复杂网络中蠕虫的传播行为研究
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摘要
互联网(Internet)已经成为当今社会最有用的工具之一,它改变了人们的生活方式和工作方式。Internet本身所具有的开放性、优越性和实用性使其成为人类进入到信息社会的重要标志。Internet在方便快捷地提供给人们各种信息和各种服务的同时,也给恶意代码的传播和蔓延提供了有利的条件。恶意代码的肆意传播给网络安全造成了严重的威胁,给人们的工作和生活造成了严重的影响。其中以蠕虫造成的危害最为严重。Internet的拓扑结构非常复杂,使得蠕虫的传播行为也不尽相同。因此本文主要研究复杂网络中蠕虫的传播行为。
本文针对蠕虫在复杂网络中的传播行为这个问题,采取从经典的传染病模型入手对复杂网络中蠕虫的传播行为进行了深入研究。全文分为四大部分。第一部分,介绍了复杂网络的基本理论知识,重点描述了几种基本的复杂网络模型。第二部分,详细描述了经典传染病模型,在此基础上,利用复杂网络的传播临界值理论分析研究复杂网络中蠕虫的传播临界值。第三部分,分别利用SIS模型和SIR模型分析研究了蠕虫在复杂网络和移动网络中的传播行为。蠕虫在复杂网络中的传播行为分为三个阶段,并提出相对应的传播模型。蠕虫在移动网络中的传播行为则受到节点密度、节点的移动速度和节点长距离移动的概率的影响,并提出相对应的模型。第四部分,分别利用SIS模型和SIR模型对电子邮件网络中和无线网络中蠕虫的传播行为进行模拟仿真并分析实验结果。
Internet has become one of the most useful tools of social.It has changed people's lifestyles and ways of working. The Internet is a sign of human access to the information society because of its openness, superiority and practicality. Internet provides conveniently various information and services to people, meanwhile, it also gives favorable conditions for the dissemination and spread of malicious code. Wanton spread of malicious code has caused a serious security threat to networks and affected severely the life and work of people. the most serious damage is caused by worms. Internet topology is very complex, making the propagation of worms different. This article researches mainly the worm propagation behavior of complex networks.
This article studies the question which the worm propagation behavior of the complex networks based the classic epidemic model. The paper is divided into four parts. The first part introduces the basic theory of complex networks, focusing on the basic description of several complex network models. The second part describes in detail the classical epidemic model, on this basis, analyses the epidemic threshold of worms in complex networks using the theory of epidemic threshold in complex networks. The third part analyses the epidemic behavior of worms in complex networks and mobile networks using SIR model and SIS model respectively. The epidemic behavior of worms in complex networks is divided into three phases, and proposed the corresponding propagation model of each phases. The epidemic behavior of worms in mobile networks is affected by the density of nodes, the speed of nodes and the probability of node’s long-distance movement, and proposed the corresponding models. The fourth part simulates the propagation of worms in e-mail networks and wireless networks using SIS model and the SIR model respectively, and analyses the experimental results.
本文针对蠕虫在复杂网络中的传播行为这个问题,采取从经典的传染病模型入手对复杂网络中蠕虫的传播行为进行了深入研究。全文分为四大部分。第一部分,介绍了复杂网络的基本理论知识,重点描述了几种基本的复杂网络模型。第二部分,详细描述了经典传染病模型,在此基础上,利用复杂网络的传播临界值理论分析研究复杂网络中蠕虫的传播临界值。第三部分,分别利用SIS模型和SIR模型分析研究了蠕虫在复杂网络和移动网络中的传播行为。蠕虫在复杂网络中的传播行为分为三个阶段,并提出相对应的传播模型。蠕虫在移动网络中的传播行为则受到节点密度、节点的移动速度和节点长距离移动的概率的影响,并提出相对应的模型。第四部分,分别利用SIS模型和SIR模型对电子邮件网络中和无线网络中蠕虫的传播行为进行模拟仿真并分析实验结果。
Internet has become one of the most useful tools of social.It has changed people's lifestyles and ways of working. The Internet is a sign of human access to the information society because of its openness, superiority and practicality. Internet provides conveniently various information and services to people, meanwhile, it also gives favorable conditions for the dissemination and spread of malicious code. Wanton spread of malicious code has caused a serious security threat to networks and affected severely the life and work of people. the most serious damage is caused by worms. Internet topology is very complex, making the propagation of worms different. This article researches mainly the worm propagation behavior of complex networks.
This article studies the question which the worm propagation behavior of the complex networks based the classic epidemic model. The paper is divided into four parts. The first part introduces the basic theory of complex networks, focusing on the basic description of several complex network models. The second part describes in detail the classical epidemic model, on this basis, analyses the epidemic threshold of worms in complex networks using the theory of epidemic threshold in complex networks. The third part analyses the epidemic behavior of worms in complex networks and mobile networks using SIR model and SIS model respectively. The epidemic behavior of worms in complex networks is divided into three phases, and proposed the corresponding propagation model of each phases. The epidemic behavior of worms in mobile networks is affected by the density of nodes, the speed of nodes and the probability of node’s long-distance movement, and proposed the corresponding models. The fourth part simulates the propagation of worms in e-mail networks and wireless networks using SIS model and the SIR model respectively, and analyses the experimental results.
引文
[1]王小帆,李翔,陈关荣.复杂网络理论及其应用[M].北京:清华大学出版社,2006:1-94.
[2]郑辉.学位论文Internet蠕虫研究[D].天津:南开大学信息技术科学学院,2003:30-48.
[3]D. Moore,C. Shannon. Code-Red: a Case Study on the Spread and Victims of an Internet Worm[C]. ACM SICGOMM Internet Measurement Workshop, Marseille, France, 2002:273-284.
[4]D. Moore, V. Paxson, S. Savage, C. Shannon, S. Staniford, N. Weaver,Inside the slammer worm[C]. IEEE Magazine of Security and Privacy,2003,1(4):33-39.
[5]A. Mackie, J. Roculan, R.Russell, M.VanVelzen. Nimda Worm Analysis[J].Security Focus,2001(21):8-16.
[6]Weixiang,qian.http://baike.baidu.com/view/697258.htm.
[7]文伟平,卿汉斯,蒋建春,王业君.网络蠕虫研究与进展[J].软件学报. 2004,15(8):1208-1209.
[8]郑辉,李冠一,涂奉生.蠕虫的行为特征描述和工作原理分析[C].第三届中国信息与通信安全学术会议CCICS,2003(3)3515348:2-11.
[9]周涛,傅忠谦,牛永伟等.复杂网络上传播动力学研究综述[J].自然科学进展,2005(5):513-516.
[10]王平.学位论文大规模网络蠕虫检测与传播抑制[D].哈尔滨:哈尔滨工业大学,2006:4-41.
[11]X.F. WANG, X. LI,G.R. CHEN. Theory and Applications of Complex Networks[M]. Beijing, Tsinghua University Press,2006:5-24.
[12]陈德伟.学位论文复杂网络度分布的研究[D].天津:河北工业大学,2007.
[13]Watts D J, Strogatz S H. Collective dynamics of‘small-world’networks[J].Nature,1998,393(6684):440-442.
[14]Barabasi A-L, Albert R. Emergence of scaling in random networks[J].Science, 1999(286):509–512.
[15]M.E.J. Newman. The Structure and Function of Complex Networks[J].SLAMReview,2003(45):5-46.
[16]陈煌琼.学位论文复杂网络中的病毒传播研究[D].武汉:华中科技大学,2009:7-27.
[17]Barrat A, Weigt M. On the properties of small-world network model[J].Eur Phys J,2000(B13):547–600.
[18]Duncan J.Watts, Steven H.Strogatz. Collective dynamics of‘small-world’networks[J].Nature,1998(393):246-253.
[19]何敏华.学位论文复杂网络上传播动力学研究[D].武汉:华中科技大学,2009:1-10.
[20]覃森.学位论文无标度网络及其应用研究[D].西安:西北工业大学,2006:6-22.
[21]沈维.学位论文恶意代码的分析和防治[D].上海:上海交通大学,2007:14-16.
[22]原野.解析恶意代码的特征与发展趋势[J].计算机安全杂志,2005:387-390.
[23]韩筱卿,王建峰,钟玮等.计算机病毒分析与防范大全[M].北京:电子工业出版社,2006:85-93.
[24]张运凯.学位论文网络蠕虫传播与控制研究[D].西安:西安电子科技大学,2005:13-41.
[25]丁昆.学位论文恶意代码传播机理及其检测防御技术研究[D].北京:北京邮电大学,2008:4-32.
[26]王晓勇.学位论文计算机恶意代码传播及防御技术研究[D].重庆:西南大学,2007:16-24.
[27]史江明.学位论文学位论文复杂网络中的病毒传播研究[D].上海:上海交通大学,2007:8-21.
[28]M.E.J. Newman, C. Moore, D.J. Watts. Mean-field solution of the small-world network model. Physical Review Letters,2000(84):3201-3204.
[29]Eguiluz VM, Klemm K. Epidemic threshold in structured scale-free networks[J]. Phys,Rev,Lett,2002(89)204612:1-4.
[30]J. O. Kephart. How topology affects population dynamics[C].In C. Langton, ed. Artificial Life III, Studies in the Sciences of Complexity,1994,pp.447–463.
[31]梁芳.学位论文复杂网络拓扑结构与流行病动力学相互作用的研究[D].武汉:华中科技大学,2007:8-14.
[32]彭俊.学位论文复杂网络的拓扑结构与传播模型的研究[D].西安:西安电子科技大学,2009:2-32.
[33]李平.学位论文复杂网络的动力学行为研究[D].成都:电子科技大学,2009:3-16.
[34]M. Barthelemy, A. Barrat, et al. Velocity and Hierarchical Spread of Epidemic Outbreaks in Scale-Free Neworks[J]. Phys Re Lett,2004,92(17)178701:1-4.
[35]Watts D J. Small Worlds: The Dynamics of Networks Between Order and Randomness[M]. Princeton, NJ: Princeton Univ. Press,1999:166-180.
[36]M. E. J. Newman, D. J. Watts. Scaling and percolation in the small-world network model[J].Phys Rev E,1999(60):7332–7342.
[37]Chen Qinghua, Shi Dinghua, The modeling of scale-free networks[J], Physica A,2004(335):240-248.
[38]R, Pastor-Satorras, A. Vespignani. Epidemic spreading in scale-free networks[J].Physical Review Letters,2001,86(14),pp:3200-3203.
[39]Y. Moreno, R. Pastor, A. Vespignani. Epidemic outbreaks in complex heterogeneous networks[J].The European Physical Journal B,2002(26), pp:521-529.
[40]Romualdo Pastor-Satorras, Alessandro Vespignani. Epidemic dynamics and endemic states in complex networks[J].Physical Review E,2001(63)066117:1-7.
[41]M. Boguna, R. Pastor-Satorras. Epidemic spreading in correlated complex networks[J].Phys Rev E,2002(65)047104:1-4.
[42]May R M, Lloyd A L. Infection dynamics on scale-free networks[J].Phys Rev E,2001(64)066112:1-4.
[43]Newman M E J. Spread of epidemic disease on networks[J].Phys Rev E, 2002(66)016128:1-2.
[44]J. O. Kephart, S. R. White. Measuring and Modeling Computer Virus Prevalence[C].Proceedings of the 1993 IEEE Symposimum on Security and Privacy,1993,p.2.
[45]Barthelemy M, Amaral LAN. Small world networks: evidence for a crossover picture[J].Phys,Rev,Lett,1999(82):3180–3183.
[46]Vazquez A. Pastor-Satorras R, Vespignani A. Large-scale topological and dynamical properties of the Internet[J].Phys Rev E,2002(65):1103-1113.
[47]Chang-guang Wang, Jian-feng Ma. Modeling Malicious code spread in scale-free networks of moving agents[C].International Conference on Computer Science and Software Engineering, 2008:546-549.
[48]M.E.J. Newman, Stephanie Forrest, Justin Balthrop. Email networks and the spread of computer viruses[J]. Physical Review E,2002(66)035101:1-4.
[49]Cliff C, Zou Don Towsley, Weibo Gong. Modeling and Simulation Study of the Propagation and Defense of Internet Email Worm[C].IEEE Transactions on Dependable and Secure Computing,2007,4(2):105-118.
[2]郑辉.学位论文Internet蠕虫研究[D].天津:南开大学信息技术科学学院,2003:30-48.
[3]D. Moore,C. Shannon. Code-Red: a Case Study on the Spread and Victims of an Internet Worm[C]. ACM SICGOMM Internet Measurement Workshop, Marseille, France, 2002:273-284.
[4]D. Moore, V. Paxson, S. Savage, C. Shannon, S. Staniford, N. Weaver,Inside the slammer worm[C]. IEEE Magazine of Security and Privacy,2003,1(4):33-39.
[5]A. Mackie, J. Roculan, R.Russell, M.VanVelzen. Nimda Worm Analysis[J].Security Focus,2001(21):8-16.
[6]Weixiang,qian.http://baike.baidu.com/view/697258.htm.
[7]文伟平,卿汉斯,蒋建春,王业君.网络蠕虫研究与进展[J].软件学报. 2004,15(8):1208-1209.
[8]郑辉,李冠一,涂奉生.蠕虫的行为特征描述和工作原理分析[C].第三届中国信息与通信安全学术会议CCICS,2003(3)3515348:2-11.
[9]周涛,傅忠谦,牛永伟等.复杂网络上传播动力学研究综述[J].自然科学进展,2005(5):513-516.
[10]王平.学位论文大规模网络蠕虫检测与传播抑制[D].哈尔滨:哈尔滨工业大学,2006:4-41.
[11]X.F. WANG, X. LI,G.R. CHEN. Theory and Applications of Complex Networks[M]. Beijing, Tsinghua University Press,2006:5-24.
[12]陈德伟.学位论文复杂网络度分布的研究[D].天津:河北工业大学,2007.
[13]Watts D J, Strogatz S H. Collective dynamics of‘small-world’networks[J].Nature,1998,393(6684):440-442.
[14]Barabasi A-L, Albert R. Emergence of scaling in random networks[J].Science, 1999(286):509–512.
[15]M.E.J. Newman. The Structure and Function of Complex Networks[J].SLAMReview,2003(45):5-46.
[16]陈煌琼.学位论文复杂网络中的病毒传播研究[D].武汉:华中科技大学,2009:7-27.
[17]Barrat A, Weigt M. On the properties of small-world network model[J].Eur Phys J,2000(B13):547–600.
[18]Duncan J.Watts, Steven H.Strogatz. Collective dynamics of‘small-world’networks[J].Nature,1998(393):246-253.
[19]何敏华.学位论文复杂网络上传播动力学研究[D].武汉:华中科技大学,2009:1-10.
[20]覃森.学位论文无标度网络及其应用研究[D].西安:西北工业大学,2006:6-22.
[21]沈维.学位论文恶意代码的分析和防治[D].上海:上海交通大学,2007:14-16.
[22]原野.解析恶意代码的特征与发展趋势[J].计算机安全杂志,2005:387-390.
[23]韩筱卿,王建峰,钟玮等.计算机病毒分析与防范大全[M].北京:电子工业出版社,2006:85-93.
[24]张运凯.学位论文网络蠕虫传播与控制研究[D].西安:西安电子科技大学,2005:13-41.
[25]丁昆.学位论文恶意代码传播机理及其检测防御技术研究[D].北京:北京邮电大学,2008:4-32.
[26]王晓勇.学位论文计算机恶意代码传播及防御技术研究[D].重庆:西南大学,2007:16-24.
[27]史江明.学位论文学位论文复杂网络中的病毒传播研究[D].上海:上海交通大学,2007:8-21.
[28]M.E.J. Newman, C. Moore, D.J. Watts. Mean-field solution of the small-world network model. Physical Review Letters,2000(84):3201-3204.
[29]Eguiluz VM, Klemm K. Epidemic threshold in structured scale-free networks[J]. Phys,Rev,Lett,2002(89)204612:1-4.
[30]J. O. Kephart. How topology affects population dynamics[C].In C. Langton, ed. Artificial Life III, Studies in the Sciences of Complexity,1994,pp.447–463.
[31]梁芳.学位论文复杂网络拓扑结构与流行病动力学相互作用的研究[D].武汉:华中科技大学,2007:8-14.
[32]彭俊.学位论文复杂网络的拓扑结构与传播模型的研究[D].西安:西安电子科技大学,2009:2-32.
[33]李平.学位论文复杂网络的动力学行为研究[D].成都:电子科技大学,2009:3-16.
[34]M. Barthelemy, A. Barrat, et al. Velocity and Hierarchical Spread of Epidemic Outbreaks in Scale-Free Neworks[J]. Phys Re Lett,2004,92(17)178701:1-4.
[35]Watts D J. Small Worlds: The Dynamics of Networks Between Order and Randomness[M]. Princeton, NJ: Princeton Univ. Press,1999:166-180.
[36]M. E. J. Newman, D. J. Watts. Scaling and percolation in the small-world network model[J].Phys Rev E,1999(60):7332–7342.
[37]Chen Qinghua, Shi Dinghua, The modeling of scale-free networks[J], Physica A,2004(335):240-248.
[38]R, Pastor-Satorras, A. Vespignani. Epidemic spreading in scale-free networks[J].Physical Review Letters,2001,86(14),pp:3200-3203.
[39]Y. Moreno, R. Pastor, A. Vespignani. Epidemic outbreaks in complex heterogeneous networks[J].The European Physical Journal B,2002(26), pp:521-529.
[40]Romualdo Pastor-Satorras, Alessandro Vespignani. Epidemic dynamics and endemic states in complex networks[J].Physical Review E,2001(63)066117:1-7.
[41]M. Boguna, R. Pastor-Satorras. Epidemic spreading in correlated complex networks[J].Phys Rev E,2002(65)047104:1-4.
[42]May R M, Lloyd A L. Infection dynamics on scale-free networks[J].Phys Rev E,2001(64)066112:1-4.
[43]Newman M E J. Spread of epidemic disease on networks[J].Phys Rev E, 2002(66)016128:1-2.
[44]J. O. Kephart, S. R. White. Measuring and Modeling Computer Virus Prevalence[C].Proceedings of the 1993 IEEE Symposimum on Security and Privacy,1993,p.2.
[45]Barthelemy M, Amaral LAN. Small world networks: evidence for a crossover picture[J].Phys,Rev,Lett,1999(82):3180–3183.
[46]Vazquez A. Pastor-Satorras R, Vespignani A. Large-scale topological and dynamical properties of the Internet[J].Phys Rev E,2002(65):1103-1113.
[47]Chang-guang Wang, Jian-feng Ma. Modeling Malicious code spread in scale-free networks of moving agents[C].International Conference on Computer Science and Software Engineering, 2008:546-549.
[48]M.E.J. Newman, Stephanie Forrest, Justin Balthrop. Email networks and the spread of computer viruses[J]. Physical Review E,2002(66)035101:1-4.
[49]Cliff C, Zou Don Towsley, Weibo Gong. Modeling and Simulation Study of the Propagation and Defense of Internet Email Worm[C].IEEE Transactions on Dependable and Secure Computing,2007,4(2):105-118.