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Generic Reliability Trust Model

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Generic Reliability Trust Model

Glenn Mahoney

Wendy Myrvold

Gholamali (Ali) Shoja

Department of Computer Science,

University of Victoria

Email: {gmahoney,wendym,gshoja}@cs.uvic.ca

Presented at:

Third Annual Conference on Privacy, Security and Trust (PST’05)

St. Andrews, New Brunswick

October 12-14, 2005

Agenda

Problem and Background

- Abstract computational trust model
Generic Reliability Trust Model

- Definition
- Metric
- Algorithms
- Experimental results
- Comparison to other trust models.
Conclusion

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Problem…

(Channel) security ≠ trust

Just because your connection is secure, it doesn’t mean you can trust who you are connected to.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Problem: (Lack of) Trust in Networks

- Economic activity involving
- operations on digital objects,
- network-mediated interactions between digital entities.

- Trust as a prerequisite for value-based interaction.
- Limited and/or application-specific capabilities for automated handling of trust.
- Security trust.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Example: eBay

- An effectively anonymous community of ad-hoc buyers and sellers.
- Created in 1995; by 2002 had:
- 61.7 million registered users,
- 638 million listed items,
- facilitated $14.9 billion dollars (US) in gross sales.
``The key to eBay's success is trust. Trust between the buyers and sellers who make up the eBay community. And trust between the user and eBay, the company.''-- eBay Web Site

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Bob

Alice

M2

M1

Channel

Network

Tom

Sue

Fred

Practical goal: Computational Trust (not human trust)Goal: create a generalized, decentralized, application-independent trust reasoning capability for use in ad-hoc, network-mediated environments -- a simulant useful for trust-related decisions.

Distributed entities exchanging messages.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Abstract Trust Model

Generic Reliability Trust Model, Glenn Mahoney, PST'05

The Generic Reliability Trust Model (GRTM)

- Definition
- Metric
- Algorithms

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Reliability

Reliability theory is the study of the performance of a system of failure-prone elements.

Given the graph G=( V(G), E(G) ), where pe is the probability that edge e is operational,

Rel(G) =

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Trust Graph

A trust graph is a labeled digraph G=( V(G), E(G) )

V(G) represents the entities

E(G) represents statements or beliefs

Each arc e=(u,v) in E(G) represents a trust statement or belief by u about v, and has a label <l,c>:

l 0 is a trust level (generally, amount of indirect trust)

c is a confidence value, c [0,1]

ce = pe is the probability of operation of this arc/link.

A trust metric defines the operational criteria -- what edges are required for any trust to exist.

The reliability model is used to calculate a value:

Trust(G) = Rel(G)

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Example Trust Graph

Alice trusts Sally with a confidence of 0.8, and at the level 2, etc.

Assumes common subject matter.

Need something more to say whether Alice trusts Bob.

Sally

Sue

1,.8

2,.8

0,.8

Alice

0,.8

Bob

2,.8

0,.8

Tom

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Generalized Operational Criteria

Can also represent a trust graph as a set of statements:

- The derived statement for the arc e=(u,v) with label <l,c> is <u,v,l>
- There are transitivity rules R for derived statements given a trust graph G and vertices s (source) and t (target or sink).
A state S in E(G) is operational iff the derived statement <s,t,0> exists in the reflexive, transitive closure of S, under R.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Hop-count Limited Transitive Trust (HLTT)

Let i>0, j ≥ 0, and k=min(i-1, j),

If <u,v,i> and <v,x,j> are derived statements

then <u,x,k> is a derived statement.

E.g. Given <Alice,Tom,1> and <Tom,Bob,0>

then <Alice,Bob,0>.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Example

The HLTT transitivity rule produces the following minimal operational states for trust from Alice to Bob:

S1 = { (Alice,Sally), (Sally,Sue), (Sue,Bob) }

S2 = { (Alice,Tom), (Tom,Bob) }

Sally

Sue

1

2

0

Alice

0

Bob

2

0

Tom

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Exact Algorithms All exact methods are #P-complete

Inclusion-exclusion:

First, find all possible operational states T, k=|T|.

- Exponential in time and memory
Then, calculate probability using inclusion-exclusion.

- Enumerate all 2k-1 subsets, alternately add and subtract product of probabilities of the union of arcs in the k-subsets
Factoring:

Recursively simplify the graph G:

Rel(G) = peRel(G * e) + (1-pe)Rel(G - e);

- Still enumerates 2k-1 subsets (worst-case), but does not require pre-generation of operational states

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Example

Recall,

S1 ={ (Alice, Sally), (Sally, Sue), (Sue, Bob) }

S2 ={ (Alice, Tom), (Tom, Bob) }

Assume pe is 0.8,

Trust(G,HLTT,Alice,Bob) is

= Pr(S1) + Pr(S2) - Pr(S1 S2)

= .512 + .64 - .327

= .824

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Approximation The result will be less-or-equal to exact result.

Use the inclusion-exclusion approach but truncate the computation:

During search phase -

- Discard candidate operational states if probability product falls below some threshold or maximum time limit reached.
- Stop if a single operational state exceeds minimum desired confidence.
After search phase -

- Prune operational states to some maximum number before performing inclusion-exclusion.
During inclusion-exclusion phase -

- Stop if lower-bound meets the desired confidence.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

SimulatedTrust Graph Data

- Straightforward representation in XML using the semantics of Graph eXchange Language (GXL).
<node id=“Alice"/>

<edge from=“Alice" to=“Sally">

- Generate graph data using a random power law (RPLG):
- Generate desired number of vertices
- Randomly generate arcs between vertices such that the probability there exists some vertex of degree k is roughly
Prob(degree k) ~ k-

- where = 0.7 and = 0.8 .

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Performance of Approximation

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Comparison

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Conclusion

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Summary of Results

- New trust model: Generic reliability trust model (GRTM)
- Appling reliability model to solve problem of computational trust

- New trust metric: Hop-count limited transitive trust (HLTT)
- Practical approximation
- Trust graph simulation as a scale-free network:
- Random power-law graphs (RPLG)
- XML/GXL representation

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Potential Application Areas

- eCommerce
- Reputation systems
- Agent-Based Systems (Social Agents)
- Delegated Rights
- Computer-based collaboration
- Distributed resource management / Grids
- Ad-hoc networking

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Future Research

- Use GRTM+HLTT within some application
- Trust model quality measure?
- Improve approximation techniques
- Use of multiple subject-matters
- Distrust?
- Standardized representation and exchange protocol
- Trust establishment in ad-hoc networks

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Generic Reliability Trust Model

Glenn Mahoney

Wendy Myrvold

Gholamali (Ali) Shoja

Department of Computer Science,

University of Victoria

Email: {gmahoney,wendym,gshoja}@cs.uvic.ca

Presented at:

Third Annual Conference on Privacy, Security and Trust (PST’05)

St. Andrews, New Brunswick

October 12-14, 2005

additional material

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Trust Definition (informal)

Trust is one's reasonable expectation of a positive outcome in a situation where there is less than full control over the actions of the participants.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

References

[colbourn87] Colbourn, C. “The Combinatorics or Network Reliability”, Oxford University Press, 1987

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Network Reliability…

“…is some measure of the ability of a network to carry out a desired network operation.”[colbourn87]

Operational Criterion is the distinguishing feature of different metrics

Probability of “operation” of the arc e.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

An example of 2-terminal reliability

RelAlice,Bob = Prob( any path from Alice to Bob )

= 1-Prob( all paths failed )

= 1 – (1 - .81)(1 - .81)

= .9639

Generic Reliability Trust Model, Glenn Mahoney, PST'05

XML/GXL Representation

<gxl>

<graph id="PowerLaw_10_09:31:48 (MCVs)">

<attr name="Model">

<string>MCVs</string>

</attr>

<attr name="Note">

<string>

Power law random graph, size 10, alph=0.7, beta=0.8, maxLevel=4, fixed conf=0.8, generated Thu Apr 22 09:31:48 PDT 2004 by models.algo.GraphGen

</string>

</attr>

<node id="V1"/>

<node id="V3"/>

…

<edge from="V1" to="V3">

<attr name="Level">

<int>4</int>

</attr>

<attr name="Confidence">

<float>0.8</float>

</attr>

</edge>

…

</gxl>

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Implementation Verification

- Three types of input data sets:
- Manually created examples.
- Generated complete graphs.
- Generated RPLGs.

- Compare results:
- Two exact algorithms.
- Manual calculations.
- Examples in Maurer's paper.
- 2-terminal reliability
- Setting approximation parameters to product exact result.

- Inspect debug/trace output.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Verification Example: D.Shier

Example from section 4.1 of D.Shier,"Network Reliability and Algebraic Structures",1991.

4 pathsets:

{(s,a),(a,t)}

{(s,a),(a,b),(b,c),(c,t)}

{(s,b),(b,c),(c,t)}

{(s,b),(b,c),(c,a),(a,t)}

p=0.6,

Rel(s,t)=0.53971

D:\gmahoney\projects\UVic\trust_modeling\source>java dtrust.maintest runverify

Generic Reliability Trust Model, Glenn Mahoney, PST'05

**** Test Run #1****

*********************

runTest: model=null, options= s t -uprob comb -noapprox -maxloop -1 -nosubsetr

runTest: inputdata=testcases\MCVs\shier_example_4_1.xml

runTest: graph note=

Example take from section 4.1 of D.Shier,"Network Reliability and Algebraic Structures",1991.4 pathsets: {(s,a),(a,t)}{(

s,a),(a,b),(b,c),(c,t)}{(s,b),(b,c),(c,t)}{(s,b),(b,c),(c,a),(a,t)} p=0.6, Rel(s,t)=0.53971

runTest: graph Shier Example 4.1 vertices=5 arcs=7

runTest: start calculation...

...calculation completed; result=[TrustMetricBasic: conf=0.539712, local=s, remote=t, subject=ID, model=MCVs]

algorithm results:

time Fri Dec 10 14:52:00 PST 2004

datafile testcases\MCVs\shier_example_4_1.xml

graph id Shier Example 4.1

vertices 5

arcs 7

completed Exhaustive support search with Uprobability using ksubset generation

allow approx(p) false

total loops 44

elapsed(ms) 60

Memory usage summary: max 282344 average 261256

- Exhaustive Search counters -

MSS count 4

elapsed(support) 10

elapsed(prob) 10

loops(support) 12

loops(prob) 32

dropped subsets 0

total elements 13

elements reduced 0

uprob type ksubset generation

- MCVs Exhaustive counters -

num minpath 4

num MSS 4

loop count(path) 12

***************************

**** End of Test Run #1****

***************************

*********************

**** Test Run #2****

*********************

runTest: model=null, options= s t -noapprox

runTest: inputdata=testcases\MCVs\shier_example_4_1.xml

runTest: graph note=

Example take from section 4.1 of D.Shier,"Network Reliability and Algebraic Structures",1991.4 pathsets: {(s,a),(a,t)}{(

s,a),(a,b),(b,c),(c,t)}{(s,b),(b,c),(c,t)}{(s,b),(b,c),(c,a),(a,t)} p=0.6, Rel(s,t)=0.53971

runTest: graph Shier Example 4.1 vertices=5 arcs=7

runTest: start calculation...

...calculation completed; result=[TrustMetricBasic: conf=0.539712, local=s, remote=t, subject=ID, model=MCVs]

algorithm results:

time Fri Dec 10 14:52:00 PST 2004

datafile testcases\MCVs\shier_example_4_1.xml

graph id Shier Example 4.1

vertices 5

arcs 7

completed Factoring calculation successful.

allow approx(p) false

total loops 49

elapsed(ms) 30

- Factoring counters -

selection method random

- MCVs Model counters -

generic 0

supportExists 98

- MCVs Transitivity counters -

full passes 25

inner loops 471

***************************

**** End of Test Run #2****

***************************

Verification Example: D.Shier (2)Generic Reliability Trust Model, Glenn Mahoney, PST'05

General Characteristics of Potential Application

- Value-based interaction,
- Involving human proxies or digital agents,
- Using open, distributed, or ad-hoc architectures,
- Require flexibility and maximization of the number of potential interactors,
- Desire to leverage pools of local or private knowledge,
- High-control, high-security solutions are inappropriate.

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Inclusion-Exclusion Example: Sets

From set theory;

|E1E2E3| = |E1| + |E2| + |E3|

- |E1E2| - | E1E3| - |E2E3|

+ |E1 E2 E3|

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Inclusion-Exclusion applied to operational probabilities

Another way to derive the inclusion-exclusion algorithm:

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Alice

Bob

Tom

Sally

Bob

Alice,Tom

Sally

Bob

Alice,Tom

Alice,Tom,Sally

Bob

Sally

Alice

Bob

Tom

Sally

Alice

Tom,Bob

Alice,Sally

Tom,Bob

Sally

Alice

Bob

Tom

Alice,Sally

Bob

Tom

Factoring ExampleGeneric Reliability Trust Model, Glenn Mahoney, PST'05

Primary Graph Reductions

- Irrelevant – do not contribute to any operational state; remove
- Series – sequence of edges are required simultaneously; combine with axiom of probability:
P(AB) = P(A)P(B)

- Parallel – network is operational if any of these edges are operational; combine with axiom of probability:
P(AB) = P(A) + P(B) – P(AB)

Sequential reduction

Parallel reduction

Generic Reliability Trust Model, Glenn Mahoney, PST'05

Related Research Projects

Generic Reliability Trust Model, Glenn Mahoney, PST'05

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