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Towards Optimal Firewall Rule Ordering Utilizing Directed Acyclical Graphs

Towards Optimal Firewall Rule Ordering Utilizing Directed Acyclical Graphs. Author: Ashish Tapdiya, Errin W. Fulp Publisher: ICCCN 2009 Presenter: Yu-Ping Chiang Date: 2009/09/30. Outline. Related work – Directed Acyclical Graph (DAG) Sub-Graph Merging (SDM) Algorithm

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Towards Optimal Firewall Rule Ordering Utilizing Directed Acyclical Graphs

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  1. Towards Optimal Firewall Rule Ordering Utilizing Directed Acyclical Graphs Author: Ashish Tapdiya, Errin W. Fulp Publisher: ICCCN 2009 Presenter: Yu-Ping Chiang Date: 2009/09/30

  2. Outline • Related work – Directed Acyclical Graph (DAG) • Sub-Graph Merging (SDM) • Algorithm • Non-optimal ordering • Time complexity • Experimental results • Number of breaks • Percentage improvement

  3. Directed Acyclical Graph (DAG) • DAG G = (R,E) • R = rules • E exists if • . • i < j

  4. Outline • Related work – Directed Acyclical Graph (DAG) • Sub-Graph Merging (SGM) • Algorithm • Non-optimal ordering • Time complexity • Experimental results • Number of breaks • Percentage improvement

  5. Sub-Graph Merging (SGM) • Definition • Sub-graph of rule ri : G(ri) • Ex: G(r2) = {r1, r2}, G(r4) = {r1, r2, r4} • Sum of probability of G(ri) : X(ri) • Ex: X(r2) = 0.0645+0.161 = 0.2255 • Cardinality of G(ri): C(ri) • Ex: C(r2) = 2

  6. Sub-Graph Merging (SGM) • Definition • DEP • Ex: • PROB(ri) • R(π) • Ex: R(π) = 0.0645*1 + 0.161*2 + … + 0.029*5 = 3.5487

  7. Sub-Graph Merging - Algorithm 0.11275 0.1614 0.0645 0.14515 0.2

  8. Sub-Graph Merging - Algorithm R(π) = 3.5487 R(π) = 3.4839

  9. SGM – non-optimal ordering 0.072886 0.058533 0.2 0.096061 0.09094

  10. SGM – time complexity O(n) O(n) O(n)

  11. Outline • Related work – Directed Acyclical Graph (DAG) • Sub-Graph Merging (SDM) • Algorithm • Non-optimal ordering • Time complexity • Experimental results • Number of breaks • Percentage improvement

  12. Edge density versus # of breaks

  13. Percentage improvement • Average number of rule comparisons was used to evaluate performance

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