1. Panel: Theory and fundamental understanding of network system resiliency, performance and usability
Ness B. Shroff
Electrical and Computer Engineering & Computer Science and Engineering

2. Question 1
Modeling
When performance and security both come as priorities for the system design, how should we proceed to understand the optimality or tradeoff in such design?
Network behaviors (e.g., random access or queuing) can be usually (and sometimes relatively easily) characterized by a good analytical framework (e.g., using queuing, control, information, or game theories). Are they still vital tools in the presence of an attacker?
In addition, the attacker’s behavior can be rather ad-hoc or unpredictable. Is it time to have a fresh look at defining a comprehensive network adversary model?
So, I’m going to take an opportunity to answer the first two questions. The first question is about modeling.

3. Existing analytical tools are still important in modeling in the presence of attackers
Queueing Theory and Models
Capture Delays, Throughput, Data freshness/age …
Can be used as tools to understand normal vs abnormal behavior in the presence of an attacker
Useful in analyzing data retrieval in coded data systems (robustness)
Useful in developing algorithms to react to network attacks (e.g., re- routing, cong. control…)
Information Theory
Provides a methodology to communicate with guaranteed perfect secrecy regardless of computational power of attackers
Ideas from Shannon and Wyner can be combined with optimization, network control, and queueing theory to achieve real- time secret communication [Shroff et. al, Tran. on Info. Theory 2013].
Recent extensions to active attackers and MIMO [Koksal et. al]
Can use signals at physical layer to develop techniques for not only covert communication, but also authentication, message integrity…
I argue that we don’t need to throw away our existing analytical tools. They are still important …

4. Existing analytical tools still important in modeling in the presence of attackers
Control and optimization theory
Useful in designing robust algorithms (e.g., robust opt/control)
Understanding how to react to adversarial attacks (congestion control, prioritization/scheduling, dynamic control…)
Characterize the tradeoffs between resources/redundancies needed to protect network and loss in network performance
Useful in designing systems with both security and performance
Game theory
Considers the strategic behavior of the attackers and defenders
Used to develop dominated equilibrium strategies
Recent advances under limited rationality (ad hoc or unpredictable behavior)
Can model dependencies at additional computational cost…
Network theory + Machine Learning = Yes!
Traditional Approaches + Learning  Develop Comprehensive Network Adversary Models

5. Comprehensive Network Adversary Model
Multi-Stage Multi-Party Bayesian Security Game
Time-scales: the network and actions can be dynamic
Interdependencies:
Between different nodes: Non-additive utility functions
Between different networks: Power Grid, Comm. Network, water network, social network
Between different agents: classes of adversaries, defenders, neutral players, etc.
Between agents and networks: social network and attackers/defenders, etc.
Uncertainties:
Attacker Type
Attacker’s action (level of rationality)
Learning (and luring) can be used to estimate:
Agent behavior, inter-dependencies, structure …
Here is a candidate comprehensive network adversary model…

6. Challenges and Open problems
Curse of dimensionality
Complexity is linear in the time dimension.
We need to dynamically solve a Bayesian security game.
Complexity could be exponential in action space.
Dependencies complicate this. From Harsanyi transformation, the uncertainty will in the attacker lead to explosion of action space.
Complexity is exponential in number of players (parties).
Open problems:
There are many open problems here:
Baysian comes from which attacker will have highest probability to attack. Comes from the uncertainty in the attacker type.
Dependency complicates the action space. Dependencies complicate network behavior.
Multi-scale: time, type of attacker, multiple party (attacker, defender, neutral, social links between players in different groups).
Does this multi-scale modeling increase the efficacy of our security defense?
How can we efficiently output the security policy from this model? What is the complexity of solving this game?
Preliminary results shows that the solving complexity of some classes can be reduced to polynomial time via a low-rank decomposition technique [Wang & Shroff Sigmetrics 2017]

7. Proactive and Dynamic Defense
Question 2
Proactive and Dynamic Defense
Recent proactive defense suggests constantly and proactively changing network configurations for security (e.g., a node keeps changing its route/path).
How can we fully understand the benefits, costs, and/or usability behind making defense dynamic and proactive?
Baysian comes from which attacker will have highest probability to attack. Comes from the uncertainty in the attacker type.
Dependency complicates the action space. Dependencies complicate network behavior.
Multi-scale: time, type of attacker, multiple party (attacker, defender, neutral, social links between players in different groups).

8. Proactive defense with game theory
Proactively change the routing path (e.g., among each of the above config.)
Alternate among four routing paths with some pre-defined probability.
On a ”shallow level”: a good strategy to confuse the attacker.
Deeper level: stealthy attacker can observe and predicts the strategy.
Combine Game theory + learning to develop a more reliable strategy
A new framework against stealth attacker: periodically update the strategy based on online learning [Zheng & Shroff, AAAI 17’].
Path A
Path B
Path C
Path D
4 figures describing 4 possible paths from source to destination.

9. Challenges and Open problems
Current results are limited to independent targets
We need to extend to the dependent targets in the network.
Attacker behavior is highly dynamic and non-stationary.
Most online learning algorithms require stationary assumptions.
Open problems:
How can we learn in non-stationary environments?
Preliminary work for change detection in non-stationary environments [Liu, Lee, and Shroff, AAAI’18]
How do we characterize the dependency among targets in the network?
Use non-additive utility functions? [Wang and Shroff, Sigmetrics 2017]

10. Characterizing Dependencies: Non-additive utility functions
Toy example: security game on a network
Targets: 1,2,3,4
Strategies: {1}, {2}, {3}, {4}, {1,2}, {3,4}
Utilities: network value function where is number of nodes in the ith connected component
For example, the network value of the original network is
After removing node 3, the network is one 18-nodes network and one isolated node, the network value is
A. Gueye and J. C. Walrand. Towards a metric for communication network vulnerability to attacks: A game theoretic approach. In Game Theory for Networks, pages 259–274. Springer, 2012.

11. Characterizing Dependencies: Non-additive utility functions
Why are non-additive utility functions important?
The non-additive strategy is more reliable!
Why?
Synergy effect!
The benefit of 1,2 >> benefit of 1 + benefit of 2
Additive vs Non-additive
The NE under additive case is that defender choose strategy {1,2} with probability and strategy {3,4} with probability 0.66.
The NE under non-additive case is that defender choose strategy {1,2} with probability 0.63 and strategy {3,4} with probability 0.37.

12. Non-additive security game has many non-networking applications
Security game is two-player normal form game between an attacker and a defender.
Select a subset of targets to defend.
Select target to attack and avoid being trapped by defender
Targets
Attacker
(Limited Budget)
Defender
(resource allocation constraint)
The classic security game model is a 2-player normal form non-zero-sum game. With one player is attacker, the other player is the defender.
There exists number of n targets, each target is indexed by 1,2,…,n.
The defender is assumed to have limited resources…
The goal is to determine the the equilibrium strategy such as Nash equilibrium and Stackelberg equilibrium to protect the critical infrastructure.
Efficiently determine the equilibrium strategy (NE, SSE) to protect the critical infrastructure.

13. Federal Air Marshal Service (FAMS)
Allocate limited number of Air Marshals to protect the flights.
Defender pure strategy space:
Only 100 flights and 10 air marshals yields 1013 pure strategies.
Real problem size: over flights per day.
[2]:
Target: flights
Resource: air marshal.
Resource
Schedules
Targets
The first application is the IRIS system in the FAMS.
The goal is to…
In this problem,
[1] Tsai J, Rathi S, Kiekintveld C, et al. IRIS-A Tool for Strategic Security Allocation in Transportation Networks[J]. AAMAS 09.

14. Game theory & National security
Other applications

15. Non-additive Security Game Model
Complete pure strategy space:
Attacker and defender’s pure strategy space is the power set of [n]:
Non-additive utility function:
Benefit function:
Attacker cost function:
Defender cost function:
Mixed strategies
It specifies the probabilities of playing each pure strategies
Attacker and defender’s mixed strategy is a vector
Bilinear form
Defender’s pure strategy is is a feasible assignment of resources to targets

16. Challenges and main results
Both exponential large attacker’s and defender’s pure strategy space
Exponential number of utility functions
Some Progress:
Decomposition-based compact representation technique in the NASG.
An oracle-based algorithm to efficiently compute the mixed strategies of NASG.
The complexity of computing the mixed strategies of NASG.
Some important cases are polynomial

17. Conclusion
Traditional analytical tools are useful in designing networks in presence of attackers
Queueing, Information Theory, Control, Game Theory, …
Full power can be harnessed by using the right combination of these tools (problem specific) and learning and luring (e.g., honeypots)
Need to develop tractable models that can characterize network/agent dependencies, handle multi-scale dynamics, and account for intelligent/patient adversaries

18. Thank you