Diithium rapid side channel attack analysis method

Abstract

The invention discloses a Diithium rapid side channel attack analysis method, which belongs to the technical field of information security, and comprises the following steps of: detecting leakage by adopting a Gaussian mixture difference method to complete detection and selection of feature points; the signature information is used to classify the actual leakage in which the private key participates, and the distribution difference is used to recover the normal domain private key. According to the method, the problem of high time overhead under small sample leakage of the existing non-template attack is solved. A complete private key can be recovered within a few minutes at a high noise level by using side information leakage generated by a small amount of signatures. Compared with an existing leakage detection method, the Gaussian mixture difference method can complete detection and selection of feature points without obtaining a sensitive intermediate value. The method can be used for detecting whether the password equipment and the password chip are safe and reliable or not, such as the fields of bank cards of financial economy, physical digital currency cards, mobile phone chips of mobile communication and the like, so as to detect whether the equipment has security risks or not.

Description

Technical Field

[0001] The present invention belongs to the field of information security technology, and in particular relates to a Dilithium fast side channel attack analysis method. Background Art

[0002] Quantum computers have developed rapidly in recent years. Once a general-purpose quantum computer is successfully developed, traditional public key cryptographic algorithms based on difficult problems such as large integer factorization and discrete logarithms using the quantum algorithm proposed in 1994 may be cracked in polynomial time, and widely deployed cryptographic systems will face huge risks.

[0003] In order to meet the challenges of the quantum computing era, the National Institute of Standards and Technology of the United States issued a global solicitation announcement for post-quantum public key cryptographic algorithm standards in December 2016. The first batch of PQC standard documents were announced in August 2024, including the signature standard algorithm DL-DSA (formerly known as CRYSTALS-Dilithium, hereinafter referred to as Dilithium), SLH-DSA (formerly known as SPHINCS+), and the key encapsulation standard algorithm ML-KEM (formerly known as CRYSTALS-Kyber). To ensure timely response to the threats posed by quantum computing, countries are stepping up the research and implementation of post-quantum cryptography.

[0004] Although post-quantum algorithms have the ability to resist attacks from traditional computers and quantum computing in theory, they will inevitably be subject to actual attacks during algorithm implementation and actual deployment. The most typical and common type of actual attack is side channel analysis. Side channel analysis will actively or passively generate various forms of information leakage during the operation of cryptographic devices and platforms, and directly or indirectly obtain secret information during the operation of the chip by combining cryptography and statistics knowledge.

[0005] The cryptography community and the chip industry have long reached a broad consensus on the significant and real threat posed by side-channel attacks to the security of cryptographic implementations, and have proposed specific security requirements and recommended evaluation processes. For example, China's "Security Chip Cryptography Testing Guidelines" GM / T 0008-2012 and "Cryptographic Module Security Technical Requirements" GM / T0028-2014 clearly stipulate that cryptographic modules must have security protection capabilities against typical side-channel attacks (including energy analysis attacks, electromagnetic analysis attacks, and timing attacks, etc.).

[0006] Therefore, studying the ability of Dilithium, the first batch of standard post-quantum signature algorithms, to resist side-channel analysis is of great significance to the actual security of public key cryptographic systems in the post-quantum era, and will promote the development and application of post-quantum cryptographic technology. Summary of the invention

[0007] The technical problem solved by the present invention is: to provide a Dilithium fast side channel attack analysis method for ARM platform that can detect and select feature points without obtaining sensitive intermediate values, and can be used to detect whether the cryptographic device and cryptographic chip are safe and reliable.

[0008] Technical solution: In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0009] A Dilithium fast side channel attack analysis method uses Gaussian mixture difference method to detect CS leakage, completes the detection and selection of feature points; uses signature information to classify the actual leakage involved in the private key, and uses the difference in distribution to restore the normal domain private key. Specifically, it includes the following steps:

[0010] S1: Collect the power consumption curve of the cryptographic device platform running Dilithium and obtain the corresponding signature information c;

[0011] S2: Use static alignment to align and segment the power consumption curves for subsequent analysis;

[0012] S3: Use Gaussian mixture model difference method to detect feature points of power consumption curve and determine cs 1 and cs 2 Feature points that can be used for side channel analysis;

[0013] S4: For recovering the i-th private key coefficient s i , classify the side information leakage of the feature point according to whether the i-th coefficient in the signature information c is 1 or -1, and calculate the difference between the non-negative and negative numbers of the two types of data after classification and record them as s i The corresponding results;

[0014] S5: Loop through step S4 until all private keys s are obtained. 1 ,s 2 The coefficient results of

[0015] S6: Use Gaussian mixture model to identify the private key s 1 ,s 2 The coefficient results are classified and the specific value of each coefficient is given, and finally the complete private key is recovered.

[0016] Furthermore, in step S3, after the complete leakage information is obtained, a Gaussian mixture model is used to fit the data, the overall distribution is split into two Gaussian distributions, and the expected values ​​corresponding to the two Gaussian distributions are calculated.

[0017] Furthermore, the overall energy leakage model of cs is:

[0018]

[0019] in, and They represent the overall leakage distribution when cs is non-negative and negative, L(x) represents the leakage model corresponding to the value x, P(x) is the probability of occurrence of different x, and is a fixed coefficient

[0020] Furthermore, in step S4, the classification of feature points includes the following three types:

[0021] When c i =1, the linear combination is

[0022] When c i = 0, the linear combination is

[0023] When c i = -1, the linear combination is

[0024] Furthermore, the distribution of three groups of data is calculated according to the classification of feature points:

[0025]

[0026] Where N represents Gaussian distribution, s i Represents the i-th coefficient in the private key;

[0027] For energy leakage, there are the following forms:

[0028]

[0029] Where i represents the i-th coefficient of the private key and signature c, and x represents cs 1 and cs 2 Possible value range, P(xc i s i ) means cs 1 and cs 2 The probability of each possible value of the coefficient outcome.

[0030] Furthermore, record The difference in the number of samples within the interval is calculated using The difference in the number of samples within the interval is used to recover s i ; First calculate In the interval, c i = -1 and c i =1, denoted as Δ ni ; Then calculate In the interval, ci =1 and c i = -1 is recorded as Δ pi ; will eventually Recorded as s i The corresponding sum difference sample size.

[0031] Furthermore, after obtaining all Finally, a Gaussian mixture model is used to complete classification; through the expectation maximization algorithm, the expectation, variance and weight of each Gaussian distribution are iteratively estimated to find the optimal parameters.

[0032] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0033] (1) The present invention uses Dilithium's signature information c to 1 and cs 2 The actual leaks are classified and the differences in distribution are used to recover the Dilithium normal domain private key, which solves the problem of high time overhead under small sample leaks of existing non-template attacks. The side information leaks generated by a small number of signatures can recover the Dilithium complete private key within minutes under high noise levels.

[0034] (2) In the actual side channel analysis process, the attacker needs to determine the exact leakage location of the target data. The present invention proposes a Gaussian mixture difference method for detecting CS leakage. Compared with the existing leakage detection method, the detection and selection of feature points can be completed without obtaining sensitive intermediate values.

[0035] (3) The present invention uses Dilithium's signature information c to 1 and cs 2 The actual leakage is classified and the difference in distribution is used to quickly determine the private key. Compared with the common non-template side channel analysis that determines the correct private key by enumerating all candidate values, the present invention does not need to enumerate all candidate values.

[0036] (4) The present invention can still complete fast private key recovery with a small amount of leakage even when the noise level of information leakage on the acquisition side is high. By combining multiple feature points, the present invention is still effective under high noise levels and can be applied to actual attacks on ARM platforms in different actual scenarios.

[0037] (5) The present invention can be used to analyze cryptographic devices that deploy the Dilithium algorithm to detect whether the cryptographic device is safe and reliable. Specifically, it can be applied to the reliability detection of cryptographic chips, such as bank cards in the financial economy, physical digital currency cards, and mobile phone chips in mobile communications, to detect whether the device has security risks.

[0038] (6) The Dilithium fast side channel attack analysis method of the present invention focuses on the actual side channel analysis of Dilithium and provides suggestions for the secure deployment of post-quantum cryptography. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is an overall flow chart of the method of the present invention;

[0040] Figure 2 Part of the power consumption curve graph collected by the present invention;

[0041] Figure 3 This is a comparison diagram of feature point detection using the Gaussian mixture model difference method of the present invention;

[0042] Figure 4 For the present invention 0 = -2, according to c i =1,-1 distribution diagram of power consumption curve after classification;

[0043] Figure 5 For the present invention 0 = -1, according to c i =1,-1 distribution diagram of power consumption curve after classification;

[0044] Figure 6 For the present invention 0 = 0, according to c i =1,-1 distribution diagram of power consumption curve after classification;

[0045] Figure 7 For the present invention 0 = 1, according to c i =1,-1 distribution diagram of power consumption curve after classification;

[0046] Figure 8 For the present invention 0 =2, according to c i =1,-1Distribution diagram of power consumption curve after classification. DETAILED DESCRIPTION

[0047] The present invention is further illustrated below in conjunction with specific examples. The examples are implemented based on the technical solutions of the present invention. It should be understood that these examples are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0048] Example 1

[0049] like Figure 1As shown, this embodiment discloses a Dilithium fast side channel attack analysis method implemented on the ARM platform. This method is a new type of non-template side channel attack method. By using the signature information c of Dilithium, the cs involved in the private key is analyzed. 1 and cs 2 The actual leakage is classified and the difference in distribution is used to recover the Dilithium normal domain private key, which solves the problem of high time overhead under small sample leakage of existing non-template attacks. Using the side information leakage generated by a small number of signatures, the Dilithium complete private key can be recovered within minutes under high noise levels. The specific steps include:

[0050] S1: Collect the power consumption curve of the cryptographic device platform running Dilithium and obtain the corresponding signature information c;

[0051] S2: Use the static alignment method recognized in the side channel field to align and segment the power consumption curves for subsequent analysis;

[0052] S3: Use Gaussian mixture model difference method to detect feature points of power consumption curve and determine cs 1 and cs 2 Feature points that can be used for side channel analysis;

[0053] S4: For recovering the i-th private key coefficient s i (vector s 1 ,s 2 Contains multiple elements, each element contains 256 polynomial coefficients), classifies the side information leakage of the feature point according to whether the i-th coefficient in the signature information c is 1 or -1, and calculates the difference between the non-negative and negative numbers of the two types of data after classification and records them as s i The corresponding results;

[0054] S5: Loop through step S4 until all private keys s are obtained. 1 ,s 2 The coefficient results of

[0055] S6: Use the Gaussian mixture model proposed in the present invention to identify the private key s 1 ,s 2 The coefficient results are classified and the specific value of each coefficient is given, and finally the complete private key is recovered.

[0056] Example 2

[0057] Based on Example 1, this example provides a more preferred implementation method.

[0058] In step S1, the power consumption curve of the cryptographic device platform running Dilithium2 is collected, and the corresponding signature information c is obtained; in this embodiment, the Dilithium reference implementation is compiled and run on the ARM Cortex-M4 platform recommended by the National Institute of Standards and Technology of the United States, and the power consumption curve of cs is collected by an oscilloscope. 1 and cs 2 The power consumption curve of the operation, where cs 1 and cs 2 Represents signature c and private key s respectively 1 ,s 2 Polynomial rings in finite fields The multiplication result appears in the Dilithium signature process.

[0059] Step S2: Use the static alignment method recognized in the side channel field to align and segment the power consumption curve for subsequent analysis;

[0060] In this embodiment, the collected information about cs 1 and cs 2 After the power consumption curve is obtained, the power consumption curve is segmented using the static alignment method, that is, a small part of the power consumption curve is first selected, and then the Pearson correlation coefficient of the power consumption curve of this part and the power consumption curve at different time points is calculated, and the larger time point in an interval is used as the segmentation point. Finally, the power consumption curve can be segmented, such as Figure 2 shown.

[0061] Step S3: Use the Gaussian mixture model difference method to detect the characteristic points of the power consumption curve and determine cs 1 and cs 2 Feature points that can be used for side channel analysis;

[0062] Among the 256 coefficients of the signature information c in Dilithium, only a few τ are 1 or -1, and the rest are 0. The value range of each coefficient of its private key also obeys the uniform distribution on [-η,η], so cs can be calculated. 1 and cs 2 The distribution of each coefficient in is a Gaussian distribution with the following parameters:

[0063]

[0064] Among them, E[cs] represents expectation, cs represents signature c and private key s 1 ,s 2 Polynomial rings in finite fields The variable consisting of the multiplication result of i represents the i-th coefficient of the signature information c; s irepresents the i-th coefficient in the private key; Var[cs] represents the variance; τ represents the number of non-zero elements in the signature information c in Dilithium, and η represents the value range of each coefficient of the private key in Dilithium.

[0065] In the 32-bit ARM platform recommended by NIST, the calculation and storage of cs are all completed in the form of complement code, so for different values ​​in t 0 The energy leakage model at the moment can be expressed as:

[0066]

[0067] Among them, a t0 Indicates t 0 The proportional coefficient at the time, x represents the actual value of cs, b t0 Indicates t 0 The constant variable at time, δ t0 Indicates t 0 The variance of the Gaussian noise at time , HW represents the Hamming weight of the corresponding value.

[0068] The overall energy leakage model of CS in statistical sense can be obtained from this:

[0069]

[0070] in, and Represents the overall leakage distribution when cs is non-negative (including 0 and positive) and negative. Since the leakage model L(x) is Gaussian distribution, P(x) represents the probability of x appearing, which is a fixed coefficient. The linear combination of multiple Gaussian distributions still obeys Gaussian distribution. and

[0071] Therefore, after obtaining the complete leakage information, the Gaussian mixture model is used to fit the data, splitting the overall distribution into two Gaussian distributions and calculating and The expectation corresponding to the distribution when The larger the value, the more and The smaller the distribution overlap is, the method is named Gaussian mixture difference method in the present invention.

[0072] In this embodiment, after the power consumption curve is collected and segmented, the Gaussian mixture model difference method of the present invention is used to determine the feature points. Figure 3 As shown in the figure, the calculation results using 1,000 samples are shown. The blue curve is the Gaussian mixture model difference method, and the red curve is the Hamming weight model. 1 and cs2 The Pearson correlation coefficient of the value and the power consumption curve is a common deterministic leakage detection method in side channel analysis.

[0073] pass Figure 3 The analysis shows that the Gaussian mixture model difference method accurately detects the most significant leakage, that is, the interval between sampling points 280 and 400. The Pearson correlation coefficient is very high in the interval between sampling points 400 and 500, but the Gaussian mixture model difference method detects a small leakage level, which means that there is a significant leakage in this interval, but after fitting and The expected difference of the distributions is small and there is overlap, which is not conducive to subsequent analysis.

[0074] Step S4: Recover the i-th private key coefficient s i , classify the side information leakage of the feature point according to whether the i-th coefficient in the signature information c is 1, 0 or -1, and calculate the difference between the non-negative and negative numbers of the two types of data after classification and record them as s i The corresponding results.

[0075] The specific contents are:

[0076] When c i =1, the linear combination is

[0077] When c i = 0, the linear combination is

[0078] When c i = -1, the linear combination is

[0079] Obviously, the main difference between the three classifications is the existence of 0 The constant offset of , analogous to the previous derivation process, the distributions of the three sets of data are:

[0080]

[0081] Where N represents Gaussian distribution, s i Represents the i-th coefficient in the private key;

[0082] For energy leakage, there are the following forms:

[0083]

[0084] Among them, i represents the i-th coefficient of the private key and signature information c, and x represents cs 1 and cs 2 Possible value range, P(xc i si ) means cs 1 and cs 2 The probability of each possible value of the coefficient outcome.

[0085] When c i s i >0 o'clock, The amount of data will increase. The amount of data will decrease, and the amount of change will increase as the value increases. i s i When <0, the opposite result will be obtained, which can help the attacker to determine s i The value of .

[0086] Next record The difference in the number of samples within the interval. The difference in the number of samples within the interval is used to recover s i .

[0087] First calculate In the interval, c 0 = -1 and c 0 =1, recorded as:

[0088]

[0089] Then calculate In the interval, c 0 =1 and c 0 =-1 is recorded as:

[0090]

[0091] Eventually Recorded as s 0 The corresponding sum difference sample size.

[0092] In this embodiment, the characteristic points where leakage is more significant (corresponding to Figure 3 Point Index = 316), s 0 =-2,-1,0,1,2, according to c i =1,-1The power consumption distribution after the power consumption curve is classified, the results are Figures 4 to 8 As shown. The horizontal axis is power consumption, i.e., energy leakage, and the vertical axis is the number of samples with the energy leakage. It can be found that the actual leakage can be clearly divided into two parts, where the left side represents the non-negative leakage, i.e. The right-hand bit represents the leakage of negative numbers, that is, When 0 = -2, if attached Figure 4 As shown, in Part c0 = -1 obviously has more samples. Part c 0 = 1, the sample size will be larger. 0 = -1, if attached Figure 5 As shown, in Part c 0 = -1 also has more categories, but now at c 0 =1 is smaller than s 0 = -2, it becomes smaller. The same results are obtained for the 0 = 0, as shown in the figure Figure 6 As shown, c 0 =1, -1 are almost the same. 0 The results when =1,2 are as shown in the attached Figure 7 , as shown in 8, its distribution is exactly opposite to the negative case.

[0093] S5: Loop through step S4 until all private keys s are obtained. 1 ,s 2 The coefficient results of

[0094] In this embodiment, by analogy with step S4, for different c i Classify, and then attack to get all

[0095] Circular calculation Private Keys 1 ,s 2 All coefficients of get corresponding values. Under high noise level, the actual analysis can be completed by combining multiple noise points.

[0096] S6: Use Gaussian mixture model to identify the private key s 1 ,s 2 The coefficient results are classified and the specific value of each coefficient is given, and finally the complete private key is recovered.

[0097] In getting all Finally, a Gaussian mixture model is used to complete This method is a very mature probability-based clustering technology, based on the assumption that data is composed of a linear combination of multiple Gaussian distributions. Its basic principle is to iteratively estimate the expectation, variance, and weight of each Gaussian distribution through the expectation maximization algorithm to find the optimal parameters. It is very suitable for clustering tasks in scenarios where data has overlapping features in this attack.

[0098] Gaussian mixture model (GMM) models the distribution of data through a weighted combination of multiple Gaussian distributions. Suppose there is a data set X containing N data points = {x1 ,x 2 ,...,x N}, each data point is a D-dimensional vector The parameters of the GMM model include the mixing coefficient π of each Gaussian distribution k (representing the weight of the distribution), the mean vector μ k and the covariance matrix Σ k The goal is to estimate these parameters by maximizing the log-likelihood function so that the model can best fit the data. Since the log-likelihood function is nonlinear, the commonly used optimization method is the expectation maximization (EM) algorithm.

[0099] The EM algorithm performs optimization in an iterative manner, which includes two main steps: the expectation step (E step) and the maximization step (M step). In the E step, based on the current parameters Calculate for each data point x i The posterior probability of belonging to each Gaussian distribution, i.e., the responsibility γ ik , where m represents the number of iterations. Responsibility γ ik Represents data point x i The probability of belonging to the kth Gaussian distribution is calculated as:

[0100]

[0101] in, is the probability density function of the kth Gaussian distribution, and its specific form is:

[0102]

[0103] In the M step, the responsibility degree γ calculated in the E step is used ik , update the parameters of the model. First, update the mixing coefficient π of each Gaussian distribution k :

[0104]

[0105] Next, update the mean μ of each Gaussian distribution k :

[0106]

[0107] Finally, the covariance matrix Σ of each Gaussian distribution is updated k :

[0108]

[0109] In the formula, m represents the number of iterations.

[0110] The EM algorithm will continue to repeat the E step and the M step until the log-likelihood function converges or reaches the preset maximum number of iterations. Each iteration will increase the value of the log-likelihood function, so that the parameters gradually approach the optimal solution. Through this iterative optimization process, the EM algorithm can eventually find the model parameters that maximize the log-likelihood, so that the GMM fits the data optimally.

[0111] In this embodiment, since the private key of Dilithium2 has only five values, namely -2, -1, 0, 1, and 2, and the overall distribution obeys Gaussian distribution, after obtaining all Δ si Finally, the Gaussian mixture model is executed to cluster the data, obtain the classification results, and then recover the complete private key.

[0112] Table 1 shows the attack success rate of different security levels of Dilithium in this embodiment. A 100% success rate can be obtained under a small amount of power consumption curve. Table 2 shows the time to recover the complete private key. The complete private key can be recovered within 1 minute. The present invention is still effective in scenarios with high noise levels (corresponding to low signal-to-noise ratios). Table 3 shows the actual attack results of Dilithium2 under different signal-to-noise ratios.

[0113] Table 1 Dilithium2,3,5 attack success rate (%)

[0114]

[0115] Table 2 Dilithium2,3,5 single feature point attack time (s)

[0116]

[0117]

[0118] (Note: The superscript * indicates that the private key can be recovered with a 100% success rate at this time)

[0119] Table 3 Dilithium2 multi-feature point attack success rate with different signal-to-noise ratios (%)

[0120]

[0121] Starting from the implementation security of the post-quantum cryptographic algorithm Dilithium, the present invention proposes an actual attack on the Dilithium algorithm based on the ARM platform. The existing non-template side channel analysis for Dilithium has a large attack time overhead when there is less side information leakage. Under high noise levels, the existing non-template attack methods require a large amount of side information leakage, while the present invention requires very little side information leakage. The existing non-template attacks do not have a clear feature point selection method, and a new feature point detection method is invented. The present invention has the characteristics of low attack time overhead, low amount of side information leakage required, accurate feature points, and is still applicable to high noise levels. It can quickly complete the actual analytical analysis implemented by Dilithium in low leakage scenarios.

[0122] The implementation method of the present invention is applicable to Dilithium implementation based on ARM platform, as well as other cryptographic analysis platforms based on pre-charge architecture.

[0123] Example 3

[0124] An electronic device includes: at least one processor; and a memory, wherein the memory stores instructions, and when the instructions are executed by the at least one processor, the at least one processor executes the Dilithium fast side channel attack analysis method of Example 1 or Example 2.

[0125] Example 4

[0126] A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the Dilithium fast side channel attack analysis method of Example 1 or Example 2 are implemented.

[0127] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A Dilithium fast side channel attack analysis method, characterized by: The Gaussian mixture difference method is used to detect the leakage of CS and complete the detection and selection of feature points; the signature information is used to classify the actual leakage involved in the private key, and the difference in distribution is used to restore the normal domain private key.

2. The Dilithium fast side channel attack analysis method according to claim 1, characterized in that: The specific steps include: S1: Collect the power consumption curve of the cryptographic device platform running Dilithium and obtain the corresponding signature information c; S2: Use static alignment to align and segment the power consumption curves for subsequent analysis; S3: Use the Gaussian mixture model difference method to detect feature points of the power consumption curve and determine the feature points of cs1 and cs2 that can be used for side channel analysis; S4: For recovering the i-th private key coefficient s i , classify the side information leakage of the feature point according to whether the i-th coefficient in the signature information c is 1 or -1, and calculate the difference between the non-negative and negative numbers of the two types of data after classification and record them as s i The corresponding results; S5: Execute step S4 repeatedly until the coefficient results of all private keys s1 and s2 are obtained; S6: Use the Gaussian mixture model to classify the coefficient results of private keys s1 and s2, give the specific value of each coefficient, and finally complete the recovery of the complete private key.

3. The Dilithium fast side channel attack analysis method according to claim 2, characterized in that: In step S3, after obtaining the complete leakage information, a Gaussian mixture model is used to fit the data, the overall distribution is split into two Gaussian distributions, and the expected values ​​corresponding to the two Gaussian distributions are calculated.

4. The Dilithium fast side channel attack analysis method according to claim 3, characterized in that: The overall energy leakage model of cs is: in, and They represent the overall leakage distribution when cs is non-negative and negative, respectively. L(x) represents the leakage model corresponding to the value x. P(x) represents the probability of x appearing, which is a fixed coefficient.

5. The Dilithium fast side channel attack analysis method according to claim 2, characterized in that: In step S4, for the i-th coefficient s in the private key i There are three types of feature points: When c i =1, the linear combination is When c i = 0, the linear combination is When c i = -1, the linear combination is 6. The Dilithium fast side channel attack analysis method according to claim 5, characterized in that: Calculate the distribution of three groups of data based on the classification of feature points: Where N represents Gaussian distribution, s i Represents the i-th coefficient in the private key; For energy leakage, there are the following forms: Where i represents the i-th coefficient of the private key and signature c, x represents the possible value range of cs1 and cs2, P(xc i s i ) represents the probability of each coefficient result of cs1 and cs2.

7. The Dilithium fast side channel attack analysis method according to claim 6, characterized in that: Record The difference in the number of samples within the interval is calculated using The difference in the number of samples within the interval is used to recover s i ; First calculate In the interval, c i = -1 and c i =1, denoted as Δ ni ; Then calculate In the interval, c i =1 and c i = -1 is recorded as Δ pi ; will eventually Recorded as s i The corresponding sum difference sample size.

8. The Dilithium fast side channel attack analysis method according to claim 2, characterized in that: In getting all Finally, a Gaussian mixture model is used to complete classification; through the expectation maximization algorithm, the expectation, variance and weight of each Gaussian distribution are iteratively estimated to find the optimal parameters.

9. An electronic device, characterized in that: include: at least one processor; And a memory, the memory storing instructions, when the instructions are executed by the at least one processor, the at least one processor executes the Dilithium fast side channel attack analysis method as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the Dilithium fast side-channel attack analysis method as described in any one of claims 1 to 8.

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