2003_ч2_Защита информации в многоканальных телекоммуникационных системах. Ч.2

BWHHCJieHHblfi

+

4

^

^X

4)

(M

X

T.e. HCKOMOC npoi

TIpH BblHHCJlCHHJlX

TOHKOCTb.

OflHy

O

paspaflHC-

Ci

uZ

V

n

onepaHflOB

C

4

x"

HOJIHHOM

4

23

"HHCJIO

nOJIHHOM

"nOJIHHOM

"HHCJIO"

II

KOJIOHK3

KOJIOHKa

t|

KOJ1OHK3

KOJIOHKa

3

->

4

-=X

15

+x

x

=

9

*x"=x'

8

=>x

5*14

4

-BblMHCJl

*14=3:

:eHHCnpOHSBeaeHHa5

nOJIb3OB3XbCa

BblHHCJlCHHH

apyrux

Flpn

HHCJIO

"IIOJIHHOM"

nojiHHOM

"MHCJIO"

n

KOJIOHK3

KOJIOHKE

KOJIOHKa

KOJIOHK3

=>

5+14

MOJKHOnoxaSjiHue4:.5

npeflcxasjieHHeBBHaeOOJIHHOMOB,nanpHMep,naftxHcyMMyHHCCJI5+14=11

HX

3JieMCHXOByfloSHOHCnOJIbSOBaXb

BblHHXaHHH

H

CJI05K6HHH

HpH

4

GF(2

.)

BHOJISK

HJUirocipHpyexTa6jiHHHbiHcnoco6

Ta6jinua4.5

rao6oro'mcjia.n

—x

x

nM5+'Z

v

-,Z_

nojio>KeHne,Boo6merosopa,cxporo^OKasyeMo);sxoo3HaHaex,Hxo

(3x0

15

nopaflKa

rpynny

iiHKJiHMecKyio

cocxasjiarox

nona

neMeHXM.3

HXO

BIWHO,

aaHHbiM

4.5

Bxa6nHue

npHBeaeHHWM

no

-pasniWHbie

aBKOJiOHKax"BCKTOP","flBOHMHoeMHCJIO"H"HHCJIO"

H,

onHcaHHWMH

paHec

c

BcooxBexcxBHH

1

x+

+

4

Mbifi

TPHHOMx

na

z

ocxaxKHoxfleneHHa

npeacxaBJieHu

xa6jiHui>i

"IIOJIHHOM"

KOJIOHKC

(x')

B

.cxeneneH

cooxBexcxByiomHx

BOBxopoH-noicasaxejiH

a

,

K>

(x')

)40

1

(x

ox

BjrieBOHKOJIOHKBnpHBeaenbicxenennnonHHOMaX

BTa6^Hue4.5

npeacxanneHOBxaGjinue.4.5

1

x

3JieM6HxoM

nopoac^eHHoe

1);none,

x+

+

2

X

x'+

+

4

X

no,nwHOMa

,

KOXOpHHHB^aeXCanpHMHXHBHbIM(BOXJ1HHHC,HanpHMCp,OX

\,

nOJIHHOM

MOJKCX6wxbHcnojibsoBaH,nanpHMep,

nonaGF(2)

nocxpoeHHa

.6

HBnpocxuxnojiaxFajiya,noapo6HeesxoxeonpocpaccMoxpenaajieeB

"'noHaxnenpHMHXHBHoro3JieM6HTa,HJIHrenepaxopa,ncnojibsyexcaxaxace

n

GF(2)npHMHXHBHbiii3J16MCHXHasbiBaexcanopo>KflaiomHM3JieweHXOM.nojia

.HyjieBoroHcnoJitsyeMbiHananocxpoenHa

HCicnioHeHHeM

noJia,sa

3JICMCHX(nojiHHOM),cxeneHHKoxoporopasuHHHWHo6pa3yioxsee

*',noRnoxopbiMnoHHMaexca

noHHXHenpHMHTHBHOroMCMCHxanona

Hcnojibsyexca

Tanyanacxo

no/left

pacuiHpeHHbix

IlpHnocrpoeHHH

=x+1.

5

MSKoxoporoHenocpeacTBCHHOcjieayerpaBCHCTBOX

+x+1)=.0,

6

+x+I)mod(x

6

(x

modq=0;

q

onpeaejieHHaMHoroijiena-

paBHO.3IlpaBOMepHOCTbonHcaHHoro^encTBHaBbireKaerHS

1,HHCKOMOC

ITOJIHHOMX+

(})opMnpyeTca

pesyjibraxeBocrarKe

B

-OCTaTOK

X"I-1

+X+1

6

X

6yaexpaBHO64,npeacxaBnem/ieKoxoporoxpeSyexCBMHfleonnHbix

=>64,

s

*X=X

5

X

=>

32*2

6

nojieGF(2)npOHSBeaeimeiHceji32H2:

Hanpmviep,By*epaccMOxpCHHowpaeee

.ocxaxoKTaK,

npeacxasjiaioxcoSofl

yxe

L,HeeSHpaanaTO,HTOOHH

+

X

+

n

X

HOJIHHOM

na

aneayexaejmxb

HX

n

K

ocxaxKOB

/^nanpHBeaeHHaxaKHx

BHayajieiueHTOBnonsGF(2)

n

He6yaexanHCbraaxtcsi

BnojieGF(2.)

X+1,6yaex3aHHM3Tbn+1paspaaHaa>Ke

qqq;

module/ram/abs=0.

Mower6wTbpeajiHsoaaHononpuHUHnaivi,HsnoxceHHWMaaneeBpaanene.6

HHyjTCBbiMHB.ocTanbHbixYMHo»ceHHenonHHOMOB6ojibuieflwiHHbi

n

...D

ls

D

eflHHHMHbiMHsHaneHHaMHBpaspa^ax

6biTbsanHcanaflBOHHHaaKOM6HHaunsc

aneMCHTaaflonacHO6wn>saneceHoBperHCTpAR,aBperacrpAYOaojwcHa

ADSP-2181Mower6wrbBbinojineHaBBHflenporpaMMHpnc..5.5SimeHHe

npoiieaypbiBCHCTevieKOMaHMnpoueccopa

PeajiH3aunaormcaHnoH

+(^+.a,,)*x+,.a,,

2

+...+a,*x

1

2

n

(a*x)mod(x

*x"'

+x+1)=.\

MOMCCT6wrbsanncancneflyrouwMoGpasoia:

JiK>6oro3HaMeHH»,.Bj,

mod(x"+X+1)fliw

*x)

OopMajiBHOpesyjibTaTonepaumi(a

x"=x+.1

=>

1=0

+X+

n

X

1BcnjiyTore,HTO

npaBHjiaMHTpe6yercyMMHpOBaHHflcflBHHyrorononHHOMacIKWIHHOMOMX+

n

KOTOporoonq)auneHmod(x+x+1)BcooTBercrBHHcpaneeHanoKeHHMMH

0

HJICH

coaepacHT

TOHOJIHHOM

ace3^,=!,

eaiH

-

X,yHHMTOxceHHe

n

(a*x)mod(x

+x-M)=a*x;

+x+!)H

n

(x

HH>KCcrenenH,nonHHOMa

*x)

-ecjiH1.&0-0,TO.CTenemnojiHHOMa(a

cneflyromeenojio»eHHesemeft:

1)CJieflyeTHMCTbB

mod(x"+X+

(a*x)

TIpHBMHHCJI6HHH

1

2

11

2

n

n1

(a*x)=

+...+a,*x+a,,*x.

*x"

a.*x+.\

nosnuHioBcropouycrapiDHX

oflHy

aa

anevteHTa

Kc^BHry

xnpHBeaer

na

1

2

n

1

a

a,,*x°

x

=,.a,,*x"-+

+...+a,*x

-

n

aneMeirraanonaGF(2)

MpeajiHsauHHBbWHCjieHHSBnpocrtix.nojiax

paciimpeHHbixnojiaxFarayaMoryrOKaaaTtcaBpaflecnynaeB6oneenpocTHMH,

-2181)BUHHCjiemiiiB

npoqeccopaADSP

B03MO3KHOCTeii

HcnoJibSOBaHHCM

c

(nanpuMep,

peanHsamm

nporpaMMnaa

H

Annaparaaa

creneHb

creneHb

no.Hnc

7

1

x

2

20

2

15+5

2

5

2

"=>

)"=(x)"=

=>(x)"=(x

6"

-BblHHCJieHHeKOpHa:

creneHb

creneHb

=>

3

-'°=

5

x-'°=x'

=

1

10

x

>(x)-

=6:

7"'

ofipaTHoroaneMenxa

2

j

0010

0100

I

I

x

16

x

x

y

16

1

0001

1000

1

15

X

15

9

1001

1001

+1

3

x

14

x"

13

1101

1011

+1

2

+x

x

13

X

3

13

15

1111

1111

2

+X

3

X

12

+X+1

12

X

14

1110

0111

+x

2

3

11

x"

+x

x

7

0111

1110

+x+1

x

10

X

2

10

10

1010

0101

+x

3

x

9

9

x

5

0101

+1

2

8

1010

8

x

11

1011

1101

1

•»

x3+x

7

X7

12

1100

0011

2

+X

3

X

-:•

6

6

X

6

0110

0110

+x

2

5

5

x

X

3

0011

1100

x-t-1

4

x4

i

8

1000

0001

X

3

3

3

x

^

i

0100

0010

2

X

2

x2

2

0010

0100

X

1

1

x

1

0001

1000

1

0

1=x°

o

i

0000

r

0000

0

—00

o=x"00

4HCJ1O

MMC/IO

flBOH4HOe

Beicrop

j

no/ii/iHOM

j

JlorapucJjM

CieneHb

j

.4.5

o

o

0

H

-f

+

-)-

(5

o

?

f^)

+

+

+

I

c^

o

g £ 1

o+

*- xu,

£ re

4-

?

+

-(-

^t i l l

o

*r

° X4,

0

o

_,

+

+

?

q o S

x

o x

*w

*M 0

iiig•S S *

X

X

0

o

+

+

+

+

+

+

M

o

t—*

l«*

ID

o X00

X OO

-1-

+

T 1

*, x^ 0 X

+

+

+

+

0 0

0 o

+

+

+

+

<=>

x.,

^ o

+

-r

,

+

+

X. 0

X•t*

X-t*

+

+

*l

*~

Xw

+

+

o

o

+

+

0

o

+

+

31

ifnejumpobrl,

af=tstbitOxfofmr1,

}

ecnnOHpaseH1,o6pa6QTKaKopoMe

npoaHanM3npOBaxbCTapujnwpaapnflflennxena

disar_sat;

crapiueMpaapafle}

mrO=0x8000;

pdelen:

AFMROSR1SROSE

-BARnonymonoprnrcoflep>KMMoe

nonpasunaMflenem/iaHOJIMHOMOB;BoaapamaeTocraroK

16-paapflflHoronoriMHOMaMSAY1naaHanon/mHbiiiusMR1

noflnporpaMMaBbimicneHUHocraxKaoxfleneHns

{

pdelen;

entry.

delenie;

module/ram.

.7.5

MC.

P

«a

0.noMombnporpaMMH,xeKCXKoxopoft

OT

°^™™™»™<*»»

3)Hs^enHbiftn

BoiiepauHH

AeJiHxejib

,c«BHHyx

8)OoBTopHTbonepauHH6)H7)npas,wen-KOH^CTBOpaspwOB,na

n..5)

onepauHK)"ncKJiioHaiomeroHJIH"anajiornHHO

paBHOe^HHHue,Bb,nonHHTb

ec™OHO

pJo*CCTKH«enHMoro,H,

pa3

fl

.7npoaHajiHSHpoBaxbSHOTCHHCcjieyiomeronocxapuiHHCTBypaapw

a1paapw.BnpaBO

H

6)CflBHHyxbflejiHxenb

.genHMOro

M

H

,bxax.pesysanecxnnoMecry

onepan^^HMoroH«e

Fc«OHOpaBHOe^HHHue,HHXb.no.Bb.onepauHK"HCKnmaKnuero

CCTKH

npoaHMHSHpoBaxbSHaneHHecxapuieropaspwapaapaflHOH

5^

noaxoH

IiyJ

ee.6onpaBHX

H

JieBOH

B

enHMoro

fl

fl

3TOM6yexpaBHO

30

ECJIH3HaneHnepaspa^a

.HOSHUHIO

paspa/ioMBKpafiHioiojiesyio

cxapiiiHM

cexice

paspa^Hofi

no

ae^mxejib

CaBHHyxb

4)

ycKopaexBbinojineHHe.nporpaMMW

BOMHOFHX

3)

Hoco6eHHo

2)

onepauHH

BbinojiHCHHe

.aenHMOMy

HC6ojibiiiecxenenHaejiHMoro,BHPOTHBHOMcjiyiaeOCXBXOKoxaejieHHa

3),HonanajiauejieHnacneayery6ejinxbCflBXOM,MXOcxenenbaeJiHTejia

(BnporpaMMyHe.BioiKmeHo)

Hyjiio

ECJIH*ezieJiHMoepasnoHyjiio,ocxaxoKox^ejienHapaseu

paBHO.Hyjiio

He

MXOaenHtaoe

BXOM,

y6eanxi>ca

cjieayer

^eJienHfl

Hanajia

flo

2)

HCBosMOacHocxn^eJieHHH(BnpprpaMMyne.BKraoHeno)

cj)jiar

BbicxaeHTb

cjicflyex

Hyjiio,

OHpascH

*e

paBCH.nyjnoECJIH

ne

HXOaejiHxejib

BXOM,

y6ea<tnbcn

cneayer

aeneiuia

Havana

Ro

1)

aejieHHHITOJIHHOMOB:

ocxaTKaox

Herpy;iHoBWBCCXHcjieflyromHHo6mHHanropHXMonepaimK

ocraxoK

0

0

1

0

0

0

0

0

0

1

1

0

0

1

1

1

1

0

1

0

0

0

0

1

1

0

0

1

1

1

0

0

0

1

1

0

0

0

1

1

0

0

1

1

0

0

1

0

1

0

1

0

1

1

0

0

1

1

0

0

1

1

0

0

1

1

paccMOrpeHHflnopaaoicBbiMHCJierowHacxnoro:

H3

Bnpoueccope)HycxpaHfls

(npuBeaeHHeB4>opMynpeflcraBJieHHa

ezuiHfflibi

onepauHefl"ucKjiioHaiomee.HJIH"3aMCHHHSHanamHeHOSHUHHMHoronjieHaHa

peajiHSOBana

6biTb

MOJKCX

H

nepenocoB

MeacpaspaflHbix

c

caasaHa

;

paMKaMn)

(noMCHCHa

saicoHOMepHocxb

cooTBercTByercxapuieMySHaiameMy(neHyneBOMy)paapa^ynenmem,paBHO

Koxoporo

SHaHCHHepaapa^aaenwMoro,nosHiwia

ec;in

jiesunesia,

HenyneBHx

nosHUHSM

cooTBexcxByromHX

paspnaax,

B

TOJibKO