Non‐profiled Deep‐Learning‐Based Power Analysis of the SM4 and DES Algorithms

Chinese Journal of ElectronicsVolume 30, Issue 3 p. 500-507 Original Research PaperFree Access Non-profiled Deep-Learning-Based Power Analysis of the SM4 and DES Algorithms MA Xiangliang, Corresponding Author MA Xiangliang maxiangliang@163.com School of Integrated Circuits, Tsinghua University, Beijing, 100084 China National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorLI Bing, Corresponding Author LI Bing lb0682@126.com National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorWANG Hong, Corresponding Author WANG Hong wh@nitsrc.cn National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorWU Di, Corresponding Author WU Di wudi_dizi@163.com China Cybersecurity Review Technology and Certification Center, Beijing, 100020 ChinaSearch for more papers by this authorZHANG Lizhen, Corresponding Author ZHANG Lizhen 806271113@qq.com National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorHUANG Kezhen, Corresponding Author HUANG Kezhen huangkezhen@tca.iscas.ac.cn Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, 100190 China University of Chinese Academy of Sciences, Beijing, 100049 ChinaSearch for more papers by this authorDUAN Xiaoyi, Corresponding Author DUAN Xiaoyi duanxiaoyi@besti.edu.cn Department of Electronics and Information Engineering, Beijing Electronic Science and Technology Institute, Beijing, 100070 ChinaSearch for more papers by this author MA Xiangliang, Corresponding Author MA Xiangliang maxiangliang@163.com School of Integrated Circuits, Tsinghua University, Beijing, 100084 China National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorLI Bing, Corresponding Author LI Bing lb0682@126.com National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorWANG Hong, Corresponding Author WANG Hong wh@nitsrc.cn National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorWU Di, Corresponding Author WU Di wudi_dizi@163.com China Cybersecurity Review Technology and Certification Center, Beijing, 100020 ChinaSearch for more papers by this authorZHANG Lizhen, Corresponding Author ZHANG Lizhen 806271113@qq.com National Research Center for Information Technology Security, Beijing, 100084 ChinaSearch for more papers by this authorHUANG Kezhen, Corresponding Author HUANG Kezhen huangkezhen@tca.iscas.ac.cn Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, 100190 China University of Chinese Academy of Sciences, Beijing, 100049 ChinaSearch for more papers by this authorDUAN Xiaoyi, Corresponding Author DUAN Xiaoyi duanxiaoyi@besti.edu.cn Department of Electronics and Information Engineering, Beijing Electronic Science and Technology Institute, Beijing, 100070 ChinaSearch for more papers by this author First published: 01 May 2021 https://doi.org/10.1049/cje.2021.04.003 This work is supported by the National Key Research and Development Program of China(No.2018YFB0904901, No.2019QY1302), and National Natural Science Foundation of China (No.61802404). AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Abstract Power analysis methods are commonly used for evaluating the security of cryptographic devices. They are characteristically low-cost and display a high success rate and the ability to obtain important device information, e.g., keys. Given the current wide application of deep-learning technology, there is a growing tendency to incorporate power-analysis technology in development. This study investigates non-profiled deep-learning-based power analysis. The labels used in this attack are uncertain, and the attack conditions required are greatly reduced. We choose the Recurrent neural network (RNN), multilayer perceptron, and convolutional neural network algorithms, which use the same network structure, to recover the keys for the SM4 software and DES hardware implementations. We propose combining the RNN algorithm with power analysis, and validate the benefits experimentally. The experimental results show that they all successfully recover the correct key for the SM4 software implementation, although the RNN algorithm by itself achieves a better effect. This conclusion also applies to attacks on the DES hardware implementation but is limited to labels based on the bit model. I. Introduction The power analysis[1] method was first proposed in 1999 by Paul C. Kocher et al., who successfully recovered the key for Data encryption standard (DES) implementations[2]. Power analyses[3,4] have two main categories: profiled attacks[4], which include template attacks and machine-learning-based attacks, and non-profiled attacks[5], which include Correlation power analysis (CPA) and differential power analysis. Profiled attacks require attackers to obtain two identical devices, with sufficient control on one device so that the attackers can use power-trace patterns for modelling. The power traces collected by the other target device are matched, and the key with the highest matching probability is identified as the correct key. Non-profiled attack only requires the collection of many power traces, corresponding to random plaintexts of the target device, to recover the target key. To date, power analysis has been applied to many block ciphers and public key cryptography algorithms, including Advanced encryption standard (AES), SM4[6], DES, and Rivest-Shamir-Adleman (RSA). In 2014, machine learning was first introduced to attack the AES implementation with a mask countermeasure[7]. Only eight traces were required to extract the key. The number of traces required when using the support-vector machine method to perform an attack was significantly reduced compared with other methods such as template attacks in a profiled-attack scenario. Profiled deep-learning-based attacks[8] were introduced in 2016. Researchers used Convolutional neural networks[9] (CNN), Multilayer perceptrons[10] (MLP), Long- and short-term memory units (LSTM), Automatic encoders (AE), Random forests (RF), and template attacks[11] to attack the unprotected AES software and hardware implementations, respectively. Besides LSTM, researchers used five other algorithms to attack the AES implementation with a first-order mask countermeasure. Their conclusions were as follows. Firstly, the CNN algorithm was more effective at attacking the AES hardware implementation than the template and RF algorithms. Secondly, the template and RF algorithms were not more effective at attacking the AES software implementation than other algorithms. Finally, the template and RF algorithms were not more effective at attacking the first-order mask AES implementation than other algorithms. Deep-learning-based power analysis[12] was introduced in 2018, prompting researchers to discuss some parameter selection and evaluation criteria. Emmanuel demonstrated that a CNN produced the same attack effect as an MLP if the power traces were aligned. The effect of a CNN was better otherwise. Therefore, a CNN was recommended as the algorithm of choice for performing deep-learning-based attacks. In 2018, Benjamin Timon proposed NDLPA[5], the attack steps of which are similar to CPA. The assumed power consumption values were used as the labels, which were mapped with the intermediate results based on the bit or Hamming weight (HW) model. The accuracy and loss values were used as the key discriminators. Two algorithms were proposed to recover the key, with and without validation data. After using the MLP and CNN algorithms to perform NDLPA, the AES key was successfully recovered. It was concluded that the bit model was better than the HW model, and that the absolute-value model was not suitable for NDLPA. In the present study, the labels used for performing the NDLPA were uncertain, and the required attack conditions were greatly reduced. Recurrent neural network[13] (RNN), MLP, and CNN algorithms were used to perform the NDLPA to attack the SM4 software implementation and the DES hardware implementation. The output accuracy and loss values were used as the key discriminators, and the assumed power consumption values as the training labels. We chose the RNN, MLP, and CNN algorithms, which use the same network structure, to recover the key, respectively, for the SM4 software implementation and DES hardware implementation. We propose combining the RNN algorithm with power analysis and verify the advantages of this approach by experiments. The key discriminators were the output accuracy and loss values as in Ref.[13], and the training labels are the assumed power consumption values. As demonstrated experimentally, they all successfully recover the correct SM4 software implementation key. However, the RNN algorithm used for performing the NDLPA achieves a better attack effect. This conclusion also applies to the attack on the DES hardware implementation but is limited to labels based on the bit model. II. Preliminaries This section briefly introduces the SM4 and DES algorithms. 1. SM4 algorithm The SM4 algorithm is a commercial and symmetric cipher algorithm in China. Its block length and key length are both 128 bits, using a 32-round iterative structure. The input plaintexts are set to ( X 0 , X 1 , X 2 , X 3 ) ∈ ( Z 2 32 ) 4 and the output cipher text to ( Y 0 , Y 1 , Y 2 , Y 3 ) ∈ ( Z 2 32 ) 4 . Then, the round keys used for encryption and decryption are r k i ∈ Z 2 32 , i = 0 , 1 , . . . , 31 . 1) The 32-round iterative function is X i + 4 = F ( X i , X i + 1 , X i + 2 , X i + 3 , r k i ) , i = 0 , 1 , . . . , 31 . 2) The inverse transformation function is ( Y 0 , Y 1 , Y 2 , Y 3 ) = R ( X 32 , X 33 , X 34 , X 35 ) = ( X 35 , X 34 , X 33 , X 32 ) . The 32-round iterative function is F ( X 0 , X 1 , X 2 , X 3 , r k i ) = X 0 ⊕ T ( X 1 ⊕ X 2 ⊕ X 3 ⊕ r k i ) . The composite function T: Z 2 32 → Z 2 32 is an invertible substitution. The T function consists of a linear transformation L and a non-linear substitution τ, T ( . ) = L ( τ(.)). a) Non-linear substitution τ The non-linear substitution τ is composed of four parallel identical S-boxes. The input is set to A = ( a 0 , a 1 , a 2 , a 3 ) ∈ ( Z 2 8 ) 4 , and the output to B = ( b 0 , b 1 , b 2 , b 3 ) ∈ ( Z 2 8 ) 4 . Hence, τ ( A ) = ( b 0 , b 1 , b 2 , b 3 ) = ( S b o x ( a 0 ) , S b o x ( a 1 ) , S b o x ( a 2 ) , S b o x ( a 3 )). b) Linear transformation L The input to the linear transform L is the output B of the non-linear transformation τ. The output C of the linear transformation L is set such that C = L ( B ) = B ⊕ ( B < < < 2 ⊕ ( B < < < 10 ) ⊕ ( B < < < 18 ) ⊕ ( B < < < 24 ) . 2. DES algorithm The DES algorithm is also a symmetric encryption algorithm with a Feistel structure. Its block size and key size are both 64 bits, but the key size used in the operation is 56 bits. The decryption and encryption operations use the same structure, but the round key is used in reverse order. The DES operation is divided into three main stages as follows: 1) The DES algorithm performs an initial permutation of the 64 bits of plaintext, and then splits the result into L 0 left 32 bits and R 0 right 32 bits. 2) The initial permutation results serve as the input to 16 rounds of identical iterative operations. The 16 iterative rounds proceed as follows: a) L i = R i − 1 . b) R i = L i − 1 ⊕ F ( R i − 1 , K i ) for i = 1 , 2 , . . . , 16 . Both L i and R i are 32-bit-long outputs of each iterative round. F is a non-linear encryption function, and K i is the key encryption for round i. The output R i is the result of a series of functional operations performed on R i − 1 , such as the extension permutation, xor with round key K i , S-box substitution, P-box substitution, and xor with L i − 1 . In addition, the S-box in DES is composed of 8 different S-boxes. 3) The 64-bit ciphertext is generated when performing the initial inverse permutation of the results of the 16 rounds of iterations. III. Non-profiled Deep-Learning-Based Power Analysis The non-profiled scenario does not require a training device for modelling. Instead, the keys must be recovered directly by analyzing the power consumption of the attacked device. The conditions for key recovery, based on the non-profiled power analysis, are greatly reduced, which makes the attack very threatening. In this section, we describe the key recovery step (algorithm[5]) in detail, the key discriminator, the advantages of the RNN algorithm used for power analysis, and deep learning. 1. Key recovery steps and algorithm Deep learning has been gradually applied to power analysis in recent years using various approaches. A profiled deep-learning-based power analysis method is undeniably very powerful. However, its inability to meet the requirements makes this attack method ineffective. In 2018, Benjamin Timon proposed NDLPA. The labels used in this attack are uncertain, and the required attack conditions are greatly reduced. CPA is the most common attack method used in power analysis. Its success at recovering the correct key stems from the hypothetical power consumption values that accurately characterize the realistic power consumption. The attack steps of NDLPA are similar to those of CPA. Measuring the power consumption of the attacked device while attack steps of NDLPA encrypts plaintexts. The S-box output is chosen as the intermediate result of the cryptographic algorithm. The hypothetical intermediate values for plaintexts and the key guess are then obtained. The next step of the attack is to map each intermediate value to the hypothetical power-consumption value based on the bit or HW model. The hypothetical power-consumption values are taken as the training labels for NDLPA. The power traces, training labels, and a number of number of training epochs are used for NDLPA. Then, the accuracy or loss value of each epoch is obtained during the training. The correct key is recovered from the key guess with the steady highest accuracy or the lowest loss, as it corresponds to the power consumption related to the realistic power consumption of the intermediate result. The key recovery steps based on deep learning (see Fig.1) and the NDLPA algorithm feature in Algorithm 1[5]. Fig. 1Open in figure viewerPowerPoint Key recover steps based on deep learning Algorithm 1 NDLPA[5] Require: T random plaintexts, number of epochs en; Ensure: Correct key Step 1: Choose the intermediate result of the encryption algorithm; Step 2: Collect T power traces of the device when it encrypts random plaintexts; Step 3: While key < 256 do Step 4: Compute hypothetical intermediate results for the key guess and Step 2 random plaintexts; Step 5: Map the intermediate results to the hypothetical power consumption as labels based on the bit or HW model; Step 6: Accuracy, loss=deep learning( 0 . 8 × T , 0 . 8 × labels , 0 . 2 × T , 0 . 2 × labels , en); Step 7: End while Step 8: The correct key is recovered if it corresponds to accuracy is the steady highest or the lowest loss values. If the correct key is not discriminated with the other key (and unless the numbers of power traces or epochs are insufficient), it is possible that the power-consumption model of the intermediate value cannot characterize the realistic power consumption of the attacked device. Notably, the absolute-value model is unsuitable for NDLPA (see Section III.2). The deep-learning algorithm and labels are different from CPA. CPA can work because the correct key corresponds to the highest correlation coefficient between the power hypothetical consumption values and the power traces. 2. Deep-learning algorithm Several papers have been published on deep-learning-based power analysis. Among these, the MLP and CNN algorithms have been widely used for deep learning to recover the key of an attacked device. The attacked effect is good, and the algorithms have been recommended by many authors[13]. In addition, because of the existence of the pooling layer, the CNN algorithm has the natural translation characteristics, implying no need to align training data such as traces[12]. Although many deep-learning algorithms have been applied to power analysis, no study based on RNN has so far been reported. The RNN algorithm differs from the MLP and CNN algorithms in that it has a memory function and stores the previous output in the hidden layer. Some authors argue that there is some relationship between the next training and the previous output. In the non-profiled scenario, the labels used for training are the hypothetical power-consumption mappings of the intermediate results, which are based on a power-consumption model. Since intermediate results are correct only if their calculation is based on a guess of the correct key, the labels corresponding to the correct key guess are themselves all correct. Other labels are only partially correct. It is known that the one with the steady highest accuracy or the lowest loss value recovers the correct key. If the memory function of the RNN algorithm is considered, the last training result impacts the next training result, causing a greater discrepancy in the accuracy, relative to the correct key. The RNN algorithm is more suitable for key recovery based on NDLPA. Therefore, we chose the RNN, MLP, and CNN algorithms to recover the key. 3. Key discriminator and labels During training, the accuracy and loss value of each epoch can be recorded. The accuracy represents the average rate of successful predictions for each label, whereas the loss value represents the training process. The smaller the loss value, the better the training effect. Therefore, the accuracy and the loss value together constitute the training outcomes of the deep-learning process, and both can be used to discriminate a correct key from an incorrect key. The loss function is the objective of the training-process optimization. In a given training round, the derivative of the loss function with respect to the weight determines the gradient of the weight parameters that replace those of the previous round. In the present study, the cross-entropy loss function was used to compute the loss value during the training, and the Keras open-source framework was used to perform the training. The accuracy was determined as the average value of the correct prediction results of the labels number N. If there are N labels, the training will produce N predictions. If M of these are correct predictions, the accuracy is then given by M/N. Thus, the key is correct if it corresponds to the accuracy that is the steady highest or loss values lowest. In the non-profiled scenario, the labels used in this study to conduct the training were uncertain. As we know, the power trace corresponds to plaintext one by one. Thus, for a given plaintext, different key guesses can yield different labels. A given trace corresponds to many labels, which makes the labels uncertain and not unique. The hypothetical intermediate results are random when considering random plaintexts and key guesses. This in turn introduces randomness in the hypothetical consumption values, and hence the labels themselves become random data. Therefore, neither the accuracy nor the loss value for each key guess can serve as a key discriminator or effectively recover the correct key. IV. Practical Results The SM4 and DES algorithms are standard block ciphers widely used in smart cards. This section considers the key-recovery experiment in the non-profiled scenario, performed for the SM4 software and the DES hardware implementations. The effects of applying the RNN, MLP, and CNN algorithms are also compared. The experimental results show that all these algorithms successfully recover the correct key in the case of the SM4 software implementation, although the RNN algorithm for NDLPA achieves a better attack effect. This conclusion also applies to the attack on the DES hardware implementation but is limited to labels based on the bit model. Notably, labels based on the HW model are unsuitable for NDLPA to attack the DES hardware implementation because this model is unable to characterize the power consumption of the DES hardware implementation. 1. Key recovery for the SM4 implementation This subsection introduces the key recovery experiment for the SM4 software implementation using NDLPA. The attacked device in this experiment was a smart card with a 32-bit CPU and 0.13 μm processing. Following Algorithm 1, the S-box output was chosen as the intermediate result in Step 1. In Step 2, the data-acquisition platform consisted of four parts: the Personal computer (PC), the measurement circuit, the smart card, and the oscilloscope. The PC sent plaintexts to the smart card, and the smart card encrypted them and sent the cipher back to the PC. During the execution of this algorithm, the oscilloscope recorded the smart-card power consumption and sent the traces to the PC. The oscilloscope sampling rate was set 100 MS/s and 805 samples were collected. A power trace of the power consumption during the first round of SM4 is shown in Fig.2. In Step 3, applying the idea of "divide and conquer", we obtained 256 key guesses for the first byte of the secret key. In Step 4, we computed the hypothetical intermediate results for the random plaintexts in Step 2. In Step 5, the intermediate results were mapped onto the hypothetical power consumption as labels based on the bit or HW model. In Step 6, the power traces, training labels, and the number en of training epochs were used for deep learning. Then, the accuracy or loss value for each epoch was obtained during the training. Fig. 2Open in figure viewerPowerPoint Power consumption during the first round of SM4 To perform NDLPA, we chose the RNN, MLP, and CNN algorithms, which are all composed of one hidden layer of 64 neurons with en=100 epochs with a set of T = 5000 traces of 800 points. Henceforth, we write RNN-NDLPA, MLP-NDLPA, and CNN-NDLPA to denote NDLPA using these algorithms. In the following figures, the red curves are associated with the correct key guess, corresponding to the accuracy or the loss, whereas the blue curves represent other candidates. In this experiment, the S-box outputs were chosen as the intermediate results, and the labels were obtained based on the bit model. From the outcomes of these experiments, shown in Figs.3–5, it can be concluded that RNN-NDLPA, MLP-NDLPA, and CNN-NDLPA all successfully recover the correct key of the SM4 implementation, because the correct key is the steady highest or the training loss value is the steady lowest after training. However, compared with MLP-NDLPA or CNN-NDLPA, RNN-NDLPA performs better with regard to the discrepancy between the correct key guess and other candidates separately corresponding to the accuracy or the loss value. In this experiment, NDLPA was performed with a set of T = 2000 traces of 800 points, and the labels were obtained based on the HW model. From the experimental outcomes displayed in Figs.6–8, it can be concluded that, when using the accuracy as the key discriminator, the correct key is not recovered by all NDLPA. However, when using the loss value as the key discriminator, the correct key is recovered by all the NDLPA. Compared with MLP-NDLPA and CNN-NDLPA, RNN-NDLPA performs slightly better from the point of view of difference. Fig. 3Open in figure viewerPowerPoint Loss (left) and accuracy (right) when applying RNN-NDLPA using labels based on the bit model for SM4 Fig. 4Open in figure viewerPowerPoint Loss (left) and accuracy (right) when applying MLP-NDLPA using labels based on the bit model for SM4 Fig. 5Open in figure viewerPowerPoint Loss (left) and accuracy (right) when applying CNN-NDLPA using labels based on the bit model for SM4 Fig. 6Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of RNN-NDLPA using labels based on the HW model for SM4 Fig. 7Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of MLP-NDLPA using labels based on the HW model for SM4 Fig. 8Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of CNN-NDLPA using labels based on the HW model for SM4 2. Key recovery for the DES implementation This section introduces the key-recovery experiment for the DES hardware implementation using NDLPA. The attacked device in this experiment was also a smart card with a 32-bit CPU and 0.13 m processing. The experimental steps and network structure were the same as with the key recovery for the SM4 implementation. The power consumption of a full DES encryption is plotted in Fig.9. Fig. 9Open in figure viewerPowerPoint Power consumption of a full DES encryption Fig.9 shows no obvious features of the DES hardware implementation, and the operation time is very short. In this experiment, we performed NDLPA with e n = 100 epochs using a set of T = 100000 traces consisting of 350 points. The labels were based on the bit model. From the experimental outcomes shown in Figs.10–12, it can be concluded that, regardless of whether the accuracy or loss value was used as the key discriminator, the correct key was successfully recovered by both RNN-NDLPA and MLP-NDLPA. However, RNN-NDLPA performed better than MLP-NDLPA in terms of difference, while the correct key could not be recovered by CNN-NDLPA. Fig. 10Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of RNN-NDLPA using labels based on the bit model for the DES Fig. 11Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of MLP-NDLPA using labels based on the bit model for the DES Fig. 12Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of CNN-NDLPA using labels based on the bit model for the DES In this experiment, we performed NDLPA with e n = 100 epochs using a set of T = 100000 traces consisting of 350 points. The labels were based on the HW model. From the experimental outcomes displayed in Figs.13–15, it can be concluded that, regardless of whether the accuracy or loss value was used as the key discriminator, all the NDLPA failed to recover the correct key because the hypothetical power-consumption values, based on the HW model, could not characterize the realistic power consumption properly. Fig. 13Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of RNN-NDLPA using labels based on the HW model for the DES Fig. 14Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of MLP-NDLPA using labels based on the HW model for the DES Fig. 15Open in figure viewerPowerPoint Loss (left) and accuracy (right) resulting from the application of CNN-NDLPA using labels based on the HW model for the DES The experimental results for the SM4 software implementation show that all three NDLPA recovered the correct key of the SM4 software implementation based on the bit or HW model. The experimental results for the DES hardware implementation show that the correct key was successfully recovered by both RNN-NDLPA and MLP-NDLPA, but that NDLPA was limited to labels based on the bit model. Above all, in the non-profiled scenario, RNN-NDLPA performed better than MLP-NDLPA and CNN-NDLPA, and indeed, labels for training provided better results based on the bit model than on the HW model[5]. V. Conclusions In the non-profiled scenario, the required attack conditions are greatly reduced, such as NDLPA and CPA. As we know, CPA can recover the correct key when the key guess corresponds to the maximum correlation coefficient. However, NDLPA can recover the correct key if it corresponds to the steady highest accuracy or the lowest loss value. It can be concluded that NDLPA and CPA both exploit the data-dependence of the power consumption of the device, and it is therefore necessary to find one power-consumption model that can characterize the realistic power consumption well. In this study, we chose the RNN, MLP, and CNN algorithms to perform NDLPA to recover the SM4 and AES keys. We proposed combining the RNN algorithm with power analysis and validated this approach experimentally. The NDLPA conditions can easily be satisfied, thereby providing a new effective attack method for evaluating smart-card security. The benefits of this approach warrant its in-depth study. Biographies MA Xiangliang received the Ph.D. degree from University of Chinese Academy of Sciences in 2020. He is now a postdoctoral researcher in Tsinghua University. His research interests include information security and side channel attack. LI Bing is now a senior engineer in National Research Center for Information Technology Security. His research interests include cyberspace security and cryptographic algorithm application. WANG Hong received the Ph.D. degree from Xidian University in 2001. He did post-doctoral research at Chinese Academy of Sciences (2001–2005). He is now a senior engineer in National Research Center for Information Technology Security. His research interests include cryptography, cyberspace security and information security evaluation. WU Di received the Ph.D. degree from University of Chinese Academy of Sciences in 2013. She is now a senior engineer in China Cybersecurity Review Technology and Certification Center. Her research interests include information security evaluation. ZHANG Lizhen is now a cryptography engineer in National Research Center for Information Technology Security. Her research interests include cryptographic algorithm application and side channel attack. HUANG Kezhen is now a Ph.D. candidate of Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences. His research interests include network security situation and cyber threat intelligence. DUAN Xiaoyi (corresponding author) received the Ph.D. degree from Beihang University in 2009. He is now a lecturer in Beijing Electronic Science and Technology Institute. 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