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Leveraging AI to Address Global Security Challenges V.S. Subrahmanian Dartmouth College [email protected] Joint Work with Many Collaborators to be Listed

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Leveraging AI to Address Global Security Challenges

V.S. Subrahmanian

Dartmouth College

[email protected]

Joint Work with Many Collaborators to be Listed

Talk Outline

• Selected Vignettes in which AI is Leveraged to Address Global Security Issues▫ Terrorism

▫ Systemic Banking Crises

▫ Anti-Poaching Engine

• Disclose or Exploit: How Should Governments Decide whether to Disclose a Vulnerability they Discover or Exploit it against Adversaries?

CSIRO - Australia Feb 2021 @vssubrah

2

Geospatial Abduction

• INPUTS:▫ Observations (attacks) O▫ “Map” of the area▫ Historical attack and cache data

• OUTPUT: Identify locations of caches• Invented “geospatial abduction” to predict locations of IED caches

in Baghdad and Afghanistan▫ Learned model of relationship b/w attack location and cache

location (14 mths of data)▫ Used model to generate constraints▫ Caches must lie in purple “annulus” donut shaped regions▫ Caches locations must satisfy some constraints

must lie in Sunni regions cannot be in the water or on coalition bases

▫ Reduced problem to vertex cover• Solved using fast approx algorithms leveraging set cover• Accuracy of 700m in Baghdad.• 35x higher density of caches in Afghanistan• Code shipped to over a dozen defense/law enforcement/

intel agencies

CSIRO - Australia Feb 2021 @vssubrah

Shakarian, P., Subrahmanian, V.S. and Sapino, M.L., 2011. GAPs: Geospatial abduction problems. ACM Transactions on Intelligent Systems and Technology (TIST), 3(1), pp.1-27.Shakarian, P., Dickerson, J.P. and Subrahmanian, V.S., 2012. Adversarial geospatial abduction problems. ACM Transactions on Intelligent Systems and Technology (TIST), 3(2), pp.1-35.

3

Predicting, Explaining, and Reshaping Terror Group Behavior

• Invented Stochastic Opponent Modeling Agents (SOMA) and Temporal Probabilistic (TP) rules.

• Used them to explain/predict behaviors of Hezbollah, Lashkar-e-Taiba, Indian Mujahideen, Boko Haram (in press.

• Developed PAGE (Policy Analytics Generation Engine) to generate policies that satisfy various goals.

CSIRO - Australia Feb 2021 @vssubrah

4

Reshaping Terrorist Networks

Predict Successor of a Removed Vertex

• Suppose we choose to remove a person from the network.

• Who will replace that node?

Predict how a network will re-structure itself when multiple vertices are removed

• Induce a probability distribution over a space of possible networks that result

Identify nodes to remove that minimize “expected lethality” of the resulting network

• Each possible new network has a lethality

• The value of removing a set of vertices is an expected value computation

CSIRO - Australia Feb 2021 @vssubrah

Learn model of lethality of a terrorist network

5

Network Lethality MeasureCSIRO - Australia Feb 2021

@vssubrah

Person P1 removed

Person P2 removed

Network N1

A1 Attacks

Network N2

A2 Attacks• We have different networks as people are removed from the

network.• We measure various properties of these networks• Initially, we have network N1 and during this time, K1 attacks

occur. Network N1 has property values 𝑣11, 𝑣2

1, . . , 𝑣𝑛1

• When person P1 was removed, we have a new network N2 and during the time N2 existed, there were K2 attacks. Network N2 has property values 𝑣1

2, 𝑣22, … , 𝑣𝑛

2

• We build a regression model to predict number of attacks from historical data about variables involved.

Predictive regression model is highly accurate.• 0.83 Pearson Correlation Coefficient for

LeT network.• 0.652 for AQ network

Spezzano, F., Subrahmanian, V.S. and Mannes, A., 2014. Reshaping terrorist networks. Communications of the ACM, 57(8), pp.60-69.

6

STONE System

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7

Forecasting Systemic Banking Crises

• Joint work with the International Monetary Fund.

• 30+ years of inter-country financial exposure data (but with huge holes).

• Developed new network indicators for tracking SBCs

• Out-of-sample predictions for systemic banking crises were near perfect.

CSIRO - Australia Feb 2021 @vssubrah

Minoiu, C., Kang, C., Subrahmanian, V.S. and Berea, A., 2015. Does financial connectedness predict crises?. Quantitative Finance, 15(4), pp.607-624.

8

Forecasting Systemic Banking Crises• Learned new factors linked to financial

contagion.

• Improvement in predictive accuracy over traditional macro-economic fundamentals was almost 10%.

• Key factors:

▫ Degree and strength go up steeply before a crisis and then level off.

▫ CCs peak before – a later drop signals a crisis shortly afterwards. Turbulence between a country’s financial partners precedes crises.

▫ Crises occur a couple of years after neighbors’ degree and strength start dropping

CSIRO - Australia Feb 2021 @vssubrah

9

APE: Anti-Poaching Engine

• Goal: Generate a coordinated schedule for tomorrow for D drones and P ground patrols to maximize the expected number of rhinos protected.

• To generate a schedule for tomorrow, we need to:▫ Predict where the rhinos will be tomorrow on

an hourly basis (avg error < 1km)▫ Predict which cells the poachers will strike

(predictive accuracy > 80%)▫ Ensure drone/patrol schedules are

coordinated▫ Maximize expected number of protected

animals.

CSIRO - Australia Feb 2021 @vssubrah

Park, N., Serra, E., Snitch, T. and Subrahmanian, V.S., 2015. APE: A data-driven, behavioral model-based anti-poaching engine. IEEE Transactions on Computational Social Systems, 2(2), pp.15-37.

Park, N., Serra, E. and Subrahmanian, V.S., 2015. Saving rhinos with predictive analytics. IEEE Intelligent Systems, 30(4), pp.86-88.

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APE: Anti-Poaching Engine

• Proposed the novel notion of a Spatio-Temporal Graph to represent how rhinos could move during a day through a park.

• Data from Oliphants West▫ Past poaching incidents▫ Location data for some rhinos from the past

• Plus terrain, vegetation, settlement, road, and other data.

• Improvement ratio = E(% of animals that would have survived with our algo)-E(% of animals that would survive with our algo).

• Accuracy(d) = 𝐼.𝑅.𝑢𝑠𝑖𝑛𝑔 𝑑𝑎𝑡𝑎 𝑢𝑝𝑡𝑜 𝑑𝑎𝑦 𝑑

𝐼.𝑅.𝑢𝑠𝑖𝑛𝑔 𝑑𝑎𝑡𝑎 𝑢𝑝𝑡𝑜 𝑑𝑎𝑦 𝑑+1

• Results showed high IRs, in the 0.99 range.

CSIRO - Australia Feb 2021 @vssubrah

11

Talk Outline

• Selected Vignettes in which AI is Leveraged to Address Global Security Issues▫ Terrorism

▫ Systemic Banking Crises

▫ Anti-Poaching Engine

• Disclose or Exploit: How Should Governments Decide whether to Disclose a Vulnerability they Discover or Exploit it against Adversaries?

CSIRO - Australia Feb 2021 @vssubrah

Chen, H., Han, Q., Jajodia, S., Lindelauf, R., Subrahmanian, V.S. and Xiong, Y., 2020. Disclose or Exploit? A Game-Theoretic Approach to Strategic Decision Making in Cyber-Warfare. IEEE Systems Journal, Vol 14 Nr. 3, Sep 2020.

12

Disclose or Exploit? NSA Point of View

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The NSA discovers a vulnerability in a globally used software product produced by a US company

Excited NSA hackers believe it provides a perfect opportunity to hack important adversary nation-state

networks in order to gather intelligence

What should they do? What process/method should they use in order to arrive at a decision?

Chen, H., Han, Q., Jajodia, S., Lindelauf, R., Subrahmanian, V.S. and Xiong, Y., 2020. Disclose or Exploit? A Game-Theoretic Approach to Strategic Decision Making in Cyber-Warfare. IEEE Systems Journal, Vol 14 Nr. 3, Sep 2020.

Disclose or Exploit? Adversary Point of View

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Adversary nation state discovers a vulnerability in a globally used software product from their country

Excited adversarial hackers believe it provides a perfect opportunity to hack important US defense networks in

order to gather intelligence.

What should they do? What process/method should they use in order to arrive at a decision?

Background: Vulnerability Equities Program (VEP)

• The US Government’s VEP is a pioneering program that tries to answer this question.

• Inter-agency Equities Review Board meets monthly to discuss this question.

• But colossal blunders occur…..

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15

The US Government Vulnerability Equities Program

• Prior to 2013: The NSA reportedly ▫ developed three exploits (Eternal Blue) targeting various Microsoft and

other systems

▫ Leveraged 5 vulnerabilities in all

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https://foreignpolicy.com/2017/09/25/is-the-nsa-doing-more-harm-than-good-in-not-disclosing-exploits-zero-days/

16

The US Government Vulnerability Equities Program

• Sometime in 2014-2017: Eternal Blue stolen by “The Shadow Brokers”

• 2017: Dumped for use by 3rd parties leading to Wannacry

NotPetya

AES-NI Ransomware

Double Pulsar trojan/backdoor

And more….

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https://www.trendmicro.com/vinfo/pl/security/news/cybercrime-and-digital-threats/malware-using-exploits-from-shadow-brokers-in-the-wild

https://www.avast.com/c-eternalblue

17

Why Should Country C Disclose Vulnerabilities it Discovers?

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Discover Vuln v in Product P

Users of P deploy

patch

Disclose v to

Company X

Company X builds (?) patch

SAFER !

X builds safer

products, C gets safer

Economic benefits to X and

C

18

Questions to ask when Country C finds a New Vulnerability• If C Exploits▫ What would be the payoff to country C ?▫ What is the probability that an adversary or 3rd party discloses the vulnerability,

reducing the effectiveness of any exploit developed and deployed?• Stockpile? ▫ What is the probability that an adversary will discover and exploit the

vulnerability if stockpiled but not disclosed by country C ? ▫ How damaging would that be?

• Disclose?▫ How much benefit would company X get out of the disclosure? ▫ How much safer would country C be?▫ Ethical/moral/legal/political payoffs ?

CSIRO - Australia Feb 2021 @vssubrah

19

Vulnerabilities and Exploits

• What percentage of vulnerabilities are actually exploited?

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SOURCE H. Chen, R. Lui, N. Park, and V.S. Subrahmanian. Using Twitter to Predict When Vulnerabilities will be Exploited, accepted for publication (poster) in Proc. 2019 ACM Conference on Knowledge Discovery & Data Mining (KDD ’19), Anchorage, Alaska, Aug 2019.

20

Vulnerabilities and Exploits

• What percentage of vulnerabilities are actually exploited?▫ 9.2%

• What percentage of vulnerabilities are exploited before they are officially published in the National Vulnerability Database?

CSIRO - Australia Feb 2021 @vssubrah

SOURCE H. Chen, R. Lui, N. Park, and V.S. Subrahmanian. Using Twitter to Predict When Vulnerabilities will be Exploited, accepted for publication (poster) in Proc. 2019 ACM Conference on Knowledge Discovery & Data Mining (KDD ’19), Anchorage, Alaska, Aug 2019.

21

Vulnerabilities and Exploits

• What percentage of vulnerabilities are actually exploited?▫ 9.2%

• What percentage of vulnerabilities are exploited in the real world before being published in the National Vulnerability Database?▫ 49.46%

CSIRO - Australia Feb 2021 @vssubrah

SOURCE H. Chen, R. Lui, N. Park, and V.S. Subrahmanian. Using Twitter to Predict When Vulnerabilities will be Exploited, accepted for publication (poster) in Proc. 2019 ACM Conference on Knowledge Discovery & Data Mining (KDD ’19), Anchorage, Alaska, Aug 2019.

22

Vulnerabilities and Exploits

• What percentage of vulnerabilities are actually exploited?▫ 9.2%

• What percentage of vulnerabilities are exploited before they are officially published in the National Vulnerability Database?▫ 49.46%

• For vulnerabilities that are exploited after Mitre discloses the vulnerability, what is the average period of time for the exploit to occur?

CSIRO - Australia Feb 2021 @vssubrah

SOURCE H. Chen, R. Lui, N. Park, and V.S. Subrahmanian. Using Twitter to Predict When Vulnerabilities will be Exploited, accepted for publication (poster) in Proc. 2019 ACM Conference on Knowledge Discovery & Data Mining (KDD ’19), Anchorage, Alaska, Aug 2019.

23

Vulnerabilities and Exploits

• What percentage of vulnerabilities are actually exploited?▫ 9.2%

• What percentage of vulnerabilities are exploited before their reports are officially published in the National Vulnerability Database?▫ 49.46%

• For vulnerabilities that are exploited after Mitre discloses the vulnerability, what is the average period of time for the exploit to occur?▫ 24.05 days

CSIRO - Australia Feb 2021 @vssubrah

SOURCE H. Chen, R. Lui, N. Park, and V.S. Subrahmanian. Using Twitter to Predict When Vulnerabilities will be Exploited, accepted for publication (poster) in Proc. 2019 ACM Conference on Knowledge Discovery & Data Mining (KDD ’19), Anchorage, Alaska, Aug 2019.

24

Life-cycle of an Exploited Vulnerability before Disclosure

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CreationTime𝑇𝑐𝑟𝑒𝑎𝑡𝑒

DiscoveryTime𝑇𝑑𝑖𝑠𝑐𝑜

Exploit Available𝑇𝑎𝑣𝑎𝑖𝑙

Exploit Starts𝑇𝑒𝑥𝑝𝑙𝑜𝑖𝑡

PUBLICNOT

PUBLIC

DiscloseTime

𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒

• Exploit development time𝑇𝑑𝑒𝑣 = 𝑇𝑎𝑣𝑎𝑖𝑙 − 𝑇𝑑𝑖𝑠𝑐𝑜

• Exploit duration𝑇𝑒𝑥𝑝 = (𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒 − 𝑇𝑒𝑥𝑝𝑙𝑜𝑖𝑡)

In DiscX:• It is a dominant strategy to use the

exploit as soon as it is available, i.e. 𝑇𝑒𝑥𝑝𝑙𝑜𝑖𝑡 = 𝑇𝑎𝑣𝑎𝑖𝑙.

Repeated Cyber Warfare Game Model, I

• DiscX models the situation as a repeated 2-player game 𝐺 = (𝐼, 𝒂, 𝒖) where▫ 𝐼 = {1,2} are the two players

▫ 𝒂 = (𝑎1, 𝑎2) is the joint strategy of the two players

▫ 𝒖 = (𝑢1 𝒂 , 𝑢2 𝒂 ) denotes a payoff function that assigns a payoff to each player under an input joint strategy 𝒂.

• Pure strategy for a player 𝑖 is given by 𝑎𝑖 = (𝑏𝑖 , 𝑡𝑒𝑥𝑝𝑖 ) where

▫ 𝑏𝑖 = ቊ0 𝑖𝑓 𝑝𝑙𝑎𝑦𝑒𝑟 𝑖 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑒𝑥𝑝𝑙𝑜𝑖𝑡

1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

▫ 𝑡𝑒𝑥𝑝𝑖 = ቊ

0 𝑖𝑓 𝑏𝑖 = 0𝑖𝑛𝑡𝑒𝑔𝑒𝑟 > 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

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How long to exploit

26

Repeated Cyber Warfare Game Model, I

• Development cost: 𝑐𝑑𝑒𝑣𝑖 , cost for player 𝑖 to develop an exploit e.g. Kaspersky

Lab estimates a team of 10 people took 2-3 years to build Stuxnet

• Exploit payoff: Suppose 𝑡𝑒𝑥𝑝𝑖,∗ is the actual time for which player 𝑖 exploits a

given vulnerability – could be different than 𝑡𝑒𝑥𝑝𝑖 .

▫ The payoff is 𝑟𝑒𝑥𝑝𝑖 𝑡𝑒𝑥𝑝

𝑖,∗ .

▫ 𝑟𝑒𝑥𝑝𝑖 is a non-decreasing function.

• Disclosure payoff: 𝑟𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒𝑖 comes from three sources

▫ Benefit to the company X whose product contains the vulnerability▫ Reduction of exposure to the vulnerability of relevant user population▫ Improved reputation for disclosing the vulnerability

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27

RCWG Overall Payoff

• 4 cases to consider depending upon whether the two players decide to exploit▫ Case 1 Neither player exploits

▫ Case 2 Player 1 exploits, player 2 does not exploit

▫ Case 3 Player 2 exploits, player 1 does not exploit

▫ Case 4 Both players decide to exploit

• Note 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒𝑖 = 𝑇𝑑𝑖𝑠𝑐𝑜

𝑖 + 𝑇𝑑𝑒𝑣𝑖 + 𝑡𝑒𝑥𝑝

𝑖

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Case 1: Neither Player Exploits

• Whoever discloses first gets the reward!

𝑢1 𝑎1, 𝑎2 = ൝𝑟𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒1 𝑖𝑓 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒

1 ≤ 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒2

0 𝑖𝑓 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒1 > 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒

2

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Case 2: Player 1 exploits, but player 2 does not

• Player 1 gets the reward for exploiting – and possibly for disclosing

𝑢1 𝑎1, 𝑎2 = ൝−𝑐𝑑𝑒𝑣

1 + 𝑟𝑒𝑥𝑝1 𝑡𝑒𝑥𝑝

1 + 𝑟𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒1 𝑖𝑓 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒

1 ≤ 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒2

−𝑐𝑑𝑒𝑣1 + 𝑟𝑒𝑥𝑝

1 𝑡𝑒𝑥𝑝1,∗ 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

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Reward for disclosure

Reward for exploiting

Cost of exploiting

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Case 3: Player 2 exploits, but player 1 does not

• Player 1 only gets a reward if he discloses before player 2

𝑢1 𝑎1, 𝑎2 = ቊ𝑟𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒1 𝑖𝑓 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒

1 ≤ 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒2

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

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Reward for disclosure

31

Case 4: Both players exploit

• Both players may get some reward

𝑢1 𝑎1, 𝑎2 = ൝−𝑐𝑑𝑒𝑣

1 + 𝑟𝑒𝑥𝑝1 𝑡𝑒𝑥𝑝

1 + 𝑟𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒1 𝑖𝑓 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒

1 ≤ 𝑇𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒2

−𝑐𝑑𝑒𝑣1 + 𝑟𝑒𝑥𝑝

1 𝑡𝑒𝑥𝑝1,∗ 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

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Pure Strategy 1-Stage Game

• Best response of player 𝑖, given fixed strategy of player 𝑗

𝑎𝑖,∗ = 𝑎𝑟𝑔𝑚𝑎𝑥𝑎𝑖 𝑢𝑖(𝑎𝑖 , 𝑎𝑗)

• Nash equilibrium of 1-stage game

𝑎1,∗ = 𝑎𝑟𝑔𝑚𝑎𝑥𝑎1 𝑢1 𝑎1, 𝑎2,∗

𝑎2,∗ = 𝑎𝑟𝑔𝑚𝑎𝑥𝑎2 𝑢2 𝑎1,∗, 𝑎2

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RCWG Nash Equilibrium

• 𝑉 = 1,2,3, … is a sequence of vulnerabilities that emerge over time.• RCWG is a sequence ෨𝐺 = {𝐺𝑣|𝑣 ∈ 𝑉} where 𝐺𝑣 = (𝐼, 𝒂𝑣, 𝒖𝑣). Each

vulnerability is a 1-stage game.• Player 𝒊’s objective: Maximize overall payoff by playing a pure strategy 𝑎𝑣,𝑖

for each vulnerability, i.e. max⟨𝑎𝑣,𝑖⟩

σ𝑣∈𝑉 𝑢𝑣,𝑖 𝑎𝑣,1, 𝑎𝑣,2 .

• Corresponding Nash Equilibrium:

𝑎𝑣,1,∗ = argmax⟨𝑎𝑣,1⟩

𝑣∈𝑉

𝑢𝑣,1(𝑎𝑣,1, 𝑎𝑣,2,∗)

𝑎𝑣,2,∗ = argmax⟨𝑎𝑣,2⟩

𝑣∈𝑉

𝑢𝑣,2(𝑎𝑣,1,∗, 𝑎𝑣,2)

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IN THEORY: RCWG can be solved by independently solving each of the 1-stage gamesIF the probability distribution of the parameter space for both players is known to both players.

34

Solving the 1-Stage Game

• Assumption (for now): Both players have complete knowledge of the

others’ parameters 𝛼 = 𝑇𝑑𝑖𝑠𝑐𝑜, 𝑇𝑑𝑒𝑣 , 𝑐𝑑𝑒𝑣, 𝑟𝑒𝑥𝑝, 𝑟𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒 .

• Payoff function of each player depends on both▫ Joint strategy 𝒂𝑣 of the players and

▫ The parameters 𝛼

• The latter is generally unknown to the other player.

• Let 𝑓𝑖,𝑘(𝛼𝑘) be a pdf for the 𝑖’th player and 𝑘’th parameter and 𝑓𝑖 𝛼be a joint distribution over all parameters.

• Suppose these pdfs are known to both players.

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Solving the One Stage Game

If both players know each others’ PDFs, then the best responses are:

𝑎𝑖,∗ = arg max𝑎𝑖:𝛼∼𝑓𝑖(𝛼)

𝑢𝑖(𝑎𝑖 , 𝑎𝑗; 𝛼)

where 𝑓𝑖 𝛼 = ς𝑘 𝑓𝑖,𝑘(𝛼𝑘) is the joint pdf over all

the parameters.

• The problem is a stochastic optimization problem as the objective function is stochastic.

• Use Monte Carlo sampling to estimate the reward function 𝑢1(𝑎1, 𝑎2; 𝛼) using N samples.

• Proposition: Computational complexity of this approach is 𝑶(𝑁 × 𝑨𝒊 ) where 𝑨𝒊 is the cardinality of the feasible action space for player 𝑖.

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Solving the One Stage Game

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Compute the best response for each player

Randomly choose feasible action for each player

Iteratively update the best response for each player till convergence

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Solving the One Stage Game

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Compute the best response for each player

Randomly choose feasible action for each player

Iteratively update the best response for each player till convergence

Complexity: Algorithm 1 (best response) has complexity 𝑶(𝑁 ∗ 𝐴𝑖 ) where 𝐴𝑖 is the size of the feasible action space for player 𝑖.

• Algorithm NE is not theoretically guaranteed to converge.• But our very extensive experiments show that it converges in 220 iterations or less, in under

20 seconds.

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Learning the Model Parameters

• In the pure strategy NE, we assume that both players know the parameter distributions (i.e. the 𝑓(𝛼)’s).

• But this is not true in the real world

• How can we learn these as the RCWG proceeds?

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Learning While Competing Approach

• At the start of the game: ▫ We have a known set V of vulnerabilities.▫ Fit a “prior” belief (pdf ሚ𝑓(𝛼) over parameter space) about the adversary

from V [in our experiments, we used both Gaussian and Beta distributions, but any distributions can be used]

• While the RCWG game is being played out▫ When a new vulnerability emerges in the game, update the Nash

equilibrium and associated payoffs using ሚ𝑓(𝛼)▫ Set 𝑉 = 𝑉 ∪ {𝑣}▫ Recompute ሚ𝑓(𝛼), i.e. update the pdf over the parameter space.

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Repeatforever

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Experimental Settings

• Rand Corporation report looks at 200 zero-day exploits (and relevant disclosures) between 2002 and 2016.

• Parameters derived from Rand report▫ 𝑡𝑑𝑖𝑠𝑐𝑜 ∼ 𝑁(200,40), min=40, max=360▫ 𝑡𝑑𝑒𝑣~𝑁(22,4.4), min = 4.4, max = 36. Median time to develop exploit = 22 days.▫ 𝑟𝑒𝑥𝑝𝑙𝑜𝑖𝑡 = 0.95𝑡𝑒𝑥𝑝 captures the fact that the reward decreases with time. We normalize each

day’s payoff relative to the first day’s payoff.▫ 𝑐𝑑𝑒𝑣~𝑁 6,1.2 . Rand report states mean development cost is $30K. Mean dev cost is 6 times the

value of the first day’s payoff, so this is a normalized factor.▫ 𝑟𝑑𝑖𝑠𝑐𝑙𝑜𝑠𝑒~𝑁 10,2 . Rand estimates reward for disclosure is $50K which is 5/3 of the value of

development cost.▫ Time for a vulnerability to be disclosed. Rand estimates this at 1.5 years. We set the time period

for emergence of a vulnerability to 600 days.▫ Initial number of vulnerabilities set to 10 and more.

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L. Ablon and A. Bogart. Zero Days, Thousands of Nights: TheLife and Times of Zero-Day Vulnerabilities and Their Exploits. Rand Corporation, 2017.

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Run Time Experiments

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RCWG converges in a bit over 20 seconds RCWG converges in 220 iterations

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Vulnerability Discovery Rate and Exploit Development Rates

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If player #1 discovers vulnerabilities faster than player #2, then his payoff is higher. RCWG generates the best payoffs compared to some baselines.

RCWG generates the best payoffs compared to the baselines.But because development time is small compared to discovery and other times, the ability to develop exploits fast does not seem to provide a huge benefit.

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Vulnerability Discovery Rate and Exploit Development Rates

CSIRO - Australia Feb 2021 @vssubrah

If player #1 discovers vulnerabilities faster than player #2, then his payoff is higher. RCWG generates the best payoffs compared to some baselines.

RCWG generates the best payoffs compared to the baselines.But because development time is small compared to discovery and other times, the ability to develop exploits fast does not seem to provide a huge benefit.

Global Implications

The US and its allies will need to increase investment in vulnerability discovery (either human or AI) if it wishes to beat out adversaries. Vulnerability Discovery Rate will level the playing field and will likely work against the US at least for the coming years.

Countries that benefit from vulnerability sharing will be able to “punch above their weight”. The US and its allies need to watch for covert vulnerability proliferation.

Countries that do not discover cyber-vulnerabilities quickly and which have strong IT businesses (e.g. Austria, Scandinavia) may want to pursue an “always disclose” strategy. These countries should push for a global “disclose” policy.

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Impact of Cost Ratios & Initial Stockpile Sizes on Payoffs

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As 𝑐𝑑𝑒𝑣 ratio increases, the payoff of all approaches decreases.

RCWG generates the best payoffs.

When the 𝑐𝑑𝑒𝑣 ratio is large, always disclose is probably a good idea.

RCWG generates the best payoffs, regardless of the number of vulnerabilities assumed to exist in the initial set 𝑉0.

Initial stockpile size helps better estimate adversary’s capabilities.

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Impact of Cost Ratios & Initial Stockpile Sizes on Payoffs

CSIRO - Australia Feb 2021 @vssubrah

As 𝑐𝑑𝑒𝑣 ratio increases, the payoff of all approaches decreases.

RCWG generates the best payoffs.

When the 𝑐𝑑𝑒𝑣 ratio is large, always disclose is probably a good idea.

RCWG generates the best payoffs, regardless of the number of vulnerabilities assumed to exist in 𝑉0.

Global Implications

If country A’s exploit development cost is lower than that of country B, then A will be able to beat B.

This suggests that US vulnerability to adversaries with lower development costs will increase in coming years.

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Selected Ongoing Projects

• Predicting Cyber-Attacks Before they Occur (KDD’19, IJCAI’19, ICDM’19), runner up in IJCAI’19 most innovative demo competition

• Deterring Nation State Cyber Attacks Intended to Steal IP and Data (IEEE Trans. on Dep. & Secure Computing, ACM Trans. on MIS, IJCAI ‘19)

• Explaining Predictions Made by ML Algorithms (BEEF, GEMA)

• Review Fraud (RF) in Online Platforms: Predict fraudsters, understand how they will attack RF detection systems, an suggest alternatives. (WSDM’18, TIST’20).

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Demo of VEST & DiscX Systems

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Contact Information

V.S. SubrahmanianDept. of Computer Science & ISTSDartmouth College Hanover, MH 03755.

[email protected]

http://home.cs.dartmouth.edu/~vs/

https://ists.dartmouth.edu/

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