Out-of-band signal analysis method, electronic equipment and medium

Abstract

The invention discloses an out-of-band signal analysis method, electronic equipment and a medium. The out-of-band signal analysis method comprises the following steps: acquiring a known information column vector and an out-of-band signal matrix generated when a cryptographic algorithm runs for t times; performing high-order combination on the out-of-band signal points in each row in the out-of-band signal matrix to obtain a combined signal column vector, and sequencing to obtain a sequence number vector; and selecting a correlation operation and a signal simulation function of column vectors of to-be-analyzed information and known information in a cryptographic algorithm. For each candidate value of a to-be-analyzed information guessing space in a cryptographic algorithm, an analog signal column vector is calculated based on correlation operation and a signal analog function. And calculating a Pearson correlation coefficient of each analog signal column vector and a serial number vector to obtain a score of each candidate quantity, and selecting a candidate value corresponding to the score with the maximum absolute value as a guess value with analysis information. And finally analyzing to obtain target information.

Description

Technical Field

[0001] The present invention belongs to the field of out-of-band signal analysis, and in particular relates to an out-of-band signal analysis method, electronic equipment, and a medium. Background Art

[0002] In the field of out-of-band signal analysis, in order to prevent the leakage of information corresponding to the out-of-band signal, such as the cryptographic algorithm, some strategies and methods that increase the difficulty of analysis are added to the cryptographic algorithm. Among them, a type of strategy that has a relatively large influence and is recognized to be effective is called "masking". "Masking" means splitting the sensitive variable x in the algorithm operation process into n "shared" variables, so that through any of d(d <n)个“分摊”变量无法得知敏感变量x的信息。我们将敏感变量x到n个分摊变量的映射称为编码函数。我们将d的最大值称为探测模型下的安全阶d max One has d max The masking scheme of the order security can enable d max The high-order analysis of out-of-band signals based on the Pearson correlation coefficient is completely ineffective at d max Higher-order analysis of out-of-band signals based on Pearson correlation coefficients of order +1 and above is still available.

[0003] Boolean masking is the simplest and easiest to implement masking scheme because its encoding function consists only of XOR operations. In addition to XOR operations, encoding functions can also be composed of more complex algebraic operations, such as multiplication masks, affine masks, polynomial masks, and inner product masks. More complex algebraic operations mean smaller leakage than Boolean masks, and therefore are more difficult to parse through out-of-band signals. Among them, some complex algebraic masks represented by inner product masks have the characteristic of "safe order amplification" under the condition that the out-of-band signal is leaked as a linear function (hereinafter referred to as linear leakage). "Safe order amplification" refers to the existence of certain d max A masking scheme that is secure by order, which can enable d max +1 level or even d max The high-order analysis of out-of-band signals based on the Pearson correlation coefficient above +1 completely fails, which greatly increases the difficulty of analyzing out-of-band signals. Summary of the invention

[0004] The purpose of the present invention is to provide an out-of-band signal analysis method, electronic device and medium in view of the deficiencies in the prior art.

[0005] The objective of the present invention is achieved through the following technical solutions:

[0006] In a first aspect, an embodiment of the present invention provides an out-of-band signal analysis method, the method comprising:

[0007] Get the cryptographic algorithm The known information column vector generated by running t times and the cryptographic algorithm The out-of-band signal matrix T generated by running t times on the electronic device;

[0008] Perform high-order combination on all out-of-band signal points in each row of the out-of-band signal matrix T to obtain a combined signal column vector For the combined signal column vector Perform sorting to obtain a sequence number vector

[0009] Select the cryptographic algorithm in which is related to the information to be analyzed the known information column vector related operation S; and select a signal simulation function f;

[0010] For the cryptographic algorithm the guess space of the information to be analyzed For each candidate value k, based on the related operation S and the signal simulation function f, calculate the corresponding simulated signal column vector Calculate each simulated signal column vector and the sequence number vector Pearson correlation coefficient, so as to obtain a score d; according to the score d, select the candidate value k corresponding to the score with the largest absolute value as the output information to be analyzed.

[0011] In a second aspect, an embodiment of the present invention provides an electronic device, including a memory and a processor, the memory is coupled to the processor; wherein, the memory is used to store program data, and the processor is used to execute the program data to implement the above out-of-band signal parsing method.

[0012] In a third aspect, an embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the above out-of-band signal parsing method is implemented.

[0013] In a fourth aspect, an embodiment of the present invention provides a computer program product, including computer programs / instructions, and when the computer programs / instructions are executed by a processor, the above out-of-band signal parsing method is implemented.

[0014] Compared with the prior art, the beneficial effects of the present invention are:

[0015] The present invention provides a method for out-of-band signal analysis. By analyzing the out-of-band signal information during the operation of a cryptographic algorithm on an electronic device, combining analog signal functions and correlation analysis, and integrating the advantages of Pearson correlation coefficient and Spearman correlation coefficient, the accuracy and efficiency of out-of-band signal analysis are effectively improved. The method of the present invention can break through the "security order amplification" characteristic and successfully analyze a complex algebraic masking of order d under a detection model with a computational complexity of d max +1 under linear leakage conditions, greatly improving the analysis ability and efficiency of out-of-band signal analysis. max order secure complex algebraic masking, greatly enhancing the analysis ability and efficiency of out-of-band signal parsing. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0017] Figure 1 is a flowchart of the out-of-band signal analysis method provided by the embodiment of the present invention;

[0018] Figure 2 is a schematic diagram of an electronic device provided by the embodiment of the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0020] It should be noted that, without conflict, the features in the following embodiments and implementation manners can be combined with each other.

[0021] As Figure 1 shown, the embodiment of the present invention provides an out-of-band signal analysis method, which is applicable to any high-order analysis of out-of-band signals for cryptographic algorithms, especially for analyzing complex algebraic masking schemes with the "security order amplification" characteristic; the method includes the following steps:

[0022] Step S1, obtaining the known information column vector generated by running the cryptographic algorithm t times and the out-of-band signal matrix T with t rows and d + 1 columns generated by running the cryptographic algorithm t times on an electronic device.

[0023] Among them, the cryptographic algorithm is a cryptographic algorithm protected by a mask with an encoding function f enc The cryptographic algorithm has a guess space for the information to be parsed as

[0024] The expression of the encoding function f Enc is as follows:

[0025]

[0026] Among them, is a variable in the cryptographic algorithm ; is the Galois field; is a d + 1-dimensional spreading factor vector and satisfies The encoding function f Enc ensures that any d spreading factors extracted from the spreading factor vector will not leak any information related to x; The encoding function f Enc has a corresponding decoding function f Dec such that

[0027] Furthermore, the known information column vector is the plaintext information or ciphertext information of the cryptographic algorithm . The out-of-band signal matrix T is, when the cryptographic algorithm runs on an electronic device, through tools such as an oscilloscope for analog-to-digital conversion, converting the physical out-of-band signals generated during its operation, such as power consumption, electromagnetic, etc., into data that can be processed on the electronic device.

[0028] The element value of the out-of-band signal matrix T is T i,j ; The element value of the known information column vector is 1 ≤ i ≤ t, 1 ≤ j ≤ d + 1. corresponds one-to-one with each row of T; 1 ≤ i ≤ t.

[0029] Step S2, perform high-order combination on all out-of-band signal points in each row of the out-of-band signal matrix T to obtain a combined signal column vector Perform sorting processing on the combined signal column vector to obtain a sequence number vector

[0030] Specifically, through a combination function C, perform high-order combination on d + 1 out-of-band signal points in each row of the out-of-band signal matrix T to obtain a combined signal column vector of dimension t​​ Among them, the \(i\)-th element in the combined leakage column vector where \(d + 1\) is the number of columns of the out-of-band signal matrix \(T\).

[0031] Furthermore, the process of sorting the combined signal column vector to obtain the sequence number vector includes:

[0032] Sort all the element values of the combined signal column vector in ascending order, label the sequence number of its minimum value as 1, ……, until the sequence number of the maximum value is labeled as \(t\); calculate the expectation \(e\) of the sequence numbers of the elements with the same value in the combined signal column vector , and label the sequence numbers of these elements as the corresponding expectation \(e\), thereby obtaining the sequence number vector

[0033] Exemplarily, assume that the combined signal column vector Sort all the element values of the combined signal column vector in ascending order to get \(\{1, 1, 2, 3, 6, 6, 6, 6, 8, 9, 9, 9\}\), calculate the expectation \(e\) of the sequence numbers of the elements with the same value in the combined leakage column vector , and label the sequence numbers of these elements as the corresponding expectation \(e\), thereby obtaining the sequence number vector

[0034] Step S3, select the cryptographic algorithm and the relevant operation \(S\) with the information to be analyzed the known information column vector ; and select a signal simulation function \(f\).

[0035] Step S4, for each candidate value \(k\) in the guess space of the information to be analyzed in the cryptographic algorithm , calculate the corresponding simulated signal column vector with dimension \(t\) based on the relevant operation \(S\) and the signal simulation function \(f\) Calculate the Pearson correlation coefficient between each simulated signal column vector and the combined signal column vector

[0036] to obtain the score \(d\); according to the score \(d\), select the candidate value \(k\) corresponding to the largest absolute value of the score as the final guessed value of the information to be analyzed. Furthermore, the expression of the simulated signal column vector is as follows:

[0037]

[0038] In the formula, represents the simulated signal column vector The i-th element, f represents the signal simulation function, S represents the correlation operation, where 1 ≤ i ≤ t.

[0039] The expression of the fraction d is as follows:

[0040]

[0041]

[0042] In the formula, represents taking the absolute value, calculating the covariance of the same-dimensional column vectors , and are calculated separately, and the standard variances of

[0043] Example 1

[0044] The success rate of the method of the present invention is related to the specific masking scheme, cryptographic algorithm the noise level generated by the electronic device during operation, and the signal leakage function of the electronic device, and is affected by the combination function C, the correlation operation S between the information to be parsed and the known information, the signal simulation function f, and the number of runs t.

[0045] Exemplarily, the present application provides the out-of-band signal parsing success rate for a specific cryptographic algorithm under a specific instance. The classical symmetric block encryption algorithm AES is selected as the cryptographic algorithm, and the inner product mask with two sharing vectors with a parameter of 3 (i.e., the second element value of the inner product mask common vector is 3) is selected as the masking scheme. Therefore, the AES encryption algorithm protected by the inner product mask is The information to be parsed is the first-byte key k of the AES algorithm. Assume that the signal leakage function of the electronic device during the operation of AES is the Hamming weight function, and its noise follows a Gaussian distribution where the expected value μ = 0 and the standard variance σ 2 = 0.01. The combination function C selects the commonly used central product function in the art where E(X i ) represents the expected value of X i , where 1 ≤ i ≤ d + 1. The S-box substitution operation of the first byte in the first round of the AES algorithm is selected as the correlation operation The signal simulation function selects the commonly used Hamming weight function f(X) = HW(X) in the art, and the Hamming weight of X is the total number of 1s when X is represented in binary. In this example, the trend of the success rate of parsing the first-byte key k with the increase in the number of runs t is shown in Table 1.

[0046] Previously, the success rate of the commonly used Pearson correlation coefficient parsing in the art was close to 0 for any number of runs t in this instance.

[0047] Table 1: Table of success rate of out-of-band signal parsing

[0048]

[0049] In summary, the out-of-band signal parsing method proposed in this application is applicable to the out-of-band signal parsing of cryptographic algorithms that apply complex algebraic masking schemes, achieving a breakthrough in the parsing success rate of 0, making it possible to parse out-of-band signals in this scenario. The out-of-band signal parsing method proposed in this application breaks through the "security order amplification" characteristic of complex algebraic masking schemes, greatly improving the parsing ability and parsing success rate for out-of-band signals, and making a certain contribution to the theoretical analysis of out-of-band signals.

[0050] Correspondingly, this application also provides an electronic device, including: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the out-of-band signal parsing method as described above. As Figure 2 shown, it is a hardware structure diagram of any device with data processing capabilities where the out-of-band signal parsing method provided by the embodiment of the present invention is located. In addition to Figure 2 the processors, memory, and network interfaces shown, any device with data processing capabilities where the device in the embodiment is located usually also includes other hardware according to the actual functions of the device with data processing capabilities, which will not be elaborated here.

[0051] Correspondingly, this application also provides a computer-readable storage medium, on which computer instructions are stored, and when the instructions are executed by a processor, the out-of-band signal parsing method as described above is implemented. The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device, such as a plug-in hard disk, a Smart Media Card (SMC), an SD card, a Flash Card, etc. equipped on the device. Further, the computer-readable storage medium may also include both an internal storage unit of any device with data processing capabilities and an external storage device. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or will be output.

[0052] Other embodiments of the present application will occur to those skilled in the art upon considering the specification and practicing the disclosure herein. The present application is intended to cover any variations, uses, or adaptations of the present application, which follow the general principles of the present application and include known common general knowledge or conventional technical means in the technical field not disclosed in the present application. The specification and examples are to be considered illustrative only.

[0053] It should be understood that the present application is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope.

Claims

1. A method for parsing out-of-band signals, characterized in that The method includes: Obtain a cryptographic algorithm Known information column vectors generated by running t times And a cryptographic algorithm Out-of-band signal matrix T generated by running t times on an electronic device; Perform high-order combination on all out-of-band signal points in each row of the out-of-band signal matrix T to obtain a combined signal column vector For the combined signal column vector Perform sorting processing to obtain a sequence number vector Select a cryptographic algorithm with parsed information Known information column vector for the related operation S; and select a signal simulation function f; For the cryptographic algorithm the guessing space of the information to be parsed For each candidate value k, the corresponding simulated signal column vector is calculated based on the relevant operation S and the signal simulation function f Calculate each simulated signal column vector and the sequence number vector to obtain the Pearson correlation coefficient, thereby obtaining the score d; according to the score d, the candidate value k corresponding to the score with the largest absolute value is selected as the information to be parsed for output.

2. The out-of-band signal method according to claim 1, wherein The cryptographic algorithm is the cryptographic algorithm protected by a mask with an encoding function of f Enc The cryptographic algorithm has a guess space for the information to be parsed of ​​ 3. The out-of-band signal parsing method according to claim 2, wherein The encoding function f Enc has the following expression: Among them, is a variable in the cryptographic algorithm, is the Galois field; is a d + 1-dimensional amortization factor vector and satisfies The encoding function f Enc has a corresponding decoding function f Dec such that f Dec :

4. A method for parsing out-of-band signals according to claim 1, characterized in that, The known information column vector is the plaintext information or ciphertext information of the cryptographic algorithm; The out-of-band signal matrix T is a cryptographic algorithm When running on an electronic device, the power consumption data and / or electromagnetic signal data of the electronic device collected 5. A method for parsing out-of-band signals according to claim 1, characterized in that, Obtain the combined signal column vector The process includes: All out-of-band signal points in each row of the out-of-band signal matrix T are subjected to high-order combination through a set of combination functions C to obtain a combined signal column vector with a dimension of t Among them, the i-th element in the combined signal column vector is the number of columns of the out-of-band signal matrix T.

6. The out-of-band signal parsing method according to claim 1 or 5, characterized in that, Sort the combined signal column vector to obtain the sequence number vector The process includes: For all the element values of the combined signal column vector , sort them in ascending order from small to large. Label the serial number of its minimum value as 1, ……, until the serial number of the maximum value is labeled as t; calculate the expectation e of the serial numbers of the same element values in the combined signal column vector , and label the serial numbers of these same element values as the corresponding expectation e, so as to obtain the serial number vector 7. A method for parsing out-of-band signals according to claim 1, characterized in that The expression of the analog signal column vector is as follows: In the formula, represents the i-th element of the analog signal column vector, f represents the signal analog function, S represents the correlation operation, and 1 ≤ i ≤ t.

8. An electronic device, comprising a memory and a processor, characterized in that, The memory is coupled to the processor; wherein, the memory is used to store program data, and the processor is used to execute the program data to implement the out-of-band signal parsing method according to any one of claims 1-7 above.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the out-of-band signal parsing method according to any one of claims 1-7.

10. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, it implements the out-of-band signal parsing method according to any one of claims 1-7.

Images