Multi-Stage Dynamic Information Flow Tracking...
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Multi-Stage Dynamic Information Flow Tracking Game Payoffs consists of tagging costs, rewards and penalties to players • ScreenGrab results for data from RAIN • Results for two different trap settings • D. Sahabandu, B. Xiao, A. Clark, S. Lee, W. Lee, and R. Poovendran. “DIFT Games: Dynamic Information Flow Tracking Games for Advanced Persistent Threats." to appear in Conference on Decision and Control (CDC), 2018. • S. Moothedath, D. Sahabandu, A. Clark, S. Lee, W. Lee, and R. Poovendran. “Multi Stage Dynamic Information Flow Tracking Game." In proceedings of the Conference on Decision and Game Theory for Security (GameSec), 2018. • D. Sahabandu, S. Moothedath, J. Allen, A. Clark, L. Bushnell, W. Lee, and R. Poovendran, “Multi-stage dynamic information flow tracking game,” Submitted. Establishing foothold C&C Server Exfiltration root@localhost: Lateral movement Infected hardware Social engineering Phishing e-mail shared folder privilege escalation Infected computer Connection to C&C • Attacks consist of multiple stages between entry and exit points • Target multiple entry points simultaneously at each stage • Interact with system to achieve goals while remaining undetected Adversarial cyber interactions: At each stage adversary and system play a strategic game in which the goal of the - Adversary is to evade detection and achieve targets in each . . stage of the attack - Defender is to detect adversary before it achieves the goal Information structure: Complete: both players know the system, payoff of other player Imperfect: defender is unaware of the stage of attack, which flow is malicious and adversary does not know actions of defender Objective: Develop a game theoretic framework to model adversarial cyber interactions such that: - Detection probability is maximized - Cost of detection is minimized Shana Moothedath, Postdoctoral Scholar, Network Security Lab, UW Collaborators: Dinuka Sahabandu (UW), Joey Allen (GA), Andrew Clark (WPI), Linda Bushnell (UW), Wenke Lee (GA), and Radha Poovendran (UW) Tag sources tag vulnerable I/O channels Tag sinks/Traps verify authenticity of tagged flows Tag propagation rules specify data- and control-flow-based tag propagation policy Defense Scheme: Dynamic Information Flow Tracking (DIFT) Abstract information flow graph Record system logs using RAIN 2 Multi-stage dynamic game Defender policy Key Steps of our Approach • Nonzero-sum imperfect information game • Solution to the game gives actionable cyber defense against multi-stage adversarial attacks U D (p D , p A )= X s2S p D (s)C D (s)+ M X j =1 p T (j )↵ D + p R (j )β j D U A (p D , p A )= M X j =1 p R (j )β j A + p T (j )↵ A Theorem 1. For a given adversary strategy , ⎼ The defender’s utility function is submodular in . ⎼ There exists an algorithm that computes at least a 1/2-optimal best response solution to the defender in poly-time. p A U D (p D , p A ) p D Theorem 2. For a given defender’s strategy , the best response of the adversary is obtained from a shortest path algorithm on the information flow graph with edge weight to every incoming edge to . - log(1 - p D (s i )) s i p D Theorem 3. For any , with probability , an -correlated equilibrium can be obtained in number of utility computations. ✏ ✏ > 0 1 - δ Case I Case II ↵ A = -100 ↵ D = 100 β 1 A = β 2 A = 300 β 1 D = β 2 D = -300 c = -100 • Choice of traps locations are critical for security • Optimal selection of traps leads to effective detection • We proposed a multi-stage dynamic game model to evaluate the performance cost and effectiveness of information flow-based ... . detection • We ground the approach on data collected using RAIN framework • We computed the best response of the players; a shortest path algorithm for the adversary and a submodularity-based 1/2-optimal approach for the defender • We gave a polynomial-time algorithm to compute the correlated equilibrium of the game • We tested our approach on ScreenGrab attack data obtained from Refinable Attack Investigation (RAIN) framework O ⇣ (N 2 (M + 1) + N ) ✏ 2 ln ⇣ N 2 (M + 1) + N δ ⌘⌘ Multi-stage dynamic game: At each stage adversary and system play a strategic game in which the goal of the - Adversary selects an attack path in the information flow graph - Defender (DIFT) tags a subset of nodes - Each stage of attack is defined by a set of destinations which . . must be achieved sequentially CONCLUSIONS PROBLEM FORMULATION RESULTS REFERENCES INTRODUCTION PROPOSED APPROACH EXPERIMENTAL RESULTS
Transcript of Multi-Stage Dynamic Information Flow Tracking...
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Multi-Stage Dynamic Information Flow Tracking Game
Payoffs consists of tagging costs, rewards and penalties to players
• ScreenGrab results for data from RAIN• Results for two different trap settings
• D. Sahabandu, B. Xiao, A. Clark, S. Lee, W. Lee, and R. Poovendran. “DIFT Games:Dynamic Information Flow Tracking Games for Advanced Persistent Threats." toappear in Conference on Decision and Control (CDC), 2018.
• S. Moothedath, D. Sahabandu, A. Clark, S. Lee, W. Lee, and R. Poovendran. “MultiStage Dynamic Information Flow Tracking Game." In proceedings of the Conferenceon Decision and Game Theory for Security (GameSec), 2018.
• D. Sahabandu, S. Moothedath, J. Allen, A. Clark, L. Bushnell, W. Lee, and R.Poovendran, “Multi-stage dynamic information flow tracking game,” Submitted.
Establishing foothold
C&C Server
Exfiltration
root@localhost:
Lateral movement
Infected hardware
Social engineering
Phishing e-mail
shared folder
privilege escalation
Infectedcomputer
Connection to C&C
• Attacks consist of multiple stages between entry and exit points• Target multiple entry points simultaneously at each stage• Interact with system to achieve goals while remaining undetected
Adversarial cyber interactions: At each stage adversary and system play a strategic game in which the goal of the
- Adversary is to evade detection and achieve targets in each .. stage of the attack
- Defender is to detect adversary before it achieves the goal
Information structure:Complete: both players know the system, payoff of other playerImperfect: defender is unaware of the stage of attack, which flow is malicious and adversary does not know actions of defender
Objective: Develop a game theoretic framework to model adversarial cyber interactions such that:
- Detection probability is maximized- Cost of detection is minimized
Shana Moothedath, Postdoctoral Scholar, Network Security Lab, UW Collaborators: Dinuka Sahabandu (UW), Joey Allen (GA), Andrew Clark (WPI),
Linda Bushnell (UW), Wenke Lee (GA), and Radha Poovendran (UW)
Tag sources tag vulnerableI/O channels
Tag sinks/Traps verify authenticityof tagged flows
Tag propagation rules specify data- and control-flow-based tag propagation policy
Defense Scheme: Dynamic Information Flow Tracking (DIFT)
Abstract information flow graph
Record system logs using RAIN2
Multi-stage dynamic game
Defender policy
Key Steps of our Approach
• Nonzero-sum imperfect information game
• Solution to the game gives actionable cyber defense against multi-stage adversarial attacks
UD(pD,pA) =X
s2SpD(s)CD(s) +
MX
j=1
pT (j)↵D + pR(j)�jD
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UA(pD,pA) =MX
j=1
pR(j)�jA + pT (j)↵A
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
Theorem 1. For a given adversary strategy ,
⎼ The defender’s utility function is submodular in .⎼ There exists an algorithm that computes at least a 1/2-optimal
best response solution to the defender in poly-time.
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Theorem 2. For a given defender’s strategy , the best response of the adversary is obtained from a shortest path algorithm on the information flow graph with edge weight to every incoming edge to .
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Theorem 3. For any , with probability , an -correlatedequilibrium can be obtained innumber of utility computations.
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1� �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
Case I Case II↵A = �100
AAACEXicbZDLSsNAFIYnXmu9RV26GSxCN5ZEBN0IVTcuK9gLNCFMppN26OTCzIkQQl/Bja/ixoUibt25822ctFlo6w8zfPznHGbO7yeCK7Csb2NpeWV1bb2yUd3c2t7ZNff2OypOJWVtGotY9nyimOARawMHwXqJZCT0Bev645ui3n1gUvE4uocsYW5IhhEPOCWgLc+sO0QkI+LljqKSJ1DekAmGryaX+MS2rGohz6xZDWsqvAh2CTVUquWZX84gpmnIIqCCKNW3rQTcnEjgVLBJ1UkVSwgdkyHra4xIyJSbTzea4GPtDHAQS30iwFP390ROQqWy0NedIYGRmq8V5n+1fgrBhZvzKEmBRXT2UJAKDDEu4sEDLhkFkWkgOgr9V0xHRBIKOsQiBHt+5UXonDZszXdnteZ1GUcFHaIjVEc2OkdNdItaqI0oekTP6BW9GU/Gi/FufMxal4xy5gD9kfH5A2Sjm1k=AAACEXicbZDLSsNAFIYnXmu9RV26GSxCN5ZEBN0IVTcuK9gLNCFMppN26OTCzIkQQl/Bja/ixoUibt25822ctFlo6w8zfPznHGbO7yeCK7Csb2NpeWV1bb2yUd3c2t7ZNff2OypOJWVtGotY9nyimOARawMHwXqJZCT0Bev645ui3n1gUvE4uocsYW5IhhEPOCWgLc+sO0QkI+LljqKSJ1DekAmGryaX+MS2rGohz6xZDWsqvAh2CTVUquWZX84gpmnIIqCCKNW3rQTcnEjgVLBJ1UkVSwgdkyHra4xIyJSbTzea4GPtDHAQS30iwFP390ROQqWy0NedIYGRmq8V5n+1fgrBhZvzKEmBRXT2UJAKDDEu4sEDLhkFkWkgOgr9V0xHRBIKOsQiBHt+5UXonDZszXdnteZ1GUcFHaIjVEc2OkdNdItaqI0oekTP6BW9GU/Gi/FufMxal4xy5gD9kfH5A2Sjm1k=AAACEXicbZDLSsNAFIYnXmu9RV26GSxCN5ZEBN0IVTcuK9gLNCFMppN26OTCzIkQQl/Bja/ixoUibt25822ctFlo6w8zfPznHGbO7yeCK7Csb2NpeWV1bb2yUd3c2t7ZNff2OypOJWVtGotY9nyimOARawMHwXqJZCT0Bev645ui3n1gUvE4uocsYW5IhhEPOCWgLc+sO0QkI+LljqKSJ1DekAmGryaX+MS2rGohz6xZDWsqvAh2CTVUquWZX84gpmnIIqCCKNW3rQTcnEjgVLBJ1UkVSwgdkyHra4xIyJSbTzea4GPtDHAQS30iwFP390ROQqWy0NedIYGRmq8V5n+1fgrBhZvzKEmBRXT2UJAKDDEu4sEDLhkFkWkgOgr9V0xHRBIKOsQiBHt+5UXonDZszXdnteZ1GUcFHaIjVEc2OkdNdItaqI0oekTP6BW9GU/Gi/FufMxal4xy5gD9kfH5A2Sjm1k=AAACEXicbZDLSsNAFIYnXmu9RV26GSxCN5ZEBN0IVTcuK9gLNCFMppN26OTCzIkQQl/Bja/ixoUibt25822ctFlo6w8zfPznHGbO7yeCK7Csb2NpeWV1bb2yUd3c2t7ZNff2OypOJWVtGotY9nyimOARawMHwXqJZCT0Bev645ui3n1gUvE4uocsYW5IhhEPOCWgLc+sO0QkI+LljqKSJ1DekAmGryaX+MS2rGohz6xZDWsqvAh2CTVUquWZX84gpmnIIqCCKNW3rQTcnEjgVLBJ1UkVSwgdkyHra4xIyJSbTzea4GPtDHAQS30iwFP390ROQqWy0NedIYGRmq8V5n+1fgrBhZvzKEmBRXT2UJAKDDEu4sEDLhkFkWkgOgr9V0xHRBIKOsQiBHt+5UXonDZszXdnteZ1GUcFHaIjVEc2OkdNdItaqI0oekTP6BW9GU/Gi/FufMxal4xy5gD9kfH5A2Sjm1k=
↵D = 100AAACEHicbZDLSsNAFIYn9VbrLerSzWARXZVEBN0IRV24rGAv0IQwmU7aoZMLMydCCH0EN76KGxeKuHXpzrdx0mahrT/M8PGfc5g5v58IrsCyvo3K0vLK6lp1vbaxubW9Y+7udVScSsraNBax7PlEMcEj1gYOgvUSyUjoC9b1x9dFvfvApOJxdA9ZwtyQDCMecEpAW5557BCRjIiXO4pKnkB5QyYYvplcYtuyaoU8s241rKnwItgl1FGplmd+OYOYpiGLgAqiVN+2EnBzIoFTwSY1J1UsIXRMhqyvMSIhU24+XWiCj7QzwEEs9YkAT93fEzkJlcpCX3eGBEZqvlaY/9X6KQQXbs6jJAUW0dlDQSowxLhIBw+4ZBREpoHoJPRfMR0RSSjoDIsQ7PmVF6Fz2rA1353Vm1dlHFV0gA7RCbLROWqiW9RCbUTRI3pGr+jNeDJejHfjY9ZaMcqZffRHxucP8iibJQ==AAACEHicbZDLSsNAFIYn9VbrLerSzWARXZVEBN0IRV24rGAv0IQwmU7aoZMLMydCCH0EN76KGxeKuHXpzrdx0mahrT/M8PGfc5g5v58IrsCyvo3K0vLK6lp1vbaxubW9Y+7udVScSsraNBax7PlEMcEj1gYOgvUSyUjoC9b1x9dFvfvApOJxdA9ZwtyQDCMecEpAW5557BCRjIiXO4pKnkB5QyYYvplcYtuyaoU8s241rKnwItgl1FGplmd+OYOYpiGLgAqiVN+2EnBzIoFTwSY1J1UsIXRMhqyvMSIhU24+XWiCj7QzwEEs9YkAT93fEzkJlcpCX3eGBEZqvlaY/9X6KQQXbs6jJAUW0dlDQSowxLhIBw+4ZBREpoHoJPRfMR0RSSjoDIsQ7PmVF6Fz2rA1353Vm1dlHFV0gA7RCbLROWqiW9RCbUTRI3pGr+jNeDJejHfjY9ZaMcqZffRHxucP8iibJQ==AAACEHicbZDLSsNAFIYn9VbrLerSzWARXZVEBN0IRV24rGAv0IQwmU7aoZMLMydCCH0EN76KGxeKuHXpzrdx0mahrT/M8PGfc5g5v58IrsCyvo3K0vLK6lp1vbaxubW9Y+7udVScSsraNBax7PlEMcEj1gYOgvUSyUjoC9b1x9dFvfvApOJxdA9ZwtyQDCMecEpAW5557BCRjIiXO4pKnkB5QyYYvplcYtuyaoU8s241rKnwItgl1FGplmd+OYOYpiGLgAqiVN+2EnBzIoFTwSY1J1UsIXRMhqyvMSIhU24+XWiCj7QzwEEs9YkAT93fEzkJlcpCX3eGBEZqvlaY/9X6KQQXbs6jJAUW0dlDQSowxLhIBw+4ZBREpoHoJPRfMR0RSSjoDIsQ7PmVF6Fz2rA1353Vm1dlHFV0gA7RCbLROWqiW9RCbUTRI3pGr+jNeDJejHfjY9ZaMcqZffRHxucP8iibJQ==AAACEHicbZDLSsNAFIYn9VbrLerSzWARXZVEBN0IRV24rGAv0IQwmU7aoZMLMydCCH0EN76KGxeKuHXpzrdx0mahrT/M8PGfc5g5v58IrsCyvo3K0vLK6lp1vbaxubW9Y+7udVScSsraNBax7PlEMcEj1gYOgvUSyUjoC9b1x9dFvfvApOJxdA9ZwtyQDCMecEpAW5557BCRjIiXO4pKnkB5QyYYvplcYtuyaoU8s241rKnwItgl1FGplmd+OYOYpiGLgAqiVN+2EnBzIoFTwSY1J1UsIXRMhqyvMSIhU24+XWiCj7QzwEEs9YkAT93fEzkJlcpCX3eGBEZqvlaY/9X6KQQXbs6jJAUW0dlDQSowxLhIBw+4ZBREpoHoJPRfMR0RSSjoDIsQ7PmVF6Fz2rA1353Vm1dlHFV0gA7RCbLROWqiW9RCbUTRI3pGr+jNeDJejHfjY9ZaMcqZffRHxucP8iibJQ==
�1A = �2A = 300
AAACMXicdVDLSgNBEJyNrxhfUY9eBoPgKexGQS9C1EuOEcwDkhhmJ51kyOyDmV4hLPklL/6JeMlBEa/+hJPNHjTRgm6Kqm5mutxQCo22PbUyK6tr6xvZzdzW9s7uXn7/oK6DSHGo8UAGqukyDVL4UEOBEpqhAua5Ehru6HbmNx5BaRH49zgOoeOxgS/6gjM0UjdfabuA7MHpxm3NlQgx7TiWQK8nV3Tul/7zz2w7l6CbL9hFOwFdJk5KCiRFtZt/afcCHnngI5dM65Zjh9iJmULBJUxy7UhDyPiIDaBlqM880J04uXhCT4zSo/1AmfKRJurPjZh5Wo8910x6DId60ZuJf3mtCPuXnVj4YYTg8/lD/UhSDOgsPtoTCjjKsSHMJGH+SvmQKcbRhDwLwVk8eZnUS0XH8LvzQvkmjSNLjsgxOSUOuSBlUiFVUiOcPJFX8kberWdran1Yn/PRjJXuHJJfsL6+AUR1qNE=AAACMXicdVDLSgNBEJyNrxhfUY9eBoPgKexGQS9C1EuOEcwDkhhmJ51kyOyDmV4hLPklL/6JeMlBEa/+hJPNHjTRgm6Kqm5mutxQCo22PbUyK6tr6xvZzdzW9s7uXn7/oK6DSHGo8UAGqukyDVL4UEOBEpqhAua5Ehru6HbmNx5BaRH49zgOoeOxgS/6gjM0UjdfabuA7MHpxm3NlQgx7TiWQK8nV3Tul/7zz2w7l6CbL9hFOwFdJk5KCiRFtZt/afcCHnngI5dM65Zjh9iJmULBJUxy7UhDyPiIDaBlqM880J04uXhCT4zSo/1AmfKRJurPjZh5Wo8910x6DId60ZuJf3mtCPuXnVj4YYTg8/lD/UhSDOgsPtoTCjjKsSHMJGH+SvmQKcbRhDwLwVk8eZnUS0XH8LvzQvkmjSNLjsgxOSUOuSBlUiFVUiOcPJFX8kberWdran1Yn/PRjJXuHJJfsL6+AUR1qNE=AAACMXicdVDLSgNBEJyNrxhfUY9eBoPgKexGQS9C1EuOEcwDkhhmJ51kyOyDmV4hLPklL/6JeMlBEa/+hJPNHjTRgm6Kqm5mutxQCo22PbUyK6tr6xvZzdzW9s7uXn7/oK6DSHGo8UAGqukyDVL4UEOBEpqhAua5Ehru6HbmNx5BaRH49zgOoeOxgS/6gjM0UjdfabuA7MHpxm3NlQgx7TiWQK8nV3Tul/7zz2w7l6CbL9hFOwFdJk5KCiRFtZt/afcCHnngI5dM65Zjh9iJmULBJUxy7UhDyPiIDaBlqM880J04uXhCT4zSo/1AmfKRJurPjZh5Wo8910x6DId60ZuJf3mtCPuXnVj4YYTg8/lD/UhSDOgsPtoTCjjKsSHMJGH+SvmQKcbRhDwLwVk8eZnUS0XH8LvzQvkmjSNLjsgxOSUOuSBlUiFVUiOcPJFX8kberWdran1Yn/PRjJXuHJJfsL6+AUR1qNE=AAACMXicdVDLSgNBEJyNrxhfUY9eBoPgKexGQS9C1EuOEcwDkhhmJ51kyOyDmV4hLPklL/6JeMlBEa/+hJPNHjTRgm6Kqm5mutxQCo22PbUyK6tr6xvZzdzW9s7uXn7/oK6DSHGo8UAGqukyDVL4UEOBEpqhAua5Ehru6HbmNx5BaRH49zgOoeOxgS/6gjM0UjdfabuA7MHpxm3NlQgx7TiWQK8nV3Tul/7zz2w7l6CbL9hFOwFdJk5KCiRFtZt/afcCHnngI5dM65Zjh9iJmULBJUxy7UhDyPiIDaBlqM880J04uXhCT4zSo/1AmfKRJurPjZh5Wo8910x6DId60ZuJf3mtCPuXnVj4YYTg8/lD/UhSDOgsPtoTCjjKsSHMJGH+SvmQKcbRhDwLwVk8eZnUS0XH8LvzQvkmjSNLjsgxOSUOuSBlUiFVUiOcPJFX8kberWdran1Yn/PRjJXuHJJfsL6+AUR1qNE=
�1D = �2D = �300
AAACM3icdVDLSgNBEJz1GeNr1aOXwSB4MexGQS9CUA/iKYJ5QBLD7KSTDJl9MNMrhCX/5MUf8SCIB0W8+g9Okj1oogXdFFXdzHR5kRQaHefFmptfWFxazqxkV9fWNzbtre2KDmPFocxDGaqaxzRIEUAZBUqoRQqY70moev2LkV+9B6VFGNziIIKmz7qB6AjO0Egt+7rhAbI7t5U0NFciwrTjQAK9HJ7RiV/41z88cpzsGC075+SdMegscVOSIylKLfup0Q557EOAXDKt664TYTNhCgWXMMw2Yg0R433WhbqhAfNBN5PxzUO6b5Q27YTKVIB0rP7cSJiv9cD3zKTPsKenvZH4l1ePsXPaTEQQxQgBnzzUiSXFkI4CpG2hgKMcGMJMFuavlPeYYhxNzKMQ3OmTZ0mlkHcNvznOFc/TODJkl+yRA+KSE1IkV6REyoSTB/JM3si79Wi9Wh/W52R0zkp3dsgvWF/fQgWpOA==AAACM3icdVDLSgNBEJz1GeNr1aOXwSB4MexGQS9CUA/iKYJ5QBLD7KSTDJl9MNMrhCX/5MUf8SCIB0W8+g9Okj1oogXdFFXdzHR5kRQaHefFmptfWFxazqxkV9fWNzbtre2KDmPFocxDGaqaxzRIEUAZBUqoRQqY70moev2LkV+9B6VFGNziIIKmz7qB6AjO0Egt+7rhAbI7t5U0NFciwrTjQAK9HJ7RiV/41z88cpzsGC075+SdMegscVOSIylKLfup0Q557EOAXDKt664TYTNhCgWXMMw2Yg0R433WhbqhAfNBN5PxzUO6b5Q27YTKVIB0rP7cSJiv9cD3zKTPsKenvZH4l1ePsXPaTEQQxQgBnzzUiSXFkI4CpG2hgKMcGMJMFuavlPeYYhxNzKMQ3OmTZ0mlkHcNvznOFc/TODJkl+yRA+KSE1IkV6REyoSTB/JM3si79Wi9Wh/W52R0zkp3dsgvWF/fQgWpOA==AAACM3icdVDLSgNBEJz1GeNr1aOXwSB4MexGQS9CUA/iKYJ5QBLD7KSTDJl9MNMrhCX/5MUf8SCIB0W8+g9Okj1oogXdFFXdzHR5kRQaHefFmptfWFxazqxkV9fWNzbtre2KDmPFocxDGaqaxzRIEUAZBUqoRQqY70moev2LkV+9B6VFGNziIIKmz7qB6AjO0Egt+7rhAbI7t5U0NFciwrTjQAK9HJ7RiV/41z88cpzsGC075+SdMegscVOSIylKLfup0Q557EOAXDKt664TYTNhCgWXMMw2Yg0R433WhbqhAfNBN5PxzUO6b5Q27YTKVIB0rP7cSJiv9cD3zKTPsKenvZH4l1ePsXPaTEQQxQgBnzzUiSXFkI4CpG2hgKMcGMJMFuavlPeYYhxNzKMQ3OmTZ0mlkHcNvznOFc/TODJkl+yRA+KSE1IkV6REyoSTB/JM3si79Wi9Wh/W52R0zkp3dsgvWF/fQgWpOA==AAACM3icdVDLSgNBEJz1GeNr1aOXwSB4MexGQS9CUA/iKYJ5QBLD7KSTDJl9MNMrhCX/5MUf8SCIB0W8+g9Okj1oogXdFFXdzHR5kRQaHefFmptfWFxazqxkV9fWNzbtre2KDmPFocxDGaqaxzRIEUAZBUqoRQqY70moev2LkV+9B6VFGNziIIKmz7qB6AjO0Egt+7rhAbI7t5U0NFciwrTjQAK9HJ7RiV/41z88cpzsGC075+SdMegscVOSIylKLfup0Q557EOAXDKt664TYTNhCgWXMMw2Yg0R433WhbqhAfNBN5PxzUO6b5Q27YTKVIB0rP7cSJiv9cD3zKTPsKenvZH4l1ePsXPaTEQQxQgBnzzUiSXFkI4CpG2hgKMcGMJMFuavlPeYYhxNzKMQ3OmTZ0mlkHcNvznOFc/TODJkl+yRA+KSE1IkV6REyoSTB/JM3si79Wi9Wh/W52R0zkp3dsgvWF/fQgWpOA==
c = �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
• Choice of traps locations are critical for security• Optimal selection of traps leads to effective detection
• We proposed a multi-stage dynamic game model to evaluate theperformance cost and effectiveness of information flow-based . . .
. detection• We ground the approach on data collected using RAIN framework• We computed the best response of the players; a shortest path
algorithm for the adversary and a submodularity-based 1/2-optimalapproach for the defender
• We gave a polynomial-time algorithm to compute the correlatedequilibrium of the game
• We tested our approach on ScreenGrab attack data obtained fromRefinable Attack Investigation (RAIN) framework
O
⇣ (N2(M + 1) +N)✏2
ln⇣N
2(M + 1) +N
�
⌘⌘
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
Multi-stage dynamic game: At each stage adversary and system play a strategic game in which the goal of the
- Adversary selects an attack path in the information flow graph- Defender (DIFT) tags a subset of nodes- Each stage of attack is defined by a set of destinations which .
. must be achieved sequentially
CONCLUSIONS
PROBLEM FORMULATION
RESULTS
REFERENCES
INTRODUCTION PROPOSED APPROACH EXPERIMENTAL RESULTS
