1. Privacy-Preserving Cross-Domain Network Reachability Quantification
Fei Chen
Computer Science and Engineering
Michigan State University
Joint work with
Bezawada Bruhadeshwar and Alex X. Liu

2. Background Network reachability can be defined as
What packets can pass through a given network path
Network reachability quantification is very important for
Understanding end-to-end network behavior
Detecting the violation of security policies
Business
Network 1
Home
Network 2
Internet

3. Motivation (1/2)
Many solutions have been proposed to quantify the network reachability
The main assumption of these solutions
All the reachability information from these network devices is known
Collecting such information could be very difficult
Due to the privacy and security concerns
Subnet1
ISP
Subnet2
Firewall
Router
Switches
User1 S1
FW1 R1
FW2
FW3
FW4 S2
User2

4. Motivation (2/2)
Subnet1
ISP
Subnet2
Firewall
Router
Switches
User1 S1
FW1 R1
FW2
FW3
FW4 S2
User2
Can we achieve the two following goals at the same time?
Quantify the network reachability for a given path, and
Preserve privacy of reachability information belong to different parties

5. Problem Statement Assumption
For each party, the reachability information is converted to an ACL
Static reachability information
Employ the network reachability approach [Khakpour et al., 2010]
Let M(A) denote the set of packets that are accepted by ACL A
We aim to design a privacy preserving protocol which
Enables User1 to compute M(A1) ∩ M(A2) ∩ M(A3)
No party can reveal the ACLs of other parties

6. Threat Model We consider semi-honest model
Each party must follow our protocol correctly
Input its ACL to our protocol without cheating
Follow the process of our protocol
Each party may try to learn the ACL rules of other parties
Analyze the intermediate messages when running the protocol

7. Related work Probing Network reachability quantificaiton
Current practice of verifying reachability
Expensive to quantify network reachability
Because it needs to generate and send significant amount of packets.
Inaccurate
E.g., it cannot probe the open ports with no server listening on them.
Network reachability quantificaiton
Estimate bounds of network reachability
[Xie et al. 2005, Ingols et al. 2006, Matousek et al. 2008]
Quantify the network reachability
[Al-Shaer et al. 2009, Sung et al. 2009, Khakpour et al. 2010]
Major assumption is not practical
All reachability information is known
No prior work studies privacy preserving reachability quantification

8. Basic building blocks (1/2)
Prefix membership verification P1 P2
[3, 7] 5
Prefix format
Prefix family
S([3,7])={011, 1**}
T(5)={101, 10*,1**,***}
Prefix numericalization
Prefix numericalization
N(S([3,7]))={0111, 1100}
N(T(5))={1011,1010, 1100,1000}
If N(S([3,7]))∩N(T(5)) ≠ , then 5[3, 7]

9. Basic building blocks (2/2)
Range intersection
Suppose the domain of this field is [0, 7] P1 P2
[3, 7]
[2, 5]
Generate ranges
Retrieve boundaries
[0, 2] , [3, 7]
2, 5
Prefix format and numericalize
Prefix family and numericalize
N(S([0,2])) , N(S([3,7]))
N(T(2)), N(T(5))
Because (1) N(S([0,2]))∩N(T(2)) ≠ , then 2[0, 2]
(2) N(S([3,7]))∩N(T(5)) ≠ , then 5[3, 7]
From 2[0, 2] and 5[3, 7], we have
[3, 7] ∩ [2, 5] = [3, 5]

10. Privacy preserving range intersection
Employ commutative encryption
For a number x, ((x)K1)K2 = ((x)K2)K1
For ease of presentation, let (x) K12 denote ((x)K1)K2
P1 (K1)
P2 (K2)
[3, 7]
[2, 5]
N(S([0,2])) , N(S([3,7]))
N(T(2)), N(T(5))
(1) Encrypt by P1
(2) Encrypt by P2
(1) Encrypt by P2
(2) Encrypt by P1
N(S([0,2]))K12 , N(S([3,7])) K12
N(T(2)) K21 , N(T(5)) K21
If P1 does the comparison, it can conclude that
[3,7] ∩ [2, 5] = [3, the original number of N(T(5)) K21]

11. Range intersection of multiple parties
P1 (K1)
P2 (K2)
P3 (K3)
[4, 7]
[3, 7]
[2, 5]
N(S([0,3])) N(S([4,7]))
N(S([0,2])) N(S([3,7]))
N(T(2)) N(T(5))
(1) Encrypt by P1
(2) Encrypt by P2
(3) Encrypt by P3
(1) Encrypt by P2
(2) Encrypt by P3
(1) Encrypt by P3
(2) Encrypt by P2
N(S([0,3]))K123 N(S([4,7])) K123
N(S([0,2]))K23 N(S([3,7])) K23
N(T(2)) K32 N(T(5)) K32
Comparison
3, N(T(5)) K32
Prepare for further
comparison
N(T(3)) K231 N(T(5)) K321
Comparison
4, N(T(5)) K321

12. Decryption of the comparison result
N(T(5)) K321
Decrypt by P3
N(T(5)) K21
Decrypt by P2
N(T(5)) K1
Decrypt by P1
N(T(5))
Decode 4 5
[4, 5]
= [4, 7] ∩ [3, 7] ∩ [2, 5]

13. ACL preprocessing ACL consists of multi-dimensional overlapping rules
Convert it to non-overlapping rules with accept decision
FDD construction
[0, 4]
[8, 15] F1
[0,15] F2
[0,4]
[5,15]
[5, 7] a d
Extract non-overlapping rules
with the accept decision

14. Experiment Setup
We conducted experiments on both real and synthetic ACLs
Each ACL examine five fields,
Source and destination IPs, source and destination ports, protocol type
The number of rules ranges from dozens to thousands
For effectiveness, we verified the correctness
For efficiency, we evaluate the computation and communication costs of the core operations
Processing each ACL
Comparing every two ACLs

15. Experimental Results (1/3)
For real ACLs with the average number of rules 806
Both offline and online Computation costs are less than 2 seconds
Communication cost is less than 60 KB
Comparison cost is less than 1 second
Our approach is efficient for the conversion and comparison of two real ACLs
Processing real ACLs

16. Experimental Results (2/3)
For synthetic ACLs with number of rules from 200 to 2000
One-time offline computation cost is less than 400 seconds
The online computation cost is less than 5 seconds
Communication cost is less than 450 KB
Processing synthetic ACLs

17. Experimental Results (3/3)
For synthetic ACLs with number of rules from 200 to 2000
The comparison time of two synthetic firewalls is less than 4 seconds
Comparing synthetic ACLs

18. Conclusion
Investigate privacy preserving quantification of network reachability for the first time
Propose an efficient and secure protocol to quantify the network reachability accurately
Conduct experiments on both real and synthetic ACLs to demonstrate the effectiveness and efficiently of our protocol

19. Future work Dynamic routing information Topological variations
Dynamic routing table
Topological variations
Links go down
New links get added
Malicious model
Some party cheats its ACL

20. Questions
Thank you!