A method and system for estimating the highest order of side channel moment information

Abstract

The present invention proposes a method and system for estimating the highest order of side channel moment information. The present invention calculates the data distribution frequency of each subinterval and the midpoint value of the subinterval; calculates the origin moment of each order in combination with the midpoint value of each subinterval, and calculates the power consumption value matrix of each order; solves by the conjugate gradient method to obtain the parameter weight vector in the maximum entropy model after solution, calculates the entropy value of each subinterval at each order, and further calculates the maximum entropy value at each order; calculates the difference between the maximum entropy values ​​of two adjacent orders, and calculates the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders. If the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders is less than a threshold, the corresponding order is used as the highest order after solution; the highest order after solution is further used to set the highest value of the moment information order used in the side channel leakage assessment, attack, and modeling process, reducing unnecessary consumption of computing resources for higher-order information.

Description

Technical Field

[0001] The present invention relates to the field of information security and is a method for side channel modeling using information entropy and moment information. The model can more accurately characterize the amount of information contained in each order moment of a leakage sample. Background Art

[0002] An accurate leakage model is needed in the side channel security assessment to evaluate the security of the cryptographic implementation in the face of side channel attacks. At present, most models for power consumption side channel assessment assume that the leakage obeys a normal distribution. However, it may not be enough to describe the leakage by only using the mean and variance of the two parameters in the model. In this case, the assumption error of the model is introduced. At the same time, the amount of data required for modeling is also an aspect that needs to be considered in the side channel security assessment. If the highest order used is lower than the required one, the modeling is not accurate enough and the variation is large. If the highest order used is higher than the required one, the computational overhead is increased. At present, the highest order of moment information used in the side channel field is relatively low, generally only up to the fourth order, and there are problems such as large model calculation overhead and easy occurrence of singular value matrix termination iteration. In order to solve the assumption error in the model, the present invention determines the highest order information required for modeling, proposes a maximum entropy modeling method, and evaluates the amount of information contained in each order moment by calculating the difference in model information entropy. Summary of the Invention

[0003] To overcome assumption errors and simultaneously measure the information contained in different moments of the leaked sample to guide modeling, this paper uses information moments as a modeling reference, establishes a maximum entropy model, uses the conjugate gradient method to introduce parameters and iterates the model, and finally determines the information content of each moment by the difference in information entropy between models. This paper proposes a method and system for estimating the highest order of side-channel moment information.

[0004] The technical solution of the method of the present invention is a method for estimating the highest order of side channel moment information, comprising the following steps:

[0005] Step 1: Use the maximum and minimum normalization method and correlation coefficient analysis method to obtain the most leaked power consumption data in each normalized power consumption data. Count the number of power consumption data with the most leaked power consumption data in each subinterval, calculate the data distribution frequency of each subinterval, and calculate the midpoint value of the subinterval.

[0006] Step 2: Calculate the origin moment of each order by combining the midpoint value of each subinterval, and calculate the power consumption value matrix of each order;

[0007] Step 3: Initialize the highest order, combine the origin moment of each order and the power consumption value matrix of each order to solve it through the conjugate gradient method, obtain the parameter weight vector in the maximum entropy model after solution, calculate the entropy value of each subinterval at each order, and further calculate the maximum entropy value at each order;

[0008] Step 4: Calculate the difference between the maximum entropy values ​​of two adjacent orders, and calculate the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders. If the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders is less than the threshold, the corresponding order is taken as the highest order after solution.

[0009] Step 5: The highest order after the solution is further used to set the maximum value of the moment information order used in the side channel leakage assessment, attack, and modeling process, reducing unnecessary higher-order information consumption of computing resources;

[0010] Step 1 is processed by the maximum and minimum normalization method and the correlation coefficient analysis method, as follows:

[0011] Acquire multiple power consumption data sequences, perform maximum and minimum normalization on each power consumption data sequence to obtain each normalized power consumption data, calculate each normalized power consumption data sequence through a correlation coefficient analysis method, and obtain the power consumption data sequence with the most obvious leakage in each normalized power consumption data sequence;

[0012] The value range of each power consumption data value in each normalized power consumption data in step 1 is [0, 1];

[0013] The range of each subinterval is:

[0014]

[0015] Where N is the number of subintervals;

[0016] The number of power consumption data with the most obvious leakage in each subinterval is counted in step 1, as follows:

[0017] Evenly divide the interval [0,1] into multiple subintervals, match the subintervals corresponding to the most obvious power consumption data in each normalized power consumption data, and count the number of power consumption data with the most obvious leakage in each subinterval;

[0018] The data distribution frequency of each subinterval counted in step 1, the data distribution frequency of the i-th subinterval is defined as p i ;

[0019] Calculate the midpoint value of each subinterval as described in step 1, as follows:

[0020]

[0021] Among them, x i is the midpoint value of the i-th subinterval;

[0022] Preferably, the calculation of the origin moment of each order in step 2 is as follows:

[0023]

[0024] Among them, μ k represents the origin moment of order k, k∈[1,K], x i is the midpoint value of the i-th subinterval, i∈[1,N], p i is the data distribution frequency of the i-th subinterval:

[0025] The power consumption matrix of each order is calculated as described in step 2, as follows:

[0026] If the first k-order origin moments are used for modeling, the details are as follows

[0027]

[0028] Among them, matrix k Represents the power consumption value matrix of order k;

[0029] Preferably, the conjugate gradient method is used to solve the matrix of the origin moment of each order and the power consumption value of each order in step 3, as follows:

[0030] Substitute the origin moment of each order and the power consumption value matrix of each order into the maximum entropy model formula in turn, as follows:

[0031] Respectively {μ2, matrix2}, {μ3, matrix3}, {μ4, matrix4}, {μ5, matrix5}, ..., {μ K , matrix K}, substitute into the maximum entropy model, K represents the highest order of initialization;

[0032] The maximum entropy model is defined as follows:

[0033]

[0034] Among them, the matrix k Substitute X into it, transpose it into μ K Substitute Y;

[0035] The parameter weight vector λ in the maximum entropy model is {λ1, λ2, λ3, ..., λ K} as the variable to be solved;

[0036] λ k Represents the k-th order parameter weight in the parameter weight vector in the maximum entropy model, k∈[1,K];

[0037] Set the maximum number of iterations and the minimum error;

[0038] The conjugate gradient method is used to perform nonlinear iterative solution on the model, and the parameter weight vector λ*={λ1*,λ2*,λ3*,……,λ K *},λ k Represents the k-th order parameter weight in the parameter weight vector of the maximum entropy model after solution, k∈[1,K];

[0039] After obtaining λ in the parameter weight, the probability formula corresponding to each interval of the maximum entropy model is as follows, where K is the maximum order corresponding to the modeling:

[0040]

[0041] The entropy value of each subinterval at each order is calculated as described in step 3, as follows:

[0042] H i,k =-p i ·log(p i )

[0043] Among them, H i,k represents the entropy value of the i-th subinterval under the k-th order, p i The corresponding probability of the i-th subinterval;

[0044] The maximum entropy value at each level is calculated as described in step 3, as follows:

[0045]

[0046] Among them, H k It represents the maximum entropy value at the kth order.

[0047] An embodiment of the system of the present invention is a side channel moment information highest order estimation system, comprising:

[0048] The sub-interval calculation module is used to obtain the most obvious power consumption data in each normalized power consumption data through the maximum and minimum normalization method and the correlation coefficient analysis method, count the number of power consumption data with the most obvious leakage in each sub-interval, calculate the data distribution frequency of each sub-interval, and calculate the midpoint value of the sub-interval;

[0049] The module for calculating the origin moment and power consumption value matrix of each order is used to calculate the origin moment of each order and the power consumption value matrix of each order by combining the midpoint value of each sub-interval;

[0050] The maximum entropy value calculation module is used to initialize the highest order, combine the origin moment of each order and the power consumption value matrix of each order to solve it through the conjugate gradient method, obtain the parameter weight vector in the solved maximum entropy model, calculate the entropy value of each subinterval at each order, and further calculate the maximum entropy value at each order;

[0051] The highest order calculation module is used to calculate the difference between the maximum entropy values ​​of two adjacent orders and the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders. If the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders is less than a threshold, the corresponding order is taken as the highest order after solution.

[0052] The maximum value calculation module of the moment information order is used to calculate the maximum order after solution, which is further used to set the maximum value of the moment information order used in the side channel leakage assessment, attack, and modeling process.

[0053] The advantages of the present invention are that it can iterate quickly when calculating the maximum entropy model, with less resource consumption, and the fitting effect of the maximum entropy model is better than the original calculation method in the KS test. The information amount of each order moment information is accurately measured, and the calculated highest order is of guiding significance for side channel modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 : Schematic diagram of the method flow of an embodiment of the present invention.

[0055] Figure 2 : An example diagram of frequency statistics and interval division of original leakage samples in an embodiment of the present invention.

[0056] Figure 3 : An example diagram of using different moment information to generate a maximum entropy model in an embodiment of the present invention.

[0057] Figure 4 : Schematic diagram of the numerical results of the maximum entropy of each order moment in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0059] In specific implementation, the method proposed in the technical solution of the present invention can be automatically run by those skilled in the art using computer software technology. System devices that implement the method, such as computer-readable storage media that store the corresponding computer program of the technical solution of the present invention and computer equipment that runs the corresponding computer program, should also be within the scope of protection of the present invention.

[0060] The core of the design idea and method of the present invention is to design a modeling method that uses moment information as the initial parameter of the model and uses information entropy modeling to solve the hypothesis error. By using different order moment constraints to participate in the modeling process, the amount of information contained in each order moment is measured and the model error is reduced.

[0061] The following is combined with Figure 1-4 The specific embodiment of the present invention is a method and system for estimating the highest order of side channel moment information, as follows:

[0062] like Figure 1 As shown, a method for estimating the highest order of side channel moment information is provided as a technical solution of an embodiment of the method of the present invention, comprising the following steps:

[0063] like Figure 1 FIG. 1 is a flow chart of a method according to an embodiment of the present invention.

[0064] Step 1: Use the maximum and minimum normalization method and correlation coefficient analysis method to obtain the most leaked power consumption data in each normalized power consumption data. Count the number of power consumption data with the most leaked power consumption data in each subinterval, calculate the data distribution frequency of each subinterval, and calculate the midpoint value of the subinterval.

[0065] Step 1 is data preprocessing, which involves normalizing the collected power consumption data and converting all the original power consumption data into values ​​between 0 and 1. Figure 2 As shown, the new frequency distribution and the corresponding frequency of each statistical interval are counted.

[0066] Step 1 is processed by the maximum and minimum normalization method and the correlation coefficient analysis method, as follows:

[0067] Acquire multiple power consumption data sequences, perform maximum and minimum normalization on each power consumption data sequence to obtain each normalized power consumption data, calculate each normalized power consumption data sequence through a correlation coefficient analysis method, and obtain the power consumption data sequence with the most obvious leakage in each normalized power consumption data sequence;

[0068] The value range of each power consumption data value in each normalized power consumption data in step 1 is [0, 1];

[0069] The range of each subinterval is:

[0070]

[0071] Where N is the number of subintervals;

[0072] The number of power consumption data with the most obvious leakage in each subinterval is counted in step 1, as follows:

[0073] Evenly divide the interval [0,1] into multiple subintervals, match the subintervals corresponding to the most obvious power consumption data in each normalized power consumption data, and count the number of power consumption data with the most obvious leakage in each subinterval;

[0074] The data distribution frequency of each subinterval counted in step 1, the data distribution frequency of the i-th subinterval is defined as p i ;

[0075] Calculate the midpoint value of each subinterval as described in step 1, as follows:

[0076]

[0077] Among them, x i is the midpoint value of the i-th subinterval;

[0078] Step 2: Calculate the origin moment of each order by combining the midpoint value of each subinterval, and calculate the power consumption value matrix of each order;

[0079] Step 2 is to calculate the moment constraints. The normalized power consumption data is used to calculate the moment constraint information of each order, and the power consumption value matrix used to generate the model is calculated. The upper limit of the order used needs to be determined based on the complexity of the frequency distribution of the leakage samples.

[0080] Step 2 calculates the origin moment of each order as follows:

[0081]

[0082] Among them, μ k represents the origin moment of order k, k∈[1,K], x i is the midpoint value of the i-th subinterval, i∈[1,N], p i is the data distribution frequency of the i-th subinterval:

[0083] The power consumption matrix of each order is calculated as described in step 2, as follows:

[0084] If the first k-order origin moments are used for modeling, the details are as follows

[0085]

[0086] Among them, matrix k Represents the power consumption value matrix of order k;

[0087] Step 3: Initialize the highest order, combine the origin moment of each order and the power consumption value matrix of each order to solve it through the conjugate gradient method, obtain the parameter weight vector in the maximum entropy model after solution, calculate the entropy value of each subinterval at each order, and further calculate the maximum entropy value at each order;

[0088] Step 3 is model calculation. Using the data generated in step 2, different amounts of moment constraint information and power consumption value matrices are brought into the pre-set program. The model is iterated nonlinearly using the conjugate gradient method, and the maximum iteration rounds and minimum error are set. The maximum entropy model generated using different amounts of moment information is obtained, as shown in the following example. Figure 3 As shown;

[0089] Step 3 combines the origin moment of each order and the power consumption value matrix of each order to solve the problem through the conjugate gradient method, as follows:

[0090] Substitute the origin moment of each order and the power consumption value matrix of each order into the maximum entropy model formula in turn, as follows:

[0091] Respectively {μ2, matrix2}, {μ3, matrix3}, {μ4, matrix4}, {μ5, matrix5}, ..., {μ K , matrix K}, substitute into the maximum entropy model, K represents the highest order of initialization;

[0092] The maximum entropy model is defined as follows:

[0093]

[0094] Among them, the matrix k Substitute X into it, transpose it into μ K Substitute Y;

[0095] The parameter weight vector λ in the maximum entropy model is {λ1, λ2, λ3, ..., λ K} as the variable to be solved;

[0096] λ k Represents the k-th order parameter weight in the parameter weight vector in the maximum entropy model, k∈[1,K];

[0097] Set the maximum number of iterations and the minimum error;

[0098] The conjugate gradient method is used to perform nonlinear iterative solution on the model, and the parameter weight vector λ*={λ1*,λ2*,λ3*,……,λ K *},λ k Represents the k-th order parameter weight in the parameter weight vector of the maximum entropy model after solution, k∈[1,K];

[0099] After obtaining λ in the parameter weight, the probability formula corresponding to each interval of the maximum entropy model is as follows, where K is the maximum order corresponding to the modeling:

[0100]

[0101] The entropy value of each subinterval at each order is calculated as described in step 3, as follows:

[0102] H i,k =-pi ·log(p i )

[0103] Among them, H i,k represents the entropy value of the i-th subinterval under the k-th order, p i The corresponding probability of the i-th subinterval;

[0104] The maximum entropy value at each level is calculated as described in step 3, as follows:

[0105]

[0106] Among them, H k It represents the maximum entropy value at the kth order.

[0107] Step 4: Calculate the difference between the maximum entropy values ​​of two adjacent orders, and calculate the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders. If the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders is less than the threshold, the corresponding order is taken as the highest order after solution.

[0108] Step 4 is model testing. Using the model generated in step 3, we perform a KS test on models generated with different amounts of moment information. To better verify the accuracy of the model, we need to generate the model multiple times and take the average value. We calculate its cumulative distribution function and compare it with the leaked samples to verify the model's fitting effect.

[0109] Step 5: The highest order after the solution is further used to set the maximum value of the moment information order used in the side channel leakage assessment, attack, and modeling process, reducing unnecessary higher-order information consumption of computing resources;

[0110] Step 5 is the information calculation. According to the models of each order generated in step 3, the maximum entropy value corresponding to the model generated using different amounts of moment information is calculated, such as Figure 4 As shown, the amount of information contained in each order moment constraint is obtained by subtracting them step by step from large to small, and the number of moment constraints required for modeling and the corresponding amount of information are obtained by comparing the results of the KS test in step 4.

[0111] Figure 2 The frequency distribution of power consumption values ​​after normalization of the original data is determined. During normalization, all values ​​must be distributed between 0 and 1, with no values ​​outside the range. Intervals with discrete distributions on either side should be excluded, ensuring that the selected intervals have as few as possible intervals with a frequency of 0. The number of intervals can be increased appropriately; a larger number of intervals results in better model fit. However, avoid subintervals with a frequency of 0 within the overall interval.

[0112] Figure 3This is the maximum entropy model fit obtained using different amounts of moment information. Different curves correspond to different amounts of moment information. In this figure, for example, up to 7th-order moment information is used. Each additional order of moment information improves the model fit. However, it is important to note that the model fit cannot be judged solely by visual observation. It should be combined with the KS test calculation model in step 4 and the cumulative distribution function of the original data to determine the model fit.

[0113] Figure 4 It is the difference between the model entropy and the original data entropy calculated after the model is obtained by using different amounts of moment information for modeling. As the order of moment information used increases, the amount of information used for modeling also increases, and the model begins to fit the distribution of the original data. The change in the information entropy difference brought about by each increase in the first-order moment constraint can represent the amount of information contained in the moment constraint of that order. For example, in this example, the information contained in the third-order moment constraint is greater than the information contained in the sixth-order moment constraint. At the same time, according to this figure, it can be judged that the information contained in the seventh-order moment constraint and higher-order constraints is no longer sufficient to bring obvious optimization to the model, which can be used to guide maximum entropy modeling.

[0114] The method for estimating the highest order of side-channel moment information of the present invention can avoid artificial assumptions in the model and reduce the model's assumption error, thereby obtaining a more accurate model. Simultaneously, modeling using moment information of different orders can effectively compare the degree of model fit and calculate the amount of information contained in each order moment constraint, quantitatively measuring the model error to a certain extent. This information can also guide the amount of data used in maximum entropy modeling. The order of the moment constraint used in the present invention can be adjusted according to the complexity of the leaked sample and does not need to be restricted to the order used in the sample.

[0115] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0116] It should be understood that the above description of the embodiments is relatively detailed and cannot be regarded as limiting the scope of protection of the patent of the present invention. Under the guidance of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which all fall within the scope of protection of the present invention. The scope of protection requested by the present invention shall be based on the attached claims.

Claims

1. A method for estimating the highest order of side channel moment information, characterized in that: The following steps are involved: Step 1: Use the maximum and minimum normalization method and correlation coefficient analysis method to obtain the most leaked power consumption data in each normalized power consumption data. Count the number of power consumption data with the most leaked power consumption data in each subinterval, calculate the data distribution frequency of each subinterval, and calculate the midpoint value of the subinterval. Step 2: Calculate the origin moment of each order by combining the midpoint value of each subinterval, and calculate the power consumption value matrix of each order; Step 3: Initialize the highest order, combine the origin moment of each order and the power consumption value matrix of each order to solve it through the conjugate gradient method, obtain the parameter weight vector in the maximum entropy model after solution, calculate the entropy value of each subinterval at each order, and further calculate the maximum entropy value at each order; Step 4: Calculate the difference between the maximum entropy values ​​of two adjacent orders, and calculate the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders. If the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders is less than the threshold, the corresponding order is taken as the highest order after solution. Step 5: The highest order after solution is further used to set the maximum value of the moment information order used in the side channel leakage assessment, attack, and modeling process, reducing unnecessary higher-order information consumption of computing resources.

2. The method for estimating the highest order of side channel moment information according to claim 1, wherein: Step 1 is processed by the maximum and minimum normalization method and the correlation coefficient analysis method, as follows: Obtain multiple power consumption data sequences, perform maximum and minimum normalization on each power consumption data sequence to obtain each normalized power consumption data, calculate each normalized power consumption data sequence through a correlation coefficient analysis method, and obtain the power consumption data with the most obvious leakage in each normalized power consumption data sequence.

3. The method for estimating the highest order of side channel moment information according to claim 2, wherein: The value range of each power consumption data value in each normalized power consumption data in step 1 is [0, 1]; The range of each subinterval is: Where N is the number of subintervals; The number of power consumption data with the most obvious leakage in each subinterval is counted in step 1, as follows: The [0,1] interval is evenly divided into multiple subintervals. The subintervals corresponding to the power consumption data with the most obvious leakage in each normalized power consumption data are matched in sequence. The number of power consumption data with the most obvious leakage in each subinterval is counted.

4. The method for estimating the highest order of side channel moment information according to claim 3, wherein: The data distribution frequency of each subinterval counted in step 1, the data distribution frequency of the i-th subinterval is defined as p i ; Calculate the midpoint value of each subinterval as described in step 1, as follows: Among them, x i is the midpoint value of the i-th subinterval.

5. The method for estimating the highest order of side channel moment information according to claim 4, wherein: Step 2 calculates the origin moment of each order as follows: Among them, μ k represents the origin moment of order k, k∈[1,K], x i is the midpoint value of the i-th subinterval, i∈[1,N], p i is the data distribution frequency of the i-th subinterval.

6. The method for estimating the highest order of side channel moment information according to claim 5, wherein: The power consumption matrix of each order is calculated as described in step 2, as follows: If the first k-order origin moments are used for modeling, the details are as follows Among them, matrix k Represents the k-order power consumption value matrix.

7. The method for estimating the highest order of side channel moment information according to claim 6, wherein: Step 3 combines the origin moment of each order and the power consumption value matrix of each order to solve the problem through the conjugate gradient method, as follows: Substitute the origin moment of each order and the power consumption value matrix of each order into the maximum entropy model formula in turn, as follows: Respectively {μ2, matrix2}, {μ3, matrix3}, {μ4, matrix4}, {μ5, matrix5}, ..., {μ K , matrix K }, substitute into the maximum entropy model, K represents the highest order of initialization; The maximum entropy model is defined as follows: Among them, the matrix k Substitute X into it, transpose it into μ K Substitute Y; The parameter weight vector λ in the maximum entropy model is {λ1, λ2, λ3, ..., λ K } as the variable to be solved; λ k Represents the k-th order parameter weight in the parameter weight vector in the maximum entropy model, k∈[1,K]; Set the maximum number of iterations and the minimum error.

8. The method for estimating the highest order of side channel moment information according to claim 7, wherein: The conjugate gradient method is used to perform nonlinear iterative solution on the model, and the parameter weight vector λ*={λ1*,λ2*,λ3*,……,λ K *}, λ k Represents the k-th order parameter weight in the parameter weight vector of the maximum entropy model after solution, k∈[1,K]; After obtaining λ in the parameter weight, the probability formula corresponding to each interval of the maximum entropy model is as follows, where K is the maximum order corresponding to the modeling:

9. The method for estimating the highest order of side channel moment information according to claim 8, wherein: The entropy value of each subinterval at each order is calculated as described in step 3, as follows: H i,k =-p i ·log(p i ) Among them, H i,k represents the entropy value of the i-th subinterval under the k-th order, p i The corresponding probability of the i-th subinterval; The maximum entropy value at each level is calculated as described in step 3, as follows: Among them, H k It represents the maximum entropy value at the kth order.

10. A side channel moment information highest order estimation system, characterized by: include: The sub-interval calculation module is used to obtain the most obvious power consumption data in each normalized power consumption data through the maximum and minimum normalization method and the correlation coefficient analysis method, count the number of power consumption data with the most obvious leakage in each sub-interval, calculate the data distribution frequency of each sub-interval, and calculate the midpoint value of the sub-interval; The module for calculating the origin moment and power consumption value matrix of each order is used to calculate the origin moment of each order and the power consumption value matrix of each order by combining the midpoint value of each sub-interval; The maximum entropy value calculation module is used to initialize the highest order, combine the origin moment of each order and the power consumption value matrix of each order to solve it through the conjugate gradient method, obtain the parameter weight vector in the solved maximum entropy model, calculate the entropy value of each subinterval at each order, and further calculate the maximum entropy value at each order; The highest order calculation module is used to calculate the difference between the maximum entropy values ​​of two adjacent orders and the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders. If the absolute value of the difference between the maximum entropy values ​​of two consecutive groups of adjacent orders is less than a threshold, the corresponding order is taken as the highest order after solution. The maximum value calculation module of the moment information order is used to calculate the maximum order after solution, which is further used to set the maximum value of the moment information order used in the side channel leakage assessment, attack, and modeling process.

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