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Extending An+cipa+on Games with Loca+on, Penalty and Timeline
Elie Bursztein LSV, ENS-‐Cachan
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I. Background II. Loca+on III. Timeline IV. Penalty
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Background
The art of war is of vital importance to the State. Sun Tzu, The art of war I.1
I. Background II. Framework III. Loca+on IV. Timeline V. Penalty
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Network is geJng more and more complex
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Opte project
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AMack techniques are geJng more and more sophis+cated
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Cert/ Carnegie Mellon University
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Sandia Red Team “White Board” a;ack graph from DARPA CC20008 InformaFon ba;le space preparaFon experiment
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Take into account the collateral damages
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Deal with the interac+on of users
Exploit vulnerabili+es
Abuse trust rela+ons
Patch
Firewall
Restore
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Model the temporal dimension
Cert/ Carnegie Mellon University
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Take into account the financial dimension
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Network are very big so usual techniques does not work well
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Framework
In war, then, let your great object be victory, not lengthy campaigns.
Sun Tzu, The art of war II.19
I. Background II. Framework III. Loca+on IV. Timeline V. Penalty
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NetQi is a framework for network risk analysis
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its a 4th genera+on* framework
*Baskerville classifica+on 1993
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Previous framework
AMack graph NetSpa MulVal Cauldron
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SEIR model
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its model is based on game theory and modal logic
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An an+cipa+on game is a dual layer structure
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The lower layer called dependency graph is used to represent the network
state
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The upper layer called an+cipa+on game is used to model the network
evolu+on
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1 2 3 4 5 6 7
ρ(Public) T T T T T T T
ρ(Vuln) ⊥ ⊥ T ⊥ ⊥ T ⊥
ρ(Compr) ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
ρ(Detected) ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
ρ(Monitored) ⊥ T T T ⊥ ⊥ ⊥
1 2 3 4 5 6 7
ρ(Odayavail) ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
ρ(CustomAvail) ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
ρ(PubAvail) ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
ρ(PubPatch) ⊥ ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
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Exploit web server
1 2 3
54
6
Patch Email server
Exploit email server
Patch web server Patch Email server
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1 2 3 4 5 6 ρ(Public) ⊥ ⊥ ⊥ T T ⊥ ρ(Vuln) ⊥ ⊥ ⊥ T T ⊥ ρ(Compr) ⊥ ⊥ ⊥ ⊥ ⊥ ⊥
ρ(NeedPub
) ⊥ ⊥ ⊥ T T ⊥
1 2 3 4 5 6 ρ(Public) ⊥ ⊥ ⊥ T T ⊥ ρ(Vuln) ⊥ ⊥ ⊥ T T ⊥ ρ(Compr) ⊥ ⊥ ⊥ T ⊥ ⊥
ρ(NeedPub
) ⊥ ⊥ ⊥ T T ⊥
Rule Execu+on
State 1 State 2
Precondi+ons Effects Time
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A successor node is compromised
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Precondi+ons Time Player Ac+on name Cost Postcondi+ons
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Network Exploit 4 in 3 unit Firewall 4 in 1 unit
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Loca+on
I. Background II. Framework III. Loca+on IV. Timeline V. Penalty
The highest form of generalship is to balk the enemy's plans Sun Tzu, The art of war VIII.31
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Rules by defini+on can be applied to any vertex
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Some+me you need to be able to restrict their scope
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Scope restric+on are enforced by loca+on
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A rule is global if no loca+on is specified
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A rule is local if the same loca+on is specified for the node and its
successors
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A rule is transi+ve if a different loca+on is specified for the node and its
successors
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Timeline
I. Background II. Framework III. Implementa+on IV. Applica+ons
Success in warfare is gained by carefully accommodaFng ourselves to the enemy's purpose.
Sun Tzu, The art of war IV.13
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In order to express a causal rela+on between ac+on we need to be able to
model a +meline
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Penality
I. Background II. Framework III. Implementa+on IV. Applica+ons
To secure ourselves against defeat lies in our own hands Sun Tzu, The art of war IV.2
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A Penalty allows to add a dura+on based cost
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Model-‐checking an+cipa+on game with loca+on and penalty is EXPTIME-‐
Complete
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A counter-‐example is an aMack and there can be a lot of counter-‐example
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How do you know which counter-‐example is the most relevant one?
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Strategy objec+ves mix constraints with costs and rewards
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S: (name, P, O, R, C)
name Player Numerical objec+ves Objec+ves order Constraintes
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General op+ons
Set of states
Players Rules
Dependency graph
Penalty
Goal
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Demonstra+on
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Analysis services Network Time
Exact 30 3 0.03
Exact 40 3 0.1
Exact 20 4 1020
Approx 2000 1 0.48
Approx 5000 4 0.82
Approx 10000 3 2.26
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Conclusion
If you know the enemy and know yourself, your victory will not stand in doubt; if you know Heaven and know Earth, you may make your victory complete.
Sun Tzu, The art of war VIII.31
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