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Криптографические методы защиты информации. Метод комбинированного шифрования

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AAAAeAIEA.

E?eioia?aoe/aneay caueoa eioi?iaoeee.

E?eioia?aoey – iaoea i caueoa eioi?iaoeee io i?i/oaiey aa
iinoi?iiieie. Caueoa aeinoeaaaony oeo?iaaieai, o.a. i?aia?aciaaieai,
eioi?ua eioi?ua aeaeatho caueuaiiua aoiaeiua aeaiiua
o?oaeii?ane?uaaaiuie ii aoiaeiui aeaiiui aac cia-iey niaoeeaeueiie
eeth/aaie eioi?iaoeee – eeth/a. Iiae eeth/ii iiieiaaony eaaei
ec-iaiyaiay /anoue e?eioinenoaiu, o?aiyuayny a oaeia e ii?aaeaeythuay,
eaeia oeo?o-thuea i?aia?aciaaiea ec aiciiaeiuo auiieiyaony a aeaiiii
neo/aa. E?eioinenoaia – naiaenoai auae?aaiuo n iiiiuueth eeth/a
ia?aoeiuo i?aia?aciaaiee, eioi?ua i?aia?acotho caueuaaiue ioe?uoue oaeno
a oeo?ia?aiio e ia?aoii.

AEaeaoaeueii, /oiau iaoiaeu oeo?iaaiey iaeaaeaee ieieioi aeaoiy
naienoaa-ie:

caeiiiue iieo/aoaeue niiaeao auiieieoue ia?aoiia i?aia?aciaaiea e
?anoeo?i-aaoue niiauaiea;

e?eioiaiaeeoee i?ioeaieea, ia?aoaaoeaoee niiauaiea, ia niiaeao
ainnoaiiaeoue ii iaio enoiaeiia niiauaiea aac oaeeo cao?ao a?aiaie e
n?aaenoa, eioi?ua naea-eatho yoo ?aaioo ?aaioo iaoeaeaniia?aciie.

Iaeaieaa ecaanoiua e?eioinenoaiu.

Eeanneoeeaoeey e?eioinenoaiu.

Ii oa?aeoa?o eniieueciaaiey eeth/a ecaanoiua e?eioinenoaiu iiaeii
?ac-aeaeeoue ia aeaa oeia: neiiao?e/iua (iaeiieeth/aaua, n nae?aoiui
eeth/ii) e ianei-iao?e/iua (n ioe?uoui eeth/ii).

A ia?aii neo/aa a oeo?aoi?a ioi?aaeoaey e aeaoeo?aoi?a iieo/aoaey
eniieue-coaony iaeei e oio aea eeth/. Oeo?aoi? ia?acoao oeo?oaeno,
eioi?ue yaeyaony ooi-eoeeae ioe?uoiai oaenoa, eiie?aoiue aeae ooieoeee
oeo?iaaiey ii?aaeaeyaony nae?ao-iui eeth/ii. Aeaoeo?aoi? iieo/aoaey
niiauaiey auiieiyao ia?aoiia i?aia?aci-aaiea aiaeiae/iui ia?acii.
Nae?aoiue eeth/ o?aieony a oaeia e ia?aaeaaony ioi?a-aeoaeai niiauaiey
iieo/aoaey ii eaiaeo, eneeth/athuaio ia?aoaao eeth/a e?eioi-aiaeeoeeii
i?ioeaieea. Iau/ii i?aaeiieaaaaony i?aaeei Ee?oaioa:

noieeinoue oeo?a ii?aaeaeyaony oieueei nae?aoiinoueth eeth/a,o.a.
e?eioiaiaeeoeeo ecaanoiu ana aeaoaee i?ioeanna oeo?iaaiey e
aeaoeo?iaaiey, e?iia nae?aoiiai eeth/a.

Ioe?uoue oaeno iau/ii eiaao i?iecaieueioth aeeeio: anee aai ?acia?
aaeee e ii ia iiaeao auoue ia?aaioai au/eneeoaeueiui ono?ienoaii
oeo?aoi?a oeaeeeii, oi ii ?acaeaaaony ia aeiee oeene?iaaiiie aeeeiu, e
eaaeaeue aeie oeo?oaony a ioaeaeueiin-oe, ia caaeneii io aai iieiaeaiey
ai aoiaeiie iineaaeiaaoaeueiinoe.Oaeea e?eioinen-oaiu iacuaathony
nenoaiaie aei/iiai oeo?iaaiey.

Ia i?aeoeea iau/ii eniieuecotho aeaa iaueo i?eioeeia
oeo?iaaiey:?annaeaaiea e ia?aiaoeaaiea. ?annaeaaiea caeeth/aaony a
?ani?ino?aiaiee aeeyiey iaeiiai nei-aiea ioe?uoiai oaenoa ia iiiai
neiaieia oeo?oaenoa: yoi iicaieyao ne?uoue noaoen-oe/aneea naienoaa
ioe?uoiai oaenoa. ?acaeoeai yoiai i?eioeeia yaeyaony ?ani?in-o?aiaiea
aeeyiey iaeiiai neiaiea eeth/a ia iiiai neiaieia oeo?ia?aiiu, /oi
iic-aieyao eneeth/eoue ainnoaiiaeaiea eeth/a ii /anoyi. Ia?aiaoeaaiea
ninoieo a eniieueciaaiee oaeeo oeo?othueo i?aia?aciaaiee, eioi?ua
eneeth/atho ainnoaiia-eaiea acaeiinayce noaoenoe/aneeo naienoa
ioe?uoiai e oeo?iaaiiiai oaenoa. ?an-i?ino?aiaiiue niinia aeinoeaeaiey
oi?ioaai ?annaeaaiey ninoieo a eniieueciaaiee ninoaaiiai oeo?a,
eioi?ue iiaeao auoue ?aaeeciaai a aeaea iaeioi?ie iineaaeiaa-oaeueiinoe
i?inouo oeo?ia, eaaeaeue ec eioi?uo aiineo iaaieueoie aeeaae a
cia/e-oaeueiia noiia?iia ?annaeaaiea e ia?aiaoeaaiea. A ea/anoaa i?inouo
oeo?ia /a-ua anaai eniieuecotho i?inoua iiaenoaiiaee e ia?anoaiiaee.
Ecaanoiu oaeaea iaoiaeu aiaeeoe/aneiai i?aia?aciaaiey, aaiie?iaaiey, a
oaeaea iaoiae eiiaeie?iaaiiiai oeo?iaaiey.

Caueoa eioi?iaoeee

iaoiaeii eiiaeie?iaaiiiai oeo?iaaiey.

Aaaeiaeoei o?aaiaaieai e nenoaia oeo?iaaiey yaeyaony noieeinoue aeaiiie
nenoaiu. E niaeaeaieth, iiauoaiea noieeinoe i?e iiiiue ethai-ai iaoiaea
i?eai-aeeo, eae i?aaeei, e o?oaeiinoyi e i?e oeo?iaaiee ioe?uoiai oaenoa
e i?e aai ?an-oeo?iaea. Iaeiei ec iaeaieaa yooaeoea-iuo iaoiaeia
iiauoaiey noieeinoe oeo?-oaenoa yaeyaony iaoiae eiiaeie?iaaiiiai
oeo?iaaiey. Yoio iaoiae caeeth/aaony a eniieueciaaiee e eiiaeie?iaaiee
ianeieueeeo i?inouo niiniaia oeo?iaaiey Oae iai?eia? iiaeii
eniieueciaaoue iaoiae oeo?iaaiey i?inoie ia?anoaiiaeie a ni/aoa-iee n
iaoiaeii aiaeeoe/aneeo i?aia?aciaaiee eee oaeno, caoeo?iaaiiue iaoiaeii
aaiie?iaaiey, aeiiieieoaeueii caueoeoue i?e iiiiue iiaenoaiiaee.

?anniio?ei ianeieueeieueei i?eia?ia :

Aicueiai a ea/anoaa ioe?uoiai oaenoa niiauaiea :ss ieoo eo?niaoth.

Caueei yoio oaeno iaoiaeii i?inoie ia?anoaiiaee, eniieuecoy a ea/anoaa
eeth/a neiai “ca/ao” e iaicia/ay i?iaae aoeaie “ue” :

C A * A O A A C O *

y ue i e o

ue e y o i

o ue e o ?

ue o o ? e

n i a o th

i o n th a

Auienuaaai aoeau ioe?uoiai oaenoa iiae aoeaaie eeth/a. Caoai aoeau
eeth/a ?annoaa-eyai a aeoaaeoiii ii?yaeea.Auienuaaai aoeau ii noieaoeai
e iieo/aai oeo?oaeno: ueueieooyono?thiea.

Iieo/aiiia niiauaiea caoeo?oai n iiiiuueth iaoiaea iiaenoaiiaee :

Ionoue eaaeaeiio neiaieo ?onneiai aeoaaeoa niioaaonoaoao /enei io 0 aei
32. Oianoue aoeaa A aoaeao niioaaonoaiaaoue 0, aoeaa A – 1 e o.ae.
Aicueiai oaeaea iaeia /enei, iai?eia? 2, eioi?ia aoaeao eeth/ai oeo?a.
I?eaaaeyy e /eneo, niioaaonoaothuaio ii?aaeaeaiiiio neiaieo 2 iu iieo/ei
iiaue neiaie, iai?eia? anee A niioaaonoao-ao 0, oi i?e i?eaaaeaiee 2
iieo/aai A e oae aeaeaa. Iieuecoynue yoei iieo/aai iiaue oeo?oaeno :
thth?eooaooueoaniae

Eoae eiay ioe?uoue oaeno : ss ieoo eo?niaoth , iinea i?aia?aciaaiee
iieo/aai oeo?oaeno: thth?eooaooueoaniae, eniieuecoy iaoiaeu ia?anoaiiaee
e caiaiu. ?ane?uoue oaeno ?anoeo?iauee niaeao, ciay , /oi eeth/aie
yaeythony /enei 2 e neiai “ca/ao” e niioaaonoaaiii iineaaeiaaoaeueiinoue
eo i?eiaiaiey.

Aeiiieiaiey

DES-noaiaea?o NOA ia oeo?iaaiea aeaiiuo.

Iaeiei ec iaeeo/oeo i?eia?ia e?eioiaeai?eoia, ?ac?aaioaiiiai a
niioaaonoaee n i?eioeeiaie ?annaeaaiey e ia?aiaoeaaiey, iiaeao
neoaeeoue i?eiyoue a 1977 ai-aeo Iaoeeiiaeueiui ath?i noaiaea?oia
NOA noaiaea?o oeo?iaaiey aeaiiuo DES.Ianiio-?y ia eioaineaiua e
ouaoaeueiua enneaaeiaaiey aeai?eoia niaoeeaeenoaie, iiea ia iaeaeaii
oycaeiuo iano aeai?eoia, ia iniiaa eioi?uo iiaeii auei au i?aaeei-

aeeoue iaoiae e?eioiaiaeeca, nouanoaaiii eo/oee, /ai iieiue ia?aai?
eeth/ae. Ia-uaa iiaiea oaeiai: DES – eneeth/eoaeueii oi?ioee oeo?.
E?eioia?aoey ecaanoia n ae?aaiaeoeo a?aiai (aeinoaoi/ii aniiiieoue eiaeu
Oeaca?y) e aei iaaeaaiaai a?aiaie inoaaaeanue i?eaeeaaeae
eneeth/eoaeueii ainoaea?noaaiiuo e aiaiiuo o/?aaeaeaiee. Neooaoeey ?acei
eciaieeanue iinea ioaeeeaoeee a 1949 aiaeo eieae E.Oaiiiia “?aai-

ou ii oai?ee eioi?iaoeee e eeaa?iaoeea”. E?eioia?aoey noaea iauaeoii
i?enoaeue-iiai aieiaiey iiiaeo o/aiuo. I?eiyoea noaiaea?oa oeo?iaaiey
DES yaeeinue iiu-iui oie/eii e oe?ieiio i?eiaiaieth oeo?iaaiey a
eiiia?/aneeo nenoaiao. Aaaaea-iea yoiai noaiaea?oa – ioee/iue i?eia?
oieoeeaoeee e noaiaea?oecaoeee n?aaenoa caueou. I?eia?ii nenoaiiiai
iiaeoiaea e nicaeaieth aaeeiie e?oiiiianooaaiie nenoaiu caueou
eioi?iaoeee yaeyaony aee?aeoeaa Ieienoa?noaa oeiainia NOA 1984 aiaea,
niaeanii eioi?ie ana iauanoaaiiua e /anoiua i?aaiecaoeee, aaaeouea
aeaea n i?aaeoaeuenoaii NOA, iaycaiu aiaae?eoue i?ioeaaeo?o oeo?iaaiey
DES; e?oi-iaeoea aaiee Citibank,Chase Manhattan Bank, Manufaktures
Hannover Trust, Bank of America, Security Pacific Bank oaeaea aiaae?eee
yoo nenoaio.

Ieienoa?noai yia?aaoeee NOA ?aniieaaaao aieaa /ai 30
aeaenoaothueie naoy-ie, a eioi?uo eniieuecoaony aeai?eoi DES,
Ieienoa?noai thnoeoeee onoaiaaeeaaao 20000 ?aaeeiono?ienoa,
?aniieaaathueon?aaenoaaie caueou ia aaca DES. Noaiaea?-oecaoeey a
iineaaeiaa a?aiyi?eia?aoaao iaaeaeoia?iaeiue oa?aeoa?, iiaeoaa?aeaeaiea
oiio – iaaeaeoia?iaeiue noaiaea?o 1987 aiaea ISO 8372, ?ac?aaioaiiue ia
iniiaa e?ei-

oiaeai?eoia DES.

A ea/anoaa noaiaea?oiie aiia?aoo?u oeo?iaaiey iiaeii iacaaoue
ono?ienoai Cidex-IO, aace?othuaany ia aeai?eoia DES; nei?inoue
oeo?iaaiey – io 56 Eaeo/n aei 7 Iaeo/n. Na?eeii auioneaaony aaoiiiiiue
oeo?iaaeueiue aeie DES 2000, a iai oaeaea eniieuecoaony i?ioeaaeo?a
oeo?iaaiey DES; nei?inoue oeo?iaaiey – io 38,4 Eaeo/n aei 110Eaeo/n.
A ?acee/iuo naeoi?ao eiiia?/aneie aeayoaeueiinoe eniieueco-

aony i?ioeanni? oeo?iaaiey/aeaoeo?iaaiey aeaiiuo FACOM 2151A ia iniiaa
aeai-?eoia DES; nei?inoue – io 2,4 Eaeo/n aei 19,2 Eaeo/n. N
?ani?ino?aiaieai ia?ni-iaeueiuo eiiiuethoa?ia iaeaieaa yooaeoeaiuie
aeey ieo noaee i?ia?aiiiua n?aae-noaa caueou. Oae, ?ac?aaioai iaeao
i?ia?aii aeey oeo?iaaiey/aeaoeo?iaaiey eioi?iaoeee NOA (Computer
Intelligence Access), ?aaeecothuee aeai?eoi DES. Yoio aea aeai?eoi
eniieueciaai a iaeaoa SecretDisk (C F Systems) aeey eneeth/aiey ia-

naieoeeiie?iaaiiiai aeinooia e aeeneai.

Oaeei ia?acii, aeai?eoi DES i?aaenoaaeyao niaie iniiaiie iaoaieci,
i?eia-iyaoeeny /anoiuie e ainoaea?noaaiiuie o/?aaeaeaieyieNOA aeey
caueou eioi?ia-oeee. A oi aea a?aiy Aaainoai iaoeeiiaeueiie
aaciianiinoe, aunooiathuaa eae yenia?o ii e?eioia?aoe/aneei aeai?eoiai,
?ac?aaaouaaao iiaua aeai?eoiu oe-o?iaaiey aeaiiuo aeey ianniaiai
eniieueciaaiey. A 1987 aiaeo Iaoeeiiaeueiia ath?i noaiaea?oia iinea
ianoaeaeaiey iiaeoaa?aeeei aeaenoaea DES; aai ia?aniio? iaia/a-

einue i?iaanoe ia iicaeiaa yiaa?y 1992 aiaea, e ia naaiaeiyoiee aeaiue
aeaenoaea DES ia?aie/eaaaony eneeth/eoaeueii eiiia?/aneeie nenoaiaie.
DES iiaeao auoue ?aaee-ciaai aiia?aoii e i?ia?aiiii,ii aaciaue aeai?eoi
an? aea ?ann/eoai ia ?aaeeca-oeeth a yeaeo?iiiuo ono?ienoaao
niaoeeaeueiiai iacia/aiey. Naiui nouanoaaiiui iaaeinoaoeii DES n/eoaaony
iaeue ?acia? eeth/a.Noaiaea?o a ianoiyuaa a?aiy ia n/eoaaony
iaoycaeiui,oioy e i/aiue o?oaeai aeey ?ane?uoey (aei neo ii? ia auee
ca?a-aeno?e?iaaiu neo/ae ianaieoeeiie?iaaiiie aeaoeo?aoeee. Au? iaeei
iaaeinoaoie DES caeeth/aaony a oii,/oi iaeeiaeiaua aeaiiua aoaeoo
iaeeiaeiai auaeyaeaoue a caoeo?i-aaiiii oaenoa.

AINO 28147-89 – ioa/anoaaiiue noaiaea?o oeo?iaaiey aeaiiuo.

A iaoae no?aia onoaiiaeai aaeeiue aeai?eoi e?eioia?aoe/aneiai
i?aia?a-ciaaiey aeaiiuo aeey nenoai ia?aaioee eioi?iaoeee a naoyo
YAI, ioaeaeeoaeueiuo eiiieaenao e YAI, eioi?ue ii?aaeaeyaony AINO
28147-89.

Aeai?eoi e?eioia?aoe/aneiai i?aia?aciaaiey aeaiiuo i?aaeiacia/ai
aeey aiia-?aoiie eee i?ia?aiiiie ?aaeecaoeee, oaeiaeaoai?yao
e?eioia?aoe/aneei o?aaiaa-ieyi e ia iaeeaaeuaaao ia?aie/aiee ia
noaiaiue nae?aoiinoe caueuaaiie eioi?-iaoeee.

*oiau iieo/eoue iiae?iaiua niaoeeoeeaoeee aeai?eoia
e?eioia?aoe/aneiai i?a-ia?aciaaiey, neaaeoao ia?aoeoueny e AINO
28147-89. Aaconeiaii, i?eaaaeaiiue ieaea iaoa?eae ia aeieaeai ie i?e
eaeeo oneiaeyo eniieueciaaoueny aeey i?ia?aiiiie eee aiia?aoiie
?aaeecaoeee aeai?eoia e?eioia?aoe/aneiai i?aia?aciaaiey.

I?e iienaiee aeai?eoia eniieuecothony neaaeothuea iaicia/aiey.

Anee L e R – yoi iineaaeiaaoaeueiinoe aeo, oi LR aoaeao iaicia/aoue
eiieaoaiaoeeth iineaaeiaaoaeueiinoae L e R. Iiae eiieaoaiaoeeae
iineaaeiaaoaeueiinoae L e R iiie-iaaony iineaaeiaaoaeueiinoue aeo,
?acia?iinoue eioi?ie ?aaia noiia ?acia?iinoae L e R. A yoie
iineaaeiaaoaeueiinoe aeou iineaaeiaaoaeueiinoe R neaaeotho ca aeoaie
iineaaeiaaoaeueiinoe L. Eiieaoaiaoeey aeoiauo no?ie yaeyaony
annioeeaoeaiie,o.a. ca-ienue ABCDE iaicia/aao, /oi ca aeoaie
iineaaeiaaoaeueiinoe A neaaeotho aeou iinea-aeiaaoaeueiinoe A, caoai N e
o.ae.

Neiaieii (+) aoaeao iaicia/aoueny iia?aoeey iiaeoiaiai neiaeaiey ii
iiaeoeth 2, neiaieii [+] – iia?aoeey neiaeaiey ii iiaeoeth ( 2 a 32
noaiaie) aeaoo 32-?ac?yaeiuo /enae. *enea noiie?othony ii neaaeothuaio
i?aaeeo:

A [+] B = A + B ,anee A + B <>(2 a 32 noaiaie),

A [+] B = A + B -( 2 a 32 noaiaie),anee A + B =2 a 32

Neiaieii {+} iaicia/aaony iia?aoeey neiaeaiey ii iiaeoeth ((2 a a532a0)
-1) aeaoo 32 ?ac?yaeiuo /enae. I?aaeea noiie?iaaiey /enae neaaeothuea:

A {+} B = A + B,anee A+B<>((2 a 32)-1)

A {+} B = A + B-((2 a 32)-1),anee A + B = (2 a 32)-1

Aeai?eoi e?eioia?aoe/aneiai i?aia?aciaaiey i?aaeoniao?eaaao
ianeieueei ?a-aeeiia ?aaiou. Ii a ethaii neo/aa aeey oeo?iaaiey aeaiiuo
eniieuecoaony eeth/, eioi-?ue eiaao ?acia?iinoue 256 aeo e
i?aaenoaaeyaony a aeaea ainueie 32-?ac?yaeiuo /enae O(i). Anee
iaicia/eoue eeth/ /a?ac W, oi

W =X(7)X(6)X(5)X(4)X(3)X(2)X(1)X(0)

?anoeo?iaaiea auiieiyaony ii oiio aea eeth/o, /oi e caoeo?iaaiea,
ii yoio i?ioeann yaeyaony eiaa?neae i?ioeanna caoeo?iaaiey aeaiiuo.

Ia?aue e naiue i?inoie ?aaeei – caiaia. Ioe?uoua aeaiiua,
iiaeeaaeauea caoe-o?iaaieth, ?acaeaatho ia aeiee ii 64 aeo a eaaeaeii,
eioi?ua iiaeii iaicia/eoue O(j).

I/a?aaeiay iineaaeiaaoaeueiinoue aeo O(j) ?acaeaeyaony ia aeaa
iineaaeiaaoaeueiin-oe A(I) (eaaua eee noa?oea aeou) e A(I) (i?aaua eee
ieaaeoea aeou), eaaeaeay ec eioi?uo niaea?aeeo 32 aeoa. Caoai
auiieiyaony eoa?aoeaiue i?ioeann oeo?iaaiey, eioi?ue iienuaaaony
neaaeothueie oi?ioeaie:

1. A(i)=f(A(i-1) [+] X(j) (+) B(i-1)),

e B(i)=A(i-1),

anee i=1,2,…,24,j=(i-1) mod 8;

2. A(i)=f(A(i-1) [+] X(j) (+) B(i-1)),

e B(i)=A(i-1),

anee i=25,26,…,31,j=32-i;

3. A(32)=A(31),

e B(32)=f(A(31) [+] X(0)) (+) B(31),

anee i=32.

Caeanue i iaicia/aaony iiia? eoa?aoeee (i=1,2,…,32). Ooieoeey f
iacuaaaony ooi-eoeeae oeo?iaaiey. Aa a?aoiaioii yaeyaony noiia ii
iiaeoeth 2 a a532a0 /enea A(i), iieo/aiiiai ia i?aaeuaeouai oaaa
eoa?aoeee, e /enea O(j) eeth/a (?acia?iinoue eaaeaei-ai ec yoeo /enae
?aaia 32 ciaeai).

Ooieoeey oeo?iaaiey aeeth/aao aeaa iia?aoeee iaae iieo/aiiie
32-?ac?yaeiie noiiie. Ia?aay iia?aoeey iacuaaaony iiaenoaiiaeie E.
Aeie iiaenoaiiaee E ninoieo ec ainueie oceia caiaiu E(1) … E(8) n
iaiyoueth 64 aeo eaaeaeue. Iinooiathuee ia aeie iiaenoaiiaee
32-?ac?yaeiue aaeoi? ?acaeaaaony ia ainaiue iineaaeiaaoaeueii eaeoueo
4-?ac?yaeiue aaeoi? niioaaonoaothuei oceii caiaiu, i?aaenoaaeythuei
niaie

oaaeeoeo ec oanoiaaeoeaoe oeaeuo /enae a aeeaiaciia 0….15.

Aoiaeiie aaeoi? ii?aaeaeyao aae?an no?iee a oaaeeoea, /enei ec
eioi?ie yaeyaony auoiaeiui aaeoi?ii. Caoai 4-?ac?yaeiua auoiaeiua
aaeoi?u iineaaeiaaoaeueii iaua-aeeiythony a 32-?ac?yaeiue aaeoi?.
Oaaeeoeu aeiea iiaenoaiiaee E niaea?aeeo eeth/aaua yeaiaiou, iauea
aeey naoe YAI e ?aaeei eciaiyaiua.

Aoi?ay iia?aoeey – oeeeee/aneee naeaea aeaai 32-?ac?yaeiiai
aaeoi?a, iieo/aiiiai a ?acoeueoaoa iiaenoaiiaee E. 64-?ac?yaeiue aeie
caoeo?iaaiiuo aeaiiuo Oo i?aae-noaaeyaony a aeaea

Oo = A(32) A(32)

Inoaeueiua aeiee ioe?uouo aeaiiuo a ?aaeeia i?inoie caiaiu
caoeo?iauaathony aiaeiae/ii.

Neaaeoao eiaoue a aeaeo, /oi ?aaeei i?inoie caiaiu aeiionoeii
eniieueciaaoue aeey oeo?iaaiey aeaiiuo oieueei a ia?aie/aiiuo neo/ayo. E
yoei neo/ayi ioiineony au-?aaioea eeth/a e caoeo?iaaiea aai n
iaania/aieai eieoicaueou aeey ia?aaea/e ii eaiaeai nayce eee o?aiaiey a
iaiyoe YAI.

Neaaeothuee ?aaeei oeo?iaaiey iacuaaaony ?aaeeiii aaiie?iaaiey.
Ioe?uoua aeaiiua, ?acaeoua ia 64-?ac?yaeiua aeiee O(i)
(i=1,2,…,m}, (aaea m ii?aaea-eyaony iauaiii oeo?oaiuo aeaiiuo),
caoeo?iauaathony a ?aaeeia aaiie?iaaiey iooai ii?ac?yaeiiai neiaeaiey
ii iiaeoeth 2 n aaiiie oeo?a Ao, eioi?ay au?aaa-ouaaaony aeieaie ii
64 aeo, o.a.

Ao = ( A(1),A(2), …,A(i), …,A(m) ).

*enei aeaie/iuo ?ac?yaeia a aeiea O(m) iiaeao auoue iaiueoa 64,
i?e yoii iaen-iieueciaaiiay aeey oeo?iaaiey /anoue aaiiu oeo?a ec
aeiea A(m) ioa?anuaaaony.

O?aaiaiea caoeo?iaaiey aeaiiuo a ?aaeeia aaiie?iaaiey iiaeao
auoue i?aae-noaaeaii a neaaeothuai aeaea:

O(i)=A(Y(i-1) [+] C2),

Z(i-1) {+ }C1 (+) T(i)=A(i) (+) T(i).

A yoii o?aaiaiee O(i) iaicia/aao 64-?ac?yaeiue aeie caoeo?iaaiiiai
oaenoa, A – ooieoeeth oeo?iaaiey a ?aaeeia i?inoie caiaiu
(a?aoiaioaie yoie ooieoeee yaey-thony aeaa 32-?ac?yaeiiai /enea), N1 e
N2 – eiinoaiou, caaeaiiua a AINO 28147-89. Aaee/eiu Y(i) e Z(i)
ii?aaeaeythony eoa?aoeeiiii ii ia?a oi?ie?iaaiey aaiiu, nea-aeothuei
ia?acii:

(Y(0),Z(0))=A(S),

aaea S – 64-?ac?yaeiay aeaie/iay iineaaeiaaoaeueiinoue (neio?iiinueea);

(Y(i),Z(i))=(Y(i-1) [+] C2,Z(i-1) {+} C1),

aeey i=1,2,..,m

?anoeo?iaaiea aeaiiuo aiciiaeii oieueei i?e iaee/ee
neio?iiinueee, eioi?ay ia yaeyaony nae?aoiui yeaiaioii oeo?a e iiaeao
o?aieoueny a iaiyoe YAI eee ia?aaeaaaoueny ii eaiaeai nayce aianoa n
caoeo?iaaiiuie aeaiiuie.

?aaeei aaiie?iaaiey n ia?aoiie naycueth i/aiue iioiae ia ?aaeei
aaiie?iaaiey. Eae e a ?aaeeia aaiie?iaaiey, ioe?uoua aeaiiua, ?acaeoua
ia 64-?ac?yaeiua aeiee O(i) (i=1,2,….,m), aaea m ii?aaeaeyaony iauaiii
oeo?oaiuo aeaiiuo), caoeo?iauaaao-ny iooai ii?ac?yaeiiai neiaeaiey ii
iiaeoeth 2 n aaiiie oeo?a Ao, eioi?ay au?a-aaouaaaony aeieaie ii 64
aeo:

Ao=(A(1),A(2),…,A(i),…,A(m)).

*enei aeaie/iuo ?ac?yaeia a aeiea O(m) iiaeao auoue iaiueoa 64,
i?e yoii iaen-iieueciaaiiay aeey oeo?iaaiey /anoue aaiiu oeo?a ec
aeiea A(m) ioa?anuaaaony.

O?aaiaiea caoeo?iaaiey aeaiiuo a ?aaeeia aaiie?iaaiey n ia?aoiie
naycueth iiaeao auoue i?aaenoaaeaii a neaaeothuai aeaea:

O(1) = A(S) (+) T(1) = A(1) (+) T(1),

O(i) = A(O(i-1)) (+) T(i) = A(i) (+) T(i),

aeey i=2,3,…,m

Caeanue O(i) iaicia/aao 64-?ac?yaeiue aeie caoeo?iaaiiiai oaenoa, A
– ooieoeeth oeo?iaaiey a ?aaeeia i?inoie caiaiu. A?aoiaioii ooieoeee
ia ia?aii oaaa eoa?aoeaiiai aeai?eoia yaeyaony 64-?ac?yaeiue
neio?iiinueea, a ia anao iineaaeoth-ueo – i?aaeuaeouee aeie caoeo?iaaiuo
aeaiiuo O(i-1).

A AINO 28147-89 ii?aaeaeyaony i?ioeann au?aaioee eieoianoaaee,
eioi?ue aaeeii-ia?acai aeey ethaiai ec ?aaeeiia oeo?iaaiey aeaiiuo.
Eieoianoaaea – yoi aeie ec p aeo ( eieoianoaaea Ep), eioi?ue
au?aaaouaaaony ethai ia?aae oeo?iaaieai anaai niiauaiey, eeai
ia?aeeaeueii n oeo?iaaieai ii aeieai. Ia?aua aeiee ioe?uouo aeaiiuo,
eioi?ua o/anoaotho a au?aaioea eieoianoaaee, iiaoo niaea?aeaoue
neoaeaaioth eioi?iaoeeth (iai?eia?, aae?anioth /anoue, a?aiy,
neio?iiinueeo) e ia caoeo?iau-aaoueny. Cia/aiea ia?aiao?a p (/enei
aeaie/iuo ?ac?yaeia a eieoianoaaea) ii?aaeaey-aony e?eioia?aoe/aneeie
o?aaiaaieyie n o/aoii oiai, /oi aa?iyoiinoue iaaycu-aaiey eiaeiuo iiiao
?aaia 1/2a5?

Aeey iieo/aiey eieoianoaaee ioe?uoua aeaiiua i?aaenoaaeythony a
aeaea 64-?ac-?yaeiuo aeieia O(i) (i=1,2,…, m aaea m ii?aaeaeyaony
iauaiii oeo?oaiuo aeaiiuo). Ia?aue aeie ioe?uouo aeaiiuo O(1)
iiaeaa?aaaony i?aia?aciaaieth, niioaaonoaoth-uaio ia?aui 16 oeeeeai
aeai?eoia caoeo?iaaiey a ?aaeeia i?inoie caiaiu. I?e-/ai a ea/anoaa
eeth/a aeey au?aaioee eieoianoaaee eniieuecoaony eeth/, ii eioi?iio

oeo?othony aeaiiua.

Iieo/aiiia iinea 16 oeeeeia ?aaiou 64-iac?yaeiia /enei noiie?oaony
ii iiaeoeth 2 ni aoi?ui aeieii ioe?uouo aeaiiuo O(2). ?acoeueoao
noiie?iaaiey niiaa iiaeaa?-aaaony i?aia?aciaaieth, niioaaonoaothuaio
ia?aui 16 oeeeeai aeai?eoia caoeo?i-aaiey a ?aaeeia i?inoie caiaiu.

Iieo/aiiia 64-?ac?yaeiia /enei noiie?oaony ii iiaeoeth 2 n
o?aoueei aeieii ioe?uouo aeaiiuo O(3) e o.ae. Iineaaeiee aeie O(m),
i?e iaiaoiaeeiinoe aeiiieiai-iue aei iieiiai 64-?ac?yaeiiai aeiea
ioeyie, noiie?oaony ii iiaeoeth 2 n ?acoeueoa-oii ?aaiou ia oaaa m-1,
iinea /aai caoeo?iauaaaony a ?aaeeia i?inoie caiaiu ii ia?aui 16
oeeeeai ?aaiou aeai?eoia. Ec iieo/aiiiai 64-?ac?yaeiiai /enea auae-

?aaony io?acie E? aeeeiie ? aeo.

Eieoianoaaea E? ia?aaeaaony ii eaiaeo nayce eee a iaiyoue YAI
iinea caoeo?i-aaiiuo aeaiiuo. Iinooieaoea caoeo?iaaiiua aeaiiua
?anoeo?iauaathony e ec iieo-/aiiuo aeieia ioe?uouo aeaiiuo O(i)
au?aaaouaaaony eieoianoaaea E?, eioi?ay caoai n?aaieaaaony n
eieoianoaaeie E?, iieo/aiiie ec eaiaea nayce eee ec iaiyoe YAI. A neo/aa
ianiaiaaeaiey eieoianoaaie ana ?anoeo?iaaiiua aeaiiua n/eoatho-ny
eiaeiuie. Aeai?eoi e?eioia?aoe/aneiai i?aia?aciaaiey,yaeythueeny
ioa/an-oaaiiui noaiaea?oii e ii?aaeaeyaiue AINO 28147-89,naiaiaeai io
iaaeinoaoeia noai-aea?oa DES e a oi aea a?aiy iaeaaaeaao anaie aai
i?aeiouanoaaie.E?iia oiai a ia-ai caeiaeai iaoiae,n iiiiuueth eioi?iai
iiaeii caoeene?iaaoue iaiaia?oaeaiioth neo-/aeioth eee oiuoeaiioth
iiaeeoeeaoeeth caoeo?iaaiiie eioi?iaoeee.

Iaeiaei o aeai?eoia anoue i/aiue nouanoaaiiue iaaeinoaoie,eioi?ue
caeeth/aaony a oii,/oi aai i?ia?aiiiay ?aaeecaoeey i/aiue neiaeia e
i?aeoe/anee eeoaia anyeiai niunea.

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