Unintentional vs. intentional impacts No impact strategy Attacker’s strategy maximizing the expected damage.

Unintentional vs. intentional impacts

No impact strategy

Attacker’s strategy maximizing the

expected damage

Basic Definitions

lowest-level part of system, which is characterized by its inherent value, availability and performance distribution

collection of elements with the same functionality connected in parallel in reliability logic-diagram sense

quantitative measure of task performing intensity of element or system (capacity, productivity, processing speed, task completion time etc.)

Basic Definitionstechnical or organizational measure aimed at reduction of destruction probability of a group of system elements in the case of attack

action aimed at preventing simultaneous destruction of several elements in the case of single attack (can be performed by spatial dispersion, by encapsulating different elements into different protective casings, by using different power sources etc.)

group of system elements separated from other elements (and possibly protected) so that a single external impact destroying elements belonging to a certain group cannot destroy elements

from other groups

object that imitates protected group of system elements, but does not contain any element (the total damage caused by the destruction of any false target is much lower than the damage

caused by the destruction of any protection group)

Defense strategyDamageSeparation

Protection

Destruction probability

False targets

Impact probability

Disinformationpp

gg

vv

Defense Strategy

F

nM

mnnm ΦΦ

1,

|)|,( nmnmn bo dF

|)|,(),,(1 1

nm

N

n

nM

mnmnodFFO

Defense Strategy Cost

Expected damage model

Cumulative performance of the

group

Attack probabilityProtection vulnerability

System performance

reduction

Equipment losses

Expected damage

Failures

ppvvgg

Functional losses

S

sss Wgc,,qW,,,C

1),()()( γβαγβα

Expected Damage Cost

ss g,,q ,)( γβα

Wg

WgW,gc

s

ss ,

,0)(

WggW

WgW,gc

ss

ss

),(

,0)(

Unsupplied demand

Loss of demand

).()()()(11

,W,,ChHvHFF,,DnmΦknknm

nM

mnmnnm

N

nFF γβαγ,βα

Expected Damage Cost

Destruction of false targets

System destruction

Protections and infrastructure

Elements Functional losses

min})())((arg{* ,F,,D,F,O,F, γβαγβ*γ*β

Optimal defense strategy

*))(1())(( O,F,O,F,O γβγβ Limited defense budget

)())(( ,F,O,F,O γβγβ Unlimited defense budget

Single attack strategy

Perfect knowledge about the system

No knowledge about the system

p=p=11/N/N

p=p=11

pp

Imperfect knowledge about the system

pppp

pi=1

Multiple attack strategyUnlimited resource

p=p=11

pppp

pp

Limited resource + perfect knowledge about the system

p=p=11

Limited resource + imperfect knowledge about the system

pi>1

Attacker’s Strategy

Single Attack

.111

F

nM

mnm

N

nF

Perfect attacker’s knowledge about the system

max})),(({arg),(

);,(,0

1,1

γβα ,,mnDmn

mnF

nMmNn

Multiple Attacks

.111

FnM

mnm

N

nF

}),(,0

;),(,1{)(,0

mn

mn

nm

nmF

max}))((arg{ γβ,,D

.)),((11 1

EmnN

n

nM

m

Attacker’s Strategy

Single Attack

)/(11

N

nnnmF MF

No knowledge about the system

Multiple Attacks

)/(1

N

nnnmF MFE

Limited resource (E attacks)

Unlimited resource

1 nmF

Imperfect knowledge about the system

D,,mnDnm /)),(( γβα

max}))((arg{, max rD,,D γβ

,)),((11 1

EmnN

n

nM

m