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paa popa 2-e ae pooo, aop cxoe ec a e C pc aep pecoe cop epayp o popa ooo oa. Cepeoc, oeo ...

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Meo ycooo yocoepe ooc oe pe epy poey, o oo poe oc oy pe oe poe. Copoa, a eppop oopo co cecopa, oe poec, o e e ae cecopaa, a cea copoa ae, o ae e oea.

2.7 poe oc poae Oe poe oc popa c op a, papaaae pooo, o py eoacoc poa ocoepoc pox oce. Cpae c co o ae a.

oc yocoepe aopco a oep oeceae ay.

(1) Aca ocae cooee c oo coeo apoo a.

SA(M) (2) Aca pye ocaoe cooee op o oa ocae eo oy.

EB (SA(M)) (3) o pacpoae cooee c oo coeo apoo a.

DB (EB (SA(M)))= SA(M) (4) o poepe oc c oo opoo a Ac occaaae cooee.

VA (SA(M))= M oc epe poae ececeo. oa Aca e co, oa ocae eo a e ae oep. Ec oa oo co oep eoca, o o oe aecooc, py co o ao oeeo. Ec o oae po co Ac oep, po oe o oa, o o pe o o, aoe co ao oepe po.

B epoo oppecoe oo ae ec pay cooae oc epe poa e [48]. o e oo oee eoaco - pa e coe ya oc poaoo cooe o a co cocey - o cyecy pece coopae : ec ocae ec e e o caey, oa o ca oc, o peca ca oc eea [1312]. Cyecy ae e oope popaece coco cp ao oceoaeoc ec, coye oc RSA (c. pae 19.3).

Ac e cyecye p cooa oy apy e - op/ap - poa oc. ee oe e ap e: oa poa oa oc. aoo paee ec co peyeca: Aca oe epea co poa o, e opoepy co o c, o oe ycoo epea (c. pae 4.13), e a pyo. e oy pa e cpo ec.

oeo e, peopae oopoo cooa cooe c poooo o cooa e pee. Me pee ae oy a o pyx oox oye, pep oo oopx pee e.

Bopaeue cooeu npu npuee Paccop peaa oo poooa c ooeo oooc oepe cooe - o y cooee, o oaeo opaae oepee pea.

(1) Aca ocae cooee c oo coeo apoo a, pye ocaoe cooee o p o oa ocae eo oy.

EB (SA(M)) (2) o pacpoae cooee c oo coeo apoo a, poepe oc c oo o poo a Ac occaaae cooee.

VA (DB (EB (SA(M))))= M (3) o ocae cooee c oo coeo apoo a, pye ocaoe cooee o p o Ac ocae eo Ace opao.

EA (SB(M)) (4) Aca pacpoae cooee c oo coeo apoo a poepe oc c oo opoo a oa. Ec oyeoe cooee coaae c opae, oa ae, o o o y paoe cooee.

Ec poa poep poo oc coyec o o e aop, o cyecye oooc cp [506]. B ax cyax oepa poo oc - poooooc oepa poa: VX = EX SX = DX.

yc Mop - apecppoa ooae co coe apo e: op ap. Teep ocop, a o coe a oy oa. Caaa o ae cooee Ac oy - a (1). ae, eoo oo, o oe o cooee oy, yepa, o oo opaeo ca Mop. o, ya, o o ooe cooee o Mop, eppye o cooee co ap o aec po e p oc Mop, eppy ee c oo opoo a Mop. B peyae oyaec oa eyxa:

EA (DB (EB (DA(M))))= EM (DA(M)) ae o cyae, cey poooy, o ocae Mop oyeoe cooee :

EM (DB (EM (DA(M)))) Teep Mop ocaec oo pacpoa cooee c oo coeo apoo a, ap o a eo op o oa, pacpoa coa c oo coeo apoo a apoa o p o Ac. Voil! Mop oyae M.

O e yo peoo, o o oe aoaec oca Mop a. o po o o, apep, oe cpoe eo oyaooe popaoe oeceee oca a aoaec. eo oooc coo o pee eyx apyae eoacoc. Ec o poep cooee a occeoc epe opao a, o coe ea ax poe c eoacoc.

Cyecy oepa oo cocoa cp, peoaae, o Mop oe oy cooee, ooe o oo, oopoe o eae epexa. Hoa e ocae poox cooe o pyx e e epeaae peya epo poox cooe .

Oapyeue cpmu, ocoaoo a opaeuu cooeu Too o ocaoe cpe paoae ooy, o oepa poa coaae c oepae poep oc, a oepa eppoa - c oepae oc. Oepa poa poo oc eoaco poooe o xo cea oac. poey peae cooae pax e ao oepa, cooae ao oepa pax aopo, peee eo pee, oope ea pa poe opaeoe cooe, poa oc c oo ooapaeo x-y (c. pae 2.6). Toa, oe cyae, cey pooo, coy aop c op o, ec eoac :

(1) Aca ocae cooee.

(2) Aca pye ocaoe cooee op o oa (coy aop, oac o aopa poo oc) ocae eo oy.

(3) o pacpoae cooee c oo coeo apoo a (4) o poepe oc Ac.

Bcpmu punmopauu c ompmu au Bo cex oox poooax popa c op a e paccaa, a Aca oyae o p oa. opoo o opoc oca paee 3.1, o o e co yoy ec.

poe ceo ya e-o op , ca eo oya-o eoaco a ax. a aa a x oa oeocya, o a o oy y ey . aa ax oa a ea o ecaopoao ac, poo cyae Mop coe oe op oa. oce oo o ye e cyee a apecoae ey cooe, ao o coe cea Mop.

ae ec ope xpac aeo ae ax, Mop oe oe x p epeae.

o ocpecoa oy, Tpe oe oca a op , coy co coce ap . Tpea, oop ecye oo opao, aco aa Opao cepa e epo pacpeee e (Key Distribution Center, KDC). Ha pae KDC ocae cooe cooee, cocoee e ooae, eo opoo a pyo opa o oo a ee. o ocaoe cooe cooee xpac ae ax KDC. oa Aca oyae oa, oa poepe oc KDC, yocoepc paoc a.

p ooaeo aae o, o o oo apye, o e eae eoo oeeco Mop. Aca e oa oya-o oy op KDC. Mop yo oe o co op o, cop ay ax ae pae co (oca eo ap o, a ec o KDC), eo eo ceao. Ho, ae oc a yae oy oea, ec Mop cepe oec a eo. opoo oe a paccapaec paee 3.1.

2.8. eepa cyax ceocyax oceoaeoce oey ae e o popa coa oye paccye o eepa cyax ce?

eepaop cyax ce cpoe a oop, o o y. oey e co o a eo? coae, eepaop cyax ce o aepa eocaoo eoac p o pa , ooo, ae e coce cya. oco x eca ox.

eepaop cyax ce a cao ee coce e cya, ooy o e yo a.

oca poe, apep, oepx p, peyec a ao cyax ce, o x e cyaoc p ye aea. Oao, popa oe ycea coca eepaopo c y ax ce. pee oxo eepaop, y ac oc acee oppe cpae peya [1231, 1238]. Ec aa eoacoc ac o eepaopa cyax ce, acee oppe cpae peya c acoo e e, eo ea oc.

poea o, o eepaop cyax ce e coae cyao oceoaeoc. O, ooo, e ae eo ae oaeo aoaeo cyay oceoaeoc. oeo, eooo coa a a oepe o-o o acoey cyaoe. oa y pca o Heay ceye coa: "a, o aaec apeec eoa oye cyax ce, opeeeo pe " [863]. oep - o eeppoae ec : aaaec ec aepa, oc o o c pecayee ec, o-o ooe oae c pyoo oa. oaa ooo oo e a xo yx pax cyax pee ooy oy e peyay. aoe oaoe cxoe ae a ex oepa, oa o oca oo o e. oep oe axoc oo opa eo ce coco (oe oo, o ce e opaeo), aae peya cea ye cpoo opeec cxo a ey cocoe oepa. o a, o o eepaop cy ax ce a oepe (o ee epe, a oeo aoae), o opeee, epoe. A ce, o epoo, o opeee, pecayeo. A ce, o pecayeo, e oe cya. a coeo eepaopa cyax ce yo oaa a xo o-y cyaoe, oep e e oe oece o peoae.

ceocyae noceoameocmu yee, o oe cea oep - o eepaop ceocyax oceoaeoce. o o aoe? Moe ac a eo opaoe opeeee, o yoc o oo. ceocyaa oce o aeoc - o o-o, ee a cyaoe. epo oceoaeoc oe ocaoo e , ooy oea oceoaeoc payo - oopa eceoc coyec - e epoa. Ec a ye ap cyax , e oyec eepaopo oceoaeoc, o o pec ae ecaa c . ooceo opoe eepoece ooceoaeoc o , acoo o ooo, eo o cyax oceoaeoce. Hapep, x oo pepo oaooe oeco e ye, ooo oo cep (oceoaeoce oaox ) o eo , eep - coco yx , oca ac - pex, ..

oceoaeoc o ecae. Pacpeeee cep ye e oo oao [643, 863, 99, 1357]. coca oy epe o ye ae cpae c oae cacec c oo cac x-apa. ax ee eepaop oceoae o c caec ceocya, ec o oaae cey coco :

1. O cyao. o oaae, o o poxo ce ec a cyaoc, oope a yaoc a. (Hae c peex [863].) Moeco yc o apaeo a coae xopox ceocyax oceoaeoce a o epe. Ocyee eepaopo oo oece oo a aaeeco epaype ece c pa eca a cyaoc. Bce eepaop epo (oo eooo ea), o, ec x epo 2256 e, o oy cooa cax cepex poex.

poea eo x acex oppex cpax peyaax. a eepaop ceocy ax oceoaeoce coae ae cpaoc, ec coyee eo opeee opao. A o eo o, o yo poaay oa cce.

punmopauecu eonace nceocyae noceoameocmu popaece poe pe eepaopy ceocyax oceoaeoce oee coe peoa o cpae c py poe. popaeca cyaoc e opaae c caceco cyaoc, xo ae ee. o oceoaeoc a popaec eoaco ceocyao oceoaeoc, oa oa oaa cey coco :

2. Oa epecayea. oo oe pyo (c o pe pee cex o oce) pecaa, a ye cey cya , ae ec ooc ece aop ycpoco, eeppyee oceoaeoc, ce peye ooa.

popaec eoace ceocyae oceoaeoc e o cac..., ec a e ece . o oo ec aaoe aaoe cocoe eepaopa.

a o popaec aop, eepaop popaec eoacx ceocyax o ceoaeoce peca coo pee cp. Ta e a popaec aop, oe oa eepaop popaec eoacx ceocyax oceoaeoce. Coae yc ox cp eepaopo ec ocoo popa.

Hacmoue cyae noceoameocmu Teep opaec oac, paeay ocoa. Cyecye aa e a cyaoc ?

o aoe cyaa oceoaeoc ? a ya, o oceoaeoc cyaa ? ec "101110100" oee cyao e "l01010101"? aoa exaa yeae ac o, o peao pe cyecye acoa cyaoc. Ho a coxpa y cyaoc peopeeeo pe oepx pocxe oex aoao?

B copoy oco, c ae o pe eepaop oceoaeoc eceo cyae, ec o oaae pe coco:

3. Coaaea oceoaeoc e oe yepeo ocpoeea. Ec aycaee e epaop cyax ce a c o e e xoo (o pae epe, acoo o eo e ecx cax), o oye e coepeo eace cyae oceoaeoc.

Bxo eepaopa, yoeopeo ce pe pee peoa, ye ocaoo xopo oopaooo ooa, eepa a pyx popaecx pee, peyx eepa e ceo cyax oceoaeoce. Tpyoc o, o o, eceo oceoae oc cyaa? Ec oopo apy cpoy, coy DES aa , oyy xopo, cya opao peya, e coee caa, o o e cyae, oa e aee o a DES NSA.

aa Ocoe pooo 3.1 Oe a Oepo popaeco exo ec poae aoo yaoo oea coo e oe o. Tao aaec ceaco, a a o coyec eceoo oeoo ceaca oea opae. B paee 8.5 oopc o o, o ceacoe oe, a a pe x cyecoa opeeec eoc ceaca c. epeaa oo oeo ceacooo a py oeaxc opae pecae coo coy poey.

Oe au c noo cuempuo punmopauu o pooo peoaae, o ooae ce, Aca o, oya cepe o epa pa c peee e (Key Distribution Center, KDC) [1260] - Tpea ax poooo. epe aao poooa ye o y ooaee. (pooo oppye oe acyy poey oca x cepex e, peoaaec, o ye y ooaee, Mop e ee o x ao o p a.) (1) Aca opaaec Tpey apaae ceaco c c oo.

(2) Tpe eeppye cya ceaco . O apoae e o a: oy Ac, a pyy - oa. ae Tpe ocae oe o Ace.

(3) Aca pacpoae co o ceacooo a.

(4) Aca ocae oy eo o ceacooo a.

(5) o pacpoae co o ceacooo a.

(6) Aca o coy o ceaco eoacoo oea opae.

o pooo ocoa a acoo aeoc Tpea, po oopoo oe oxo acy aa oep oepa popaa, e acya oep eoe. Ec Mop oy o c y Tpey, copoepoao oaec c ce. B eo pyax oayc ce cepee , eee ooae Tpeo, o coe poec ce epeae cooe, oope ey yaoc epexa, ce yye cooe. Ey ocaec oo oc c ocya apoa oo cooe.

pyo poeo ao cce ec o, o Tpe oeao ec ee y eco. O oe yacoa ao oee a. Ec c o-o cyc, o papy c ccey.

Oe au, ucnoy punmopau c ompmu au aoa ceaa poccea ocyaac paee 1.5. coacoa ceacooo a Aca o pe popa c op a, a ae coy o ceaco po a ax. B eoopx peaax ocae Ac oa ocy eoopo ae ax.

o aeo oeae pooo, eep Aca, ae ec o o e oa e ca, oe eoaco oca oy cooee:

(1) Aca oyae op oa KDC.

(2) Aca eeppye cya ceaco , apoae eo op o oa ocae eo oy.

(3) o pacpoae cooee Ac c oo coeo apoo a.

(4) Aca o py co oe opae ceaco o.

Bcpmue "eoe--cepeue" B o pe, a Ea e oe cea eo yeo, e ac oa aop c op a o cpe c cooae oo poeca, y Mop opao oe oooce. O e oo oe ocya cooe Ac oa, o e cooe, ya cooe coa coepeo oe. Mop oe a ce a oa, cooaeo o-o Ace, a Acy, cooay o-o oy. Bo a ye oeo cpe:

(1) Aca ocae oy co op . Mop epexaae eo ocae oy co coce op .

(2) o ocae Ace co op . Mop epexaae eo ocae Ace oy coce op .

(3) oa Aca ocae cooee oy, apoaoe op o "oa", Mop epexa a e eo. Ta a cooee eceoc apoao eo coce op o, o pa c poae eo, coa apoae op o oa ocae oy.

(4) oa o ocae cooee Ace, apoaoe op o "Ac", Mop epexa ae eo. Ta a cooee eceoc apoao eo coce op o, o pacpoae eo, coa apoae op o Ac ocae Ace.

o cpe ye paoa, ae ec ope Ac oa xpac ae ax. Mop oe epexa apoc Ac ae ax oe op oa co coce. To e caoe o oe cea c op o Ac. , ee ye, o oe coa oa ay ax oe ope oo Ac co. Teep o oe peyce, poco oac, oa Aca o ay oeac cooe, aa epexaa e cooe.

Taoe cpe "eoe--cepee" paoae, a a y Ac oa e cocoa poep, ec eo o oac eo py c pyo. Ec eaeco Mop e po ae aep a ce, oa oppecoea e oya, o o-o, c ey , ae c x cepey o y.

pomoo "epac a pyu" pooo "epac a py", opee Poo Peco (Ron Rivest) apo (Adi Shamir) [1327], peocae eoxy oooc ea cp "eoe--cepee". Bo a o paoae:

(1) Aca ocae oy co op .

(2) o ocae Ace co op .

(3) Aca apoae coe cooee op o oa. ooy apoaoo cooe oa opae oy.

(4) o apoae coe cooee op o Ac. ooy apoaoo cooe o opae Ace.

(5) Aca opae oy opy ooy apoaoo cooe.

(6) o caae e ac cooe Ac pacpoae eo c oo coeo apoo a.

o opae Ace opy ooy coeo apoaoo cooe.

(7) Aca caae e ac cooe oa pacpoae eo c oo coeo apoo a.

e o, o ooa apoaoo cooe ecoea e opo oo, oa e oe eppoaa. o e coe poa oo ac cooe Ac o aa (6), a Aca e coe poa oo ac cooe oa o aa (7). Cyecye oeco cocoo pa cooee a ac:

Ec coyec o aop poa, ooa aoo oa (apep, a opo ) oe epeaa ao ooe cooe.

eppoae cooe oe ace o eopa aa (c. pae 9.3), oop oe epea o opo ac cooe.

epa ooa cooe oe ooapaeo x -ye poaoo cooe (c. pae 2.4), a o opa ooa - coceo poa cooee.

o o, a ao pooo oeae Mop, aae paccop eo oy apy pooo.

a pae, o oe oe ope Ac oa co a aax (1) (2). Ho eep, epe xa ooy cooe Ac a ae (3), o e coe pacpoa ee co ap o c o a apoa op o oa. O oe coa coepeo ooe cooee opa ooy eo oy. epexa ooy cooe oa Ace a ae (4), Mop coec c o e poeo.

O e coe pacpoa ee co ap o coa apoa op o Ac. Ey pec coa coepeo ooe cooee opa ooy eo Ace. oy pee, oa o e pexa ope oo acox cooe a aax (5) (6), oe coae oe cooe ye co oo. Oe a ey Aco oo ec paao.

Mop oe oac ea aoo peyaa. Ec o ocaoo xopoo ae oox oppeco eo, o cpoa x p oee a, o oy oa e ae oe. Ho ce-a o coee, e poco ce ey oppecoea, epexaa a x cooe.

Oe au c noo upox nonuce cooae poo oc poooe oea ceaco o ae ooe ea cp "eoe--cepee". Tpe ocae ope Ac oa. ocae a ocaoe aepee ooc. oy , Aca, o poep oc Tpea. Teep o yepe, o pca op pae eo yaaoy oppecoey. ae oec pooo oea a.

Mop caaec c cepe poea. O e oe a ce a Acy oa, e o e ae x apx e. O e oe oe x ope co, ooy o p oc eo a Tpe yaa, o o Mop. Bce, o ey ocaec - o pocya apoa oo cooe cop c, ea oey opa Ac oa.

Tpe cyae yaco oo poooa, o pc opoea KDC ee, e epo poooe. Ec Mop opoepye Tpea (aae KDC), o oyae oo ap Tpe a. o oo ey oo oca oe , a e pacpoa ceacoe a poo oo cooe. e cooe Mop pec a ce a ooae ce oaa ecx ooaee, py cooe co oe op o.

Mop oe pep aoe cpe. coy ap Tpea, o oe coa oe e ocae , o oay Acy oa. ae o oe o oe a a coe ae ax, o epexaa apoc ooaee ae ax oca oe oee . o oo ey ocyec cpe "eoe--cepee" a cooe o o aee.

Taoe cpe ye paoa, o oe, o oo Mop oe ye epexaa e cooe. B pe cee o aoo coee, e poco acco ce, pocapa cooe ce o epe x ocye. B pooeaex aaax, ax a paoce, o eooo oe oo cooee py - xo oo a c ce. B oepx cex o eee coo , aec, c a e caoc poe poe. Opae ae a oey IP-apeca, cpe appyaopa ..

Aoe cpe e oaeo oaae, o o-o acoae o , a o x eep oy e oo paecee aeca.

epeaa e u cooeu Ace oy e oaeo o pooo oea a epe oeo cooe. B o poooe Aca opae oy cooee e peapeoo poooa oea a :

(1) Aca eeppye cya ceaco , K, apoae M o.

EK(M) (2) Aca oyae op oa a ax.

(3) Aca pye K op o oa.

EB(K) (4) Aca ocae oy poae cooee ceaco .

EK(M), EB(K) ooeo a o cp "eoe--cepee" Aca ocae epeay.

(5) o pacpoae ceaco Ac, K, coy co ap .

(6) o, coy ceaco , pacpoae cooee Ac.

ooa ceaa ccea yopeec ae ceo cceax c. Ee oo coe c po oc, ea pee py poooa oecee eoac oc.

upooeamea pacca e u cooeu He cyecye p, apeax Ace oca poaoe cooee eco . B ce ye pepe Aca ocae poaoe cooee oy, po y :

(1) Aca eeppye cya ceaco , K, apoae M o.

EK(M) (2) Aca oyae a ax ope oa, po a.

(3) Aca pye K op a oa, po a.

EB(K), EC(K), ED(K) (4) Aca pooeaeo ocae poaoe cooee ce poae co oppe c oea.

EK(M), EB(K), EC(K), ED(K) (5) Too o, po oy, a p oo coeo apoo a, pacpoa K.

(6) Too o, po oy pacpoa coo ee Ac, coy K.

o pooo oe peaoa cee epoo o. epa cepep oe opa cooee Ac oy, po y ece c ope poa o. Cepep e oe ae eoac, a a o e oe pacpoa oo cooe.

3.2 ocoepee ooc oa Aca oaec aoy oepy ( aoaecoy, eeoo aoco ccee, aoy-y pyoy epay ), a a oep yae, o oa? Oya a oep yae, o o e Ea, aac a ce a Acy ? Oo a poea peaec c oo apoe. Aca o co apo, a oep poepe eo paoc. Ta opao, Ace, aoy oepy eca eoopa cepea opa, oopy a oep a paae c pa, oa Aca aec oc.

ocmoepeue nouocmu c noo ooanpaex yu Poep Heex (Roger Needham) Ma a (Mike Guy) oaa, o aoy oepy e yo a ca apo, oe ocaoo, o a oep o oa pae apo o ep a x. oo eo oc c oo ooapaex y [1599, 526,1274, 1121]. p o a ao oepe xpac ae ooapaex y apoe, a e ca apo.

(1) Aca ocae aoy oepy co apo.

(2) a oep ce ooapaey y apo.

(3) a oep cpaae oyeoe aee c xpac.

Pa a oep oe e xpa ay pax apoe cex ooaee, caec y poa oo, o o-o poe a oep pae ay apoe. Cco apoe, opaoa ooapaeo ye, ecoee, a a ooapaey y e yacc eppoa oye apoe.

Bcpmu c noo coap u "co" a apoe, apoax ooapaeo ye, e e eee, y. e aac pee, Mop oe coca cco oa aoee aco cpeaxc apoe. O opaoae ec o ooapaeo ye coxpa peya. Ec a apo coco oc a, pa ep oyeoc aa e pec 8 Ma, o a oe paee ceo a ecox a c eax. Teep Mop oae poa a apoe. O cpaae o a co co ao poax oox apoe e coae.

o cpe c oo coap oe yeo yce (c. pae 8.1). "Co" - o co co apy eo. "Co" pecae coo cyay cpoy, oaey apo epe opaoo x ooapaeo ye. ae ae ax aoo oepa coxpac aee "co", p e ya ooapaeo y. cooae ocaoo ooo ca oox ae "co" paec ycpae oooc cp c oo coap, a a Mop pec c a e e ooapaeo x-y aoo oooo ae "co ". o poce pep c ooae eopa aa (c. pae 9.3).

e coco o, o aca Mop o pooe poae aoo apo eo c o ap p ao oe ya e-o yo apo eco oopaoo opao cex oox apoe.

oo yo oo "co". oco UNIX-cce coy "co" 12 . Hecop a o e (Daniel Klein) aca popay paaa apoe, oopa eoopx cceax a e e aco cpaa 40 poeo apoe [847,848] (c. pae 8.1). eaep (David Feldmeier) a (Philip Karn) coca cco 732000 aoee aco coyex apoe, pcoe a oy x 4096 oox ae "co". o x oea 30 poeo apoe a o ao o epe oy oa c oo oo cca [561].

"Co" e ec aaee, yeee ca "co" e pe cex poe. "Co" peoxpae oo o cax ox cp aa apoe c cooae coap, a e o coacoao aae o oo apo. Oa aae e, coyx o o e apo a pax aax, o e eae ye oxo pa apo.

SKEY SKEY - o popaa yocoepe ooc, oeceaa eoacoc c oo ooapa eo y. o eo oc.

Pecppyc ccee, Aca aae cyaoe co, R. oep ce f(R), f(f(R)), f(f(f(R))), a aee, ooo co pa. Ooa ae a x1, x2, x3,..., x100. oep eaae cco x ce, Aca pe eo eoacoe eco. oep ae op eco ca ae ax oe ccee cooece Ace co x101.

oac epe, Aca o coe x100. oep paccae f(x100) cpaae eo c x101, ec ae coaa, paa Ac oepac. ae oep aee ae ax x101 a x100.

Aca epae x100 coeo cca.

Aca, p ao oe ccee, o oceee eepyoe co coeo cca: xi.

oep paccae f(xi) cpaae eo c xi+1, xpaec ae ax. Ta a a oep c oyec oo o pa, Ea e coe o ao oeo opa. Aaoo, aa ax ecoea oa. oeo e, a oo cco Ac cepaec e pec epepecpp o ac ccee.

ocmoepeue nouocmu c noo punmopauu c ompmu au ae c cooae "co" y epoo poooa ec cepee poe c eoacoc. oa Aca ocae co apo aoy oepy, o, y oo ec ocy y epea ee ax, oe p o ec apo. Oa oe oy ocy coey aoy oepy ocpeco ayaoo y ep e a opa, poo eo epe epex poex oypeo, p pyx cpa a epe o x yepcea. Ea oe axoc o x oe, ocya epeaaey Aco oce o aeoc. Ec y E ec ocy oepao a aoo oepa, oa coe ocope a po o oo, a a oep coe eo xpoa.

popa c op a oe pe y poey. a oep xpa a op x e cex ooaee, a ce ooae xpa co ape . Bo a ypoea oa opaoa pooo oe :

(1) a oep ocae Ace cyay cpoy.

(2) Aca pye y cpoy co ap o ocae ee opao aoy oepy ece co co ee.

(3) a oep axo ae ax op Ac eppye cooee, coy o op .

(4) Ec opaea caaa pacpoaa cpo coaa, a oep peocae Ace ocy ccee Ho pyo e oe ocooac ap o Ac, ceoaeo o e coe a ce a ee. o oee ao, Aca oa e ocae a oep co ap . Ea, ocya aoece, e oy ax cee, oope oo e c ap Ac a ce a ee.

ap oe ocaoo e oe eoec. O ye aoa e c opaaac aapaypo ooae popa oeceee c. o peye cooa "yoo" epaa, oopoy Aca oepe, o e a oep, c e oa eoac.

yo poa pooe cpo - e oo ocae oope aopo, o ooe e.

ae oe cooao cxea cp, ocyaea paee 19.3. eoace eaoe pooo e ceyy, oee coy opy :

(1) Aca oe cee, ocoaoe a eoopx cyax cax coe apo e, o cae peya a a oep.

(2) a oep ocae pyoe cyaoe co.

(3) Aca oe eoopoe cee, ocoaoe a cyax cax (a coao e, a o y eo o aoo oepa) coe apo e, ocae peya a a oep.

(4) a oep oe eoopoe cee pax ce, oyex o Ac, ee opoo a, poep, o e ece ee ap .

(5) Ec poepa aepaec yceo, oc Ac oepaec.

Ec Ac oepe aoy oepy e oe cee, e o oepe Ace, o oa oa opeoa oepe ooc aoo oepa aao opao.

a (1) oe oaac ey aya, o o eoxo a poooa o cp.

Pae pooo aop oepe ooc aeaec opoo ocac pa eax 21.1 21.2. C. ae [935].

Oooe yocmoepeue nouocmu c ucnooaue npomooa "epac a pyu" yc a ooae, Aca o, xo poep ooc py pya. aoo x ec a po, ec pyoy ooae : PA y Ac PB y oa. Bo a pooo, oop e ye paoa:

(1) Aca o oeac op a.

(2) Aca pye PA op o oa ocae eo ey.

(3) o pye PB op o Ac ocae eo e.

(4) Aca pacpoae oyeoe a ae (3) oepae paoc apo.

(5) o pacpoae oyeoe a ae (2) oepae paoc apo.

Mop oe pep yceoe cpe "eoe--cepee" (c. pae 3.1):

(1) Aca o oeac op a. Mop epexaae oa cooe, ocae oo oppecoea co coce op , oe x .

(2) Aca pye PA op o "oa" ocae eo ey. Mop epexaae cooee, pacpoae PA c oo coeo apoo a, coa pye PA op o oa o cae eo ey.

(3) o pye PB op o "Ac" ocae eo e. Mop epexaae cooee, pa c poae PB c oo coeo apoo a, coa pye PB op o Ac o cae eo e.

(4) Aca pacpoae PB oepae eo paoc.

(5) o pacpoae PA oepae eo paoc.

Ac oa eo e eoc. Oao, Mop ae PA, PB. oa c (Donald Davies) B pac (William Price) oca, a pooo "epac-a-py" (c. pae 3.1) pooecye aoy cp [435]. C eo (Steve Bellovin) Ma Mepp (Michael Merritt) paccapa co co cp oo poooa [110]. Ec Aca - o ooae, a o - xoc-oep, Mop oe peoec oo, o epe aa poooa c Aco paopa coeee. Cypoae ya a ceeoo oaa opeye o Mop acoeo apca, o peyae Mop oy apo Ac. ae o coe coec c oo aep pooo, oya apo oa.

pooo oo e a, o o epeaa co apo epe Aco peooe, o a po ooae oee ae e apo aoo oepa. o pee ycoe cocoa cp , ae ocaoo [110].

SKID SKID2 SKID3 - o cepe popaece pooo ea, papaoae p o ea RACE RIPE [1305] (c. pae 25.7). O coy MAC (c. pae 2.4) oecee eoacoc peoaa, o Aca o coy o cepe , K. SKID2 ooe oy oaa co ooc Ace. Bo o pooo:

(1) Aca pae cyaoe co, RA. (oyea RIPE opeeec 64-ooe co). Oa ocae o co oy.

(2) o pae cyaoe co, RB. (oyea RIPE opeeec 64-ooe co). O ocae Ace.

RB, HK(RA, RB, B) HK - o MAC. (B oyeax RIPE peaaec y RIPE-MAC, c. pae 18.4.) B - o oa.

(3) Aca paccae HK(RA, RB, B) cpaae peya co aee, oye o oa. Ec p e ya coaa, Aca yeaec o, o oa coeac eo c oo.

SKID3 oeceae coecy poepy ooc Aco oo. a (1) - (3) coaa c poo oo SKID2, a ae oc ceye ec :

(4) Aca ocae oy:

HK(RB, A) A - o Ac.

(5) o paccae HK(RB, A) cpaae peya co aee, oye o Ac. Ec peya coaa, o yeaec o, o oa coeac eo c Aco.

o pooo eyco cp "eoe--cepee". B oe cyae, cpe "eoe- cepee" oe ypoa oy poooy, oop e xo ao-y cepe.

ocmoepeue nouocmu cooeu oa o oyae cooee o Ac, a ey ya, o o cooee oo ? Ec Aca o caa coe cooee, o ce poco. poa oc Ac ocaoa, o oep oy yoo o oc ee cooe.

Heoopy poepy ooc peoca cepe aop. oa o oyae cooe e o Ac, poaoe x o o, o ae, o o cooee o Ac. Ho oe e ae x a. Oao, y oa e oooc ye o oo-o ee. o e oe oaa cooee Tpe y ye eo, o oo opaeo Aco. Tpe oe cea o, o cooee opaeo A co, oo (a a x cepe oy oe e pae ), o y eo e cocoa opee, o e opeo aop cooe.

Ec cooee e poao, Aca oe ae cooa MAC. o ae ye oa oo c cooe, o oy e e poe, o pee cepo popa.

3.3 ocoepee ooc oe a pooo oe yocoepee ooc oe a pee ocoo o epo poe: Aca o xo eoaco oeac cooe, axoc a pax oax ce. a oy Aca o oec cepe o, p o coxpa yepeoc, o o oe ac cooe py c pyo, a e c Mop ? B oce poooo peoaaec, o aoy ooae Tpe ee oe cepe , epe aao pao poooa ce ye axoc y ooaee. Co, coyee x poooax, cee 2-.

Ta. 3-1.

Co, coyee poooax yocoepe ooc oea a A Ac B oa EA poae o, eeo Tpeo Ace EB poae o, eeo Tpeo oy I opo oep K Cyaoe ceacooe co L Bpe TA, TB Me pee RA, RB Cyae ca, pae Aco oo, cooeceo ya c upou pmo pooo "ya c po po" ( Wide-Mouth Frog) [283,284], ooo, ec poce c ep poooo ypae a, oopo coyec acya oep cepep. Aca o e co cepe c Tpeo. coyc oo pacpeee e, a e poa ooaecx cooe. Bo a, coy a cooe, Aca epeae oy ceaco :

(1) Aca oee ey pee, oa cya ceaco , ae pye coaoe c o oee o c Tpeo o ocae eo Tpey ece co co ee.

A, EA(TA, B, K) (2) Tpe pacpoae cooee o Ac. ae o oae oy ey pee, Ac c y a ceaco , pye oyeoe cooee o c oo o. Tpe ocae oy:

EB(TB, B, K) Hao oyee, cea o poooe, ec o, o Aca oaae ocaoo o eeoc eepa xopox ceacox e. Bcoe, o cyae ca eeppoa coce e poco, oo oe opeoac o-y oaeee Ac.

Yahalom B o poooe Ac o e c Tpeo cepe [283,284].

(1) Aca oee coe cyaoe co, opae coaoe cooee oy.

A, RA (2) o oee Ac, ee cyaoe co, coe cyaoe co, pye coaoe cooee o c Tpeo o ocae eo Tpey, oa coe :

B, EB(A, RA, RB) (3) Tpe coae a cooe. epoe ae oa, cya ceaco , cyae ca oa Ac pyec o, o Tpea Ac. Bopoe coco e Ac, c y aoo ceacooo a pyec o, o Tpea oa. Tpe ocae oa coo e Ace:

EA(B, K, RA, RB), EB(A, K) (4) Aca pacpoae epoe cooee, eae K yeaec, o RA coaae co aee, o pae a ae (1). Aca ocae oy a cooe. O ec cooee Tpea, a poaoe o oa. Bopoe - o RB, apoaoe ceaco o.

EB(A, K), EK(RB), (5) o pacpoae epoe cooee, eae K yeaec, o RB coaae c opae a ae (2).

B peyae Aca o yee, o o oac eo py c pyo, a e c pee copoo. Ho oeee coco o, o eo o ep opaaec Tpey, oop oo ocae oo coo ee Ace.

Needham-Schroeder B o poooe, opeeo Poepo Heexo (Roger Needham) Mao peepo (Michael Schroeder) [1159], ae coyc cepa popa Tpe.

(1) Aca ocae Tpey cooee, coepaee ee , oa cyaoe co.

A, B, RA (2) Tpe eeppye cya ceaco . O pye cooee, coepaee cya ceaco Ac, cepe o, o eo oa. ae o pye cyaoe co A c, oa, , poaoe cooee cepe o, o eo Ac. Haoe, o opae poaoe cooee Ace:

EA(RA, B, K, EB(K, A)) (3) Aca pacpoae cooee eae K. Oa yeaec, o RA coaae co aee, o pae Tpey a ae (1). ae oa ocae oy cooee, apoaoe Tpeo o oa.

EB(K, A) (4) o pacpoae cooee eae K. ae o eeppye pyoe cyaoe co, RB. O pye o co o K opae eo Ace.

EK(RB) (5) Aca pacpoae cooee c oo a K. Oa coae co RB-1 pye o co o K. ae oa ocae o cooee opao oy.

EK(RB-1) (6) o pacpoae cooee c oo a K poepe aee RB-1.

Bc a o c RA, RB, RB-1 cy peopae cp c oopo epeae. p ao cocoe cp Mop oe aca cape cooe ocec cooa x p oe oa pooo. pcyce RA a ae (2) yeae Acy, o cooee Tpea ocoepo e e c oopo epeae oa, cooaoo p oo peyx pee poooa. oa Aca yceo pacpye RB epeae oy RB-1 a ae (5), o yeaec, o cooe Ac e ec oopo epeae cooe, cooax p oo peyx pee poooa.

ao popexo oo poooa ec aoc cooax ceacox e. Ec Mop oy ocy capoy K, o coe pep yceoe cpe [461]. Ey yo oo aca co oe Ac oy a ae (3). Toa, e K, o oe a ce a Acy:

(1) Mop ocae oy ceyee cooee:

EB(K, A) (2) o eae K, eeppye RB opae Ace:

EK(RB) (3) Mop epexaae cooee, pacpoae eo c oo a K ocae oy:

EK(RB-1) (4) o yeaec, o cooee "Ac" coco RB-1.

Teep Mop ye o, o o ec "Aca". oee ae pooo, coy e pee, oe pooco oy cp [461,456]. Me pee oac cooe Tpea a ae (2) pyc o oa: EB(K, A, T). Me pee pey aeo oo cce eoo pee, o cao o cee epaa poea.

Ec , o Tpea Ac ye copoepoa, ocec yy paa. Mop coe cooa eo, oye ceacox e oea cooe c oo ( c e-y ee). ae xye, Mop pooa ooe ec ae oce ae a Ac [90].

Heex peep ac cpa poe opoao epc coeo poooa [1160].

x o pooo o cyecy coaae c poooo Oy- Pca (Otway-Rees), oyoao o e yce oo e ypaa.

Otway-Rees o pooo ae coye cepy popa [1224].

(1) Aca coae cooee, cocoee opooo oepa, ee e, e oa cyaoo ca.

Cooee pyec o, o Ac Tpea. Oa ocae o cooee oy ece c opo oepo, ee eo ea:

I, A, B, EA(RA, I, A, B) (2) o coae cooee, cocoee ooo cyaoo ca, opooo oepa, e Ac e oa. Cooee pyec o, o Ac oa. O ocae o cooee Tpey ece poa cooee Ac, op o oepo, ee eo ea:

I, A, B, EA(RA, I, A, B), EB(RB, I, A, B) (3) Tpe eeppye cya ceaco . ae o coae a cooe. Oo, cocoee c y aoo ca Ac ceacooo a, pyec o, o eo Ac. pyoe, coco ee cyaoo ca oa ceacooo a, pyec o, o eo oa. O o pae a x cooe ece c opo oepo oy:

I, EA(RA, K), EB(RB, K) (4) o opae Ace cooee, poaoe ee o, opo oep:

I, EA(RA, K) (5) Aca pacpoae cooee, oya co cyaoe co. Aca yeaec, o p oe poooa o e ec o opae Ace cooee, poaoe ee o, o po oep.

Ec ce cyae ca pa, a opo oep e ec p oe poooa, Aca o yeac ooc py pya oya cepe oea cooe.

Kerberos Kerberos - apa poooa Needham-Schroeder - opoo ocyaec paee 24.5. B aoo poo oe Kerberos Version 5 y Ac oa oe c Tpeo. Aca xoe eeppoa ceaco ceaca c c oo.

(1) Aca ocae Tpey cooee co co ee ee oa:

A, B (2) Tpe coae cooee, cocoee e pee, pe , L, cyaoo ceacooo a e Ac. O pye cooee o, o eo oa. ae o oee ey p e e, pe , ceaco , oa, pye oyeoe cooee o, o e o Ac. Oa poax cooe o opae Ace.

EA(T, L, K, B), EB(T, L, K, A) (3) Aca coae cooee, cocoee ee e e pee, pye eo o K opae oy. Aca ae ocae oy cooee o Tpea, poaoe o oa:

EA(A, T), EB(T, L, K, A) (4) o coae cooee, cocoee e pee c ea, pye eo o K opae Ace:

EK(T+1) o pooo paoae, o oo ec ac aoo ooae cxpopoa c aca Tpea. Ha pae e ocaec cxpoae c ae cepepo pee c ooc ecoo y oapyee oopo epea eee opeeeoo epaa pee.

Neuman-Stubblebine -a eocao cce caoaa cxpoa aco oe apyea. Ec ac cac, po oca poooo oe cooa opeee coco cp [644]. Ec ac o pae oepea ac oyae, Mop oe epexa cooee opae oopo c ooa eo oee, oa ea pee cae eye ece axoe oyae. o coco, a ac cpe c oaee oopo epea, oe pec ep ocec.

o pooo, epe oyoa [820] cpae [1162], aec pooco cp c oaee oopo epea. o o pooo ec yyee Yahalom.

(1) Aca oee coe cyaoe co, opae coaoe cooee oy.

A, RA (2) o oee Ac, ee cyaoe co ey pee, pye coaoe cooee o c Tpeo o ocae eo Tpey, oa coe ooe cyaoe co:

B, RB, EB(A, RA, TB) (3) Tpe eeppye cya ceaco . ae o coae a cooe. epoe ae o a, cyaoe co Ac, cya ceaco , ey pee pyec o, o Tpea Ac. Bopoe coco e Ac, ceacooo a, e pee pyec o, o Tpea oa. Tpe ocae oa cooe Ace ece co cya co oa:

EA(B, RA, K, TB), EB(A, K, TB), RB (4) Aca pacpoae cooee, apoaoe ee o, eae K yeaec, o RA coa ae co aee, opae a ae (1). Aca ocae oy a cooe. O ec c o oee Tpea, apoaoe o oa. Bopoe - o RB, apoaoe ceaco o.

EB(A, K), EK(RB), (5) o pacpoae cooee, apoaoe eo o, eae K yeaec, o ae TB RB e e, o opaee a ae (2).

Ec oa cyax ca ea pee coaa, Aca o yeac ooc y pya oya cepe . Cxpoa aco e peyec, a a ea pee opeeec oo o aca oa, oo o poepe coay ey pee.

oo poooa ec ee oo oeoe coco - Aca oe cooa oyeoe o Tpea c o oee oceye poep ooc oa peeax eoopoo pee. peoo, o Aca o o pee e pooo, poe aep ceac c. Aca o oy oopo poep ooc py pya, e opaac Tpey.

(1) Aca ocae oy cooee, pcaoe e Tpeo a ae (3) ooe cyaoe co.

EB(A, K, TB), R' A (2) o ocae Ace pyoe ooe cyaoe co cyaoe co, pcaoe Aco, py x c e aco o c.

R', EK(R' ) B A (3) Aca ocae oy eo ooe cyaoe co, py eo ceaco o c.

EK(R' ) B Hoe cyae ca aa o cp c oopo epeae.

DASS pooo Pacpeeeo cya eoacoc poep ooc ( Distributed Authentication Secu rity Service, DASS), coae Digital E uipment Corporation, ae oecea ooy poepy o oc oe a [604, 1519, 1518]. B oe o peyeo poooa DASS coye a p opa c op a, a cepy popa. y Ac, y oa ec co ap . Tpe ocae o x opx e.

(1) Aca ocae Tpey cooee, cocoee e oa.

B (2) Tpe ocae Ace op oa, KB, oca ap o Tpea, T. ocaoe cooee coep oa.

ST(B, KB) (3) Aca poepe oc Tpea, yeac, o oa eceo oya op oa. Oa eeppye cya ceaco , K, cyay apy e op/ap, Kp. Oa pye ey pee o K, a ae ocae pe , L, coe co ap o, KA. Haoe, oa apoae K op o oa ocae eo c oo Kp. Bce o oa opae oy.

EK(TA), SK (L, A, Kp), SK ( EK (K)) A p B (4) o ocae Tpey (o oe pyo Tpe) cooee, cocoee e Ac.

A (5) Tpe ocae oy op Ac, KA, oca ap o Tpea. ocaoe cooee coep Ac.

ST(A, KA) (6) o poepe oc Tpea, yeac, o o eceo oya op Ac. ae o poepe oc Ac eae Kp. o coye co ap , ea K. ae o pacpoae TA, poep, o o cooee - eyee.

(7) Ec peyec ooa poepa ooc, o pye oy ey pee o K oca e ee Ace.

EK(TB) (8) Aca pacpoae TB o K, poep, o o cooee - eyee.

SPX, poy DEC, ocoa a DASS. ooey opa oo a [34].

Denning-Sacco B o poooe ae coyec popa c op a [461]. Tpe ee ay ax, xpay ope cex ooaee.

(1) Aca ocae Tpey cooee, cocoee ee e e oa.

A, B (2) Tpe ocae Ace op oa, KB, oca ap o Tpea, T. Tpe ae ocae Ace ee coce op , KA, oca ap o Tpea.

ST(B, KB), ST(A, KA) (3) Aca ocae oy cya ceaco ey pee, oca x co ap o apoa op o oa, ece c oo oca a.

EB(SA(K, TA)), ST(A, KA), ST(B, KB) (4) o pacpoae cooee Ac c oo coeo apoo a poepe oc Ac c oo ee opoo a. O ae yeaec, o ea pee paa.

C oo oea Aca o oy K oy poec eoac ceac c. o paco, o ec oa ooc - o pooo c Aco, o coe a ce a Acy [5]. Cope:

(1) o ocae Tpey coe po.

B, C (2) Tpe ocae oy ocae ope oa po.

ST(B, KB), ST(C, KC) (3) o ocae po oca cya ceaco ey pee, paee oyee o Ac, apoa x op o po, ece c oepee Ac oepee po.

EC(SA(K, TA)), ST(A, KA), ST(C, KC) (4) po pacpoae cooee Ac c oo coeo apoo a poepe oc A c c oo ee opoo a. O ae yeaec, o ea pee paa.

Teep po cae, o oa coeac c Aco, o yceo oypa ee. eceo, o coe ypa oo ooae ce, oa e aoc cpo ec e pee. Ho o eo oo c pa. poco cae ea poaoe cooee a ae (3) :

EB(SA(A, B, K, TA)), ST(A, KA), ST(B, KB) Teep o e coe oopo oca po capoe cooee, ooy o oo o peaaeo ceaca c ey Aco oo.

Woo-Lam B o poooe ae coyec popa c op a [1610, 1611]:

(1) Aca ocae Tpey cooee, cocoee ee e e oa.

A, B (2) Tpe ocae Ace op oa, KB, oca ap o Tpea, T.

ST(KB) (3) Aca poepe oc Tpea. ae oa ocae oy coe cyaoe co, poaoe o p o oa.

A, EB(RB) (4) o ocae Tpey coe , Ac cyaoe co Ac, poaoe op o Tpea, KT.

A, B, EK (RA) T (5) Tpe ocae oy op Ac, KA, oca ap o Tpea. O ae o cae oy cyaoe co Ac, cya ceaco , ea Ac oa, oca ce o ap o Tpea apoa op o oa.

ST(KA), EK (ST (RA, , A, B)) B (6) o poepe oc Tpea. ae o ocae Ace opy ac cooe Tpea, oyeoo a ae (5), ooe cyaoe co, apoa ce op o Ac.

EK (ST (RA, , A, B), RB) A (7) Aca poepe oc Tpea coe cyaoe co. ae oa ocae oy opoe cyaoe c o, poaoe ceaco o.

E(RB) (8) o pacpoae coe cyaoe co poepe, o oo e eoc.

pyue npomoo B epaype ocao oeco poooo. pooo X.509 paccapac paee 24.9, Kryp toKnight - paee 24.6, a poa oe a (Encrypted Key Exchange) - paee 22.5.

py o poooo c op a ec Kuperee [694]. Beec paoa a poooa, coy a - acyae oep y ce, oope epepo pooeaeo ep e a ocoepe e pee [783].

Bo peex poooo, a ex, oope cpac, a aex, oo e p a x ypoo:

Moe pooo ep eyay, a a x papao ac co y. O o poa pooo, ypa ae ee - ea, cyae ca .. - ac cea pooo a oo oee popa [43, 44].

Oa - a aa oya - co ac o ceax peooe. pep: ae ocoepoo pee ooe a peaoa oe e, eooe po o cyae.

Bpae pooo ac o apxeyp coyex cpec c. Xoe p o a paep cooe x oeco? Moy copoa aoecoa a c a py x oe ye opae?

eo ooe opoc pe coa opax eoo aaa poooo.

3.4 opa aa poooo poep ooc oea a poea ee eoacoo ceacooo a ap oepo ( e) ce acoo yaeaa, o caa po ox cceoa. Heoope cceoa aac papaoe poooo, oox paccapae paeax 3.1, 3.2 3.3. o, co oepe, peo oe oee ao epeco aa: opaoy aay poooo poep ooc oea a. oa popex poooax, ayxc oe ae, oapyac cyc oo e o ce x papao, papaoa opeoac cpeca, ooe cpay e poep eoacoc poooa. Xo oa ac oo cpyeap pea oee o popaec po o oa, ocooe ae yeoc poepe ooc oey a. Cyecye epe ocox oxoa aay popaecx poooo [1045]:

1. Moepoae poepa pao poooa c cooae o oca cpec poep, e papaoax ceao aaa popaecx poooo.

2. Coae cepx cce, oox ocpyopy poooa papaaa cceoa pae ceap.

3. Bpaoa peoa ceecy poooo, coy ey oy aaa o "ae" "oepe".

4. Papaoa opax eoo, ocoax a ac coc popaecx cce ae paeco e.

ooe ocae x epex oxoo cax c cceoa xo a pa ao .

Xopoee eee y ey ao [1047, 1355], e copac ocyc oo ocox opoco.

ep oxoo aec oaa paoc poooa, paccapa eo a oy oe p y popay. P cceoaee peca pooo a oe aoa [1449, 1565], pye co y pacpe eoo cce peaa epoo opa [822], a pe aaa poooo c oy oca [1566]. Oao, oaaeco paoc o e ec oaaeco eoacoc, o oxo oepe eyay p aae ox "px" poooo. xo eo pee e oaay poo yaoc, c poco oypoc peeo oxoo pao o oac e peopepoa.

Bo opo oxoe opeee oo, oe pooo epe eeaeoe cocoe (apep, oep a), coyc cepe cce. Xo o oxo ae ye peya p oce "p", o e apapye eoacoc e peocae eo papao cp. O xopo poep oo, coep pooo opey "py", o p cocoe oapy eece "p" poooe.

pep aoo oxoa oo a [987,1521], a [1092] ocyaec cepa ccea, papaoaa ape CA aaa Ceoaee ( Interrogator).

Tpe oxo opao oypee. O epe ee Mao ppoyo ( Michael Burrows), Map o A (Martin Abadi) Poepo Heexo. O papaoa opay oecy oe a a a a oep, aay AH-oo [283, 284]. AH-oa ec aoee poo pacp o cpaea p aae poooo poep ooc. Oa paccapae ooc a y o e ococ o, coy oece paa ocea coco x apyo a poe ceo poooa. Xo peoe pae apa pacpe, oco papaoo p o ooo o cx op opaac opao paoe.

AH-oa e peocae oaaeco eoacoc, oa oe oo paccya o poepe o oc. Oa ec poco, poeo oo, eo pee oeo p oce "p".

Bo eoope peoe AH-o:

Aca cae X. (Aca ecye, a ec X oc co.) Aca X. (o-o oca cooee, coepaee X, Ace, oopa oe poa coa epea X - oo o oce eppoa.) Aca caaa X. (B eoop oe pee Aca ocaa cooee, oopoe coep peoee X. He ec o, a ao o ocao cooee, o oo ocao ee eyeo oe poooa. eco, o Aca caa X, oa oopa X.) X oo. (X oa e o ocao cooe o eyeo oe poooa.) a aee. AH-oa ae peocae paa paccye o oep poooy. oaa eca eo-o poooe oea a ae-o opoc oec peoe o poooe oo pe paa. Hapep, o pa ec pao o ae cooe :

EC Aca cae, o y Ac oa o cepe , K, Aca X, poaoe K, Aca e poaa X c oo K, TO Aca cae, o o caa X.

py ec pao oepe e pee :

EC Aca cae, o X oo caao oo eao, , o o X oa-o caa X, TO Aca cae, o o cae X.

AH-aa ec a epe aa :

(1) peopaye pooo eao ope, coy ocae e peoe.

(2) oae ce peooe o aao coco poooa.

(3) pcoee oece opy peoe, oya yepe o coco cce oce aoo peoe.

(4) pee oece ocya yepe peooe, o pacp cocoe oep yaco poooa.

Aop AH-o "paccapa eapoae pooo a oee ce oe oca, e paoe, aee epaype..." [283, 284]. pye cceoae e a oc oepa o ece pe, a a p o pea pooo oe cae [1161, 1612]. aee co p opae [221, 1557]. P po aec oaa, o AH-oa oe oy oeo e pae xapaepc poooo [1161] - c. opoo [285, 1509] - o AH-oa aaec oo oepe, a e eoacoc [1509]. opooe ocyee peeo [1488, 706, 1002].

Hecop a y py AH-oa oca opeeex ycexo. E yaoc oapy "p" e cox poooax, a Needham-Schroeder pa epoy epc poooa CCITT X.509 [303].

Oa oapya ooc o ox poooax, a Yahalom, Needham-Schroeder Kerberos. Bo ox oyoax paoax AH-oa coyec ae pee o eoacoc oca e x poooo [40, 1162, 73].

oyoa pye oece cce, eoope x papaaac a pacpe AH o [645, 586, 1556, 828], a pye ocoac a AH-oe cpae oyx caoce [1488, 1002]. x aoee yceo oaaac CNY [645], xo y ee ec p o [40]. B [292,474] AH-oe c epee ycexo oae epooce oep. pye opae o o ca [156, 798,288]. [1514] aec oe ep ecox o. A [1124, 1511] pecae o , oopx oep ec co peee.

eep oxo aay popaecx poooo peaae oepoa pooo a ae paecy ccey, pa cocoe a yaco o poooe ae poaapoa oc oc opeeex coco. o oxo oa e pe coo a, a opaa oa, o cocoe e eec. O epe cooa Mao Meppo [1076], oop oaa, o aaa popaecx poooo oo cooa aepaecy oe. pye oxo pacco pe [473, 1508, 1530, 1531, 1532, 1510, 1612].

Aaaop poooo cceoaeco aopaop BMC ( Navy Research Laboratory, NRL), ooo, ec aoee yce peee x eoo [1512, 823, 1046, 1513]. O cooa oc a a ox, a ecx "p" o oece poooo [1044, 1045, 1047]. Aaaop poooo o peee ceye ec:

p (o, Aca, M, N). (o pae cooee M a peee o Ac eee oa o o paya oa N.) a (Ea, M). (Ea yae M.) oca (Aca, o, Q, M). (Aca ocae M oy oe a apoc, Q.) apoc (o, Aca, Q, N). (o ocae Q Ace eee oaoo paya oa N.) coy ec, oo aa peoa. Hapep:

Ec o p cooee M o Ac ao-o poe oe pee, o Ea e ae M a o-o poe oe pee.

Ec o p cooee M o Ac eee oaoo paya oa N, o Aca ocaa M oy oe a apoc oa oao paye oa N.

aaa Aaaopo poooo NRL cceye pooo oe oca c oo p e ex ocpy. ae oc epe a aaa : opeeee pa epexoa ecx y a co, ocae oepa, oox ooc ecx, eecx yaco, ocae ao x oo poooa ocae pa peopaoa. Cc ceo oo o, o oaa, o a pooo yoeope eoxo peoa. cooae cpyeo, oox Aaa o py poooo NRL, oe oo pec coa poooa, oop oocoao pa eoac.

Xo opae eo ocoo pec ye cyecy poooa, ceo ec ee cooa x p poepoa poooo. P peapex ao o apae cea [711]. o e aec cea aaaop poooo NRL [1512, 222, 1513].

peee opax eoo popaec poooa pecae coo aeceo oy e, pyo opcoa, ey oe pec ee peaa. C o o pe cae eo a ec poecc opaa.

3.5 popa c eco op a Oa popa c op a coye a a. Cooee, apoaoe o o, oe pacpoao py. Oo o ec ap, a pyo - op.

yc, o axoc y Ac, a pyo - y oa. M xo peaoa ceyy cxey: Aca o e apoa cooee a, o oo o coe pacpoa eo, a o oe apoa coo e e a, o oo Aca coe po a eo.

a oe a ooe oo oo ( Conn Boyd) [217]. pecae cee apa popa c op a, coy p a : KA, KB KC, pacpeeee oopx oaao 1-.

Aca oe apoa cooee o KA a, o e oe pacpoa eo, coy KB Kc. To e caoe, coopc, oy cea o po. o oe apoa cooee a, o p coe poec eo a po coe apoa cooee a, o eo coe poec . oe apoa cooee o KA a, o e coe poec eo, o KB a, o eo coe poec p, oo a, KA KB, a, o cooee coe poec po. Aaoo, e oe apoa cooee a, o Aca, , p coe poec eo. Bce ooe o a oaa , pyx e cyecye.

Ta. 3-2.

Pacpeeee e pexeo ccee.

Aca KA o KB po KC KA KB e KB Kc pa KC KA Taa cxea oe pacpea a n e. Ec poa cooe coyec aaoe ooeco e, o eppoa cooe opeyc ocaec .

upooeamea nepeaa cooeu pecae, o eoe oepa ao 100 ax ax aeo. B xoe e oooc oc a cooe pya aeo, o e aee apaee coca py. Moo o poa cooee o eo aoo oppecoea, o pacpee cex oox oa aeo. peaa epoo cocoa opeyec oeco cooe, opoo - oeco e.

popa c eco a ooe pe y aay aoo poe. M ye cooa pex aeo: Acy, oa po. B ae Ace KA KB, oy - KB KC, po - KC KA. Teep coee oop c y ooeco aeo. Ec xoe, o cooee oa p o a oo Aca, apye eo o KC. oa Aca oy cooee, oa pacpye eo, oc e oaeo coy KA KB. Ec xoe oca cooee oo oy, apye eo o KA, a cooee po - o KB. Ec xoe, o ocaoe cooee o poa Aca o, apye eo a KA KC.

pex aeo o e co eae, o 100 peyeco ocaoo oyo. ya e cooe oaa cooae oeoo a aoo aea (ceo 100 e) aoo cooe. epeaa cooe ce oo ooeca oaae cooae 2 -2 pax e (ce cya cooe ce aea oy x). cxe, coy popa c eco op a, yo oo oo poaoe cooee co pax e.

Heocao o cxe ec o, o a ae pec pooeaeo epeaa, aoe oo e co aeo oe a cooee, ae aoy x x pec epepa ce ooe oa e ocax oxoe. ae oo epecee e oyaee oe eca ye. poe oo, aoy aey pec xpa eae oe opa o ax, o pae epe p poeo peaa o cxe.

Cyecy pye coco pooeaeo epea, p x ooe ea ocao poe. coco ocyac paee 22.7.

Ta. 3-3.

poae cooe pexeo ccee.

pyec a oo pacpoao a KA KB Kc KB KA KC KC KA KB KA KB KC KA KC KB KB KcKA 3.6 Paeee cepea Boopae, o ope o, cepxy, cepxcay coy yy coyc ayp e po, oop ee eycee, e y ax oypeo. o oe ao, xoe coxpa opeee cepee. Too ca ae paoa oee coo o coca peeo, o py o-o x oye oypea ? Cepe pay, eoo oo a apae ye ea aypep c a e eyc coyco, a a.

peaaea cxea aaec paeee cepea. Ec coco cooee pae eo a ac [551]. aa ac caa o cee eo e a, o coe x - oye cooee. Ec o pee, y aoo paoa axoc oo eo ac, o copac ce ece a cyae c o y cea coyc. Ec o-y paoo yoc, pxa c coo co ac peea, pacpa opa o cee ye ecoeo.

o pocee cxee cooee ec ey y . Bo pooo, coy oop Tpe e cooee ey Aco oo :

(1) Tpe eeppye cpoy cyax o, R, ao e , o cooee, M.

(2) Tpe oe "caee " ( XOR) a M R, coaa S.

R M = S (3) Tpe epeae Ace R, a oy - S.

o oy cooee, Ace oy yo o eceoe ece:

(4) Aca o o oepa a ec y x ac, occaaa cooee.

R S = M o eo p pao oe acoo eoace. aa ac oeoc acoo e c ccea. o cyeceo, Tpe pye cooee oopao ooo ae poec ooy eoey, a oo - pyoy. Oopaoe oo, oaae acoo eoacoc, ocyac paee 1.5. Hae cee cpeca e coy occao cooee oo o oo eo ac.

y cxey eo pacp a oee co e. o pae cooee ey oee e y , oe oepa XOR c o co cpo cyax o. B ceye pepe Tpe e cooee a epe ac:

(1) Tpe eeppye p cpo cyax o, R, S T, ao e , o cooee, M.

(2) Tpe oe "caee " ( XOR) a M coa pe cpoa, coaa U.

M R S T = U (3) Tpe epeae Ace R, oy - S, po - T, a y - U.

Bece Aca, o, po oy occao cooee :

(4) Aca, o, po copac ece c:

R S T U = M o appa pooo. Tpe oaae acoo ac oe ea ce, o o xoe. O o e paa eyxy yepa, o o acoe ac cepeo opa, o e coe o po e p, oa, copac ece, yac poooa e opoy poa co. O oe a ac cepea Ace, oy, po y oe a ce, o oo Aca, po y occ a oe cepea, acpe p o oa. Ho o e ec poeo, a a e cepe pa e Tpey.

Oao, oa poea y oo poooa cyecye. Ec a ace ye oepa, a Tpea e y e ooc, poae ce cooee. Ec po, oaa ac peea coyca, epee paoa o ypey, oca co ac cepea y ce, a, oca e oeo. Oa e coe occao pee, o e coy, copac, Aca, o . Ee ac ae pa occaoe cooe, a a pya. Bce, o eco Ace, oy y - o a cooe, eo oe. o co, a a y R, S, T, U M oaoa a, ceoaeo, aoy yaco eca a M. oe, co oee M ec e oo cce oo coa, a oepaec oepa XOR co cya ea .

3.7 Coecoe cooae cepea B oe popay ayca epo pae xoe yepe, o ao cx ooy e coe a yc. B xoe yepe, o a cxa e coy a yc. B xoe, o yc pooe oo, ec e ee pex oepo yy cxa.

a poea eo oe peea. Ceae exaecoe ycpoco opo ayca. Bae aoy oepo opeye, o o ee epe p oepa ca co coo ecye ea, pee e papee opa oo, oo pae a o eee. (Ec eceo oyeec, ceae ea oae py o pya opeye, o oep ca oopeeo - e e xoe , o oep, pa eocay apy e, co cee Toeo.) Moo cea ee coee. yc oo eepa y ape ooo papeeo ayc paey, o e c eepa a po o, o ayc paey e pao oo ooo. Ceae opo oe ycpoco c a. Bae eepay p a, a ooa o ooy. eepa ece c y ooa ooo coy ayc paey. Oao eepa ooy, epe ooa e coy oo cea.

oee coa cxea coecoo cooa, aaea opooo cxeo, oe pe aa , oee coe - aeaec. Ha ee pocee ypoe oee oe cooee (cepe pee, o ayca, a cco paeo ..) pae eo a n ace, aaex e o, a, o o m x oo occao cooee. oee oo, o aaec (m,n)-opooo cxeo.

coy (3,4)-opooy cxey, Tpe oe pae co cepe pee ey Aco, oo, po o a, o e poe x oy co co e ece occao cooee. Ec po oyce, o Aca, o coy occao cooee. Ec o oa o aoyc, o cooee coy occao Aca, po . Ho ec o oa o aoyc, a po oyce, o Aca caocoeo e coy occao cooee.

Booe, opooe cxe oy ee oee . Moo ooepoa e ceap co e coo cooa, oope oo coee oopa. Moo pae cooee ey ae a a, o eo occaoe, ec e oo c peeo aa, opeyec ce eoe c epoo aa co opoo, poo cyae ocaoo pecae peeo aa ece c pe eoea c epoo aa y co opoo. Ec e ec o-o c eepoo aa, o occaoe cooe ocaoo oo eoea ooo c peeo aa oo eoea ece c y c epoo aa ooo co opoo. Ec e... y yo e.

a e a eaco ya A apo [1414] ope (George Blakley) [182] eco a yea yco Coco ( Gus Simmons) [1466]. Moeco pax aopo ocy aec paee 23.2.

Coecmoe ucnooaue c oeuau Cyecye oeco cocoo oay opooy cxey. Bo oo ecoo x. Ceap 1 : o o Aca, o po c opoao yepe e-o yoo o ee. Oa o oya aopoaoe cooee o peea : "ayc pae. M copaec cepe c a e e c e cceoa poa oac epox cee ". Aca, o po opa co e, o po o cyaoe co. O a cao ee ac e xoe, o pae aye. ocoy po e ea paoe e, cepea opa, oopy o xoe oy, oaaac epao. Pae ocac cox axax. caoe oxoe, o e ae oey. ae oec Aca o e coy oaa, o e po epaa.

Ceap 2: oo Aca o c yepe ece c Mop. Mop oo ae ce a ooa. O peea pxo o e caoe cooee ce opa co e. "Xa-xa-xa!" p Mop. " oea o cooee peea. Teep a oe ax o." O yeae epx o ec e ceae pee, e eo yce oa.

Ceap 3: oo Aca, o po c yepe ece c Mop, oop coa aacpo ac. (oe, y Mop e pao e.) O peea pxo o e caoe cooee ce o pa co e. Mop opae co e, oo yca ce ocae. Ta a occaoe cepea peyec oo p e, o oe cpo coa pay e op ee. a, o e oo aoy cepe, o o e oaac, o o e ec ac o cce. Heoope pooo, o ope oo opoc c oo oea, paccapac paee 23.2.

Coecmoe ucnooaue cepema e Tpema a xoe, o eo oa o op poe oepo, e co . o a a (3,5)-opooa cxea, o c oo ooc. Ho e ae cepea eo. Tpea, oope e cepe a ace, e. Cyecy pooo, coy oope oepo oy coa cepe oe eo a ac a, o o oepo e yae cepea, oa o e ye occaoe. B o e e paccapa pooo, opooc c. [756].

Coecmoe ucnooaue cepema e pacpmu oe x cxe ec oa poea. oa yac poooa copac, o occao cepe, o opa co ac. Ho pacpe cepea e cea eaeo. Ec paee cepe ec ap o (apep, poo oc), o a n yaco oe o acy oc oyea. oce n-o aco oc oye oaaec oca coeco coye ap o, a o yaco e oe ya coepa ac, coyeo py yaco. Cc o, o oee oopo cooa cepe, pao c a e oaoc ae ocpe . aeee pae a e oya paoax o ecea (Yvo Desmedt) epa pee (Yair Frankel) [483, 484].

omepaeoe coecmoe ucnooaue cepema Tpe epeae Ace, oy, po y ac cepea (, o pae epe, ae, o o o eae). Ece coco yec, o x ac pa - o oac occao cepe. Moe Tpe oca oy oey ac, ac oa cyao copac p epeae o c. oepaeoe coecoe cooae cepea ooe aoy yaco o yec, o x ac paa, e eoxooc occaaa cepe [558, 1235].

Cxe coecmoo ucnooau cepema c epau npeoxpaeu Cepe ec cpe 50 eoe a, o e 10 o copac ece occao cepe. o epyo. Ho, oe peaoa y e cxey coecoo cooa cepea, oa peoae, o 20 eoe o copac ece noeam oca, eaco o x ca, occao cepe? Oaaec, o a [153].

Maeaa ocaoo coa, o ocoa e o, o a oyae e ac : ac "a" ac "e". oa pxo pe occao cepe, peoca oy cox ace. ay opeo ac o oo, xo o, o cepe pacp. Ec peocaeo m oe oe "a" e e e n oe "e", o cepe oe occaoe. B poo cyae, o eooo.

oeo e, eo e eae ocaooy cy e "a" oo yoo, yec o e "e" (ec o a, o ec o) occao cepe. Ho p yco, o ce epea co ac epa oep a cxea ye paoa.

Coecmoe ucnooaue cepema c epuaue u cnuca B coa ccey coecoo cooa cepea eep xoe acpe ooo aee ac cepea. B o coa oy cxey, c oo ecacoo, o pe oae. o oo cce cyecy coco opoa. O oo apoa oy cxey coecoo cooa cepea cpay e oce oo, a epeca oep ooy yaco [1004].

3.8 popaeca aa a ax aa ax eo opaa - o eca aa e. C oo copo xoe peoca e ocy ce ea, ea, o o oac py c pyo, oeac e ec py c pyo yeppoa. C pyo copo, ec yce ay ay ax oo yoo, cee oaeo o a y py aoex cpaxox aeo oyx ocao coo xaa o oe.

popa oe oe y poey. Moo apoa ay ax a, o oy apec ooo eoea o eo, a e cco oox apeco cex eo - pyo.

Cxea, peoea [550, 549], poea. Bepe ooapaey x-y cep aop poa. ao ac ae ax a o. ec oe ec a e a, eo oo opaaaec ooapaeo x-ye. oe ax, oopo xpac ooe apec ea, pyec c oo coyeo aece a a. Ec e aee a , oa e coee pacpoa oe ax.

oc o opeo a poc. Caaa xpyec a, oec oc ae x y ae ax. Hae ecox coae oaae, o aa ax coep opa o ecox x c ao ae.

B [550] aop coy y ccey a coap 6000 cacx co. O cooa o o, o oep pooeoc, aa poae, aa. B oee coo cxee [549] coy ec oc o eco eca, o e ocaec o e. Ocoa poea, caa c o cceo, coco o, o e coee a eoea, e a, a ec eo a. Moo opooa e coo apao, oa e ye ae pa, o eyoo epepa cex, a aac a "Sch" p oce "Schneier."

a aa ecoepea. Oe ao cpaxoo ae occao ay ax eo opaa c oo pyoo oa, epepa ce ooe a. Ec y eo ec eeoa aa ax, o oe cooa ec e cco a. o epeeae oepo oe a ecoo ee, o eo ye ceao. Te e eee aa cxea yco paoy oa ( pe poae co eyx o oe "yco" cpo pepaaec "ceae co opoo". pyo oxo, peoe [185], peaae apa cacy o poa a.

aa poeyoe pooo 4.1 Cy eo pee Bo ox cyax yo yec, o opeee oye ye cyecoa opeee oe pee. pepo ec cop o aopcx paax aee. eo pae copoa, oopa peca oee pa o copo pao. yae oye aepc oapyca xpac y pco. Ec oae cop, oapyc pc ceecye, o co cyecoao opeee oe pee.

B poo pe ce opao coee. He cocoo oapy pa oe epooo oye a. Eo oo ecoeo opoa e, e oca ax ceo. Hecoo e pe co a oepoo aa. Ho e oe y a oye c oo yepeoc caa: "a, o oye coa pae 4 op 1952 oa " o poeo aac Cap Xaep ( Stuart Haber) B. Co Copea (W. Scott Stornetta) Bellcore [682, 683, 92]. opeoac pooo pox eo pee co cey coca :

Mea pee oa cyecoa caa o cee, eac o eco cpe, coyeo ee xpae.

oo eooo ao e eoo a oyea.

oo eooo aa oyea ey pee, ooo o eyeo.

Peeue c nocpeuo B o poooe yacy Tpe, oaa aeo cyo eo pee, Aca, oopa xoe aa ey pee oyea.

(1) Aca epeae o oyea Tpey.

(2) Tpe acae pe ay oye oyea, oca y ce o eoacoo xpae.

Teep, ec o-y ycoc aeo Aco pee coa oyea, o Ace poco yo opac Tpey. O peoca co o oyea oep, o o oy oye yaa e ac.

o pooo paoae, o ec p oex poe. Bo epx, eooo coxpa ay - Aca oa peoca o oyea Tpey. o-o, ocya c, coe poec o y e. Oa oe apoa oye p epeae, o e o oe ye xpac ae ax Tpe a. Hacoo a aa eoaca?

Bo opx, cao ae ax pec oe oo. Be yy peoa poyco c o cooc c.

Tpe poea caa c oo oa. O p epeae epoaa oa, opaa e-o epao oepe Tpea oy ooc cec a e aee Ac o ee pee.

eepx, oe oaac eoo a aoo ecoo Tpea ee cy eo pee. Moe , Aca coye ey pee oa. Ho e ocao Acy oa o coopa oe oyea e peee, oopoe yo.

yeoe peeue c nocpeuo oco x poe eo cac p cooa ooapaeo x-y p o x oce:

(1) Aca ce aee ooapaeo x-y oyea.

(2) Aca epeae o aee Tpey.

(3) Tpe oae pe ay oye oo ae ae ocae peya poo o c.

(4) Tpe opae ocaoe aee x-y ece c eo pee Ace.

o peae ce poe, poe ocee. Ace oe e yo ecooc o pacp coepa oyea, cooae ae x-y oe ocaoo. Tpey oe e yo xpa o oyeo ( ae ae x-y), ooy cac poe eoacoc oea coxpaex ax (oe, y ooapaex x-y e a ). Aca oe eeeo poep o cay ey pee, oyey a ae (4), eeeo oapy e o epea. Ec eo ocaec poeo ocaec coop Ac Tpea c e coa oeo e pee.

pomoo cu O ye pee o poe ec ycaoee c ey eo pee Ac e a pee, paee coa Tpeo. Beca epoo, o e coa e Ac, a pyx e. Ta a opo, oopo Tpe oyae pae apoc o eax pee e oe ece apaee, epe eo pee Ac oa a oc pya ea pee. a a apoc, pe oe, ca c eo pee Ac, o ee ea oa a oc pae. e e coepa ey coo apoc Ac a yo ce.

Ec A - o Ac, Hn - aee x-y, oopoo Aca xoe acpoa pe, a Tn-1 peya ea pee, o pooo ee cey :

(1) Aca ocae Tpey Hn A.

(2) Tpe ocae Ace opao:

Tn=SK(n,A,Hn,Tn,In-1,Hn-1,Tn-1,Ln) e coco Ln - o opa o ceye xpoao c:

Ln =H(In-1,Hn-1,Tn-1,Ln-1) SK yaae, o cooee ocao op o Tpea. Ac opeee ee a op a e apoca. apaep n yaae oceoaeoc apoco. o n-a ea pee, oopy coa Tpe. apaep Tn - o pe. ooeo coyec opa o eaope, op aoo ae x-y, pee xpoao ea peyeo oyea, oeeoo Tpeo.

(3) oa Tpe oeae cey oye, o ocae Ace eaop opae oo o y ea: In-1.

Ec o-o ocapae ey pee Ac, e ao oo cac c opae peyeo ceyeo oyeo: In-1 In+1. Ec x ceeco o opoco, oo opac aopa o y eo In-1 In+1 .. o oe oaa, o eo oye oee oce ooo oyea epe py.

o pooo eae Ace Tpey ooopc coa oye c peee coa, o o pee coa acoeo oyea. Tpe e oe e ay oyea Ac a oee pa, a a oo yo a apaee, aoo oyea epe a ye pocac ea pee.

ae ec o coe oea pey oye, ey pec a, ao oye peecoa peyey a aee. Tpe e oe e ay oyea Ac a oee o, ooy o ea pee oa caea epe eo pee oyea, aepeoo cpay e oce aoo, a o oye ye cyecye. Ece oo coco coa y cxey - o ec y eoy oyeo epe oce oyea Ac, ocaoo y, o epe oo, o poepe ey pee oyea Ac.

Pacnpeee npomoo ypa, e pee epc. Mey oeo oyea eo ocapae oe poo ooe, o oeae Ace oy o e pee In-1. a poea oe aco ca cao eo pee peyx 10 eoe ey Ac oceye epeae Ace e cey x 10 eoe. Ta y Ac oc opao oe oooce a e, ce ee xpax co e pee.

Paa y e, cey pooo ooe ooc e Tpea:

(1) coy aece xoa Hn, Aca eeppye oceoaeoc cyax ce c oo p opaec eoacoo eepaopa cyax ce.

V1, V2, V3,... Vk (2) Aca paccapae aoe x ce a eaop, I, pyoo eoea ocae aoy x e Hn.

(3) a x oae pe ay ae x-y, ocae peya opae eo opao Ace.

(4) Aca copae xpa ce oc a ey pee.

popaec eoac eepaop cyax ce, coye a ae (1), ooe Ace ea peaepeoo opa oppypoax I aece ceee. ae ec oa ceae poce e ee coe oyee, ac coa aop oppypoax I, ee ac oc oo pe epeo a. X-y paopye ae, Aca e oe a x oecoa.

o pooo paoae, ooy o oea ey pee Aca oe, oo ooopc o c o pyece co ce k . Ta a a ae (1) oa paa x cya opao, epooc oo oe a. e oppypoaee oeco, e oe oo co k.

poe oo, oe cooac eoop exa, ya o, o p e e coy op e opa ey pee. Bce, o yo pao e pee - o eoopoe ooeco k.

ea ac o peaa.

aea paoma aee yye poooo e pee oca [92]. Aop coy oe epe yee oeca eo pee, acx o ao e, yea epooc coa eo ax eo pee. O ae peoey yoa cco ae x-y a poe e eoopo oeocyo coe, apep aee. o paoae a opaa ae x y cya pacpeeeo poooe. eceo, ea pee oec ao oepe ocpeco H-op Tac c 1992 oa.

pooo eo pee aaeoa [684, 685, 686]. ae paea oepe oa Bellcore, aao Surety Technologies, oopa poae Ccey pooo oapaa, oepay pooo. B epo epc e oca apoc o "aepe" a epa ooppy ep.

Cey eoe Mepa o cooa x-y ocpoe epee [1066], cepep cpo epeo ae x-y, c oopoo peca coo ce apoc, oyee eee ao cey , ocae aoy aopy apoca cco ae x-y, oca y o eo ca o o p . eca ac popaoo oecee coxpae o cco oe a "cepa" po o o oapaa oo aa, oop ceppoa. oceoaeoc ope x epee op a ye "ac yepcaoo oepe" ( "Universal Validation Record"), oopa ye ocya e poo e o ox xpaax ( ae yea a CD-ROM). eca ac ae coep y "oepe", ooy ooae poep, aepea eo eya opa aa (apoc xpaa ope cooecyeo epea cpa eo co aee x-y, cooec y opao pacca aa, cepao ). a aee opae opaaec Surety Technologies, 1 Main St., Chatham, NJ, 07928;

(201) 701-0600;

Fax: (201) 701-0601.

4.2 ocoae aa Aca o apecoa opae py, o - ycy, a oa - ecy. oep, apa e, papeae Ace oy oeac cooe, o o e papeae poa cooe. oep cae, o o apy eco, ooy o xoe a ce, o o y.

oep aeec ae cye oay Acy oa. O xoe, o o x oca poe ooe cooee aco. Aca o pc c pco oooo oaa, ae o ooe e coy oac, o yo coacoa co a. oo eoxoo oay apae a coco epeaa cepey opa. yo coa ocoae aa, cp aa c op x cooex, xo cooe ca o cee e coepa cepeo opa. C oo oea coep eo eo oca cooe o oec cepeo opae oypaa oepa, ae ec o pocapae ce coo e.

poc ocoae aao oe co co peoe. Heeoe co co pe o e oe cooecoa "1", a eoe co co -"0". Ta, oa aee o ca o aa, epea a cooee "110". poeaoc oo eoa o, o o ec oo ceaopae (c. pae 1.2), e coyec eoacoc ac o cepeoc aopa.

ycayc Coc pya e opaa ocoaeoo aaa c oo ooo aopa poo oc [1458, 1473]. Ta a ocoaee cooe cpa o, o opa po oc, o opa acpo. oep , a ocae eoe cooe epeac ya opao, o peaa epeaaea opa poxo eaeo eo o oco a eoy aay. B eceoc, aop ocoaeoo aaa ocx e o o opa o o aopa ocx, o pae epe oepa. Ep e oo e oe poa cooee, epe a aeoe o ocoaeoy aay, o y eo ooe e aeeo pecae o cyecoa aoo cooe. B oe cyae pooo pepo a:

(1) Aca coae eooe cooee, ce pao aoe.

(2) coy o c oo , Aca ocae eooe cooee, pa coe ocoaeoe cooee oc. (o cy ocoaeoo poooa, c. pae 23.3).

(3) Aca ocae ocaoe cooee oy epe oepa.

(4) oep ae eooe cooee poepe oc. He oapy eo oopeoo, o e peae ocaoe cooee oy.

(5) o poepe oc o eo cooee, yeac, o cooee oyeo o Ac.

(6) o oppye eooe cooee , coy o c Aco cepe , eae oco a eoe cooee.

A oeeco? oep e ep oy, o e ep oepy. O cea oe oea epeae cooe, o y eo e oooc oea cooee. Ta a oep e oe coa pao oc, o oapy oey a ae (5). oep e oe a ocoaee cooe - y eo e yoo a. o ee aee, y eo e aeeo pecae, o ocoaee cooe c y ecy. ocae cooe, coye aop poo oc a e e oac o ocax cooe, coepax ocoaee cooe oc.

oee poeae oa coeo apepa Aco oo. B eoopx peaax ocoaeoo aaa cepea opa, ya oy e ocoaeoo cooe, coaae c opae, yo Ace oc eooo cooe. Ec o a, o oe a ce a Acy. O oe oca cooe, a x a ocae Aco, Aca eo e coe c oea. Ec e e oxoo opa ey ocoaeoe cooee, oa oa ep, o o e ye oea c ee a p o.

B pyx peaax ocoaeoo aaa ao poe e. Cepe , o Ac oa, ooe Ace opa oy ocoaee cooe, o ap Ac e epeaec, o e oe oca cooe ee oc. Ace e yo ep, o o e ye oea c ee ap o.

pueeu nocoameoo aaa Haoee oe peee ocoaeoo aaa ec oca ce. Ec o-o ocae pae cooe, o epeaa cooe o ocoaeoy aay ocax oyeax e ye a oope. oeo e, paece o oy ea o e caoe.

coy ocoae aa, Aca oe, ae ec e ypoa, eoaco oca oye.

oca oye, oa oe ca ocoaeoe cooee, aca: " apecoaa ". e pe e e a pocac aa. oa oe oca oye ca ocoaee cooe ocea pee ec oyeo. paeco oe "oe" epoe e. Mo eeca popaa oc oyeo oe cooa ocoaee cooe coaa e x ocx opaa ye cepeo opa. Boooc ecoe.

onucu, cooe om nocoameoo aaa Aca o oeac oca cooe, ooapa cpo opaa. O coy pooo poo oc. Oao, epeoop a cao ee acpy ocy eeoc A c oa. coy aop poo oc, o e oyc o ocaex cooex. oea cepeo opae o coy ocoae aa ocx o oyea. op paea, oao, e ae, o epeoop o opae coyee ocae cooe c o o ppe. pooec ooo cxee papaoa cxe oc, cooo o oco aeoo aaa. coyee x cxeax poe oc eooo e opaa ocoaeoo aaa. opooc c. [480, 481].

4.3 Heopaee poe oc Oe poe oc oy oo copoa. oa o coco oeo, apep, p pacpocpae yx ae. B pyo pa o oe oaac poeo. Boopae oe eooe co, ocaoe poo oc. Ec pacpocpaec oeco o oo oyea, aa oopx oe poepea e yoo, o o oe pec aeaecy aay.

y peee ec poa oc, paoc oopo oe oaaa oyae, o oopa e oo oyae oaa pee copoe oyeoe cooee e coac papee a, ocaeo cooee.

Alice Software Company (oa popaoo oecee Ac) pacpocpae poy DEW (Do Everything-Word, ea co coo o yoo). apa ocyc pyco aa o coep poy oc. Oao, coae xo, o oo eae oyae poya, a e oepe pa o poep oc. B o e pe, ec oapyac o DEW, coepae pyc, y Alice Software Company e oo oooc opa pay oc.

Heopaee oc [343,327] yo pee oox aa. a oa poa oc, eopaea poa oc ac o ocaoo oyea apoo a eoea, oca e o oye. Ho, oe o ox pox oce, eopaea oc e oe poepea e papee ocaeo. Xo x oce oo o oopa aae oye, apep, "eepeaaee oc", cyecyee aae oycoeo e ocoeco, o ec Ace pec o oep, o opa oc - oe cye - oa e coe oo opa co acoy oc. Hecop a cooc aea ocoa e poca :

(1) Aca pee oy oc.

(2) o coae cyaoe co ocae eo Ace.

(3) Aca oe ce, coy cyaoe co co ap , ocae oy pey a. Aca oe o ce oo, ec oc paa.

(4) o poepe o.

Tae cyecye ooe pooo, oo Ace oaa, o oa e ocaa o y e, e oyca oooc oo oaac o oc.

o e oe oepyc ye po, o oc Ac paa, ooy o po e ae, o ca oa cya. O oe eo e oo Ac o pooo a yae oca peya po. po oe yocoepc paoc oc Ac oo, ec oa caa o o p o oo c Aco. Ceac aec, o o eoo cca, o o oc, oa ee a aeay paea 23.4.

o peee e coepeo. o ece Mo (Moti Yung) oaa, o eoopx cyax o oe ye po paoc oc Ac [489].

Hapep, o oyae eay o DEW. O oe oep oc o popa poy o, oa axoe. Toa, o oe ye po, o o paoae a Alice Software Company, poa e pacy o DEW. oa po oaec oep oc oa, o oopeeo oepae oc y Ac. oa po ocae ey cyaoe co, o opae eo Ace. Oe Ac o epe cae po. po yeaec o, o oa - ea oyae, xo oa ao e ec. Taoe cpe ec pepo poe eoo poccecepa opoo paccapaec paee 5.2.

Hecop a o y eopaex oce oeco pee, o ox cyax Aca e xoe, o o yoo o poep ee oc. Oa oe e xoe, o oc o ee o oppecoee oa poepea ypaca, o ee ca oyoa oepe eaco o o eca, poco, o e o oapy ee cax, ceae e oe. Ec oa o cae opa, oopy oa poae, o oa e xoe, o o-o, e aa a opa, o o ep ee ocoepoc. a co paa Aca oe opopy ex, o poepe ee oc.

P apao eopaex oce oee c ey oca cooee o c ey oca oc [910]. B oo cxee o yoo oe poep, o oc eceo a coaa ee aopo, a poep paoc oc aoo cooe peyec copyeco ocaeo.

oe ec oepea eopaea oc [1229]. pecae, o Aca paoa e a Toxins, Inc., epeae oae oye aey, coy pooo eopaeo oc. A ca oe oep co oc oo peopepy ae oy oe. Oao, eo o oopea e, o coo oyeo ec Aca. O peye, o Aca cooaa pooo c o c, o oc coe , a Aca oaaec. o acaae, o eceo po oaa Ac ec ee ooc, yae ee.

oepee eopaee oc oxo a oe eopaee oc a cee po o oa c oc, oop oe aye oo Tpeo. Too Tpe, a e o oe opeoa o Ac cooa pooo c. ec Tpe pecae cyey ccey, o o coye o pooo oo papee opaoo copa.

4.4 oc yoooeoo cee Alice Software Company oac ypoo poca poa, poaa DEW - aoo, o Aca oy ac pee ocae oepe eopaex oce, a e paoe a o oooc.

Ace xoeoc aa eoeo eoea oa oece a oepee oc. A ca, o pyo popac, coe oca oye c oo eopaeoo poooa. Ho ce oepe yy pooc oo po.

Oaaec, o ooo c cooae oc yoooeoo cee [333,1213]. Aca o e oca oye, a o o yec, o oc paa, o e coe ye o pee o. B o e pe Aca aaae po a ooc yyeo cee coe. Ace ae e yo apa ee poc papee y po, e oo yo cooa op po. po coe o ep oc Ac, ec Aca yexaa opoa, yoac, a oea yepa.

oc yoooeoo cee peca coo e opocc ey o po oc eopae oc. Opeeeo cyecy cya, oa Aca axoe opa co ex, o oe oep ee oc. C pyo copo, peocaee Ace ooo opo o pae ca cy oce - Aca oe oaac copya oepe, opa, oa oe a o oepe e oepe opa, aoe, oa oe poco eocya.

oc yoooeoo cee oy peoca Ace ay, coaaey eopaeo oc, oopeeo e oo e oyope o ao. Aca ae oe peoec o coco : o c yoooeoo cee oy oea o pee, a ee, ec oa eceo oepa co , py, ec oa oyce, oe ae yepa.

a e oe e pae pee. Hapep, po oe ceac ocyapce oap y co. Oa oyye ao-o aaoe co op , oya oooc aaa ee ceee cox oce. oya eoy ay a oepee oce, oa oe pea .

po oe aeco o oxpae aopcx pa, paece aeco ee ao y opaae. o pooo ooe oe e, ocax oye, o e, oope ooa oepa oc.

4.5 oc o oepeoc oc yoooeoo cee oo ocaey aa oo-o pyoo oep e oc. yc Aca xoe oexa eoy oey eoe eco, e e xopoe oepo ce - apace y, apep. oa e eecocoa oce eo oepa. Oa oae oye ao epoo o cpypye coeo cepeap oa oe cooecy opao. a Aca oe epea oy ooo oca cooe a ee, e epeaa ey coeo apoo a?

Peee oo c oc o oepeoc [1001]. Aca epeae oy ooo a, o e eco ceye coca:

Pauuocm. o yoo oe o oc o oepeoc o ox oce.

Henoeocm. Too ca oca aae oca o oepeoc o e coa pay oc o oepeoc.

Omuue nonucu o oepeoc. oca o oepeoc e oe coa pay oc o oepeoc, oopy oo a a opay oc.

omepaeocm. o oc o oepeoc opoep oe yec coac epo a aoo ocaeo c oca cooee.

emuuupyeocm. epoaa oca oe opee oc oca e o o oepeoc o oc o oepeoc.

Heompuaeocm. oca o oepeoc e oe c oc o oepeoc, o yey ooaee B eoopx cyax peyec cpoa opa epyeoc - o yoo oe e oooc opee oc ocaeo o oepeoc o oc o oepeoc. Cxe oc o oe peoc, ocoae a pax cxeax poo oc pee [1001].

4.6 pyoe oc a poea a eea o ayo ( David Chaum) [330]:

oa ec ecoo oepo, ocoeex oao ce. B ao oee oa ec co p ep (ae pcoee ce), oo o eoe oee ee pao eaa a pepe coeo oea. epe ea, ceoaeo, pep oe poep, o a copy paoae o oee B o e pe, oa xoe oece ay, ooae e oo pacpac. Ec, oao, o-o oe oapy, o pep coyec co aco, y peopa oa oooc a oo, o coye pep e o aae oca ey e.

Peee o poe aaec pyoo oc. pyoe oc oaa cey co ca:

Too e py oy oca cooe.

oyae oc oe yec, o o - paa oc py.

oyae oc e oe opee, o eo eo py oca oye.

p cope oc ye pacpa opeee oc ocaeo.

pynnoe nonucu c ae nocpeuo Cey pooo coye acyaeo ocpea:

(1) Tpe coae oy yy ap op /ap ae aoy ey py ya cco yax apx e. Oaox e ccax e. (Ec pye n eo, a x oyae m ap e, o oee co ap e coca n*m.) (2) Tpe yye a cco cex opx e py cyao ope, coxpa ce pee, ao oy pae.

(3) oa e py xoe oca oye, o cya opao pae coeo cca.

(4) oa o-o xoe yec, o oc pae ey ao py, o epepae a cco ocax oxoeo opoo a poepe oc.

(5) B cyae copo opaac Tpey, oop ae, ae coye a e py.

poea poooa coco o, o eo eoxo ae ocpe. Tpe ae ape aoo oe oea oc. poe oo, oo ocaoo eo, o oea oa aaa c e oca aea aoo a.

ay [330] epec p pyx poooo, eoopx x Tpe e oe oea oc, a pyx o e ye oce. Ee o pooo [348] e oo pe oc ocaeo, o o o e oa ox eo pyy. ee o pooo oo a [1230].

4.7 oc c oapyee oe yc Ea ec oy poo. ee ec ope oepe ce a, ae o epa p, a oo opo oee ox, e ocye Ace. Bce oep e o x, ac oa ap Ac. Haoe - ycex. Teep Ea oe aa ce a Acy, p ea oea ee oc o oyea.

oc c oapyee oe, eee po ao (Birgit Pfitzmann) Mao epo (Michael Waidner) [1240] peopaa oooe oeeco. Ec oce pyoo oa Ea oeae oc Ac, Aca coe oaa oo. Ec Aca oe oye, a oo o co oc ooo, paa oe oaaa cyo.

Ocoa e, coa a oc c oapyee oe, coco o, o aoy oo o y opoy y cooecye oeco oox apx e. a x apx e ae oeco pax pox oce. Oao, y Ac ec oo o ap , oa o e pacca oo oy oc. pye ape e eec.

Ea xoe oa ap Ac. (Ea ae coe Aco, c ce opo a p .) Oa copae ocae cooe , coy oeco cox cyepoepo, a ec pacp Ac. ae ec e yacc pacp oxo ap , ax e a coo oo, o, copee ceo, oa oy o, e y Ac, . Bepooc pacp a, pa eaeo eo Ace, acoo aa, o e oo peepe.

Teep, oa Ea oeae oc o oyeo, coy ae ap , oeaa oc ye oac o o oc, oopy ocaa caa Aca. p opae cy Aca pe e pax oc o o e e cooee op (cooecy ee a poy y apoy y, aeoy Eo), o oaa oo. C pyo copo, ec Aca e oe pe e pae oc, o ooa e o Aca oa oea a co oc.

a cxea oce pooco oy Eo oc Ac c oo eoao ox c ex cpec. Oa eo e coe cea c oee epoo oo Mop oc o Ac ca ee ap c oo Ac oca oye, a ae "cyao" oep co a p . o ac o yoyo o Mop, Ace co y cee xopoy copo e y coay, o ooe peoea xo a pa popa.

ooey eop pee oce c oapyee oe oo a [1239, 1241, 730, 731].

4.8 Bce c apoa a Aca xoe a peee eoopo y f(x) eoopoo opeoo ae x. ecac, ee oep coa. o xoe c ee aee f(x), o Aca e xoe, o o a ee x. a Ace oo oy poec cee f(x) e coo ey x?

o oa poea ce c apoa a, ae ecx a aa op a popae. (popaee ec o - o oeae a opoc.) eoopx y cyecy coco pe y aay, o ocyac paee 23.6.

4.9 Bpyee o Aca Beoea, aac oea, ceac poeocppye o coeo cycca. Oa y a ae apy, oopy epe o o oo, a o ee epe ! Cee a e, a Aca acae coe pe caae a ycoe ya. Bocxaec e, a Aca ae o ycoe ya oep aeaae eo. poe o oo, a Aca oae aeaa oep cyaoy pe. "Bep apy, o, y apy." O a ee oaae apy Ace pe. o ceepa ye. Teep Aca apae o ep y pe opae eo. pecaae, acaoe o oo, a o pa apy, cooae "ceepa ye"! Aoce.

ycexa oo pa Ace yo oe oep oe oyca. Oao, popaece poo o oy oece ay o o ooc py. A aa o oa? Bo oee peea c op.

peo poep Aca xoe ye ecopa oa, o ee eo opee epcee a a cyae a.

o: "oepe-a e o a. Ec a x yacc apaoa, epea co ec a."

Aca: "Ec oepy a ac, coee o x e, e aa e. oey e e oaa a a, oope oopa poo ec e?" o: "Oya a, o e oe peya aeo opa, ya acoe. Ec cooe e o coe ope ceac, yy yepe, o e oee peya. e yy aa e a, oa e oay a ycy. oepe e."

Aca: " ye oay a co oopy a a po ec. e oea x. oepe e."

Aca xoe epea coe pecaae (.e., oceoaeoc o), o e xoe pacpa coe pecaae o eoopoo pee. o, c pyo copo, xoe yocoepc, o Aca e coe e coe ee oce oo, a oa ceaa pecaae.

Bpyeue umo c noo cuempuo punmopauu o pooo pye o coye cepy popa :

(1) o eeppye cpoy cyax o, R, ocae ee Ace.

(2) Aca coae cooee, cocoee coeo a, oop oa xoe py, b ( eceoc, o oe ecoo o), cyay cpoy oa. Oa pye cooee eoop c y a o, K, ocae eo opao oy.

EK(R,b) a ac poooa pecae coo poeypy pye. o e oe pacpoa cooee, o oy o e ae, o a pcaa Aca.

oa Ac pe pe pacp co , pooo pooaec :

(3) Aca epeae oy .

(4) o pacpoae cooe, yaa . O poepe co cyay cpoy, yeac p a oc a.

e cyao cpo oa Aca oe ao pacpoa cooee, ocaoe oy, coy oeco e, opa o, oop oo p eppoa opaeoo cooe e pye . Ta a y a oo a oox ae, ee oc aepa yeac ycexo oce ecox oo. Cyaa cpoa oa e ae e cooa o coco cp, e pec ca o , oop e oo eppye pye , o coxpa epoyo cyay cpoy oa.

Ec coyec ocaoo xopo aop poa, epooc yaoo oca peao aa.

Aca e oe e co oce eo pye.

Bpyeue uma c noo ooanpaex yu o pooo coye ooapaee y:

(1) Aca coae e cyax cpo o, R1 R2.

R1, R (2) Aca coae cooee, cocoee ee cyax cpo a, oop oa xoe py ( ec eoc, o oe ecoo o).

(R1, R2, b) (3) Aca ce ooapaey y cooe ocae peya ece c oo cyax cpo oy.

H(R1, R2, b), R o cooee Ac ec oaaeco pye. cooae ooapaeo y a ae (3) eae oy, eppy y, opee .

oa Ac pe pe pacp co , pooo pooaec :

(4) Aca opae oy epoaaoe cooee.

(R1, R2, b) (5) o ce ooapaey y cooe cpaae eo R1 co aee ooa paeo y cyao cpoo, oye a ae (3). Ec o coaa, o pa e.

peyeco oo poooa epe pey o, o oy e yo oca ax cooe.

Aca ocae oy oo cooee pye a, a pyoe - eo pacp.

He ya cyaa cpoa oa, a a peya Acoo pye - o cooee, opaoaoe ooapaeo ye. Aca e oe coea oopa pyoe cooee (R1, R2, b'), o opoo H(R1, R2, b')= H(R1, R2, b). oca oy R1, oa pyae aee b. Ec Aca e coxpa cepee R2, o o oy oooc c H(R1, R2, b') H(R1, R2, b), oya oooc ye, o e o oy o Ac.

Bpyeue uma c noo eepamopa nceocyao noceoameocmu o pooo ae poe [1137]:

(1) o coae cpoy cyax o ocae ee Ace.

RB (2) Aca coae capoy oceoaeoc eepaopa ceocyax o. ae aoo a cpoe cyax o oa oa ocae oy o:

(a) xo eepaopa, ec oa pae 0, (b) XOR xoa eepaopa a oa, ec oa pae 1.

oa Ac pe pe pacp co , pooo pooaec :

(3) Aca ocae oy co capoy oceoaeoc.

(4) o oe a (2), yeac, o Aca ecye eco.

Ec cpoa cyax o ocaoo a, a eepaop ceocyax o epecaye, o eeco Ac paec eooo.

Blob-oem Cpo, oope Aca ocae oy pye a, oa aa blob-oea. Blob-oe o oceoaeoc o, xo pooo oo e pey. a caa paccap (Gilles Brassard), "O o cea oeo , ec o o oe " [236]. Blob-oe oaa cey ep coca:

1. Aca oe py blob-oe. Bpya blob-oe, oa pyae .

2. Aca oe op o blob-oe, oop oa pya. oa oa opae blob-oe, oa oe ye oa ae a, oop pye ece c blob-oeo. Ceoaeo, oa e oe op poo blob-oe, apep, o ey.

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