論文進度報告

Advisor: Professor Frank Y.S. Lin Presented by G.W. Chen 陳冠瑋

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Title考慮服務品質需求下達到資訊遺漏最小化之近似最佳化機密分享與防禦資源配置規劃Near Optimal Secret Sharing and Defense Resource Allocation Plans for QoS Constrained Information Leakage Minimization

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AgendaProblem DescriptionHeuristic algorithm for outer problem (Initial)Lagrangean Relaxation problemHeuristic algorithm for inner problem

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Problem DescriptionNetwork operatorDeploy the network topology Select appropriate material in order to achieve the reliability of the networkEnforce QoS routing mechanism and the secret sharing strategyAllocate the defense budget on nodesAttackerApply attack power to compromise more valuable nodesRecover information and maximize damageSteal the threshold number of sharesGet the corresponding decrypt key

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Objective function

ZS Max ,Minpiiiimil x,a,y,Z,,b,,k

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Outer problem

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Reliability

Defense

QoS requirement

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Initial Outer problemStep 1: Determine the number of nodes and secretStep 2: Use the lowest material to construct the grid networkStep 3: Depend on the request of users to determine the candidate location which shares and keys can be placedStep 4: Check QoS requirements

if ok, go to Step 5if not, execute replication mechanism

Step 5: Execute reliability verificationStep 6: Use the remaining resource to allocate defense capability

1) Degree based 2) Uniform based 3) Share_count based

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Replication MechanismStep 1: For each user, check their receivable range, to check how many shares or key they need

Step 2: If there is the same candidate node, we assign the replicate key or share to this node, or we assign the replicate share or key in receivable range depending on their degree

Step 3: Repeat Step 1 and Step 2 until all constrain are satisfied

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User

User

Secret 1

Secret 1

Secret 2

Secret 2

Secret 2

Secret 2

Secret 1

Secret 1

User

11

j

1 2 3 4 m

22

Secretv

2

1

2

1

LLNN

Mesh networ

k

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Reliability Verification (Artificial flow)-1Step 1: Set important level: User to Secret

For each user, mark the farther node which is the most hop counts from secret to user

Step 2: Use the min cost flow algorithm to reach marked nodes (artificial capacity= 1)

Step 3: Execute step 2 until all artificial flows can be achieved then go to Step 5, if not, then go to Step 4

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User 1User 2

Secret 1

Secret 1

Secret 2

Secret 2

Secret 2

Secret 2

Secret 1

Secret 1

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Reliability Verification (Artificial flow)-2Step 4: Find the nearest distance between node (N1) where artificial flow can arrive from the user and the other node (N2) where artificial flow can arriveCheck whether the nodes exist or not

If yes, to construct the link between Node1 and Node2If no, to construct the link between User and Marked nodeAdd them to total_construction_cost

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User 1User 2

Secret 1

Secret 1

Secret 2

Secret 2

N1

N2

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Reliability Verification (Artificial flow)-3Step 5: Check the reliability of each artificial path,

If yes, go to Step 6If no, to enhance the level of the material to achieve reliability

• The rule: choose the smaller latency link to enhance Step 6: Stop

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Inner problem

18

19

20

21

1 1

1

2,3

2

2

3

3

S

key1

key2

key3

Share Key

1

2

3

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Sub-problem 11 1

1

2,3

2

2

3

3

S

key1

key2

key3

每個 Node 都會有唯一的攻擊路徑

px

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Sub-problem 2

2 3

2S

3S

1S 1S

2S

3S

1

1S

2S

3S

全部資訊皆復原Z

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Sub-problem 3 1 1

1

2,3

2

2

3

3

S

key1

key2

key3

攻擊預算為 四單位的防禦資源

ii y and a

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Heuristic AlgorithmStep 1: Make Xp’s value as the candidate attack pathStep 2: Compromise all nodes on the candidate attack pathsStep 3: If total_attack_cost >attack_budget, then go to Step 4, otherwise go to Step 6Step 4: Calculate the weight of node dynamically and choose the largest weight to remove its attack_budget Step 5: Execute step 4 repeatedly until total_attack_cost <= attack_budget

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Heuristic AlgorithmTotal_attack_cost > Budget

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1 1

1

2,3

2

2

3

3

S

key1

key2

key3

Share Key

1

2

3

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Check basket

RecoveredSecret

UnrecoveredSecret

RedundantNo Yes

Key Share

1 3 2 3

Leaf node

Node damage

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Compromised node damage (1) The recovered secret:

Shares or Key in Node i:

Redundant share or key:

2*shold[j]share_thre[j])[j](*ge[j]Secretdama mageNode[i].da 43

shold[j]share_thre

[j])[j](age[j])*(Secretdam*5 mageNode[i].da 43

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Compromised node damage (2)The unrecovered Secret

Key

Share

shold[j]share_thre

[j])[j](*ge[j]Secretdama mageNode[i].da 43

2*shold[j]share_thre

[j])[j](*ge[j]Secretdama mageNode[i].da 43

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Compromised node weightCalculate the weight of Node i

Node[i].weight)[i] u* NodeNum.damage)/(Node[i](AnCap[i] ightNode[i].we 1

2

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1 1

1

2,3

2

2

3

3

S

key1

key2

key3

Share Key

1

2

3

2,3

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1 1

1

2,3

2

2

3

3

S

key1

key2

key3

Share Key

1

2

3

2,3

1

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Heuristic AlgorithmTotal_attack_cost < Budget

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Heuristic AlgorithmStep 6: Check the basket of the attacker and recalculate the weight of the node, then set compromised node’s weight to 0 Step 7: Find shortest path using this weight by dijkstra’s algorithm and calculate each node’s path weight and sort themStep 8: For all unrecovered secret, we sum up the weight of the path until it could be recovered, and set the smallest weight to be the target secret Step 9: To find the smallest weight of the path in the target secret, if path_cost <= remaining_budget to compromise all nodes on path and set the weight of node to 0, otherwise to find next path Step 10: Execute Step 6~ Step 8 repeatedly until all secret are already checked

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Check basket UnrecoveredSecret

IS_keyin_basket IS_enough_sharein_basket

diff_threshold

NeitherKey nor en_share

diff_threshold

1 3

1 2

4 5Yes

No

Key

Yes

No

Share

Check Node

Share Key

Uncompromised node damage

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Uncompromised node damage (1)For the unrecovered secret:

If key in the basketSome shares in Node i

Acquire few shares to recover

Enough shares in the basket

re[j])basket_sha-eshold[j](share_thr[j])[j](*ge[j]Secretdama*2 mageNode[i].da 43

[j])[j](*ge[j]Secretdama*5 mageNode[i].da 43

[j])[j](*ge[j]Secretdama*5 mageNode[i].da 43

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Uncompromised node damage (2) Neither key nor enough shares

If the key in Node i

If the share in Node i

Acquire few shares to meet threshold

re[j])basket_sha-eshold[j](share_thr[j])[j](*ge[j]Secretdama*4 mageNode[i].da 43

re[j]basket_sha-shold[j]share_thre[j])[j](*ge[j]Secretdama mageNode[i].da 43

[j])[j](*ge[j]Secretdama*3 mageNode[i].da 43

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Compromised node weightCalculate the weight of Node i

Node[i].weight

path[i].weight)[i] u* NodeNum.damage)/(Node[i](AnCap[i] ightNode[i].we 1

2

iPi

ightnode[i].we ightpath[i].we

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1 1

1

2,3

2

2

3

3

S

key1

key2

key3

Share Key

1

2

3

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1 1

1

2,3

2

2

3

3

S

key1

key2

key3

Share Key

1

2

3

42

1 1

1

2,3

2

2

3

3

S

key1

key2

key3

Share Key

1

2

3

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Thanks !!