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Solution to exercises

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Exercise I, 1a) – initiate rule

What is the likelihood of the

threat scenario to the left?

If the vertices t and e are

related by initiate, we have: I.e.:

Servers infected

by malicious code[1 per year]

Malicious

code on computer

spreads via LANEmployee

0.1

Malicious

code on computer

spreads via LAN

[1 per year]

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Exercise I, 1b) – leads-to rule

What is the likelihood of the

threat scenario to the right?

If the vertices e1 and e2 are

related by leads-to, we have: 1 per 1 year × 0.1 = 1 per 10

years

Servers infected

by malicious code[1 per year]

Malicious

code on computer

spreads via LANEmployee

0.1

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2a) Leads-to + statistically independent vertices

1 per 10 years × 0.2 = 1 per 50 years

1 per 1 year × 0.1 = 1 per 10 years

If the vertices e1 and e2 are

statistically independent and

separate, we

have:

(1/50 + 1/10) =

6 per 50 years

Servers malfunctioning

Servers infected

by malicious code

[1 per 10 years]

0.1

0.2

Malicious code

traffic jams network

[1 per year]

?

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2b) Leads-to + mutually exclusive vertices

If the vertices e1 and e2 are

mutually exclusive, we have:

1 or 5 per 50 years;

alternatively between 1 and 5

per 50 years

Servers malfunctioning

Servers infected

by malicious code

[1 per 10 years]

0.1

0.2

Malicious code

traffic jams network

[1 per year]

?

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2c) Consistency check

Both 6 per 50 years and 5 per 50 years are higher values

than 1 per 20 years

The diagram is inconsistent

Servers malfunctioning

[1 per 20 years]

Servers infected

by malicious code

[1 per 10 years]

0.1

0.2

Malicious code

traffic jams network

[1 per year]

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Exercise II – computing likelihood intervals

Scale Value

1 Rarely <= 1 per 10 years

2 Seldom > 1 per 10 years & <= 1 per 5 years

3 Sometimes > 1 per 5 years & <= 1 per 1 year

4 Often > 1 per 1 year

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Exercise I, 1a) – initiate rule

What is the likelihood of the

threat scenario to the left?

If the vertices t and e are

related by initiate, we have: I.e.:

Servers infected

by malicious code[sometimes]

Malicious

code on computer

spreads via LANEmployee

0.1

Malicious

code on computer

spreads via LAN

[sometimes]

INF

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Exercise I, 1b) – leads-to rule

What is the likelihood of the

threat scenario to the right?

If the vertices e1 and e2 are

related by leads-to, we have: sometimes = <1/5,1/1]

1 per 5 years × 0.1 = 1 per 50

years

1 per 1 year × 0.1 = 1 per 10

years

<1/50,1/10] = rarely

Servers infected

by malicious code[sometimes]

Malicious

code on computer

spreads via LANEmployee

0.1

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2a) Leads-to + statistical independence

[0,1/10] × 0.2 = [0,1/50]

<1/5,1/1] × 0.1 = <1/50,1/10]

If the vertices e1 and e2 are

statistically independent and

separate, we have:

([0,1/50] + <1/50,1/10] ) =

<1/50,6/50]

1.2 per 10 years ∈ seldom

we interpret this as seldom

Servers malfunctioning

Servers infected

by malicious code

[rarely]

0.1

0.2

Malicious code

traffic jams network

[sometimes]

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2b) Leads-to + mutually exclusive vertices

If the vertices e1 and e2 are

mutually exclusive, we have:

rarely multiplied with 0.2 gives

rarely

sometimes multiplied with 0.2

gives rarely

In which case, we may deduce

rarely

?

Servers malfunctioning

Servers infected

by malicious code

[rarely]

0.1

0.2

Malicious code

traffic jams network

[sometimes]

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2c) Consistency check

seldom > rarely

The diagram is inconsistent wrt 2a)

Servers malfunctioning

[rarely]

Servers infected

by malicious code

[rarely]

0.1

0.2

Malicious code

traffic jams network

[sometimes]

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3a) Consistency check

0.5

Internal

infrastructure

Virus attack

Shared infrastructure

resources

Low

robustness

External

resource failure

U2: Unauthorized

modification of

users’ personal

information

[seldom]

1.0

U4: Unavailability

of service due to

infrastructure

failure

[sometimes]

1.0

0.2

External

resources

Internal hardware

or software failure U5: Unavailability

of service due to

malicious code

[seldom]0.2

High traffic on the

service may cause the

server to crash

[sometimes]

All active user

sessions are deleted

leaving the information

partly incorrect

Users’ personal

information

Availability of

service

moderate

major

moderate

External sources of

information fails or

malfunctions

[sometimes]

Internal parts of

the service fails or

malfunctions

[seldom]

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Consistency check

We look at max values:

1 per 1 year × 0.2 = 1 per 5 years

1 per 5 years × 1.0 = 1 per 5 years

(1 per 5 years + 1 per 5 years)

= 2 per 5 years ∈ sometimes OK

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Consistency check

1 per 1 year × 0.2 = 1 per 5 years ∈ seldom OK

1 per 1 year × 0.5 = 1 per 2 years × 1.0 = 1 per 2 years ∉

seldom Not OK

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Exercise III – associativity

Statistical independence, separate events and

frequencies: Associativity follows trivially since + is

associative

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Exercise III - associativity

Statistical independence and probabilities

Again we have associativity. We get the same expression

using the above rule twice independent of where we put

the brackets

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Exercise III - associativity

Mutual exclusion and frequencies: Associativity follows

trivially if all events have the same frequency

If they have different frequencies f_1, f_2, f_3 we get

– f_1 or f_2 or f_3

independent of where we put the brackets; hence, we

also have associativity in the general case

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Exercise III - associativity

Mutual exclusion and probabilities: Associativity follows

trivially since + is associative

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