1. Considering Multi-objective Resource Allocation Strategies under Attack-Defense Roles and Collaborative Attacks 考慮攻防雙角色與協同攻擊情況下之多目標資源分配策略
Advisor: Frank,Yeong-Sung Lin
Present by Ying-Ju Chen
Presentation date: Dec. 20, 2011

2. Agenda
Problem Description
Mathematical Formulation
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3. Agenda
Problem Description
Mathematical Formulation
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4. Problem Description Two players Two roles Defender
Attacker (Collaborative attack)
Player 1
Player 2
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5. Two Roles – Attacker & Defender
‧Normal Attack
‧Retaliation Attack
Defender
Passive Defense
‧Proactive ‧Reactive Active Defense
‧Preventive Strike
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6. Role - Defender Defense Proactive Reactive Preventive Strike (PS)
Uniformly distribute his defense resources to each node.
Reactive
Allocate reinforced resources to compromised node which has been repaired.
Preventive Strike (PS)
According to the flow of the attacker, i.e. the greater flow of the node would be allocated more resources.
Cause damage to the counterpart’s network and indirectly influence his retaliation ability.
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7. Role - Defender Reallocation Repair
The resources could be reallocated but the discount factor is also considered.
Repair
The compromised nodes could be repaired.
The reward would be retrieved back from another player.
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8. Role - Defender Update information (Unknown vulnerabilities)
Initially, the defender doesn’t know his system vulnerabilities.
The nodes successfully compromised last round imply that these nodes have vulnerabilities.
The defender can update his information about the unknown vulnerabilities on his nodes after the attacker’s attack.
Once the node be repaired, it will be reinforced more defense resources in this round. (Reactive defense)
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9. Role - Attacker Attack Normal attack Retaliation attack
Based on his local view about the vulnerabilities.
Retaliation attack
Once the node was preventively struck, he must revenge next round.
Since the network would be harmed after being preventively struck, the discount factor is considered.
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10. Role - Attacker Reward Each node in players’ topologies has a reward.
Once being successfully compromised, the reward would be gained by the attacker.
Once being repaired next round, the reward would be retrieved by the defender.
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11. Role - Attacker
Update information (Unknown vulnerabilities & Defender’s private information)
Each attacker has partial information of the defender’s system, which is called a local view.
Each attacker’s local view can grow after exploring in the beginning of each round.
The explore cost of each attacker is different and is considered.
Through the game, each attacker learns more about the defender’s vulnerabilities information and his private information.
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12. Update information (Both roles)
Defender’s information
Vulnerabilities
All information about the defender’s topology
Defender’s private information
Attacker ’s knowledge (combined local view)
Attacker 1
Attacker 1’s local view
Collaborative attack
Attacker 2
Attacker 2’s local view … …
Attacker N
Attacker N’s local view
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13. Role - Attacker Collaborative attack
There’s always a leader in the collaborative attack in every round. Different leaders have different leaderships.
Each attacker’s attack power over a node is different.
Each attacker’s cooperative effect is different.
The synergy of collaborative attack would be influenced by the cooperative effect of each attacker and the leadership of the leader in that round.
In each round, each collaborative attacker’s attack power involved and the collaborative synergy will be reflected in contest success function.
Collaborative synergy in round r = (∑ cooperative effect of each attacker ) x (The leader’s leadership)
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14. Problem Description The network survivability is measured by ADOD.
The game has two players.
Given
Both players have incomplete information of each other.
Player 1’s total budget.
Player 2’s total budget.
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15. Problem Description – Players
Objective
Minimize the damage degree of their own networks (ADOD).
Maximize the damage degree of the other player’s network (ADOD).
Budget constraint
deploying the defense budget on nodes of it’s topology
repairing the compromised nodes
reinforcing defense budget to compromised node which has been retrieved and repaired
deploying the attack budget on nodes of the defender’ topology
updating information
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16. Agenda
Problem Description
Mathematical Formulation
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17. Agenda
Problem Description
Mathematical Formulation
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18. Given Parameters Notation Description V
Index set of nodes of both players’ topologies VA
Index set of nodes of player 1’s topology VB
Index set of nodes of player 2’s topology R
Index set of rounds in the attack and defense actions
VAr
Index set of nodes of player 2’s combined local view on player 1’s topology in round r, where r ∈ R and VAr ⊆ VA
VBr
Index set of nodes of player 1’s combined local view on player 2’s topology in round r, where r ∈ R and VBr ⊆ VB
EAr
Index set of new explored nodes of player 2’s topology in round r, where r ∈ R and EAr ⊆ VA-VA-1
EBr
Index set of new explored nodes of player 1’s topology in round r, where r ∈ R and EBr ⊆ VB-VB-1 KA
Index set of collaborative attackers of player 1 KB
Index set of collaborative attackers of player 2
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19. Given Parameters Notation Description gAr
Player 1’s group of collaborative attackers in round r-1, where gAr ∈ KA and r ∈ R
gBr
Player 2’s group of collaborative attackers in round r-1, where gBr ∈ KB and r ∈ R wr
The weight of the average DOD in round r, where r ∈ R
Total budget of player 1
Total budget of player 2
tki
Attacker k’s attack power (resources) when attacking on node i, where k ∈ and i ∈ Ck
The cooperative effect of attacker k with other collaborative attackers, where k ∈ Lk
The leadership of attacker k, which could be positive or negative, where k ∈

20. Given Parameters Notation Description
The synergy of collaborative attack is as a function of the leader’s leadership and individual collaborative attacker’s cooperative effect, which could be positive or negative, when group of collaborative attackers gAr attack on node i in round r-1, where i ∈ VBr, and r ∈ R
The synergy of collaborative attack is as a function of the leader’s leadership and individual collaborative attacker’s cooperative effect, which could be positive or negative, when group of collaborative attackers gBr attack on node i in round r-1, where i ∈ VAr, and r ∈ R θi
Existing defense resource allocated on node i, where i ∈ V
eri
Repair cost of players when node i is dysfunctional in round r-1, where i ∈ V and r ∈ R
dri
The discount rate of the resources that players reallocate on node i in round r, where i ∈ V and r ∈ R
fri
The reinforcement rate above 1 represents the players reallocate more resources on the retrieved and repaired node i in round r, where i ∈ V and r ∈ R
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21. Given Parameters Notation Description lkri
Explore cost of attacker k when information of node i is updated in round r, where k ∈ , i ∈ , and r ∈ R. The cost is greatly increasing if the node is not adjacent with combined local view.
hkri
The discount rate of the attack resources that attacker k allocates on node i in round r, which is gained from exploring, where k ∈ , i ∈ V, and r ∈ R ui
The reward of compromising node i, where i ∈ V
δri
1 if node i is compromised in round r-1, 0 otherwise, where i ∈ and r ∈ R
ρri
1 if the attacker takes retaliation attack on node i in round r after the PS of the defender in round r-1, 0 otherwise, where i ∈ and r ∈ R
σri
The discount rate of the attack resources in round r after the PS of another player in round r-1, where k ∈ , i ∈ , and r ∈ R α
Player 1’s weight of ADOD β
Player 2’s weight of ADOD
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22. Decision variables Notation Description yri
Proactive defense budget allocation on node i in round r, where i ∈ V and r ∈ R
zri
PS defense budget allocation on node i in round r, where i ∈ and r ∈ R
sri
1 if node i is retrieved and repaired by another player in round r, 0 otherwise, where i ∈ and r ∈ R Ar
Total budget of player 1 in round r, where r ∈ R Br
Total budget of player 2 in round r, where r ∈ R
Player 1’s budget allocation, which is a vector of cost A1, A2 to Ar in round r, where i ∈ V and r ∈ R
Player 2’s budget allocation, which is a vector of cost B1, B2, to Br in round r, where i ∈ V and r ∈ R
Player 1’s Average DOD, which is considering under player 1’s and player 2’s budget allocation on player 1’s topology in round r, where r ∈ R
Player 2’s Average DOD, which is considering under player 1’s and player 2’s budget allocation on player 2’s topology in round r, where r ∈ R
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23. Objective function
(IP 1)
(IP 1’)
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24. Subject to
Player 1
Player 2
(IP 1.1)
(IP 1.2)
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25. Subject to
(IP 1.3)
(IP 1.4)
(IP 1.5)
(IP 1.6)
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26. Thanks so much for your listening. 
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