A Cryptographic Approach to Safe Inter-domain Traffic Engineering

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A Cryptographic Approach to Safe Inter-domain
Traffic Engineering

• Sridhar Machiraju
• SAHARA Retreat, Summer 2004

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Outline

• Motivation
• Defining the Problem
• Proposed Solution
• Random Noise
• Discussion and Conclusions

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Motivation

• In BGP, Autonomous Systems (ASs) are abstracted
  as a node in a graph

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In reality,
Peering links
AS1
Internal links
AS2
AS3
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In BGP,
Peering links
AS1
Internal links
AS2
AS3
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Motivation

• In BGP, Autonomous Systems (ASs) are abstracted
  as a node in a graph

• Why?
• Scalability
• Confidentiality of intra-domain information,
  e.g., link quality, routing, flow info, policies
  etc.
• Why is this bad? Traffic engineering by one AS
  can send flows over bad paths in neighboring ASs

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Outline

• Motivation
• Defining the Problem
• Proposed Solution
• Random Noise
• Discussion and Conclusions

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High-level Problem Statement
In A, this path has most available bandwidth
A
B
Source of flow F
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High-level Problem Statement
In A, this path has most available bandwidth
path with best end-to-end available bandwidth
B
A
Destination of flow F
Source of flow F
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High-level Problem Statement
In A, this path has most available bandwidth
path with best end-to-end available bandwidth
B
A
Destination of flow F
Source of flow F

• Design a technique so that neighboring domains
  conduct traffic engineering cooperatively in a
  scalable fashion without having to reveal
  confidential intra-domain information?

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Formalizing the Problem

• Consider traffic from A to B that can exit one of
  P peering points

• Two kinds of constraints (of A and B)
• Given demand Ti, find amount of traffic, xik of
  flow Fi to transit peering point k
• For every bottleneck link, , all traffic
  traversing it must not exceed avail b/w

Confidential information
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A Linear Programming Problem

• Constraints

Constraints in AS A (private to A)
amount of each flow exchanged at peering points
Constraints in AS B (private to B)

• Objective maximize/minimize CTX
• (minimize) maximum link utilization
• (maximize) total traffic exchanged
• (minimize) average/maximum path inflation

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Outline

• Motivation
• Defining the Problem
• Proposed Solution
• Random Noise
• Discussion and Conclusions

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Overview of Solution
LP1

• Sub-matrices of V,W are private to A, B
• A and B transform the above into
• Solve LP1 and XQX
• V, W, X, X, C, C do not reveal any
  information about private information of A and B
  to each other (almost)

LP1
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Transforming the LP problem

• A sends encrypted sub-matrix, E(VA) and E(WA) to
  B
• B chooses random invertible P and Q
• B sends E(V)PE(V)Q and E(W)PE(W)
• requires addition of encrypted values and
  multiplication by known scalars (VB, WB)
• These can be performed by homomorphic encryption
  schemes, e.g., Pailliers
• A decrypts E(V) and E(W) to obtain LP1

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The Final Solution
B
E(VA), E(WA)
E(V)PE(V)Q E(W)PE(W)
A
A
Send XQX
Solve VXltW for X
B
E() represents encryption by A
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Outline

• Motivation
• Defining the Problem
• Proposed Solution
• Random Noise
• Discussion and Conclusions

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Small random noise is OK

• LP1 does not leak any information about VB, WB
  only if V has full rank
• So, add small random noise to matrix entries
• this can be done by homomorphic encryptions
• How does this affect the LP problem?
• Constraints may not be violated by small noise
• Objective function may be affected, though

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Effect of random noise(1)

• 10 constraints objective maximize flow

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Effect of random noise(2)

• Objective maximize (1path inflation)
• About 2-3 unsolvable problems too!

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Outline

• Motivation
• Defining the Problem
• Proposed Solution
• Discussion and Conclusions
• Random Noise

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Discussion

• Scalability
• LP problem transformation is quadratic in terms
  of number of cryptographic operations
• But, traffic engineering not frequent (hourly)
• Threat model
• ASs are assumed to be rational, i.e., do not
  inject wrong inputs
• Future work Experiment with real topologies and
  quantify time complexity

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Conclusions

• Inter-domain routing could benefit a lot from
  cooperation which is hindered by confidentiality
  requirements
• We demonstrate this for the case of safe traffic
  engineering
• Other cases of inter-domain cooperation policy
  safety, resource allocation and intrusion
  detection
• checking global invariants
• computing global functions