A Method for Selecting Defense Strategies Based on Stochastic Evolutionary Game Model
HUANG Jian-ming1, ZHANG Heng-wei1,2
1. The Third Institute, Information Engineering University, Zhengzhou, Henan 450001, China;
2. State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, Henan 450001, China
Abstract:In the network attack-defense game systems,there are many stochastic factors,such as changes of attack-defense strategy sets and system operating environment.The traditional deterministic game model can not describe the game process of network attack and defense accurately.This paper constructed an attack-defense stochastic evolutionary game model by adapting the nonlinear Itó stochastic differential equations.The model can be applied to analyze the stochastic evolutionary process of network attack and defense.In addition,the stability of the strategy selection of attack and defense was analyzed according to the discriminant theorem of stochastic differential equations.Besides,an algorithm to select the security defense strategies based on stochastic attack-defense evolutionary game model was designed.Finally,the simulations demonstrate that the different intensity influences of stochastic interference on the speed of decision-making evolution of attack and defense.The attackers and defenders are more inclined to choose strong strategies when the game system has great intensity of interference.The model and the method proposed in this paper can provide guidance for attack behavior prediction and defense strategy selection.
[1] Gordon L,Loeb M,Lucyshyn W,Richardson R.2016 CSI/FBI computer crime and security survey[A].Proceedings of the 2016 Computer Security Institute[C].San Francisco:IEEE,2016.48-64.
[2] Lye K W,Jeannette W.Markov game strategies in network security[J].International Journal of Information Security,2015,4(1):71-86.
[3] Gordon L,Loeb M.Budgeting process for information security expenditures[J].Communications of the ACM,2016,51(8):395-406.
[4] Borkovsky R N,Doraszelski U,Kryukov Y.A user's guide to solving dynamic stochastic games using the homotopy method[J].Operation Research,2015,58(4):1116-1132.
[5] 朱建明,王秦.基于博弈论的网络空间安全若干问题分析[J].网络与信息安全学报,2015,1(1):43-49. ZHU Jian-ming,WANG Qin.Analysis of cyberspace security based on game theory[J].Chinese Journal of Network and Information Security,2015,1(1):43-49.(in Chinese)
[6] Nilim A,Ghaoui L E.Robust control of Markov decision processes with uncertain transition matrices[J].Operations Research,2016,53(5):780-798.
[7] 张恒巍,余定坤,韩继红.基于攻防信号博弈模型的防御策略选取方法[J].通信学报,2016,37(5):51-61. ZHANG Heng-wei,YU Ding-kun,HAN Ji-hong.Defense policies selection method based on attack-defense signaling game model[J].Journal on Communications,2016,37(5):51-61.(in Chinese)
[8] 张恒巍,李涛.基于多阶段攻防信号博弈的最优主动防御[J],电子学报,2017,45(2):431-439. ZHANG Heng-wei,Li Tao.Optimal active defense based on multi-stage attack-defense signaling game[J].Acta Electronica Sinica,2017,45(2):431-439.(in Chinese)
[9] 孙薇.基于演化博弈论的信息安全攻防问题研究[J].情报科学,2015,(9):1408-1412. SUN Wei.Research on attack and deference in information security based on evolutionary game[J].Information Science,2015,(9):1408-1412.(in Chinese)
[10] Herbert Gintis.Game Theory Evolving[M].Boston:Priceton University Press,2015.10.
[11] 朱建明,宋彪,黄启发.基于系统动力学的网络安全攻防演化博弈模型.[J].通信学报,2014,35(1):54-61. ZHU Jian-ming,SONG Biao,HUANG Qi-fa.Evolution game model of offense-defense for network security based on system dynamics[J].Information Science,2014,35(1):54-61.(in Chinese)
[12] 黄健明,张恒巍,王晋东,等.基于攻防演化博弈模型的防御策略选取方法[J].通信学报,2017,38(1):168-176. HUANG Jian-ming,ZHANG Heng-wei,WANG Jin-dong,et al.Defense strategies selection based on attack-defense evolutionary game model[J].Information Science,2017,38(1):168-176.(in Chinese)
[13] 王元卓,林闯,程学旗,等.基于随机博弈模型的网络攻防量化分析方法[J].计算机学报,2015,33(9):1748-1764. WANG Yuan-zhuo,LIN Chuang,CHENG Xue-qi,et al.Analysis for network attack-defense based on stochastic game model[J].Chinese Journal of Computers,2015,33(9):1748-1764.(in Chinese)
[14] 姜伟,方滨兴,田志宏.基于攻防随机博弈模型的防御策略选取研究[J].计算机研究与发展,2016,47(10):1714-1723. JIANG Wei,FANG Bing-xing,TIAN Zhi-hong.Research on defense strategies selection based on attack-defense stochastic game model[J].Journal of Computer Research and Development,2016,47(10):1714-1723.(in Chinese)
[15] D Cheng,F He,H Qi.Modeling,analysis and control of networked evolutionary games[J].IEEE Transactions on Automatic Control,2017,(99):41-49.
[16] 胡适耕,黄乘明,吴付科.随机微分方程[M].北京:科学出版社,2008.66-67. Hu Shi-gen,Huang Cheng-ming,Wu Fu-ke.Stochastic Differential Equation[M].Beijing:Science Press,2008.66-67.(in Chinese)
[17] Erwin A,Alex P.On the stability of evolutionary dynamics in games with incomplete information[J].Mathematical Social Sciences,2016,(58):310-321.
[18] White J,Park J S,Kamhoua C A,Kwiat K A.Game theoretic attack analysis in online social network services[A].Proceedings of the 2017 International Conference on Social Networks Technology[C].Los Angeles:IEEE,2017.1012-1019.
[19] Richard Lippmann,Joshua W.Haines.Analysis and results of the DARPA off-line intrusion detection evaluation[A].Proceedings of the 17'th International Workshop on Recent Advances in Intrusion Detection[C].New York:ACM,2016.162-182.
[20] Maleki H,Valizadeh M H,Koch W,et al.Markov modeling of moving target defense games[J].Journal of Cryptology,2017,(23):47-83.
[21] ZHANG Yong.Network security situation awareness approach based on Markov game model[J].Journal of Software,2016,22(3):495-508.