from chinese wall security policy models to granular computing

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From Chinese Wall Security Policy Models to Granular Computing

Tsau Young (T.Y.) Lin

[email protected] [email protected]

Computer Science Department, San Jose State University, San Jose, CA 95192,

and

Berkeley Initiative in Soft Computing, UC-Berkeley, Berkeley, CA 94720

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From Chinese Wall Security Policy. . .

The goal of this talk is to illustrate how granular computing can be used to solved a long outstanding problem in computer security.

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Outline

1. Overview(Main Ideas)

2. Detail Theory

Background

Brewer and Nash Vision

Formal Theory

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Overview

New Methodology: Granular Computing

Classical Problem:Trojan Horses

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Overview - Granular computing

Historical Notes

1. Zadeh (1979) Fuzzy sets and granularity

2. Pawlak, Tony Lee (1982):Partition Theory(RS)

3. Lin 1988/9: Neighborhood Systems(NS) and Chinese

Wall (a set of binary relations. A non-reflexive. . .)

4. Stefanowski 1989 (Fuzzified partition)

5. Qing Liu &Lin 1990 (Neighborhood system)

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Overview-Granular computing

Historical Notes

6. Lin (1992):Topological and Fuzzy Rough Sets

7. Lin & Liu: Operator View of RS and NS (1993)

8. Lin & Hadjimichael : Non-classificatory hierarchy (1996)

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Overview

Problem Solving Paradigm

Divide and Conquer

1. Divide: Partition (= Equivalence Relation)

2. Conquer: Quotient sets (Bo ZHANG, Knowledge Level Processing)

3. Could this be generalized?

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Overview-Example

Partition: disjoint granules(Equivalence Class)

[0]4 = {. . . , 0, 4, 8, . . .}={4n},

[1]4 = {. . . , 1, 5, 9, . . .} ={4n+1},

[2]4 = {. . . , 2, 6, 10, . . .} ={4n+2},

[3]4 = {. . . , 3, 7, 11, . . .} ={4n+3}.

Quotient set = Z/4 (Z/m)

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Overview-New Challenge?

Granulation: overlapping granules

B0 = {. . . , 0, 4, 8, 12,. . . 5, 9, }

B1 = {. . . , 1, 5, 9, . . .}

B2 = {. . . , 2, 6, 10, . . ., 7,}

B3 = {. . . , 3, 7, 11, . . ., 6, }.

Quotient ?

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Overview-

Granular Computing - New Paradigm ?

Classical paradigm is unavailable for general granulation

Research Direction: New Paradigm ?

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Overview- Granular Computing a New Problem Solving Paradigm

Divide and Conquer (incremental development)

1. Divide: Granulation (binary relation)

Topological Partition

2. Conquer: Topological Quotient Set

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Application - New Paradigm ?

Report:

Applying an incremental progress

in granulation to

Classical problem in computer security

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Overview - Trojan Horses

Classical Problem

Trojan Horses, e.g.virus propagation

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Grader G is a conscientious student but lacking computer skills.

So a classmate C sets up a tool box that includes, e.g., editor, spread sheet, …;

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C embeds a “copy program”

into G’s tool; it sends

a copy of G’s file to C

(university system normally allows students to exchange information)

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As the Grader is not aware of such

Trojan Horses, he cannot stop them;

The system has to stop them!

Can it?

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Can it?

In general, NO

With constraints, YES Chinese (Great) Wall Security Policy.

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Overview - Trojan HorsesDirect Information flow(DIF); CIF, a sequence of

DIF’s, leaks the information legally !!!

Professor

Grader

StudentCIF

DIF Trojan horse(DIF)

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Overview

End of Overview

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Details

Background

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Background

In UK, a financial service company may consulted by competing companies. Therefore it is vital to have a lawfully enforceable security policy.

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Background

Brewer and Nash (BN) proposed Chinese Wall Security Policy Model (CWSP) 1989 for this purpose

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Background

The idea of CWSP was, and still is, fascinating;

Unfortunately, BN made a technical error.

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Outline

BN’s Vision

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BN: Intuitive Wall Model

Built a set of impenetrable Chinese Walls among company datasets so that

No corporate data that are in conflict can be stored in the same side of the Walls

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Policy: Simple CWSP (SCWSP)

"Simple Security", BN asserted that

"people (agents) are only allowed access to information which is notheld to conflict with any other information that they (agents) already possess."

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Could Policy Enforce the Goal?

“YES” BN’s intent; technical flaw

Yes, but it relates an outstanding difficult problem in Computer Security

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First analysis

Simple CWSP(SCWSP):

No single agent can read data X and Y

that are in CONFLICT

Is SCWSP adequate?

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Formal Simple CWSP

SCWSP says that a system is secure, if

“(X, Y) CIR X NDIF Y “

“(X, Y) CIR X DIF Y “ (need to know may apply)CIR=Conflict of Interests Binary Relation

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More Analysis

SCWSP requires no single agent can read X and Y,

but do not exclude the possibility a sequence of agents may read them

Is it secure?

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Aggressive CWSP (ACWSP)

The Intuitive Wall Model implicitly requires: No sequence of agents can read X and Y:

A0 reads X=X0 and X1,

A1 reads X1 and X1,

. . .An reads Xn=Y

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Can SCWSP enforce ACWSP?

Related to a Classical Problem

Trojan Horses

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Current States

1.BN-Theory (Rough Computing)-failed

2.Granular Computing Method

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Formal Model

When an agent, who has read both X and Y, considers a decision for Y,

information in X may be used

consciously or unconsciously.

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Formal Model (DIF)

So the fair assumptions are:

if the same agent can read X and Y

X has direct information flowed into Y, in notation, X DIF Y

also Y DIF X . . .

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Formal Simple CWSP

SCWSP says that a system is secure, if

“(X, Y) CIR X NDIF Y “

“(X, Y) CIR X DIF Y “

CIR=Conflict of Interests Binary Relation

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Composite Information flow

Composite Information flow(CIF) is

a sequence of DIFs , denoted by such that

X=X0 X1 . . . Xn=Y

And we write X CIF Y

NCIF: No CIF

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Formal Aggressive CWSP

Aggressive CWSP says that a system is secure, if

“(X, Y) CIR X NCIF Y “

“(X, Y) CIR X CIF Y “

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The Problem

Simple CWSP ? Aggressive CWSP

This is a malicious Trojan Horse problem

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Need ACWSP Theorem

Theorem If CIR is anti-reflexive, symmetric and anti-transitive, then

Simple CWSP Aggressive CWSP

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Solution

BN’s solution

GrC Solution

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BN-Theory(failed)

BN assumed:

Corporate data are decomposed into

Conflict of Interest Classes

(CIR-classes)

(implies CIR is an equivalence relation)

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BN-Theory BN assumption: CIR-classes

Class A

Class B

f, g, h i, j, k

Class Cl, m, n

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BN-Theory Can they be partitioned?

CUS, Russia

UK?

France, German

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BN-theory

Is CIR Equivalence Relation?

NO (will prove)

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Some Mathematics

A partition Equivalence Relation

Class A

Class B

f, g, h i, j, k

Class Cl, m, n

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Some Mathematics

Partition Equivalence relation

X Y (Equivalence Relation)

if and only if

both belong to the same class/granule

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Equivalence Relation Generalized Identity X X (Reflexive)

X Y implies Y X (Symmetric)

X Y, Y Z implies X Z (Transitive)

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Is CIR Symmetric?

US (conflict) USSR

implies

USSR (conflict) US ?

YES

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Is CIR Transitive?

US (conflict) Russia

Russia (conflict) UK

UK ? US

NO

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Is CIR Reflexive?

Is CIR self conflicting?

US (conflict) US ?

NO

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Is CIR Equivalence Relation?

NO

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Overlapping CIR-classes

• CIR is not an equivalence relation, so CIR classes do overlap

US, UK, Iraq, . . .

USSR

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BN-Theory

BN-Theory Failed, but

BN’ intention is valid

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New Theory

Formalize BN’s intuition:

O: the set of objects(company datasets)

X, Y, . . . are objects

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Summary on Simple CWSP “X and Y has no conflict then they can be read by same

agent “

“(X, Y) CIR X NDIF Y” B(X) ={Y | X NDIF Y }

={Y | (X, Y ) CIR }

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Granule (“Access Lists”)

B(X) is a set of objects that information of X canNOT be flow into.

Granule / Neighborhood “Access Denied Lists”

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DAC and GrC

The association

B: O 2O ; X B(X)

DAC (Discretionary Access Control Model) Basic (binary) Granulation/Neighborhood

System

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Derived Equivalence Relation

The inverse images of B is a partition (an equivalence relation)

C ={Cp | Cp =B –1 (Bp) p V}

This is the heart of this talk

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The set C of the center sets of CIR

The set C of center sets Cp is a partition

Iraq, . . .US, UK, . . .

German, . . .

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C and CIR classes IJAR=Cp

CIR-class Cp -classes

Cp -classes

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C and CIR classes


Cp -classes

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C and CIR classes CIR: Anti-reflexive, symmetric, anti-transitive


Cp -classes

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Cp is called the center set of Bp

A member of Cp is called a center.

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The center set Cp consists of all the points that have the same granule

Center set Cp = {q | Bq= Bp}

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Aggressive CWSP Theorem

Theorem. If CIR is anti-reflexive, symmetric, anti-transitive, then

C=IJAR(=complement of CIR).

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Aggressive CWSP

CIR (with three conditions) only allows information sharing within one IJAR-class

An IJAR-class is an equivalence class; so there is no danger the information will spill to outside.

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ACWSP

Theorem If CIR is anti-reflexive, symmetric and anti-transitive, then

Simple CWSP Strong CWSP

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Conclusions

1. Classical Problem Solving Paradigm requires partitioning (equivalence relation) may be too strong

2. Classical idea is extended to granulation (binary relation)

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Conclusions

3. A small success in apply new paradigm to computer security

4. CWSP is one of the the bigger problem, managing the Information Flow Model in DAC; this was considered impossible in the past.

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Conclusions

5. BN’s requirements implies IJAR is an equivalence class. However, if we impose “need to know” constraint, then IJAR is not an equivalence class. Under such constraints, we have weaker form of CWSP theorem

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AppendixAggressive CWSP Theorem

If CIR is anti-transitive non-empty and if (u, v) CIR implies that w V (at least one of (u, w) or (w, v) belongs to CIR ). Let (x, y) and (y, z) be in IJAR, we need to show that (x, z) be in IJAR. Assume contrarily, it is in CIR, by anti-transitive, one and only one of (x, y) or (y, z) be in CIR, that is the contradiction.

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