高级搜索

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于深度学习的Android恶意软件检测:成果与挑战

陈怡 唐迪 邹维

陈怡, 唐迪, 邹维. 基于深度学习的Android恶意软件检测:成果与挑战[J]. 电子与信息学报, 2020, 42(9): 2082-2094. doi: 10.11999/JEIT200009
引用本文: 陈怡, 唐迪, 邹维. 基于深度学习的Android恶意软件检测:成果与挑战[J]. 电子与信息学报, 2020, 42(9): 2082-2094. doi: 10.11999/JEIT200009
Yi CHEN, Di TANG, Wei ZOU. Android Malware Detection Based on Deep Learning: Achievements and Challenges[J]. Journal of Electronics & Information Technology, 2020, 42(9): 2082-2094. doi: 10.11999/JEIT200009
Citation: Yi CHEN, Di TANG, Wei ZOU. Android Malware Detection Based on Deep Learning: Achievements and Challenges[J]. Journal of Electronics & Information Technology, 2020, 42(9): 2082-2094. doi: 10.11999/JEIT200009

基于深度学习的Android恶意软件检测:成果与挑战

doi: 10.11999/JEIT200009
基金项目: 中国科学院重点实验室基金(CXJJ-19S022)
详细信息
    作者简介:

    陈怡:1991年生,博士生,研究方向为移动应用安全、漏洞挖掘

    唐迪:1991年生,博士生,研究方向为基于机器学习的安全研究

    邹维:1964年生,研究员,博士生导师,研究方向为网络与软件安全

    通讯作者:

    邹维 zouwei@iie.ac.cn

  • 1)百度手机助手:https://shouji.baidu.com2)小米应用商店:http://app.mi.com3)华为应用市场:https://appstore.huawei.com4)VirusTotal:https://www.virustotal.com
  • 5)下载地址:http://R2D2.TWMAN.ORG
  • 6)表3表4表5中,加粗条目表示该指标下最优异的测试结果。
  • 中图分类号: TP309.5

Android Malware Detection Based on Deep Learning: Achievements and Challenges

Funds: Foundation of Key Laboratory of Network Assessment Technology, Chinese Academy of Sciences (CXJJ-19S022)
  • 摘要: 随着Android应用的广泛使用,Android恶意软件数量迅速增长,对用户的财产、隐私等造成的安全威胁越来越严重。近年来基于深度学习的Android恶意软件检测成为了当前安全领域的研究热点。该文分别从数据采集、应用特征、网络结构、效果检测4个方面,对该研究方向已有的学术成果进行了分析与总结,讨论了它们的局限性与所面临的挑战,并就该方向未来的研究重点进行了展望。
  • 表  1  Android恶意软件公开数据集统计表

    数据集名称恶意软件数量软件收集时间软件检测方法下载链接
    VirusShare[24]343118792011至今未说明https://virusshare.com
    AndroZoo[25]13029682011至今VirusTotalhttps://androzoo.uni.lu
    ArgusLab[26]246502010~2016VirusTotalhttp://amd.arguslab.org
    Drebin[28]55602010~2012VirusTotalhttp://contagiominidump.blogspot.com
    ISCX[29]19292012~2015VirusTotalhttps://www.unb.ca/cic/datasets/index.html
    Genome[30]12602010~2011未说明http://www.malgenomeproject.org
    Contagio[27]2522011~2018未说明http://contagiominidump.blogspot.com
    下载: 导出CSV

    表  2  公司合作及数据采集统计表

    文献合作公司良性软件恶意软件
    文献[31]腾讯安全实验室83784106912
    文献[32]McAfee1962011505
    文献[20]McAfee36272475
    文献[33]Comodo25002500
    文献[34]Comodo15001500
    文献[35]Leopard Mobile Inc2000000
    下载: 导出CSV

    表  3  在相同数据下现有深度学习模型与传统机器学习模型效果对比统计表(%)

    研究工作评价指标深度学习模型传统机器学习模型
    支持向量机决策树朴素贝叶斯逻辑回归随机森林K最近邻
    文献[12]m496.580.077.579.078.0
    文献[14]m110053.347.0
    m298.334.854.0
    m499.466.082.0
    文献[19]m195.7792.0875.0979.2264.18
    m297.8493.7598.6491.8295.91
    m496.7692.8482.9583.8671.19
    文献[22]m199.5294.2393.7795.6497.0495.40
    m299.8395.8994.6895.9094.6993.16
    m399.7495.0594.2295.7795.8594.27
    m499.6894.9794.1395.8295.9394.29
    文献[32]m194.8287.69276.593.8
    m297.7687.59276.893.8
    m590.8694.495.585.597.1
    m69.145.64.514.52.9
    m72.2424.213.93812
    注:各评价指标的含义如下。m1:精确率(Precision),m2:召回率/真正率(recall/TPR),m3:F-measure,m4:准确率(accuracy),m6:假正率(FPR),m7:假负率(FNR)
    下载: 导出CSV

    表  4  在不同数据不同特征下现有基于深度学习的方法与基于传统机器学习的方法效果对比统计表

    研究工作机器学习模型m1(%)m2(%)m3(%)m4(%)m6(%)m7(%)m8(s)
    文献[11]深度学习9899
    文献[28]支持向量机93.9
    文献[62]决策树78
    文献[63]朴素贝叶斯93
    文献[61]K最近邻99
    文献[64]极限梯度提升决策树9797
    文献[35]深度学习969390.5
    文献[28]支持向量机94.01.00.75
    文献[65]随机森林95.3920.3419.8
    文献[39]深度学习98.8498.4798.6598.86
    文献[66]逻辑回归80.9987.1183.9383.26
    文献[44]深度学习98.981.58
    文献[67]随机森林97.424.33
    文献[20]深度学习99959798
    文献[68]支持向量机98
    文献[69]朴素贝叶斯94919291
    文献[67]随机森林98979797
    注:各评价指标的含义如下。m1:精确率(Precision),m2:召回率/真正率(recall/TPR),m3:F-measure,m4:准确率(accuracy),m6:假正率(FPR),m7:假负率(FNR),m8:检测时间
    下载: 导出CSV

    表  5  基于深度学习的Android恶意软件检测工作效果互相对比统计表(%)

    研究工作m1m2m3m4m6m7
    文献[11]9998
    文献[19]96.8
    文献[20]8687
    文献[35]969390.5
    文献[20]99.39932.5
    文献[39]98.8798.4798.6598.86
    文献[13]83.2487.6785.3984.95
    文献[18]94.7691.3193.0093.10
    文献[20]6798.4771.0069.00
    文献[44]98.981.58
    文献[20]89.506.72
    文献[32]98.0999.5698.8298.5
    文献[33]93.9693.3693.6893.68
    文献[19]96.7896.7696.7696.76
    文献[20]99959798
    文献[21]95.31
    文献[35]93
    文献[33]93.68
    注:各评价指标的含义如下。m1:精确率(Precision),m2:召回率/真正率(recall/TPR),m3:F-measure,m4:准确率(accuracy),m6:假正率(FPR),m7:假负率(FNR)
    下载: 导出CSV
  • CHAU M and REITH R. Smartphone market share[EB/OL]. https://www.idc.com/promo/smartphone-market-share/os, 2019.
    Tencent Mobile Butler. Tencent mobile security lab mobile security report in the first half year of 2019[EB/OL]. https://m.qq.com/security_lab/news_detail_517.html, 2019.
    WANG Bolun, YAO Yuanshun, SHAN S, et al. Neural cleanse: Identifying and mitigating backdoor attacks in neural networks[C]. 2019 IEEE Symposium on Security and Privacy, San Francisco, USA, 2019: 707–723. doi: 10.1109/SP.2019.00031.
    SAFAVIAN S R and LANDGREBE D. A survey of decision tree classifier methodology[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1991, 21(3): 660–674. doi: 10.1109/21.97458
    SUYKENS J A K and VANDEWALLE J. Least squares support vector machine classifiers[J]. Neural Processing Letters, 1999, 9(3): 293–300. doi: 10.1023/A:1018628609742
    MCCALLUM A and NIGAM K. A comparison of event models for naive Bayes text classification[C]. AAAI-98 Workshop on Learning for Text Categorization, Madison, Isconsin, USA, 1998: 41–48.
    王鑫, 李可, 宁晨, 等. 基于深度卷积神经网络和多核学习的遥感图像分类方法[J]. 电子与信息学报, 2019, 41(5): 1098–1105. doi: 10.11999/JEIT180628

    WANG Xin, LI Ke, NING Chen, et al. Remote sensing image classification method based on deep convolution neural network and multi-kernel learning[J]. Journal of Electronics &Information Technology, 2019, 41(5): 1098–1105. doi: 10.11999/JEIT180628
    徐少平, 张贵珍, 李崇禧, 等. 基于深度置信网络的随机脉冲噪声快速检测算法[J]. 电子与信息学报, 2019, 41(5): 1130–1136. doi: 10.11999/JEIT180558

    XU Shaoping, ZHANG Guizhen, LI Chongxi, et al. A fast random-valued impulse noise detection algorithm based on deep belief network[J]. Journal of Electronics &Information Technology, 2019, 41(5): 1130–1136. doi: 10.11999/JEIT180558
    杨宏宇, 王峰岩. 基于深度卷积神经网络的气象雷达噪声图像语义分割方法[J]. 电子与信息学报, 2019, 41(10): 2373–2381. doi: 10.11999/JEIT190098

    YANG Hongyun and WANG Fengyan. Meteorological radar noise image semantic segmentation method based on deep convolutional neural network[J]. Journal of Electronics &Information Technology, 2019, 41(10): 2373–2381. doi: 10.11999/JEIT190098
    STATISTA. Number of available applications in the Google Play Store from December 2009 to June 2020[EB/OL]. https://www.statista.com/statistics/266210/number-of-available-applications-in-the-google-play-store/, 2019.
    KIM T, KANG B, RHO M, et al. A multimodal deep learning method for Android malware detection using various features[J]. IEEE Transactions on Information Forensics and Security, 2019, 14(3): 773–788. doi: 10.1109/TIFS.2018.2866319
    YUAN Zhenlong, LU Yongqiang, WANG Zhaoguo, et al. Droid-sec: Deep learning in android malware detection[C]. 2014 ACM Conference on SIGCOMM, Chicago, USA, 2014: 371–372. doi: 10.1145/2619239.2631434.
    XIAO Xi, WANG Zhenlong, LI Qing, et al. Back-propagation neural network on Markov chains from system call sequences: A new approach for detecting Android malware with system call sequences[J]. IET Information Security, 2017, 11(1): 8–15. doi: 10.1049/iet-ifs.2015.0211
    NIX R and ZHANG Jian. Classification of Android apps and malware using deep neural networks[C]. 2017 International Joint Conference on Neural Networks, Anchorage, USA, 2017: 1871–1878. doi: 10.1109/IJCNN.2017.7966078.
    HUANG Na, XU Ming, ZHENG Ning, et al. Deep android malware classification with API-based feature graph[C]. The 18th IEEE International Conference on Trust, Security and Privacy in Computing and Communications/13th IEEE International Conference on Big Data Science and Engineering, Rotorua, New Zealand, 2019: 296–303. doi: 10.1109/TrustCom/BigDataSE.2019.00047.
    ABDERRAHMANE A, ADNANE G, YACINE C, et al. Android malware detection based on system calls analysis and CNN classification[C]. 2019 IEEE Wireless Communications and Networking Conference Workshop, Marrakech, Morocco, 2019: 1–6. doi: 10.1109/WCNCW.2019.8902627.
    WANG Wei, ZHAO Mengxue, and WANG Jigang. Effective android malware detection with a hybrid model based on deep autoencoder and convolutional neural network[J]. Journal of Ambient Intelligence and Humanized Computing, 2019, 10(8): 3035–3043. doi: 10.1007/s12652-018-0803-6
    XIAO Xi, ZHANG Shaofeng, MERCALDO F, et al. Android malware detection based on system call sequences and LSTM[J]. Multimedia Tools and Applications, 2019, 78(4): 3979–3999. doi: 10.1007/s11042-017-5104-0
    YUAN Zhenlong, LU Yongqiang, and XUE Yibo. Droiddetector: Android malware characterization and detection using deep learning[J]. Tsinghua Science and Technology, 2016, 21(1): 114–123. doi: 10.1109/TST.2016.7399288
    MCLAUGHLIN N, MARTINEZ DEL RINCON J, KANG B, et al. Deep android malware detection[C]. The 7th ACM on Conference on Data and Application Security and Privacy, Scottsdale, USA, 2017: 301–308. doi: 10.1145/3029806.3029823.
    NAWAY A and LI Yuancheng. Using deep neural network for Android malware detection[EB/OL]. https://arxiv.org/pdf/1904.00736, 2019.
    WANG Zhiqiang, LI Gefei, CHI Yaping, et al. Android malware detection based on convolutional neural networks[C]. The 3rd International Conference on Computer Science and Application Engineering, Sanya, China, 2019: 1–151. doi: 10.1145/3331453.3361306.
    SABHADIYA S, BARAD J, and GHEEWALA J. Android malware detection using deep learning[C]. The 3rd International Conference on Trends in Electronics and Informatics, Tirunelveli, India, 2019: 1254–1260. doi: 10.1109/ICOEI.2019.8862633.
    MELISSA. VirusShare. Com-because sharing is caring[EB/OL]. https://virusshare.com, 2019.
    ALLIX K, BISSYANDÉ T F, KLEIN J, et al. Androzoo: Collecting millions of android apps for the research community[C]. The 13th IEEE/ACM Working Conference on Mining Software Repositories, Austin, TX, USA, 2016: 468–471.
    WEI Fengguo, LI Yuping, ROY S, et al. Deep ground truth analysis of current android malware[C]. The 14th International Conference on Detection of Intrusions and Malware, and Vulnerability Assessment, Bonn, Germany, 2017: 252–276. doi: 10.1007/978-3-319-60876-1.
    MILAPARKOUR. Contagio mobile mobile malware mini dump[EB/OL]. http://contagiominidump.blogspot.com, 2019.
    ARP D, SPREITZENBARTH M, HUBNER M, et al. Drebin: Effective and explainable detection of android malware in your pocket[C]. The 21st Annual Network and Distributed System Security Symposium, San Diego, California, USA, 2014: 23–26. doi: 10.14722/ndss.2014.23247.
    KADIR A F A, STAKHANOVA N, and GHORBANI A A. Android botnets: What URLs are telling us[C]. The 9th International Conference on Network and System Security, New York, NY, 2015: 78–79. doi: 10.1007/978-3-319-25645-0_6.
    ZHOU Yajin and JIANG Xuxian. Dissecting android malware: Characterization and evolution[C]. 2012 IEEE Symposium on Security and Privacy, San Francisco, USA, 2012: 95–109. doi: 10.1109/SP.2012.16.
    YE Yanfang, HOU Shifu, CHEN Lingwei, et al. Out-of-sample node representation learning for heterogeneous graph in real-time android malware detection[C]. The 28th International Joint Conference on Artificial Intelligence, Macao, China, 2019: 4150–4156. doi: 10.24963/ijcai.2019/576.
    ALZAYLAEE M K, YERIMA S Y, and SEZER S. DL-Droid: Deep learning based android malware detection using real devices[J]. Computers & Security, 2020, 89: 101663. doi: 10.1016/j.cose.2019.101663
    HOU Shifu, SAAS A, CHEN Lifei, et al. Deep4MalDroid: A deep learning framework for android malware detection based on Linux kernel system call graphs[C]. 2016 IEEE/WIC/ACM International Conference on Web Intelligence Workshops, Omaha, USA, 2016: 104–111. doi: 10.1109/WIW.2016.040.
    HOU Shifu, SAAS A, YE Yanfang, et al. Droiddelver: An android malware detection system using deep belief network based on API call blocks[C]. WAIM 2016 International Conference on Web-Age Information Management, Nanchang, China, 2016: 54–55. doi: 10.1007/978-3-319-47121-1_5.
    HUANG T H D and KAO H Y. R2-D2: Color-inspired convolutional neural network (CNN)-based android malware detections[C]. 2018 IEEE International Conference on Big Data, Seattle, USA, 2018: 2633–2642. doi: 10.1109/BigData.2018.8622324.
    NAUMAN M, TANVEER T A, KHAN S, et al. Deep neural architectures for large scale android malware analysis[J]. Cluster Computing, 2018, 21(1): 569–588. doi: 10.1007/s10586-017-0944-y
    DUC N V and GIANG P T. NADM: Neural network for Android detection malware[C]. The 9th International Symposium on Information and Communication Technology, Danang City, Vietnam, 2018: 449–455. doi: 10.1145/3287921.3287977.
    AAFER Y, DU WENLIANG, and YIN Heng. Droidapiminer: Mining API-level features for robust malware detection in android[C]. The 9th International Conference on Security and Privacy in Communication Systems, Sydney, Australia, 2013: 86–103. doi: 10.1007/978-3-319-04283-1_6.
    PEKTAŞ A and ACARMAN T. Deep learning for effective Android malware detection using API call graph embeddings[J]. Soft Computing, 2020, 24(2): 1027–1043. doi: 10.1007/s00500-019-03940-5
    SUN Yizhou and HAN Jiawei. Mining heterogeneous information networks: Principles and methodologies[J]. Synthesis Lectures on Data Mining and Knowledge Discovery, 2012, 3(2): 1–159. doi: 10.2200/S00433ED1V01Y201207DMK005
    FAN Yujie, HOU Shifu, ZHANG Yiming, et al. Gotcha-sly malware!: Scorpion a metagraph2vec based malware detection system[C]. The 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, London, UK, 2018: 253–262. doi: 10.1145/3219819.3219862.
    DONG Yuxiao, CHAWLA N V, and SWAMI A. Metapath2vec: Scalable representation learning for heterogeneous networks[C]. The 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Halifax, Canada, 2017: 135–144. doi: 10.1145/3097983.3098036.
    FU Taoyang, LEE W C, and LEI Zhen. Hin2vec: Explore meta-paths in heterogeneous information networks for representation learning[C]. 2017 ACM on Conference on Information and Knowledge Management, Singapore, 2017: 1797–1806. doi: 10.1145/3132847.3132953.
    MA Zhuo, GE Haoran, LIU Yang, et al. A combination method for Android malware detection based on control flow graphs and machine learning algorithms[J]. IEEE Access, 2019, 7: 21235–21245. doi: 10.1109/ACCESS.2019.2896003
    GEORGE R C and JAIN A K. Markov random field texture models[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1983, PAMI-5(1): 25–39. doi: 10.1109/TPAMI.1983.4767341
    CSÁJI B C. Approximation with artificial neural networks[D]. [Master dissertation], Eotvos Loránd University, 2001: 7.
    KRIZHEVSKY A, SUTSKEVER I, and HINTON G E. ImageNet classification with deep convolutional neural networks[C]. The 25th International Conference on Neural Information Processing Systems, Lake Tahoe, USA, 2012: 1106–1114.
    LECUN Y, BOTTOU L, BENGIO Y, et al. Gradient-based learning applied to document recognition[J]. Proceedings of the IEEE, 1998, 86(11): 2278–2324. doi: 10.1109/5.726791
    SZEGEDY C, LIU Wei, JIA Yangqing, et al. Going deeper with convolutions[C]. The 2015 IEEE Conference on Computer Vision and Pattern Recognition, Boston, USA, 2015: 1–9. doi: 10.1109/CVPR.2015.7298594.
    BERGSTRA J, BARDENET R, BENGIO Y, et al. Algorithms for hyper-parameter optimization[C]. The 25th Annual Conference on Neural Information Processing Systems 2011, Granada, Spain, 2011: 2546–2554.
    SZEGEDY C, VANHOUCKE V, IOFFE S, et al. Rethinking the inception architecture for computer vision[C]. 2016 IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, USA, 2016: 2818–2826. doi: 10.1109/CVPR.2016.308.
    HOCHREITER S and SCHMIDHUBER J. Long short-term memory[J]. Neural Computation, 1997, 9(8): 1735–1780. doi: 10.1162/neco.1997.9.8.1735
    MNIH V, HEESS N, GRAVES A, et al. Recurrent models of visual attention[C]. The 27th International Conference on Neural Information Processing Systems, Montreal, Canada, 2014: 2204–2212.
    SALAKHUTDINOV R and MURRAY I. On the quantitative analysis of deep belief networks[C]. The 25th International Conference on Machine Learning, Helsinki, Finland, 2008: 872–879. doi: 10.1145/1390156.1390266.
    ALONSO J M and CHEN Yao. Receptive field[J]. Scholarpedia, 2009, 4(1): 5393. doi: 10.4249/scholarpedia.5393
    ALLEN F E. Control flow analysis[J]. ACM SIGPLAN Notices, 1970, 5(7): 1–19. doi: 10.1145/390013.808479
    SCARSELLI F, GORI M, TSOI A C, et al. The graph neural network model[J]. IEEE Transactions on Neural Networks, 2009, 20(1): 61–80. doi: 10.1109/TNN.2008.2005605
    JIANG Bo, ZHANG Ziyan, LIN Doudou, et al. Semi-supervised learning with graph learning-convolutional networks[C]. 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, USA, 2019: 11305–11312. doi: 10.1109/CVPR.2019.01157.
    MARON H, BEN-HAMU H, SERVIANSKY H, et al. Provably powerful graph networks[C]. The 33rd Conference on Neural Information Processing Systems, Vancouver, Canada, 2019: 2153–2164.
    GORI M, MONFARDINI G, and SCARSELLI F. A new model for learning in graph domains[C]. 2005 IEEE International Joint Conference on Neural Networks, Montreal, Canada, 2005: 729–734.
    WU Dongjie, MAO C H, WEI T E, et al. Droidmat: Android malware detection through manifest and API calls tracing[C]. The 7th Asia Joint Conference on Information Security, Tokyo, Japan, 2012: 62–69. doi: 10.1109/AsiaJCIS.2012.18.
    HUANG C Y, TSAI Y T, and HSU C H. Performance evaluation on permission-based detection for android malware[C]. International Computer Symposium ICS 2012 Held at Hualien, Taipei, China, 2013: 111–120. doi: 10.1007/978-3-642-35473-1_12.
    ZHANG Mu, DUAN Yue, YIN Heng, et al. Semantics-aware android malware classification using weighted contextual API dependency graphs[C]. 2014 ACM SIGSAC Conference on Computer and Communications Security, Scottsdale, USA, 2014: 1105–1116. doi: 10.1145/2660267.2660359.
    FEREIDOONI H, CONTI M, YAO Danfeng, et al. ANASTASIA: Android malware detection using static analysis of applications[C]. The 8th IFIP International Conference on New Technologies, Mobility and Security, Larnaca, Cyprus, 2016: 1–5. doi: 10.1109/NTMS.2016.7792435.
    YANG Chao, XU Zhaoyan, GU Guofei, et al. Droidminer: Automated mining and characterization of fine-grained malicious behaviors in android applications[C]. The 19th European Symposium on Research in Computer Security, Wroclaw, Poland, 2014: 163–182. doi: 10.1007/978-3-319-11203-9_10.
    DIMJAŠEVIĆ M, ATZENI S, UGRINA I, et al. Evaluation of android malware detection based on system calls[C]. 2016 ACM on International Workshop on Security and Privacy Analytics, New Orleans, USA, 2016: 1–8. doi: 10.1145/2875475.2875487.
    YERIMA S Y, SEZER S, and MUTTIK I. High accuracy android malware detection using ensemble learning[J]. IET Information Security, 2015, 9(6): 313–320. doi: 10.1049/iet-ifs.2014.0099
    JEROME Q, ALLIX K, STATE R, et al. Using opcode-sequences to detect malicious Android applications[C]. 2014 IEEE International Conference on Communications, Sydney, Australia, 2014: 914–919. doi: 10.1109/ICC.2014.6883436.
    YERIMA S Y, SEZER S, MCWILLIAMS G, et al. A new android malware detection approach using Bayesian classification[C]. The 27th IEEE International Conference on Advanced Information Networking and Applications, Barcelona, Spain, 2013: 121–128. doi: 10.1109/AINA.2013.88.
    POWERS D M W. Evaluation: From precision, recall and F-measure to ROC, informedness, markedness & correlation[J]. Journal of Machine Learning Technologies, 2011, 2(1): 37–63.
  • 加载中
表(5)
计量
  • 文章访问数:  2812
  • HTML全文浏览量:  817
  • PDF下载量:  256
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-01-20
  • 修回日期:  2020-07-30
  • 网络出版日期:  2020-08-07
  • 刊出日期:  2020-09-27

目录

    /

    返回文章
    返回