A cluster-based cryptographic chip side information leakage quantification method and system

Abstract

The present application relates to a kind of based on clustering cryptographic chip side information leakage quantitative measurement method and system, belong to network security side channel analysis technical field.The method is divided into the waveform section with operation number by cryptographic chip collected side channel waveform, and it is reduced dimension, clustering is carried out on low-dimensional space, obtain two sets, record as set A and set B;According to known key, the correct operation of each waveform section is deduced, and is marked to the point corresponding to each waveform section, to obtain two sets, record as set C and set D;Assuming A with C corresponds, B with D corresponds, then the point belonging to A but not belonging to C and the point belonging to B but not belonging to D are added to set E.Set a threshold alpha, if the number of points in E is less than alpha, then determine that the method implementation cannot resist simple energy / electromagnetic analysis;Otherwise, the judgment is contrary.The method and system can jump out of naked eye observation and subjective judgment, with more objective and fair angle to evaluate the security of cryptographic product.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of network security side channel analysis, and relates to a method and system for clustering and dividing side information waveform segments of a cryptographic chip and giving results to verify product security, in particular to a cryptographic chip side information leakage quantitative measurement method and system based on clustering. BACKGROUND

[0002] Modern cryptographic technology is usually implemented in a cryptographic device, and its typical forms are U-shield, smart card, cryptographic card, cryptographic machine, etc., and its core includes a cryptographic chip containing cryptographic algorithms and keys. When the cryptographic chip implements cryptographic services, its input is plaintext, and its output is generally ciphertext or signature value. In the field of side channel analysis and evaluation, when the cryptographic chip is running, the detection personnel can collect the physical information such as the energy consumed by the device, the electromagnetic radiation, and the time spent, and analyze it. The detection agency can verify the security of a cryptographic chip by whether it can recover the key with the help of this information.

[0003] We take the core operation of 256-bit elliptic curve digital signature algorithm, scalar multiplication, as an example for illustration. Without adding countermeasures against side channel attacks, about 384 operations are usually required. For each bit of the key, if the value is 0, only one point addition operation is performed; if the value is 1, one point addition operation and one point multiplication operation are performed. With the addition of "pseudo-operation" type side channel protection, whether the key is 0 or 1, both point addition and point multiplication operations are required. Here we take the 384 operations in the unprotected case as an example for illustration.

[0004] When performing security verification on the simple energy analysis (similar to simple electromagnetic analysis) method for the implementation of ECC digital signature algorithm, the general steps are as follows:

[0005] First, a piece of energy waveform collected from a one-time ECC signature process of the cryptographic chip is divided into waveform segments with operation numbers according to different operations, and each waveform segment is dimensionally reduced. Here we take two dimensions as an example for illustration. The two dimensions obtained by dimensional reduction are taken as the horizontal and vertical coordinates, and the waveform segments corresponding to the 384 operations are mapped to a two-dimensional space, with each waveform segment corresponding to a point in the two-dimensional space;

[0006] Then, in the two-dimensional space, the dimensionally reduced waveform segments are clustered, and the resulting two sets are denoted as set A and set B, respectively;

[0007] Finally, by observing whether there is a certain distance between the two sets A and B, it is determined whether the enemy can recover the key through clustering analysis, and whether the cryptographic chip is secure or not.

[0008] The security verification method for this cryptographic chip is specifically referenced from the paper "Clustering Algorithms for Non-profiled Single-Execution Attacks on Exponentiations" published in CARDIS in 2013 by Johann Heyszl, Andreas Ibing, Stefan Mangard, Fabrizio De Santis, and Georg Sigl. The problem with existing methods is that professional technicians can only judge the success of clustering results by visual observation, which is highly subjective. Furthermore, due to the lack of quantifiable metrics, it is difficult to assess the security level of the device. Therefore, an objective evaluation method and a quantifiable metric are needed to better evaluate the security of cryptographic products. Summary of the Invention

[0009] The purpose of this invention is to address the shortcomings of existing evaluation schemes, such as excessive subjectivity and difficulty in classifying security levels. From an objective and impartial perspective, a quantitative measurement standard for security evaluation of information leakage on the cryptographic chip side based on clustering is established. At the same time, to ensure that the method has high usability in practical applications and simple and quick operability, a quantitative measurement system for information leakage on the cryptographic chip side based on clustering is established.

[0010] The objective of this invention is achieved through the following technical solutions.

[0011] This invention discloses a clustering-based method for quantifying information leakage on the cryptographic chip side, comprising the following steps:

[0012] Step 1: The energy or electromagnetic side channel waveforms collected during cryptographic operations by the cryptographic chip are divided into waveform segments with operation numbers according to different operations, and the dimensionality is reduced to a low-dimensional space. The waveform segment corresponding to each operation is mapped to a point in the low-dimensional space, and each point records its operation number.

[0013] Step 2: Cluster the points corresponding to each waveform segment in the low-dimensional space to obtain two sets, denoted as set A and set B;

[0014] Step 3: Based on the known key, deduce the correct operation for each waveform segment and mark the corresponding points of each waveform segment in the low-dimensional space, thus obtaining two sets, denoted as set C and set D;

[0015] Step 4: Discuss two cases. Case 1: Assume A corresponds to C and B corresponds to D. Then add the points that belong to A but not C and the points that belong to B but not D to set E. Case 2: Assume A corresponds to D and B corresponds to C. Then add the points that belong to A but not D and the points that belong to B but not C to set F.

[0016] Step 5: Set a threshold α. If the number of points in E is less than α, or the number of points in F is less than α, then the method is deemed unable to resist simple energy / electromagnetic analysis; otherwise, the method is deemed able to resist simple energy / electromagnetic analysis.

[0017] This invention also discloses a clustering-based quantitative measurement system for information leakage on the cryptographic chip side, used to implement the aforementioned clustering-based quantitative measurement method for information leakage on the cryptographic chip side. The clustering-based quantitative measurement system for information leakage on the cryptographic chip side includes a data acquisition module, a segmentation module, a dimensionality reduction module, a clustering module, and an analysis module.

[0018] The data acquisition module is used to collect side-channel information such as energy or electromagnetic interference leaked by the cryptographic chip under test during cryptographic operations. This data forms the basis for evaluating the security of the cryptographic chip. The collected information is presented as a waveform showing the leakage information changing over time.

[0019] Segmentation Module: Used to divide the energy or electromagnetic side-channel waveforms acquired by the acquisition module into multiple waveform segments according to different operations. To ensure sequential comparison, each waveform segment is assigned a number according to its arrangement on the time axis.

[0020] Dimensionality reduction module: This module reduces the dimensionality of each waveform segment obtained from the segmentation module to a lower-dimensional space, allowing the original variables to be represented using fewer variables. After dimensionality reduction, each waveform segment corresponding to an operation is mapped to a corresponding point in the lower-dimensional space. Simultaneously, each point retains its index to ensure order. After processing by the dimensionality reduction module, some redundant features can be removed from the waveform segments, while retaining most of the information from the original features.

[0021] The clustering module divides the waveform segment set obtained after dimensionality reduction into multiple distinct sets according to specified criteria, maximizing the similarity of waveform segments within the same set and maximizing the differences between waveform segments in different sets. After processing, the clustering module yields waveform segments of various types. It provides multiple clustering methods, including K-Means, DBSCAN, Mean-Shift, Gaussian mixture clustering, and hierarchical clustering.

[0022] The analysis module is used to deduce the correct operation for each waveform segment based on the known key and mark it on the corresponding point in the low-dimensional space output by the analysis module, ensuring a one-to-one correspondence between the two. Following the specific evaluation method described in the invention, points with analysis errors are marked in the low-dimensional space. The final output of the analysis module is the number of points with cluster analysis errors and its ratio to the total number of points. Based on this ratio, a quantifiable security evaluation and grading standard is established, ultimately assigning a specific security level to the tested cryptographic chip as the evaluation conclusion.

[0023] Beneficial effects

[0024] 1. Compared with existing evaluation methods, this method and system can move beyond visual observation and subjective judgment, and evaluate the security of cryptographic products from a more objective and impartial perspective.

[0025] 2. Compared with existing evaluation methods, this method and system can establish a quantifiable grading standard based on the number of points that do not match the known key, and finally give the tested cryptographic chip a specific security level as the evaluation conclusion.

[0026] 3. Compared to existing evaluation methods, this method and system establish and improve a security evaluation system. Evaluators can easily and conveniently perform a series of automated evaluation steps to quickly obtain evaluation results. Furthermore, the usability, reliability, and functionality of this evaluation system have undergone rigorous scientific testing, and the conclusions drawn by the system are considered trustworthy. Attached Figure Description

[0027] Figure 1 A flowchart of a clustering-based method for quantifying information leakage on the cryptographic chip side;

[0028] Figure 2 This is a schematic diagram of the control interface for the data acquisition module;

[0029] Figure 3 This is a schematic diagram of the control interface for the segmentation module;

[0030] Figure 4 This is a schematic diagram of the control interface for the dimensionality reduction module.

[0031] Figure 5 This is the energy waveform segment after dimensionality reduction;

[0032] Figure 6 To create visual graphics that are reduced to two dimensions;

[0033] Figure 7 This is a schematic diagram of the clustering module control interface;

[0034] Figure 8 A visualization of cluster analysis;

[0035] Figure 9 This is a schematic diagram of the clustering module control interface;

[0036] Figure 10 A visualization of the known key;

[0037] Figure 11 A visual representation of points where clustering analysis errors are identified;

[0038] Figure 12 This is the interface for the evaluation system of the first cryptographic chip.

[0039] Figure 13 This is the interface for the evaluation system of the second cryptographic chip. Detailed Implementation

[0040] The above description is merely an overview of the technical solution of the present invention. To better understand the technical means of the present invention, the method and system of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. In the implementation examples, to better demonstrate the effect of using this method to evaluate the security of cryptographic chips, experiments will be conducted on two different cryptographic chips that use the ECC algorithm for signing. All accompanying drawings show the left and right sides corresponding to different devices.

[0041] Example

[0042] like Figure 1 As shown, a clustering-based method and system for quantifying information leakage on the cryptographic chip side includes the following steps:

[0043] Step 1: Use the acquisition module to acquire the energy or electromagnetic side channel waveforms acquired when the cryptographic chip performs cryptographic operations. Use the segmentation module to divide the acquired waveforms into 384 waveform segments with operation numbers according to different operations. Use the dimensionality reduction module to reduce the dimensionality of each waveform segment to a point with a marked number in a low-dimensional space.

[0044] Step 1.1: The acquisition module of this invention can provide parameters such as oscilloscope model selection, acquisition channel, trigger channel, sampling rate, number of sampling points, time base, time delay, range, range offset, trigger voltage, trigger direction, and trigger delay. Simultaneously, a background program is written to control the effective power consumption or electromagnetic waveform acquired by the oscilloscope. The control interface for operating the acquisition module to acquire the side-channel information leaked by the smart card is as follows: Figure 2 As shown.

[0045] Step 1.2: The device under test used in this example is a smart card implemented with the ECC elliptic curve signature algorithm, with a key length of 256 bits. Without protection, performing a single signature process requires approximately 384 operations. The segmentation module of this invention divides the waveform acquired by the acquisition module into 384 waveform segments with operation numbers according to different operations. The control interface for operating the segmentation module is as follows... Figure 3 As shown.

[0046] Step 1.3: Use the dimensionality reduction module to reduce the dimensionality of each waveform segment to a labeled point in the lower-dimensional space. In the example, the original waveform segments are reduced to two-dimensional space using Principal Component Analysis (PCA). This unsupervised dimensionality reduction method can transform multiple variables into a few principal components obtained by linear combination of the original variables, and these principal components can reflect most of the information of the original variables. The control interface for operating the dimensionality reduction module is shown below. Figure 4 As shown. Taking waveform segment 0-63 as an example, the dimensionality reduction result is as follows. Figure 5 As shown.

[0047] Dimensionality reduction can use linear combinations of the original variables as new variables to represent the original data. These two variables are then used as the x and y axes to create a visualization, resulting in a point on the graph corresponding to each waveform segment, with each point numbered. The visualization result is as follows: Figure 6 As shown.

[0048] Step 2: Use the clustering module to cluster the points corresponding to each waveform segment in the low-dimensional space, resulting in two sets, denoted as set A and set B.

[0049] The clustering module of this invention provides multiple clustering methods, including K-Means, DBSCAN, Mean-Shift, Gaussian mixture clustering, and hierarchical clustering, and each method allows for setting required parameters. The example uses the Gaussian mixture clustering method, with the parameter setting specifying the number of target clusters as 2. The control interface for operating the clustering module is shown below. Figure 7 As shown.

[0050] In the visualization obtained in step 2, different colors are added to the points in clusters A and B to distinguish the two clusters. The elements in each cluster are numbered waveform segments. The resulting visualization is as follows: Figure 8 As shown.

[0051] Step 3: Use the analysis module to perform the operation, deduce the correct operation for each waveform segment based on the known key, and mark the corresponding points of each waveform segment in the low-dimensional space, thus obtaining two sets, denoted as set C and set D.

[0052] In this example, a 256-bit key is used, and the key content is F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0 F0. Enter the correct key into the analysis module. The control interface for operating the analysis module is as follows: Figure 9 As shown.

[0053] The binary data corresponding to the key is split bit by bit. If the value is 0, only one dot-mapping operation is performed; if the value is 1, a dot-mapping operation is performed first, followed by a dot-multiplying operation. A total of 384 dot-mapping and dot-multiplying operations are performed on the key, corresponding to 384 waveform segments. The key is split into two sets, denoted as set C and set D, where the elements are numbered waveform segments. Different colors are added to the points in sets C and D to distinguish the two sets. The resulting graph is shown below. Figure 10 As shown.

[0054] Step 4: Discuss two cases. Case 1: Assume A corresponds to C and B corresponds to D. Then add the points that belong to A but not C and the points that belong to B but not D to set E. Case 2: Assume A corresponds to D and B corresponds to C. Then add the points that belong to A but not D and the points that belong to B but not C to set F.

[0055] If the number of failed analyses in set E is small, it indicates that the key can be recovered with a certain fault tolerance rate using cluster analysis based on the energy leakage information collected from the side channel, thus suggesting that the security of the cryptographic chip is not high; conversely, if the number of failed analyses in E is large, the opposite is true. Mark the points in set E or set F among all points, such as... Figure 11 As shown, the red points are points in set E or set F, which are the points where the clustering analysis was incorrect, while the gray points are the points where the analysis was correct.

[0056] Step 5: Set a threshold α. If the number of points in E is less than α, or the number of points in F is less than α, then the method is deemed unable to resist simple energy / electromagnetic analysis; otherwise, the method is deemed able to resist simple energy / electromagnetic analysis.

[0057] For example, if we assume that an attacker's maximum exhaustive search capability is 50 bits (approximately 20% of a 256-bit key length), we would determine that the cryptographic implementation is insecure if the number of points in E is less than 50.

[0058] Furthermore, different quantitative metrics can be established to assess the security level of cryptographic chips. It is important to note that to ensure the objectivity of this assessment, the quantitative metric must be consistent. To make it applicable to different application scenarios, the ratio of the number of failed operations in set E to the total number of operations can be used as the rating indicator. An example rating metric is shown in Table 1.

[0059]

[0060] Table 1. Examples of Safety Assessment Rating Standards

[0061] Statistical analysis revealed that when clustering the leaked information from the left-hand cryptographic chip, the number of failed analyses was 0, accounting for 0% of the total operations. However, the number of failed analyses for the right-hand cryptographic chip was 161, accounting for 41.927% of the total operations. Therefore, the evaluation conclusion is that the device on the left has a very low security level, while the device on the right has a secure security level. The evaluation system interface for the operations on the two cryptographic chips in the example is shown below. Figure 12 , 13 As shown.

[0062] The above description is merely a preferred embodiment to demonstrate the effects of the method and system of the present invention. The present invention should not be limited to the content disclosed in this embodiment and the accompanying drawings. Any equivalent or modified embodiments made without departing from the spirit of the present invention fall within the protection scope of the present invention.

Claims

1. A clustering-based method for quantifying information leakage on the cryptographic chip side, characterized in that, Includes the following steps: Step 1: The energy or electromagnetic side channel waveforms collected during cryptographic operations by the cryptographic chip are divided into waveform segments with operation numbers according to different operations, and the dimensionality is reduced to a low-dimensional space. The waveform segment corresponding to each operation is mapped to a point in the low-dimensional space, and each point records its operation number. Step 2: Cluster the points corresponding to each waveform segment in the low-dimensional space to obtain two sets, denoted as set A and set B; Step 3: Based on the known key, deduce the correct operation for each waveform segment and mark the corresponding points of each waveform segment in the low-dimensional space, thus obtaining two sets, denoted as set C and set D; Step 4: Discuss two cases. Case 1: Assume A corresponds to C and B corresponds to D. Then add the points that belong to A but not C and the points that belong to B but not D to set E. Case 2: Assume A corresponds to D and B corresponds to C. Then add the points that belong to A but not D and the points that belong to B but not C to set F. Step 5: Set a threshold α. If the number of points in E is less than α, or the number of points in F is less than α, then the method is deemed unable to resist simple energy / electromagnetic analysis; otherwise, the method is deemed able to resist simple energy / electromagnetic analysis.

2. A cluster-based quantitative measurement system for information leakage on the cryptographic chip side, used to implement the cluster-based quantitative measurement method for information leakage on the cryptographic chip side as described in claim 1, characterized in that: It includes a data acquisition module, a segmentation module, a dimensionality reduction module, a clustering module, and an analysis module; The acquisition module is used to collect side-channel information such as energy or electromagnetic fields leaked when the cryptographic chip under test performs cryptographic operations. This information serves as the basis for evaluating the security of the cryptographic chip. The acquired information is in the form of a waveform of the leaked information changing over time. The segmentation module is used to divide the energy or electromagnetic side channel waveforms acquired by the acquisition module into multiple waveform segments according to different operations. In order to compare them in order, each waveform segment is assigned a number according to the arrangement order on the time axis to ensure order. The dimensionality reduction module is used to reduce the dimensionality of each waveform segment obtained by the segmentation module to a low-dimensional space, so as to use fewer variables to represent the original variables. After dimensionality reduction, the waveform segment corresponding to each operation is mapped to a point in the low-dimensional space. At the same time, each point still records its number to ensure order. After the dimensionality reduction module processes the waveform segment, some redundant features are removed, while most of the information of the original features is still retained. The clustering module is used to divide the waveform segment set obtained after the dimensionality reduction module into multiple different sets according to the specified division criteria, and to maximize the similarity of waveform segments within the same set, while maximizing the differences between waveform segments outside the same set. After processing by the clustering module, multiple types of waveform segments are obtained. The clustering module provides a variety of clustering methods, including K-Means, DBSCAN, Mean-Shift, Gaussian mixture clustering, and hierarchical clustering. The analysis module is used to deduce the correct operation for each waveform segment based on the known key and mark it on the corresponding point of each waveform segment in the low-dimensional space output by the analysis module, so that the two correspond one-to-one. According to the method described in claim 1, the points of analysis error are marked in the low-dimensional space. The final output of the analysis module is the number of points of cluster analysis error and its ratio to the total number of points. Based on this ratio, a quantifiable security evaluation and grading standard is formulated, and finally a specific security level is assigned to the tested cryptographic chip as the evaluation conclusion.

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