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
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 1
Internet
Business
Network 2
Home
Network 2
2
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
User1
S1
ISP
FW 1
Firewall
FW 2
R1
Router
Subnet2
FW 3
FW 4
S2
User2
Switches
3
Motivation (2/2)
Subnet1
User1
S1
ISP
FW 1
Firewall
FW 2
R1
Router
Subnet2
FW 3
FW 4
S2
User2
Switches
 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
4
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
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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
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Related work
 Probing
 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
7
Basic building blocks (1/2)
 Prefix membership verification
P1
P2
[3, 7]
5
Prefix format
S([3,7])={011, 1**}
Prefix numericalization
N(S([3,7]))={0111, 1100}
Prefix family
T(5)={101, 10*,1**,***}
Prefix numericalization
N(T(5))={1011,1010, 1100,1000}
If N(S([3,7]))∩N(T(5)) ≠ , then 5[3, 7]
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Basic building blocks (2/2)
 Range intersection
 Suppose the domain of this field is [0, 7]
P1
P2
[3, 7]
[2, 5]
Generate ranges
[0, 2] , [3, 7]
Prefix format and numericalize
N(S([0,2])) , N(S([3,7]))
Retrieve boundaries
2, 5
Prefix family and numericalize
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]
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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
N(S([0,2]))K12 , N(S([3,7])) K12
(1) Encrypt by P2
(2) Encrypt by P1
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]
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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
N(S([0,3]))K123
N(S([4,7])) K123
(1) Encrypt by P2
(2) Encrypt by P3
N(S([0,2]))K23
N(S([3,7])) K23
N(T(2)) K32
N(T(5)) K32
Comparison
3, N(T(5)) K32
Comparison
(1) Encrypt by P3
(2) Encrypt by P2
Prepare for further
comparison
N(T(3)) K231
N(T(5)) K321
4, N(T(5)) K321
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Decryption of the comparison result
N(T(5)) K321
Decrypt by P3
Decrypt by P2
Decrypt by P1
N(T(5)) K21
N(T(5)) K1
N(T(5))
Decode
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5
[4, 5] = [4, 7] ∩ [3, 7] ∩ [2, 5]
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ACL preprocessing
 ACL consists of multi-dimensional overlapping rules
 Convert it to non-overlapping rules with accept decision
r1 : F1  [0, 4]  F2  [7,15]  d
r2 : F1  [5, 7]  F2  [5,15]  d
r3 : F1  [5, 7]  F2  [0, 8]  a
r4 : F1  [0,15]  F2  [0,15]  d
FDD construction
F1
[0, 4]
[5, 7]
F2
[0,15]
d
[8, 15]
F2
F2
[0,4]
a
[5,15]
[0,15]
d
d
Extract non-overlapping rules
with the accept decision
nr1 : F1  [0, 4]  F2  [7,15]  a
nr2 : F1  [5, 7]  F2  [0,4]  a
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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
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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
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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
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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
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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
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Future work
Dynamic routing information
 Dynamic routing table
Topological variations
 Links go down
 New links get added
Malicious model
 Some party cheats its ACL
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Questions
Thank you!
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