基于元胞自动机的复杂信息系统安全风险传播研究

李钊; 徐国爱; 班晓芳; 张毅; 胡正名

doi:10.7498/aps.62.200203

摘要

基于元胞自动机建立复杂信息系统安全风险传播模型, 研究复杂信息系统安全风险在最近邻耦合网络、随机网络,　Watts-Strogatz 小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的传播问题. 通过研究安全风险传播模型在四种网络拓扑下安全风险的传播阈值, 与现有的传播阈值研究成果进行比较, 验证模型的正确性, 并分析验证网络拓扑结构中度分布的异质化程度越高传播阈值越小的结论. 通过对安全风险的传播演化趋势进行研究, 分析验证网络度分布的异质化程度越高、安全风险影响范围越小、传播速度越快的结论, 并指出度分布的异质化程度越高、模型后期的免疫机制对控制安全风险传播的效果越缓慢. 通过对安全风险在传播最早期就趋于消亡的情况进行研究, 分析得出安全风险在传播之初就趋于消亡的消亡率与传播率之间呈现近似负指数的关系, 并且初期的感染源越多安全风险的消亡率越低. 分析了影响复杂信息系统安全风险传播的关键要素, 对复杂信息系统中安全风险传播的控制具有指导作用.

关键词:

Abstract

There models of complex information system security risk propagation are proposed in this paper based on cellular automata, and the probabilistic behaviors of security risk propagation in complex information systems are investigated by running the proposed models on nearest-neighbor coupled network, Erdos-Renyi random graph network, Watts-Strogatz small world network and Barabasi-Albert power law network respectively. Analysis and simulations show that the proposed models describe the behaviors of security risk propagation in the above four kinds of networks perfectly. By researching on the propagation threshold of security risks in four kinds of network topology and comparing with the existing research result, the correctness of the models is verified. The relationship between the heterogeneity of degree distribution and the value of the propagation threshold is analyzed and verified in this paper. Through the research on the evolutionary trends of security risk propagation, the relationship between the heterogeneity of degree distribution and the influence sphere and speed of security risk propagation is analyzed and verified as well. Meanwhile, the relationship between the heterogeneity of degree distribution and the effect of the immune mechanism on controlling security risk propagation is pointed out. Furthermore, the result of simulations describes the negative exponent relationship between security risk extinction rate and the propagation rate. The key factors affecting the security risk propagation are analyzed in this paper, providing the guidance for the control of security risk propagation in complex information systems.

Keywords:

作者及机构信息

1.
北京邮电大学信息安全中心, 北京 100876;

2.
北京邮电大学, 灾备技术国家工程实验室, 北京 100876;

3.
中国信息安全测评中心, 北京 100085

基金项目: 国家自然科学基金(批准号: 60970135, 61170282)、高等学校博士学科点专项科研基金 (批准号: 20120005110017)和国家科技支撑计划 (批准号: 2012BAH06B02)资助的课题．

Authors and contacts

1.
Information Security Center, Beijing University of Posts and Telecommunications, Beijing 100876, China;

2.
National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing 100876, China;

3.
China Information Technology Security Evaluation Center, Beijing 100085, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 60970135, 61170282), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120005110017), and the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2012BAH06B02).

参考文献

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[2]	Zhang Y Z, Fang B X, Chi Y, Yun X C 2007 J. Software 18 137 (in Chinese) [张永铮, 方滨兴, 迟悦, 云晓春 2007 软件学报 18 137]
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[5]	Zou C C, Towsley D, Gong W B 2007 IEEE Trans. Depend. Secure Comput. 4 105
[6]	Zou C C, Gong W, Towsley D 2002 Proceedings of the 9th ACM Conference on Computer and Communications Security Washington, DC, USA, November 18-22, 2002 p10
[7]	Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉荣, 蒋国平2009 58 5911]
[8]	Wang Y Q, Jiang G P 2010 Acta Phys. Sin. 59 6724 (in Chinese) [王亚奇, 蒋国平2010 59 6724]
[9]	Wang Y Q, Jiang G P 2011 Acta Phys. Sin. 60 080510 (in Chinese) [王亚奇, 蒋国平2011 60 080510]
[10]	Jin Z, Liu Q X, Mainul H 2007 Chin. Phys. 16 1267
[11]	Fuentes M A, Kuperman M N 1999 Physica A 267 471
[12]	Sirakoulis G C, Karafyllidis I, Thanailakis A 2000 Ecol. Model. 133 209
[13]	White S H, del Rey A M, Sanchez G R 2009 Appl. Math. Sci. 3 959
[14]	Gagliardi H, Alves D 2010 Math. Popul. Stud. 17 79
[15]	Shan X M, Liu F, Ren Y 2002 Acta Phys. Sin. 51 1175 (in Chinese) [山秀明, 刘锋, 任勇2002 51 1175]
[16]	Kong L J, Liu M R, L X Y 2001 Acta Phys. Sin. 50 1255 (in Chinese) [孔令江, 刘慕仁, 吕晓阳 2001 50 1255]
[17]	Dai S Q, Dong L Y, Xue Y 2001 Acta Phys. Sin. 50 445 (in Chinese) [戴世强, 董力耘, 薛郁2001 50 445]
[18]	Erdos P, Rnyi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[19]	Watts D J, Strogatz S H 1998 Nature 393 409
[20]	Barabsi A L, Albert R 1999 Science 286 509
[21]	Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 035108
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[23]	Erdos P, Rnyi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[24]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117

施引文献

[1]	Feng D, Zhang Y, Zhang Y Q 2004 J. Commun. 25 10 (in Chinese) [冯登国, 张阳, 张玉清 2004 通信学报 25 10]
[2]	Zhang Y Z, Fang B X, Chi Y, Yun X C 2007 J. Software 18 137 (in Chinese) [张永铮, 方滨兴, 迟悦, 云晓春 2007 软件学报 18 137]
[3]	Kephart J O, White S R, Chess D M 1993 IEEE Spectrum 30 20
[4]	Okamura H, Kobayashi H, Dohi T 2005 Proceedings of the 16th IEEE International Symposium on Sof tware Reliability Engineering Chicago, IL, USA, November 8-11, 2005 p149
[5]	Zou C C, Towsley D, Gong W B 2007 IEEE Trans. Depend. Secure Comput. 4 105
[6]	Zou C C, Gong W, Towsley D 2002 Proceedings of the 9th ACM Conference on Computer and Communications Security Washington, DC, USA, November 18-22, 2002 p10
[7]	Song Y R, Jiang G P 2009 Acta Phys. Sin. 58 5911 (in Chinese) [宋玉荣, 蒋国平2009 58 5911]
[8]	Wang Y Q, Jiang G P 2010 Acta Phys. Sin. 59 6724 (in Chinese) [王亚奇, 蒋国平2010 59 6724]
[9]	Wang Y Q, Jiang G P 2011 Acta Phys. Sin. 60 080510 (in Chinese) [王亚奇, 蒋国平2011 60 080510]
[10]	Jin Z, Liu Q X, Mainul H 2007 Chin. Phys. 16 1267
[11]	Fuentes M A, Kuperman M N 1999 Physica A 267 471
[12]	Sirakoulis G C, Karafyllidis I, Thanailakis A 2000 Ecol. Model. 133 209
[13]	White S H, del Rey A M, Sanchez G R 2009 Appl. Math. Sci. 3 959
[14]	Gagliardi H, Alves D 2010 Math. Popul. Stud. 17 79
[15]	Shan X M, Liu F, Ren Y 2002 Acta Phys. Sin. 51 1175 (in Chinese) [山秀明, 刘锋, 任勇2002 51 1175]
[16]	Kong L J, Liu M R, L X Y 2001 Acta Phys. Sin. 50 1255 (in Chinese) [孔令江, 刘慕仁, 吕晓阳 2001 50 1255]
[17]	Dai S Q, Dong L Y, Xue Y 2001 Acta Phys. Sin. 50 445 (in Chinese) [戴世强, 董力耘, 薛郁2001 50 445]
[18]	Erdos P, Rnyi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[19]	Watts D J, Strogatz S H 1998 Nature 393 409
[20]	Barabsi A L, Albert R 1999 Science 286 509
[21]	Pastor-Satorras R, Vespignani A 2002 Phys. Rev. E 65 035108
[22]	Chakrabarti D, Wang Y, Wang C 2007 ACM Trans. Inform. Syst. Secur. 10 1
[23]	Erdos P, Rnyi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[24]	Pastor-Satorras R, Vespignani A 2001 Phys. Rev. E 63 066117

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