catching spies by math background - information …8. moat with the bridge to the main castle 9....

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Catching spies by math

Dusko PavlovicKestrel, Oxford, Twente

DagstuhlAugust 2010

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Outline

Problem: Spying, treason and betrayal

Background: Security as a process

Solution: Spectral decomposition of trust

Problem 2.0: Privacy

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Outline





Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Examples of insider threats

The insider may "write down"

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0


. . . or may cause the main damage by being caught

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0


. . . or may be used to conceal the real traitor

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0


. . . or to justify oppressive policies

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Security measures against insider threats

Quartering is reserved for the traitors

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Security measures against insider threats

. . . as well as the deepest (9th) circle of Hell.

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Questions

! Why is the insider threat so threatening?

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Questions

! Why is the insider threat so threatening?

! Do the computers bring in anything new?

Catching spies

D. Pavlovic

Problem

BackgroundStatics and dinamics

Trust

Adverse selection

Solution

Problem 2.0

Outline



Security statics and dynamics

Trust

Adverse selection of trust



Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Security architecture

! secure perimeter (! cryptography)! secure access (! protocols)

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Security architectureSchloss Dagstuhl

1. glacis

2. moat3. rampart

4. bastions

5. main castle

6. well7. artist’s cottage

8. moat with the bridge tothe main castle

9. bailey (ward)10. moat with the bridge to

the bailey

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Security architectureSchloss Dagstuhl

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Security process

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Security threats

! static:! attacks on the perimeter: cryptanalysis! attacks on the access: breaking protocols

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Security threats

! static:! attacks on the perimeter: cryptanalysis! attacks on the access: breaking protocols

! dynamic:! moles: dishonest, but trusted! defectors: first trustworthy, later dishonest

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Security threats

! static: ! outside! attacks on the perimeter: cryptanalysis! attacks on the access: breaking protocols

! dynamic: ! inside! moles: dishonest, but trusted! defectors: first trustworthy, later dishonest

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Authentication and trust! A is authenticated using A1 that she

!""#""$

knowshasis

%""&""'

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


!""#""$

knowshasis

%""&""'

! A1 is authenticated using A2 that she!""#""$

knowshasis

%""&""'

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


!""#""$

knowshasis

%""&""'


knowshasis

%""&""'


knowshasis

%""&""'

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


!""#""$

knowshasis

%""&""'


knowshasis

%""&""'


knowshasis

%""&""'

! . . .

! (turtles all the way down)

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


!""#""$

knowshasis

%""&""'


knowshasis

%""&""'


knowshasis

%""&""'

! . . .

! (turtles all the way down)

! . . .

! TRUST

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Trust cycle

Building trust

Using trustscores

feedback

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Building trust

A pattern matrix of a trust network can be built by

! trustor’s own experience! social networks

! collaborative rating and recommendation! Amazon, Ebay,. . .

! surveillance and indexing of the network! credit card operators, credit rating and directmarketing agencies, Google, Amazon, DHS, NSA,. . .

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Building trust

OS

.351.12 1.02

.211.57

".56

.35

a

b

c

d

I

II

III

.83

1.25

1.051.13

a b c dI 1.25 1.05 1.12 1.57II .83 1.13 1.02 .35III 0 .35 .21 -.56

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Building trust

OS

.351.12 1.02

.211.57

".56

.35

a

b

c

d

I

II

III

.83

1.25

1.051.13

M =

())))))))))*

1.25 1.05 1.12 1.57.83 1.13 1.02 .350 .35 .21 ".56

+,,,,,,,,,,-

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Using and updating trust

OS

Xu(t + 1) i

Prob.Xu(t + 1) = i

/= C(t)Miu(t)

(where C(t) = 1"!0i#OMiu (t)

)

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Building and updating trust

E.g., trustor’s private update rule can be

Miu(t + 1) =

!""""""""""#""""""""""$

Miu(t) if i " Xu(t + 1)0 if i = Xu, not satisfactory1 if i = Xu, satisfactory, new1+Miu(t) if i = Xu, satisfactory, not new

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


TRUSTE-certified uncertifiedhonest 94.6% 97.5%malicious 5.4% 2.5 %

Table: Trustworthyness of TRUSTE [Edelman 2007]

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


Googlesponsored organic

top 4.44% 2.73%top 3 5.33% 2.93 %top 10 5.89% 2.74 %top 50 5.93% 3.04 %

Table: Malicious search engine placements [Edelman 2007]

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


Yahoo!sponsored organic

top 6.35% 0.00%top 3 5.72% 0.35 %top 10 5.14% 1.47 %top 50 5.40% 1.55 %


Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


Asksponsored organic

top 7.99% 3.23%top 3 7.99% 3.24 %top 10 8.31% 2.94 %top 50 8.20% 3.12 %


Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0


"Pillars of the society" phenomenon

! social hubs are more often corrupt! the rich are more often thieves! the most trusted are more often traitors

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Trust is like money

Preferential attachment

The rich get richer

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Trust is like money


The rich get richer

Power law distribution

Theft is more profitable when there are very rich people(heavy tails)

Catching spies

D. Pavlovic

Problem


Trust

Adverse selection

Solution

Problem 2.0

Trust is like money


The rich get richer

Power law distribution

Theft is more profitable when there are very rich people(heavy tails)

Abstraction

Theft is easier when there are untraceable carriers("Non olet")

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Outline




Singular Value Decomposition

Find the traitor


Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Correlations

Definition

The correlations between the pairs u, v # S and i , j # Oare defined

Suv =1

i#OMiuMiv Oij =

1

u#SMiuMju

The correlation matrices are thus

S = M ·M$ O = M$ ·M

where M$ denotes the transposed matrix.

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Remarks! For a trustor u # S, the vector Su # RS consists ofthe correlations Suv for v # S.

! The vector Su can be viewed the trust communitywith the strongest correlations with u.

! For a trustor community u # RS, the vector Su # RSis the community with the strongest correlations withu.

! A community w has the strongest correlationsamong its members if Sw is colinear with w, i.e. if

Sw = "w

for some " # R.! This means that w is an eigenvector of the S.

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Communities

Definition

A community of subjects (resp. of objects) is aneigenspace of the correlation matrix S (resp. O). Wedenote by 2S (resp. 2O) the set of the trust communities ofsubjects (resp. objects).

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Concepts

Lemma

The trust communities of subjects and objects are inone-to-one correspondence: the trust matrixM = (Miu)S%O induces a bijection # : 2S "& 2O.

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Concepts

Lemma

The trust communities of subjects and objects are inone-to-one correspondence: the trust matrixM = (Miu)S%O induces a bijection # : 2S "& 2O.

Definition

A trust concept induced by the trust matrix M is a pair! = 'u, i( # 2S % 2O, such that #(u) = i.

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Concept mining by spectral decomposition

Proposition

The pattern matrix M = (Miu)O%S decomposes to

M = V"U$

RS ROM

R2S R

2O!

VV$UU$

! " is an invertible diagonal matrix, whereas! U and V are isometries.

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Concept mining by spectral decomposition

Proposition

This decomposition is unique up a permutation on 2S,which lifts to 2O along # (or the other way around).

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Find the spy

OS

.351.12 1.02

.211.57

".56

.35

a

b

c

d

I

II

III

.83

1.25

1.051.13

M =

())))))))))*

1.25 1.05 1.12 1.57.83 1.13 1.02 .350 .35 .21 ".56

+,,,,,,,,,,-

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Spectral decomposition

())))))))))*

1.25 1.05 1.12 1.57.83 1.13 1.02 .350 .35 .21 ".56

+,,,,,,,,,,-=

())))))))))*

.83 ".4

.55 .60 .7

+,,,,,,,,,,-·

()))))*3 00 1

+,,,,,- ·

())))))))))))))))*

.5 0

.5 .5

.5 .3

.5 ".8

+,,,,,,,,,,,,,,,,-

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Trust concepts

OS E

.5

.3

.5

.5

.83 I

II

III

a

b

c

d ".8

.5

.5 .55".4

.6

.7

3

1

"1

"2

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Trust concepts

OS E

.5

.3

.5

.5

.83 I

II

III

a

b

c

d ".8

.5

.5 .55".4

.6

.7

3

1

"1

"2

! traitor: 2!2 ) "!1 ) 0

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Trust concepts

OS E

.5

.3

.5

.5

.83 I

II

III

a

b

c

d ".8

.5

.5 .55".4

.6

.7

3

1

"1

"2

! traitor: 2!2 ) "!1 ) 0

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Trust concepts

OS E

.5

.3

.5

.5

.83 I

II

III

a

b

c

d ".8

.5

.5 .55".4

.6

.7

3

1

"1

"2

! traitor: 2!2 ) "!1 ) 0! disident: !2 * 2!1 * 0

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Trust concepts

Comment

The trust concepts are genuinely new information,generated by the network.

Catching spies

D. Pavlovic

Problem

Background

SolutionSVD

Find the traitor

Problem 2.0

Trust concepts

Comment

The trust concepts are genuinely new information,generated by the network.

A traitor is not recognized from a previously learnedprofile, but extracted from network dynamics as anintrinsic singularity.

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Outline





Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Problem 2.0

! detect malicious insiders

! respect the privacy of others

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Problem 2.0

! detect malicious insiders! learn the nodes from the threat simplex

! respect the privacy of others! do not learn any other predicates

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Problem 2.0: Statistical data base filtering

Dalenius’ Desideratum (1977)

"Anything that can be learned about a respondent from astatistical database should be learnable without theaccess to the database."

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Problem 2.0: Statistical data base filtering

Dalenius’ Desideratum (1977)

"Anything that can be learned about a respondent from astatistical database should be learnable without theaccess to the database."

Impossible

For every statistical database A with an incompleterecord RA + R, there is a database B with an incompleterecord RB + R such that the complete record R can bederived from RA and RB.

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Upshot

! Data privacy is like DRM! inference control against the users

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Upshot


! The insider threats are mitigated by network analysis! not data mining, but concept mining

Catching spies

D. Pavlovic

Problem

Background

Solution

Problem 2.0

Upshot


! The insider threats are mitigated by network analysis! not data mining, but concept mining

! The tradeoff between trust and privacy is not atechnical problem

! resolved through battling out the political powers ofthe stakeholders

catching spies by math background - information …8. moat with the bridge to the main castle 9....

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