intermediate value matrix; the hypothetical key space includes multiple hypothetical keys of the encryption device;

[0043] A modeling module is used to perform Hamming weight and uneven weighted bit sum modeling on each element of the hypothetical intermediate value matrix to generate a hypothetical energy consumption matrix; each element in the hypothetical energy consumption matrix represents the correlation between a sample plaintext and a hypothetical key;

[0044] An analysis module is configured to perform correlation analysis between each element of the hypothetical energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to determine a joint decision matrix; the elements in the joint decision matrix represent a correlation ranking between each hypothetical key and the encryption device;

[0045] An updating module is used to update the hypothesis key space according to the correlation ranking in the joint decision matrix, and iteratively obtain the joint decision matrix through the updated hypothesis key space;

[0046] The determination module is used to determine the hypothetical key with the highest correlation ranking in the joint decision matrix that meets the conditions as the key of the encryption device.

[0047] The present invention provides a computer-readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the side channel attack method is implemented.

[0048] The present invention provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned side channel attack method when executing the program.

[0049] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects:

[0050] In the side channel attack method provided by the present invention, a hypothetical energy consumption matrix is ​​generated by modeling the Hamming weight and the unevenly weighted bit sum, and then the modeled hypothetical energy consumption matrix is ​​jointly judged with the energy trace after noise reduction processing to obtain a correlation matrix. The correlation matrix is ​​used to update the hypothetical key space, so that the hypothetical key in the updated hypothetical key space is used as the basis for subsequent joint judgment. In this way, useful information can be extracted from a small number of samples through the hypothetical energy consumption matrix and the joint judgment, and the hypothetical key space is dynamically updated through the joint judgment matrix, which makes it unnecessary to process all keys in subsequent analysis, but can focus on the hypothetical keys that have a greater impact on the judgment result, thereby effectively reducing the sample size requirement. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0052] Figure 1 A schematic diagram of a side channel attack method provided by the present invention;

[0053] Figure 2 A schematic diagram of another side channel attack method provided by the present invention;

[0054] Figure 3 A schematic diagram of another side channel attack method provided by the present invention;

[0055] Figure 4 A schematic diagram of another side channel attack method provided by the present invention;

[0056] Figure 5 A schematic diagram of another side channel attack method provided by the present invention;

[0057] Figure 6 This is a schematic diagram of the effect of a side channel attack method provided by the present invention on selecting a plaintext strategy in a low-noise situation;

[0058] Figure 7 This is a schematic diagram of the effect of a side channel attack method provided by the present invention on selecting a plaintext strategy in a high-noise situation;

[0059] Figure 8 This is a schematic diagram of the effect of correlation joint judgment of a side channel attack method provided by the present invention in a low-noise situation;

[0060] Figure 9 This is a schematic diagram of the effect of correlation joint judgment of a side channel attack method provided by the present invention in a high-noise situation;

[0061] Figure 10 This is a schematic diagram of the effect of a key reduction strategy of a side channel attack method provided by the present invention in a low-noise situation;

[0062] Figure 11 This is a schematic diagram of the effect of a key reduction strategy of a side channel attack method provided by the present invention under high noise conditions;

[0063] Figure 12 This is a schematic diagram comparing the success rate of a side channel attack method provided by the present invention with that of traditional CPA analysis in a low-noise situation;

[0064] Figure 13 This is a schematic diagram comparing the success rate of a side channel attack method provided by the present invention with that of traditional CPA analysis in a high-noise environment;

[0065] Figure 14 This is a schematic diagram comparing the correlation between a side channel attack method provided by the present invention and traditional CPA analysis in a low-noise situation;

[0066] Figure 15 This is a schematic diagram comparing the correlation between a side channel attack method provided by the present invention and traditional CPA analysis in a high-noise situation;

[0067] Figure 16 A schematic diagram of a side channel attack device provided by the present invention;

[0068] Figure 17 A schematic diagram of a computer device for implementing a side-channel attack method provided by the present invention. DETAILED DESCRIPTION

[0069] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0070] Currently, typical chosen-plaintext attack methods include collision attacks and differential attacks. When the implementation code of some Advanced Encryption Standard (AES) algorithms is unknown, it is impossible to establish an accurate leakage model, resulting in the inability to conduct effective attack experiments.

[0071] In a data set, due to noise interference and other reasons, the measured values ​​are incorrectly observed and recorded, resulting in observation data that deviates greatly from other data values. This type of observation data is called an outlier, also known as an outlier. In the prior art, a variety of outlier detection methods have been proposed for different application scenarios, including statistical parameter methods, time series prediction methods, and data mining methods. The Z-Score outlier detection in the statistical parameter method models the data by assuming a statistical model and uses statistical parameters to judge the data as abnormal. It is also called the n-times standard deviation empirical rule. The Z-Score is a statistic that indicates the degree of deviation between the data and the mean, with the standard deviation as the unit. The standard deviation is an indicator that measures the degree of dispersion of the data distribution. The larger the value, the higher the degree of dispersion of the data.

[0072] Due to the "weak separability" of signal and noise, the signal and noise can be separated through low-rank matrix approximation based on different features. Low-rank matrix approximation (LRMA) refers to the use of the low rank of the signal matrix and the sparsity of the noise matrix to recover the data matrix. Low-rank matrix recovery is a common tool for solving denoising problems in signal processing and image enhancement. Denoising methods based on rank reduction theory mainly construct special mathematical matrices for noisy data, and then use low-rank approximation (rank reduction) methods to reduce the rank of the noisy data to remove random interference.

[0073] In cryptographic chips, digital circuits typically utilize a complementary metal oxide semiconductor (CMOS) process. CMOS circuits primarily generate two side-channel leaks: energy consumption and electromagnetic radiation. Both signals inevitably carry noise during the acquisition process. Energy analysis attacks exploit the fact that the energy consumption of a cryptographic device depends on the operations it performs and the data it processes. Therefore, the energy trace can be broken down into operation-dependent and data-dependent components. Each point in the energy trace can be characterized as the sum of the operation-dependent component, the data-dependent component, electronic noise, and a constant component. If the amplitude distribution of a noise follows a Gaussian distribution and its power spectral density is uniform, it is called Gaussian white noise. A Gaussian filter is a type of linear smoothing filter whose weights are selected based on the shape of the Gaussian function. Gaussian smoothing filters are very effective at suppressing noise that follows a normal distribution.

[0074] Information leakage models map internally processed data to hypothetical energy by assuming a mapping relationship between the device's energy and certain internal data (such as S-box outputs or intermediate values ​​during the encryption process). Information leakage models primarily include the Hamming weight model, the Hamming distance model, the bit model, and the zero-value model. In the Hamming weight model, energy is assumed to be proportional to the number of set bits in the intermediate value, which can be understood as a multi-bit model with equal weights. The unevenly weighted bit and leakage model is a generalization of the Hamming weight model, assigning different weights to each bit to represent its importance, which is closer to reality. In noisy data, different bits are affected by noise to varying degrees. Assigning specific weights can, to a certain extent, mitigate the impact of strong interference from the hypothetical key.

[0075] A discriminator is a statistical tool designed to identify the most likely correct key from a set of guesses. The optimal discriminator is the decision model that maximizes the probability of distinguishing the correct key. Building on the principles of the DPA method, Brier et al. first proposed Correlation Power Analysis (CPA), which outperforms differential power analysis in terms of attack efficiency, robustness, and experimental data size. Correlation Power Analysis is a powerful method in energy analysis attacks. It analyzes the energy consumption of cryptographic devices during encryption operations to infer sensitive data such as keys. The theoretical basis of CPA is the correlation between the leakage model of intermediate values ​​in cryptographic algorithms and the characteristic points contained in the actual power consumption trace. By analyzing the energy leakage during encryption operations on a large number of different data packets, the signal at a fixed moment is analyzed and treated as a function of the processed data. The key in the cryptographic integrated circuit can be recovered based on the leakage. CPA uses the Pearson correlation coefficient to measure the correlation between the hypothetical power leakage and the actual power leakage. Its advantage is that it can obtain key information without knowing the implementation details of the target device's encryption algorithm. Furthermore, CPA can recover key information even in the presence of noise in the leakage signal.

[0076] Based on this, the present invention provides a non-modeling side-channel attack method based on filtering, denoising, and dual-model joint judgment. First, the acquired energy trace is subjected to selected plaintext analysis to obtain the corresponding plaintext leakage that is most relevant to the encryption process execution and the key information. The energy trace after the selected plaintext is then subjected to outlier detection, singular value decomposition denoising, and Gaussian mean filtering to improve the signal-to-noise ratio of the signal. The plaintext information after the selected plaintext is generated by operating intermediate values ​​with the hypothetical key. The hypothetical intermediate values ​​are then subjected to Hamming weight, unevenly weighted bits, and dual-model modeling to generate a hypothetical energy consumption matrix. The modeled hypothetical energy consumption matrix is ​​subjected to correlation analysis with the noise-reduced signal, and the two obtained correlation matrices are jointly judged to determine the recovered key. During the step test, the size of the correlation matrix is ​​updated and used as the basis for the hypothetical key space, thereby reducing the overall computational complexity of the side-channel attack. The present invention adopts the above-mentioned non-modeling side-channel attack method based on filtering, denoising, and dual-model joint judgment. The signal-to-noise ratio of the signal and the key operation intermediate value is greatly improved, and the number of signal samples required for a successful side-channel attack and the computational time of the step test are successfully reduced.

[0077] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0078] Figure 1 The following is a flow chart of a side channel attack method in the present invention, which specifically includes the following steps:

[0079] S101, encrypting multiple sample plaintexts using each hypothetical key in a hypothetical key space to obtain a hypothetical intermediate value matrix; the hypothetical key space includes multiple hypothetical keys of an encryption device.

[0080] First, before conducting a side-channel attack, a sample plaintext used in the side-channel attack can be determined. The sample plaintext is the corresponding plaintext that is most relevant to the key information executed by the encryption device during the encryption process.

[0081] In an exemplary embodiment, a method for obtaining sample plaintext includes: encrypting multiple original plaintexts in a plaintext training set through an encryption device to obtain multiple original energy traces generated by the multiple original plaintexts during the encryption process; dividing the multiple original plaintexts into multiple groups according to Hamming weight to obtain multiple groups of plaintext data, each group of plaintext data includes at least one original plaintext and a corresponding original energy trace; performing a chosen plaintext attack on each group to obtain multiple groups of hypothetical key correlations; each group of hypothetical key correlations is a correlation under each hypothetical key; based on the hypothetical key correlations of each group, a preset number of groups of plaintext data with the largest correlation are screened from the multiple groups of data; finally, from the multiple groups of screened plaintext data, the original plaintext of each group of plaintext data corresponding to the original energy trace that conforms to the normal distribution is determined as the sample plaintext.

[0082] The encryption device is a device whose key needs to be cracked. The encryption device includes a key. When the encryption device encrypts plaintext, it encrypts the plaintext using the key therein. The assumed key is the key of the assumed encryption device.

[0083] The plaintext training set includes multiple plaintexts. This plaintext is used as the original plaintext. Multiple original plaintexts are encrypted using an encryption device to obtain multiple original energy traces generated during the encryption process. The original energy traces include two side-channel leaks: energy consumption and electromagnetic radiation. It should be noted that the same original plaintext can be encrypted multiple times, yielding multiple original energy traces corresponding to the original plaintext. Selected plaintext analysis is then performed on the obtained original energy traces to determine the corresponding plaintext leaks that are most relevant to the encryption process and key information.

[0084] Specifically, the number of bits with the same number of "1" in each original plaintext is counted, and the original plaintexts with the same number of "1" are grouped together to obtain multiple groups of plaintext data. Then, a chosen plaintext attack (CPA) is performed on each original plaintext and the corresponding original energy trace in each group to obtain multiple groups of hypothetical key correlations, where the hypothetical key correlation of each group is the correlation under each hypothetical key. For example, if there are 256 hypothetical keys, each group has 256 correlations.

[0085] Then, based on the assumed key correlation of each group, a preset number of groups of plaintext data with the greatest correlation are screened from multiple groups of data, and finally the original plaintext in the plaintext data is determined as the sample plaintext; specifically, based on the assumed key correlation of each group, the original plaintext trace and original energy trace corresponding to the Hamming weight with the most obvious leakage are screened out; optionally, the screening method can be to obtain the peak value of the assumed key correlation of each group, sort the peak values ​​in order from large to small, and screen out the groups corresponding to the preset number of peak values; finally, in the multiple groups of plaintext data preliminarily screened out, the overall statistical distribution of the original energy trace of each group of plaintext data is analyzed separately, for example, whether the original energy trace of each group of plaintext data conforms to the normal distribution, and the "P" value is used as the main reference information, and it is considered that the energy trace group greater than the "P" value is closer to the normal distribution, and the original energy trace closer to the normal distribution and the corresponding original plaintext are used as the output of the plaintext selection stage; the original plaintext output at the end is determined as the sample plaintext.

[0086] In an exemplary embodiment, multiple sample plaintexts are encrypted using each hypothetical key in the hypothetical key space to obtain a hypothetical intermediate value matrix, including: for each sample plaintext, performing a round key addition operation and a byte replacement operation on the first byte of the sample plaintext with each hypothetical key to obtain multiple encrypted sample plaintexts, and then determining the hypothetical intermediate value matrix based on each encrypted sample plaintext.

[0087] The round key addition operation and the byte replacement operation are both operations in the AES encryption algorithm, and the specific implementation methods are not repeated here in this embodiment; wherein, as shown in formula (1), S is the encrypted sample plaintext.

[0088] S=S box [plaintext^keyspace] (1)

[0089] Among them, S box [.] is the function corresponding to the target operation (byte substitution) of the cryptographic algorithm (AES algorithm), plaintext is the plaintext involved in the operation, and keyspace is the hypothetical key space. The hypothetical key space contains multiple hypothetical keys.

[0090] In essence, this embodiment performs a round key addition operation and a byte replacement operation on each sample plaintext through each hypothetical key in the hypothetical key space, thereby obtaining a hypothetical intermediate value matrix.

[0091] It should be noted that the encryption operation in this embodiment encrypts the first byte of the sample plaintext. Therefore, the final predicted key is the first byte of the key. The remaining bytes of the key can be divided and conquered, referring to this method, to obtain the individual bytes of the key. For example, if the encryption operation is performed on the second byte of the sample plaintext, the final predicted key is the second byte of the key.

[0092] S102 , inputting the assumed intermediate value matrix into a leakage model, performing Hamming weight and uneven weighted bit sum modeling on the assumed intermediate value matrix through the leakage model, and generating a assumed energy consumption matrix.

[0093] In which, each element in the assumed energy consumption matrix represents the correlation between a sample plaintext and a hypothetical key.

[0094] Specifically, the leakage model includes a Hamming weight energy consumption model and an unevenly weighted bit sum model; the energy consumption matrix includes a Hamming weight energy consumption matrix and an unevenly weighted bit sum energy consumption matrix; the hypothetical intermediate value matrix is ​​input into the leakage model, and the hypothetical intermediate value matrix is ​​subjected to Hamming weight and unevenly weighted bit sum modeling through the leakage model to generate a hypothetical energy consumption matrix, including: substituting the Hamming weight, proportional coefficient, and uncorrelated leakage and noise of each element of the hypothetical intermediate value matrix into the Hamming weight energy consumption model to obtain the Hamming weight energy consumption matrix; substituting each element value of the hypothetical intermediate value matrix, the corresponding weight, and the constant component and noise component in the actual leakage into the unevenly weighted bit sum model to obtain the unevenly weighted bit sum energy consumption matrix.

[0095] Substitute each element value in the assumed intermediate value matrix into the Hamming weight and unevenly weighted bit sum model respectively to generate the corresponding assumed energy consumption matrix as the output of the leakage model modeling phase, as shown in Formula (2) and Formula (3).

[0096] h1=aHW(v)+b (2)

[0097]

[0098] Where h1 is the element value of the Hamming weight energy consumption matrix, v is each element of the assumed intermediate value matrix, usually the function value of the assumed key and encryption operation data, HW is the Hamming weight of v (the number of 1), a is the proportional coefficient of the signal, b is the uncorrelated leakage and noise; h2 is the element value of the unevenly weighted bit and energy consumption matrix, z i For each element value of the assumed intermediate value matrix, usually the ith bit of the assumed intermediate matrix of the cryptographic algorithm target byte, a i For the corresponding assignment weights, c and n q are the constant component and noise component in the real leakage, and n is the number of bits of the assumed intermediate value matrix.

[0099] S103 , performing correlation analysis on each element of the hypothetical energy consumption matrix and energy traces corresponding to multiple sample plaintexts to determine a joint decision matrix; the elements in the joint decision matrix represent the correlation ranking of each hypothetical key and the encryption device.

[0100] In an exemplary embodiment, the original energy trace corresponding to the sample plaintext can be subjected to outlier detection, singular value decomposition denoising and Gaussian mean filtering in sequence to obtain the original energy trace after denoising, and the original energy trace after denoising is determined as the energy trace corresponding to the sample plaintext.

[0101] Specifically, the method for obtaining the energy trace of the sample plaintext includes: for any sample plaintext, performing outlier detection on multiple original energy traces of the sample plaintext to determine the original energy trace with abnormalities; replacing the original energy trace corresponding to the abnormality with the mean of the multiple original energy traces to obtain the original energy trace after anomaly detection; performing singular value decomposition denoising processing on the original energy trace after anomaly detection to obtain the original energy trace after singular value decomposition denoising; performing Gaussian mean filtering on the original energy trace after singular value decomposition denoising to obtain the original energy trace after Gaussian mean filtering; and determining the original energy trace after Gaussian mean filtering as the energy trace of the corresponding sample plaintext.

[0102] Outlier detection involves treating the original energy traces with Z-Score absolute values ​​greater than 3 as outliers (abnormal original energy traces), and then using the mean of the original energy traces under the same plaintext as filling, that is, replacing the abnormal original energy traces with the mean of the original energy traces under the same plaintext.

[0103] Optionally, the original energy trace after anomaly detection is subjected to singular value decomposition denoising processing to obtain the original energy trace after singular value decomposition denoising, including: embedding all the original energy traces after anomaly detection into a Hankel matrix point by point, and then decomposing the Hankel matrix into a low-rank signal matrix and a noise sparse matrix by truncated singular value decomposition; finally, attenuating the low-rank signal matrix by damping attenuation to obtain the original energy trace after singular value decomposition denoising.

[0104] Specifically, the original energy trace after anomaly detection is embedded into a Hankel matrix point by point. Then, the low-rank property of the signal matrix is ​​utilized to decompose the Hankel matrix into a low-rank signal matrix and a noise sparse matrix through truncated singular value decomposition, and the low-rank signal matrix is ​​attenuated by the damping term.

[0105] First, the threshold of the truncated singular value decomposition and the sequence of singular values ​​to be retained (arranged from large to small, the large ones are retained) are determined by the hard threshold method. Then, the retained singular values ​​are damped and attenuated to obtain the singular diagonal matrix after the truncated singular values ​​are damped and attenuated, that is, the singular diagonal matrix processed by the damped singular value decomposition method (also including the left singular matrix and the right singular matrix). Finally, the matrix after damped singular value decomposition denoising is obtained by matrix multiplication of the left singular matrix, the singular diagonal matrix and the right singular matrix. Then, the matrix after damped singular value decomposition denoising is converted into the original energy trace after singular value decomposition denoising.

[0106] The original energy trace after singular value decomposition denoising is subjected to Gaussian mean filtering with the original energy trace under the same plaintext to obtain the data after Gaussian mean filtering (the original energy trace after denoising), which is used as the final output of the filtering and denoising stage (the energy trace corresponding to the sample plaintext).

[0107] Therefore, a correlation analysis is performed on each element of the assumed energy consumption matrix and the energy traces corresponding to multiple sample plaintexts to determine a joint decision matrix, including: using the Pearson correlation coefficient as a discriminator, performing a correlation analysis on the Hamming weight energy consumption matrix and the energy traces corresponding to multiple sample plaintexts to obtain a first correlation matrix; using the Pearson correlation coefficient as a discriminator, performing a correlation analysis on the unevenly weighted bit and energy consumption matrix and the energy traces corresponding to multiple sample plaintexts to obtain a second correlation matrix; and adding the first correlation matrix and the second correlation matrix to obtain a joint decision matrix.

[0108] That is, the two hypothesized energy consumption matrices are correlated with the denoising filtered leakage data, and the discriminator selects the Pearson correlation coefficient. The two correlation matrices are summed and used as the basis for decision to obtain the recovered key, as shown in Formula (4).

[0109] CorrelationM key =Pearson(AssumPower1, trace)+Pearson(AssumPower2,trace) (4)

[0110] Among them, CorrelationM key is the joint decision matrix, Pearson(.) is the function of correlation analysis using the Pearson correlation coefficient as the discriminator, AssumPower1 is the Hamming weight energy consumption matrix, AssumPower2 is the unevenly weighted bit sum energy consumption matrix, and trace is the energy trace corresponding to multiple sample plaintexts (the leaked data after denoising filtering).

[0111] S104 , updating the hypothetical key space according to the correlation ranking in the joint decision matrix, and iterating through the updated hypothetical key space to obtain the joint decision matrix.

[0112] The element values ​​in the joint decision matrix represent the correlation between the hypothetical keys.

[0113] Optionally, according to the correlation ranking in the joint decision matrix, the hypothetical keys with correlation rankings after a preset number of digits are deleted from the hypothetical key space to update the hypothetical key space, and the joint decision matrix is ​​obtained by iteratively obtaining the updated hypothetical key space.

[0114] Specifically, when performing a step test, the joint decision matrix obtained from the previous correlation analysis will exclude the hypothetical keys at the end according to the size ranking, and the updated hypothetical key space will be used as the hypothetical key input for the previous round of key addition in this correlation analysis.

[0115] S105 , determining the hypothetical key with the highest correlation ranking in the joint decision matrix that meets the preset conditions as the key of the encryption device.

[0116] The preset condition may be that the number of times the joint decision matrix is ​​updated reaches a preset number, and after the joint decision matrix is ​​updated the preset number of times, the hypothetical key with the highest correlation ranking in the joint decision matrix is ​​determined as the key of the encryption device.

[0117] In an exemplary embodiment, the present invention also provides a side channel attack method. Taking the AES encryption algorithm as an example, energy information is collected for the first round of byte replacement in the algorithm encryption process. By using this method to recover the first byte of the key, the remaining bytes of the key can be divided and conquered. Refer to the analysis process, as shown in the following example. Figure 2 As shown, this embodiment includes the following steps:

[0118] S201, obtaining source data, the source data including original plaintext and corresponding energy trace, obtaining sample plaintext and corresponding energy trace from the original plaintext by selecting plaintext.

[0119] Specifically, the original plaintexts are grouped according to Hamming weight, side-channel attacks are performed on different groups of data, and the plaintexts with the most obvious Hamming weight leakage are selected; then, based on this, the corresponding energy traces of the selected plaintexts are selected according to their overall statistical distribution, and some plaintexts that are closer to the normal distribution are selected; among them, the P value of the overall statistical distribution is used as the main reference basis. The larger the P value, the closer the corresponding data is to the normal distribution.

[0120] S202 , preprocessing the energy trace corresponding to the sample plaintext to obtain a preprocessed energy trace; the preprocessing includes: outlier detection, damped singular value decomposition denoising, and Gaussian mean filtering.

[0121] Specifically, if Figure 3 As shown in the figure, first, the energy trace of the sample plaintext is subjected to outlier detection based on the Z-Score method. When the absolute value of the Z-Score of the observed data is greater than 3, it is considered an outlier, and the mean of the leaked data with the same plaintext is used as padding. Then, the energy trace is denoised by damped singular value decomposition, and the leaked data used in the attack is embedded point by point into a Hankel matrix. By utilizing the low rank property of the signal matrix, the original Hankel matrix is ​​decomposed into a low-rank signal matrix and a noise sparse matrix through damped singular value decomposition, and the matrix is ​​attenuated by the damping term. Finally, the energy trace denoised by damped singular value decomposition is subjected to Gaussian mean filtering under the same plaintext to obtain the data after Gaussian mean filtering (the energy trace after preprocessing), which is used as the final output of the filtering and denoising stage.

[0122] In step S203, the round key addition operation and the byte replacement operation are performed on the sample plaintext and the hypothetical key to obtain the corresponding hypothetical intermediate value matrix; then, the hypothetical intermediate value matrix is ​​modeled using the Hamming weight (HW model) and the uneven weighted bit sum (UWSB leakage model) dual models to generate a hypothetical energy consumption matrix.

[0123] Specifically, if Figure 4 As shown, the first byte of the sample plaintext and the first byte of the hypothetical key are subjected to round key addition and byte replacement operations to obtain a hypothetical intermediate value matrix, which is then input into the HW model and the UWSB leakage model respectively to obtain two hypothetical energy consumption matrices.

[0124] First, the generated hypothetical intermediate value matrix is ​​modeled based on the Hamming weight model to generate a hypothetical energy consumption matrix 1. In the Hamming weight model, energy is assumed to be proportional to the number of bits set in the intermediate value, and its definition can be expressed as: h = aHW(v) + b; where v is the hypothetical intermediate value of the cryptographic algorithm, usually the function value of the hypothetical key and encryption operation data, HW is the Hamming weight of v, a is the proportional coefficient of the signal, and b is the uncorrelated leakage and noise.

[0125] According to the results of correlation analysis after modeling the single-bit model and the mutual information between different bits of the intermediate value, the uneven and weighted bit sum models are weighted. Then, the generated hypothetical intermediate value matrix is ​​modeled based on the uneven weighted bit sum model to generate the hypothetical energy consumption matrix 2. The uneven weighted bit sum leakage model is a generalization of the Hamming weight and Hamming distance models, and its definition can be: Among them, z i is the ith bit of the assumed intermediate value of the target byte of the cryptographic algorithm, a i are the corresponding assignment weights, c and n q are the constant component and the noise component in the real leakage.

[0126] S204, input the preprocessed energy trace output by S202 and the two hypothetical energy consumption matrices output by S203 into two discriminators based on the Pearson correlation coefficient, and optimize the data output by the two discriminators through weights to output a correlation matrix.

[0127] Specifically, if Figure 5 As shown in the figure, the preprocessed energy trace and the assumed energy consumption matrix of the HW model are input into the discriminator 1, and the preprocessed energy trace and the assumed energy consumption matrix of the UWSB leakage model are input into the discriminator 2, and the data output by the two discriminators are weighted and optimized to obtain the correlation matrix.

[0128] A correlation analysis is performed on the modeled hypothetical energy consumption matrix and the signal after noise reduction processing, and the two correlation matrices obtained are jointly judged to determine the recovery key. The main feature of the method is that the characteristics of the intermediate value modeling by the two models are combined, and a correlation analysis is performed with the real leakage signal to obtain a more accurate correlation analysis result as the basis for the decision to recover the key.

[0129] S205 , updating the hypothetical key space according to the size ranking of the correlation matrix, and determining the key of the encryption device according to the size ranking of the correlation matrix.

[0130] S206, during the step test, the size ranking of the correlation matrix is ​​updated and used as the basis for assuming the key space.

[0131] Specifically, the correlation matrix size ranking during the step test is updated and used as the basis for the hypothetical key space. The hypothetical keys with low correlation matrix size ranking are used as non-major interference items, which increases the computational complexity of the overall side channel analysis process. By updating the ranking and screening out the hypothetical keys with low ranking, the overall analysis time of the step test is shortened. It can be defined as: S = S box [plaintext^keyspace], where S box [·] is the function corresponding to the target operation (byte replacement) of the cryptographic algorithm, plaintext is the plaintext involved in the operation, and keyspace is the hypothetical key space. The hypothetical key space will be updated according to the correlation ranking in the step test, excluding hypothetical keys with weak correlation.

[0132] In order to further verify the effectiveness of the side channel attack method provided by the present invention, Figure 6 and Figure 11 As shown, a schematic diagram of the effect of selecting a plaintext strategy in implementing the side channel attack method of the present invention in a low-noise situation, a schematic diagram of the effect of selecting a plaintext strategy in implementing the side channel attack method of the present invention in a high-noise situation, a schematic diagram of the effect of joint judgment based on correlation in implementing the side channel attack method of the present invention in a low-noise situation, a schematic diagram of the effect of joint judgment based on correlation in implementing the side channel attack method of the present invention in a high-noise situation, a schematic diagram of the effect of key reduction strategy in implementing the side channel attack method of the present invention in a low-noise situation, and a schematic diagram of the effect of key reduction strategy in implementing the side channel attack method of the present invention in a high-noise situation are given.

[0133] Furthermore, the side channel attack method of the present invention can be compared with the traditional CPA method, such as Figure 12-15 As shown, Figure 12 This is a schematic diagram comparing the success rate of the side channel attack method provided by the present invention with that of the traditional CPA analysis in a low-noise situation. Figure 13 This is a schematic diagram comparing the success rate of the side channel attack method provided by the present invention with that of the traditional CPA analysis in a high-noise situation. Figure 14This is a schematic diagram comparing the correlation between the side channel attack method provided by the present invention and the traditional CPA analysis in a low-noise situation. Figure 15 This is a schematic diagram comparing the correlation between the side channel attack method provided by the present invention and the traditional CPA analysis in a high-noise situation.

[0134] Experimental verification shows that the side-channel attack method provided by the present invention can significantly improve the relevance of the correct subkey and greatly reduce the number of samples required to guess the correct subkey. Table 1 compares the side-channel attack method provided by the present invention with traditional CPA. Table 1 shows the conclusion that the non-modeling side-channel attack method based on filtering noise reduction and dual-model joint judgment helps reduce the number of samples required to guess the correct subkey, improving the efficiency of side-channel attacks.

[0135] Table 1

[0136]

[0137] In summary, the side channel attack method provided by the present invention can better preserve the useful information in the side channel signal, improve the correlation of the correct key bytes, and greatly reduce the number of required signal samples.

[0138] Therefore, the present invention adopts the above-mentioned non-modeling side channel attack method based on filtering noise reduction and dual-model joint judgment, and uses this method to preprocess the signal data set. The signal-to-noise ratio of the intermediate value of the signal and the key operation is greatly improved, the efficiency of the side channel attack is greatly improved, and the number of signal samples required for a successful side channel attack is successfully reduced.

[0139] In summary, the side-channel attack method of the present invention can efficiently analyze cryptographic algorithm energy traces in situations with low signal-to-noise ratios and strong interference, resulting in a significant improvement in the correlation between the correct key and the noisy energy trace analysis. By combining Hamming weight, unevenly weighted bits, and dual-model modeling, and jointly determining correlations, this method compensates for leakage characteristics that are not detected by a single leakage model. Some hypothetical keys that exhibit strong interference when modeled using a single model are excluded, thereby improving the accuracy of correlation analysis and achieving better recovery results.

[0140] When applying the side channel attack method provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.

[0141] The above is a side channel attack method provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding side channel attack device, such as Figure 16 shown.

[0142] Figure 16A schematic diagram of a side-channel attack device provided by the present invention. The device 1600 includes:

[0143] The encryption module 1601 is configured to perform encryption operations on a plurality of sample plaintexts using each hypothetical key in a hypothetical key space to obtain a hypothetical intermediate value matrix; the hypothetical key space includes a plurality of hypothetical keys of the encryption device;

[0144] Modeling module 1602 is configured to perform Hamming weight and uneven weighted bit sum modeling on each element of the hypothetical intermediate value matrix to generate a hypothetical energy consumption matrix; each element in the hypothetical energy consumption matrix represents the correlation between a sample plaintext and a hypothetical key;

[0145] An analysis module 1603 is configured to perform a correlation analysis between each element of the hypothetical energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to determine a joint decision matrix; the elements in the joint decision matrix represent a correlation ranking between each hypothetical key and the encryption device;

[0146] An updating module 1604 is configured to update the hypothetical key space according to the correlation ranking in the joint decision matrix, and iteratively obtain the joint decision matrix through the updated hypothetical key space;

[0147] The determination module 1605 is configured to determine the hypothetical key with the highest correlation ranking in the joint decision matrix that meets the conditions as the key of the encryption device.

[0148] The specific definition of the side-channel attack device can be found in the definition of the side-channel attack method above and will not be repeated here. Each module in the above-mentioned side-channel attack device can be implemented in whole or in part through software, hardware, or a combination thereof. Each of the above-mentioned modules can be embedded in or independent of the processor in the computer device in hardware form, or can be stored in the memory of the computer device in software form, so that the processor can call and execute the corresponding operations of each of the above modules.

[0149] The present invention also provides a computer-readable storage medium, which stores a computer program, which can be used to execute the above Figure 1 Provided side channel attack method.

[0150] The present invention also provides Figure 17 The structural diagram of the computer equipment shown in FIG. Figure 17 As shown in the figure, at the hardware level, the computer device includes a processor, an internal bus, a network interface, a memory, and a non-volatile memory. Of course, it may also include other hardware required for the business. The processor reads the corresponding computer program from the non-volatile memory into the memory and then runs it to achieve the above Figure 1 Provided side channel attack method.

[0151] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory or optical memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0152] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A side channel attack method, characterized in that: The method comprises: Performing encryption operations on multiple sample plaintexts using each hypothetical key in a hypothetical key space to obtain a hypothetical intermediate value matrix; the hypothetical key space includes multiple hypothetical keys of the encryption device; Inputting the hypothetical intermediate value matrix into the leakage model, performing Hamming weight and uneven weighted bit sum modeling on the hypothetical intermediate value matrix using the leakage model to generate a hypothetical energy consumption matrix; each element in the hypothetical energy consumption matrix represents the correlation between a sample plaintext and a hypothetical key; Performing correlation analysis on each element of the hypothetical energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to determine a joint decision matrix; the elements in the joint decision matrix represent the correlation ranking of each hypothetical key and the encryption device; updating the hypothetical key space according to the correlation ranking in the joint decision matrix, and iterating the updated hypothetical key space to obtain the joint decision matrix; The hypothetical key with the highest correlation ranking in the joint decision matrix that meets the preset conditions is determined as the key of the encryption device.

2. The method according to claim 1, characterized in that The method of encrypting the plurality of sample plaintexts using each hypothetical key in the hypothetical key space to obtain a hypothetical intermediate value matrix includes: For each sample plaintext, perform a round key addition operation and a byte replacement operation on the first byte of the sample plaintext with each hypothetical key to obtain multiple encrypted sample plaintexts; The hypothetical intermediate value matrix is ​​determined according to each encrypted sample plaintext.

3. The method according to claim 1, characterized in that The leakage model includes a Hamming weight energy consumption model and an unevenly weighted bit sum model; the assumed energy consumption matrix includes a Hamming weight energy consumption matrix and an unevenly weighted bit sum energy consumption matrix; the assumed intermediate value matrix is ​​input into the leakage model, and the assumed intermediate value matrix is ​​subjected to Hamming weight and unevenly weighted bit sum modeling by the leakage model to generate the assumed energy consumption matrix, including: Substituting the Hamming weight, proportionality coefficient, and uncorrelated leakage and noise of each element of the assumed intermediate value matrix into the Hamming weight energy consumption model to obtain the Hamming weight energy consumption matrix; Each element value of the assumed intermediate value matrix, the corresponding weight, and the constant component and the noise component in the real leakage are respectively substituted into the unevenly weighted bit sum model to obtain the unevenly weighted bit sum energy consumption matrix.

4. The method according to claim 3, characterized in that The performing correlation analysis on each element of the assumed energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to determine a joint decision matrix includes: Using the Pearson correlation coefficient as a discriminator, performing correlation analysis on the Hamming weight energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to obtain a first correlation matrix; Using the Pearson correlation coefficient as a discriminator, performing a correlation analysis on the unevenly weighted bit and energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to obtain a second correlation matrix; The first correlation matrix and the second correlation matrix are added together to obtain the joint decision matrix.

5. The method according to claim 1, wherein The updating of the hypothetical key space according to the correlation ranking in the joint decision matrix includes: According to the correlation ranking in the joint decision matrix, the hypothetical keys with correlation rankings after a preset number of bits are deleted from the hypothetical key space.

6. The method according to claim 1, characterized in that Methods for obtaining the sample plaintext include: Encrypting multiple original plaintexts in the plaintext training set using the encryption device to obtain multiple original energy traces generated by the multiple original plaintexts during the encryption process; Dividing the plurality of original plaintexts into a plurality of groups according to Hamming weights to obtain a plurality of groups of plaintext data, each group of plaintext data including at least one original plaintext and a corresponding original energy trace; Perform a chosen plaintext attack on each group separately to obtain multiple groups of hypothetical key correlations; each group of hypothetical key correlations is the correlation under each hypothetical key; Based on the assumed key correlation of each group, a preset number of groups of plaintext data with the greatest correlation are selected from multiple groups of data; From the screened multiple groups of plaintext data, the original plaintext of each group of plaintext data corresponding to the original energy trace that complies with the normal distribution is determined as the sample plaintext.

7. The method according to claim 6, characterized in that The method for obtaining the energy trace of the sample plaintext includes: For any sample plaintext, perform outlier detection on multiple original energy traces of the sample plaintext to determine the presence of abnormal original energy traces; Replacing the original energy trace corresponding to the anomaly with the mean value of the multiple original energy traces to obtain the original energy trace after anomaly detection; Performing singular value decomposition denoising on the original energy trace after the anomaly detection to obtain the original energy trace after singular value decomposition denoising; Performing Gaussian mean filtering on the original energy trace after singular value decomposition and denoising to obtain the original energy trace after Gaussian mean filtering; The original energy trace after the Gaussian mean filtering is determined as the energy trace of the corresponding sample plaintext.

8. The method according to claim 7, characterized in that The performing singular value decomposition denoising processing on the original energy trace after the anomaly detection to obtain the original energy trace after singular value decomposition denoising includes: embedding all original energy traces after the anomaly detection into a Hankel matrix point by point; The Hankel matrix is ​​decomposed into a low-rank signal matrix and a noise sparse matrix by truncated singular value decomposition; The low-rank signal matrix is ​​attenuated by damping attenuation to obtain the original energy trace after singular value decomposition and denoising.

9. A side channel attack device, characterized in that: include: An encryption module is used to encrypt multiple sample plaintexts using each hypothetical key in the hypothetical key space to obtain a hypothetical intermediate value matrix; The hypothetical key space includes a plurality of hypothetical keys for an encryption device; A modeling module is used to perform Hamming weight and uneven weighted bit sum modeling on each element of the hypothetical intermediate value matrix to generate a hypothetical energy consumption matrix; Each element in the assumed energy consumption matrix represents the correlation between a sample plaintext and a hypothetical key; an analysis module, configured to perform a correlation analysis between each element of the hypothetical energy consumption matrix and the energy traces corresponding to the plurality of sample plaintexts to determine a joint decision matrix; the elements in the joint decision matrix represent a correlation ranking between each hypothetical key and the encryption device; An updating module, configured to update the hypothetical key space according to the correlation ranking in the joint decision matrix, and iteratively obtain the joint decision matrix through the updated hypothetical key space; The determination module is used to determine the hypothetical key with the highest correlation ranking in the joint decision matrix that meets the conditions as the key of the encryption device.

10. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

Images