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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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3. o e oe a, a opao Aca oe op blob-oe, oop oa pya. o o c aec cpae, ae oa Aca opoe pye blob-oe.

4. Blob-oe e ecy ao opa, poe pyaeoo Aco a. Ca o cee blob oe, ae a poecc, c oo oopoo Aca pyae opae x, e ca e c e py, o Aca xoea coxpa cepee o oa.

4.10 opacae "eco" oe Hacao pe popoa o aa (Joe Kilian) [831]:

Aca o xoe cpa "opa pey", o oe y x e o. Aca peoa poco coco opaca oey ceo.

"Caaa ayaee cya , ae aya cya . ae oe a a "caee ", - peoa oa.

"Ho ec o ac e ye aya cya opao?", - cpoc o.

"o e ao. Ec xo o o eceo cyae, o "caee " o oo ec eo cya", - oea Aca, oce yoo pay o coacc.

Heoo cyc Aca o ayc a y o cycceoy eey, eay a ooe opo. Aca, opoopoa paaa, caaa: "O ac oe oopa y y ca ee po axoo". o coacc, peo cooa x pooo opaca oe, o opee, o yece y.

"Ec oye ye 0, o oe y, a ec 1 - o ", - caaa Aca. " ao y e ?" o oe: "1".

"Hy o, y e ao e", - yao aea Aca. - " ya, y e ceo eya e".

Oeo, y poooa opaca oe ec cepe ee. Xo o paa, o "caee " ec eo cyaoo a, x, oo eaco pacpeeeoo a, y, ae peyae eceo cya , pooo Ac e apapye, o a a yy pacpeee eaco. Ha cao ee epyo yec, o e c y ecye ceoo poooa, oop oo y eac copoa opaca "ecy" oey. Aca o opea, oa e oy co o eecoo cyea c oo o popa. opa ce a co eopeeco, o ee oo o pe eo-o eoo, o oep, oopo po co, oaa c peao oe.

oa Aca o cey pa axoe opoc oey, o e epoaa pooo. Caaa aya o, o eco oo, o op eo eeeo, o acae co a ce ya ae co oep. ae Aca oe co . Haoe, Aca o oca oa oepa c cya .

o ye eceo cyae, eaco o ecoc pax. Aca o oy paoa pooo, c o ao aa ea popao ocyecac, ce o oo caco.

oep eca oxo a blob-oe pye a. oa May a (Manuel Blum) coyc c poeo opaca "eco" oe o oey [194], o pe ee, coy po oo pye a:

(1) Aca pyae cya , coy y cxe pye a, ocay paee 4.9.

(2) o aaae co .

(3) Aca pacpae oy. o pae poco, ec o pao aaa .

B oe cyae, a ye pooo co cey coca :

Aca oa "poc oey" o oo, a o aaae co .

Aca e oa e oooc e peya coeo poca, ya oa.

oa e oo oooc ya peya poca epe e, a o ceae coe peo o ee.

Cyecye ecoo oooce o o.

poco oem c noo ooanpaex yu Ec Aca o ooopc o ooapaeo y, pooo poc :

(1) Aca pae cyaoe co, x. Oa ce y=f(x), e f(x) - ooapaea y.

(2) Aca ocae y oy.

(3) o peoaae, o x eo eeo, ocae coe peooee Ace.

(4) Ec peooee oa pao, peyao poca ec "ope", ec epao - o "pea".

Aca oe peya poca oe ocae x oy.

(5) o poepe, o y=f(x).

eoacoc oo poooa oeceaec ooapaeo ye. Ec Aca coe a x x', ae o x - eo, a x' - eeo, y=f(x)= f(x'), o oa a pa coe oaa oa. poe oo, a e aa f(x) oe eoppepoa c x. B poo cyae o coe oaa A cy, o pae epe oa. Hapep, ec f(x) 75 poeax cyae ea, ec x, y oa ye peyec o. (oa ae aa e ec y opo cooa poe, ooy o eo cee oe oaac co poc.) poco oem c noo punmopauu c ompmu au o pooo paoae a c popae c op a, a c cepo popae.

Eceoe ycoe - epeee aopa. To ec :

DK (EK (EK ( M ))) = EK ( M) 1 2 1 B oe cyae o coco e oec cepx aopo, o cpaeo eoopx aopo c op a (apep, RSA c e oy). o pooo:

(1) Aca, o coa ap op /ap .

(2) Aca coae a cooe, oo "opa", a opoe - "pe". cooe o a eoopy cyay cpoy, o oa oa oep x ooc a oceyx aax p o ooa. Aca pye oa cooe co op o ocae x oy pooo o pe.

EA(M1), EA(M2) (3) o, oope e oe poa e oo cooee, cya opao pae oo x. (O o e oca x c oo "-e e ape", ocooac oepo oa pooo opac ae.) O pye paoe cooee co op o o cae eo opao Ace.

EB(EA(M)) e M - M1 M2.

(4) Aca, oopa e oe poa oyeoe cooee, pacpoae eo co ap o ocae opao oy.

DA(EB(EA(M)))= EB(M1), ec M = M1, EB(M2), ec M = M2.

(5) o pacpoae cooee co ap o, pacpa peya poca oe, oc a e pacpoaoe cooee Ace.

DB(EB(M1)) DB(EB(M2)) (6) Aca ae peya poca oe poepe, o cyaa cpoa paa.

(7) Aca o pacpa ap cox e, o a copo oa yec ocyc o eeca.

o pooo caoocaoe. a copoa oe eeeo oapy oeeco pyo, e peyec pe copoa yac poooe, aece appa oce aepe poooa. o ocope, a o paoae, aae oaec coea.

Ec pa, coea, xoe Aca, y ee ec p oox y o a peya. Bo e p x, oa oe apoa a cooe "opa" a ae (2). o oapy o, oa Aca pacpoe co a ae (7). Bo opx, oa oe cooa ao-o pyo pacpoa c o oe a ae (4). o pee eccce, oopy o oapy a ae (5). B pex, oa oe o epa cooee a ae (6). o ae oapy o a ae (7), oa Aca e coe oaa, epaoc cooe. oeo, Aca oe oaac o yac poooe a o ae, oa yeco Ac cae oa oe.

Ec o axoe oeec pa, eo ooee y e ye. O oe epao a poa cooee a ae (3), o Aca oapy oa, y a aeoe cooee a ae (6).

O oe a, o epao o a (5) -a aoo-o oeeca co copo Ac, o a opa yeca cpoec a ae (7). Haoe, o oe oca Aca cooee o "pee" a ae (5), eaco o pacpoaoo cooe, o Aca coe eeeo poep ocoepoc coo e a ae (6).

poco oem ooe epeco oe, o o cex x poooax Aca o ya peya poca e oopeeo. B ao poooe ec oe, oa oa copo (Aca epx yx poooax o ocee) y ae peya poca, o e oe e eo. a copoa oe, oao, aepa pacpe peyaa opo copo. o aaec poco oe ooe. pecae cee cox ooe. Aca co po c ooe, A o - eoo oae. o pocae oey, oa aae ooe. Aca oe eep ay ooe ye peya, o oa e oe cycc e eo. o e coe ye peya, oa Aca e oo ey oo ay ooe.

eepau e c noo poca oem Pea peee oo poooa cy eepa ceacooo a. pooo poca oe o o Ace oy coa cya ceaco a, o o x e coe o a o, a ye o . Ec Aca o apy co cooe, poeypa eepa a oy e c a e eoaco o oyea.

4.11 Mce oep pooo, aao poooy poca oe c oo opx e, ooe Ace oy pa py c pyo oep o epoo oe. Aca eco coa poa yx cooe, o o o "opa", a pyoo - "pe", coae 52 cooe M1, M2,..., M52, o cy ap ooe. o cy a opao pae x, pye co op o ocae opao Ace. Aca pacpoae cooe ocae x opao oy, oop pacpoae x opeee coe "py". ae o cya opao pae ee cooe , e e x, ocae Ace. Oa pacpoae x, cooecye ap caoc ee "pyo". B eee p a e poeypa peec ca poa ooex ap. B oe p Aca o pacpa co ap a p e, o a o yec ocyc oeeca.

Mce noep c mpe upoau oep epecee, ec pe yacy ecoo eoe. ao pooo ceoo oepa eo oe pacpocpae a pex oee poo. B o cyae popaec aop ae oe oya.

(1) Aca, o po coa ap op /ap .

(2) Aca coae 52 cooe, o ooy ao ap oo. cooe o a e oopy yay cyay cpoy, o Aca oa poep x ooc a oceyx aax poooa. Aca pye ce cooe co op o ocae x oy po oo ope.

EA(Mn) (3) o, oop e oe poa e oo cooee, cya opao pae x. O pye x co op o ocae opao Ace.

EB(EA(Mn)) (4) o opae po ocaec 47 cooe.

EA(Mn) (5) po, oopa e oe poa e oo cooee, cya opao pae x. Oa pye x co op o ocae Ace.

EC(EA(Mn)) (6) Aca, oopa e oe poa oo oyex cooe, pacpoae x co ap o ocae opao oy po ( cooec c e, o oo oa x oya).

DA(EB(EA(Mn)))= EB(Mn) DA(EC(EA(Mn)))= EC(Mn) (7) o po pacpoa cooe co a, o ya co ap DB(EB(Mn)) DC(EC(Mn)) (8) po cya opao pae ocaxc 42 cooe ocae Ace.

EA(Mn) (9) Aca pacpoae cooe, o ya co ap.

DA(EA(Mn)) (10) B oe p Aca, o po pacpa co ap ap e, o a o yec ocyc oeeca.

ooee ap paac oo e opao. Ec apa ya oy po, o x epe apoay ooy oope pooo c Aco, Ec apa ya Ace, o o, y oo ceac axoc apoaa ooa, ocae e cyay apy.

B eae, a (10) ec oae. Co "py" oe poooa o opa e ce po, a oo e, oope e cacoa. Ta a a (10) pooo oo opo oeeca, oo ae-y yye.

B oepe epeco oo, e coea oee. Bce ocae oy oea coo e e, pa y o ce pao popa. (B eceoc o e coce epo. o-o, popa, oe copa ae o ce p oep pyx poo.) a, e a cya pa pax poo.

Ec pae Aca, oa pacpae co "pyy" co . o oe cooa ap Ac poep paoc ec Ac a ae (2), o ec poep, o aoe 52 cooe cooecye oeo ape. po oe poep, o Aca e e o coe "pye", py ap o p o Ac poep, o o cooecy poa cooe, oope oa ocaa Ace a ae (8).

Ec pa o po, oee pacpae co ap . Aca oe yec paoc ap, poep co cyae cpo. Oa oe ae yec, o ca eo ap, py x op o oee poep, o o coaa c apoa coo e , oye a aax (3) (5).

o pooo e ae o coopa poo-oeo. Aca pyo po oy oec eaaao ece aya peeo poa. Ceoaeo, ao poep ce cyae cpo a pa, oa po pacpa co ap. ec ce a pya coo c y poa, oope oa oopeeo e pacpa co ap, pe o x cae ( peye poooe o Aca) oae py.

Bce o paco eop, o peaoa ce o a oepe eca epoco. B peaa pex poo a pex pax Sparc-cax oce aco peyec oo acoa oo, a o ye opa aco oep [513].

Bcpmu ceoo noepa popa oaa, o p cooa poooa oepa aopa c op a RSA pocxo eoa yea opa [453, 573]. opeo, ec ooe pecaee ap ec apa ocao (c pae 11.3), o apoae ap ae c apa oca o. o coco oe cooao "pae" eoopx ap - apep, cex yo. o ac e oo opa o caax, o ao pe a oep ae y-y opa ac peyeco p eo pe.

a oaccep (Shafi Goldwasser) C Ma (Silvia Micali) [624] papaoa pooo yce oo oepa yx poo, oop peae y poey, xo -a coe cooc o copee ee o o eopeecoe aee. Ooe pooo oepa n poo, ycpa poey ye opa, papaoa [389].

Peya pyx cceoa poooo p oep oo a [573, 1634, 389]. coe pooo, oo poa e pacpa cox "py", pee [390]. o oepc (Don Copper smith) paccapae a cocoa oeeca yceo oepe, coye aop RSA [370].

Aouoe pacnpeeeue e Xo eoxoe, o o-y copac cooa o pooo p oep o oey, ap eep (Charles Pfleeger) paccapae cya, oopo o poooa oe oaac o e [1244].

Paccop poey pacpeee e. Ec peoo, o e oy ca eeppoa co ( o e opeeey opy, o oca eoopo opaae, ee o-y oooe), o eepa pacc e pec coa ep pacpeee e (Key Distribution Center, KDC). poea o, o yo a ao coco pacpeee e, o o, a cepep, e coe o, oy ao ocac. Cey pooo peae y po ey:

(1) Aca coae apy op /ap . B o poooe oa coxpae cepee oa a.

(2) KDC eeppye epep oo e.

(3) KDC pye , o a py, co op o.

(4) KDC epeae apoae , o a py, o ce.

(5) Aca cya opao pae .

(6) Aca pye pa co op o.

(7) Aca e aoe-o pe (ocaoo ooe, o cepep e o opee, ao oa p a a) ocae a apoa KDC.

(8) KDC pacpoae a apoa c oo coeo apoo a, oya , apoa op o Ac.

(9) Cepep ocae poa opao Ace.

(10) Aca pacpoae c oo coeo apoo a.

axoec e-o cepee poooa E e aeeo pecae o pao Aco e. Oa epep oo e, coaaex a ae (4). oa Aca ocae cepepy a ae (7), o pyec ee op o, oop ae oo poooa xpac cepee. Co coa ca o cooee c ooo e y E e. oa opaaec Ace cepepo a ae (9), o ae apoa op o Ac. caoc ec, oo oa Aca pac poae eo a ae (10).

Ec coyee RSA, o poooe pocxo yea opa co copoc, o ee epe, o a cooee. po oo coa c apae oca. Ec copaeec coo a o coco pacpeee e, yeec, o a yea e pee a-o ocec.

poe oo, oo e, coaae KDC oe ocaoo o, o pooco cp py oo. oeo e, ec Aca e oe ep KDC, o oa e oa ooac eo a. Moea KDC oe peycopeo aca ce coaaee . Toa o c o e a cpe x , pa Aco.

o pooo ae peoaae, o Aca ye ecoa eco. p cooa RSA cyecy e p ec, oope oe pep Aca, o oy oe opa, e e yaoc p pyo eoe poa. B ae ceap a poea e cyecea, o p pyx ocoec ax oa oe ca ao.

4.12 Ooapaee cyaop Aca ec eo opaa "aoop". oa e pxoc cpeac c py ea oxo oceex pecopaax ea cepe aeo apao. ea o, o pecopa acoo oxo ocee, o oa e oe yepea, o eoe, c apo ee a coo, oe e opa a .

"aoop" oy pa ecox pee. a oe oc c coo cco eo op a a. o ee a coo e ceyx poe. Bo epx, eep a oe oc c coo oy ay ax, , o opx, pec a ceye oxpa o cco eo. py cocoo ec cooae eaox ap, yex ae cepeape. ooe pe yeco oo cocoa ec o, o ocopoe coy poep eo opaa (ce c eco aaeo ae), o oo ye ae cepeap. Hoy "aoopo" e o e p o ao cee.

Ho peee ec cooae ooapaeoo cyaopa [116]. o o-o oxoee a o oapaee x-y, oopx oec peoae oyaoc. To ec, oo x poa a ax eo opaa pooo ope oya oo o e aee. oee oo, oo oa ox eo x-ay oya ooe x-aee, coa e acee o opa.

a, o o eae Aca. Oa oe pace, coy oeco cex e eo opaa, o x o ee. ae oa coxpae o oyeoe aee ece co co ee. o pye e e a o e caoe. Teep, oa Aca o cpeac oxo oceeo pecopae, o poco oe ac py c pyo ce ae ea. Aca yeaec, o peya, oyae p oae e oa ae Ac, coaae c peyao, oyae p oae e A c ae pao ae oa. o eae o e caoe. Teep o oa a, o coece - ae e opaa. o e pe o e coe opee oc pyx eo opaa.

oee oo, paccae ae aoo ea oy a ocopo. Toa Aca coe oep coe eco ocopoey (ooo, eco c yee eco oppae ), e oaa ey ec cco eo.

Hox eo oo oa poco oca o pyy oe ea. ecac, ya ea oo oo ece ye: ce ea paccaec o cco o epeca co ae. Ho "aoopa" pec o o ece oo p ocae oo-o eo, epe e oy ocac cce. (Cpao, o o e coae poe.) o paya e peec pe poe, oa xoe oc ea poo oc e cooa epaoao cce oce.

4.13 Pacpe cepeo "ce eo" pecae cee, o Aca - ae eo Coecoo Coa, a eep epaoa. o apa oa, oa poae cepe. a, oo aa aay ey, oe y cepe. ee ae ec aao. Bce ee cepe c ae aa yopoe o oepa : "e Xoa?", "o ao opopye Tpexcopo occ ?", "oey opc E cea , a yo o po o y yy?", ..

Aca e xoe oaa a cepea o ee ooo e oaae ae ac opa, acaec oo cepeo. o, oea oyae, e xoe a a oa ee. O ae e xoe co oa Ace, ae cepeo ey y. o e ee eo, , poe oo, oa Aca coe oa co aao y "Cepe, oop epecyec o".

pooo oepa e paoae o cyae, a a oe oo poooa Aca o o pacp co ap py pyy. oy e, cyecy p, c oo oopx o oe ya cpay ecoo cepeo.

Peee aaec pacpe cepeo "ce eo" (all-or-nothing disclosure of secrets, ANDOS) [246], ooy o ec o oy y opa o o cepeo Ac, o o oep oo oc ya o-o ee o pyx ee cepeax.

B popaeco epaype oo a pae pooo ANDOS. Heoope x ocya c paee 23.9.

4.14 cooe pyee e Bo opo ee ey Co Ma [1084]:

Ceo ocyae c papee cya ec e eoo oaa pecyo py paocy.

o aey e ee oee ao, o o ae peopaae aeee pacpocpaee pecye, yepa o cooa ox cee c c eao e. Ceoaeo, cyecye oocoaoe ecooco, o pa c pocpaee popa c op a oe a pyy pecy eppopcec opaa. e ceo, o ox aoax peoaaec, o cooecye paecee eoca p opeeex yc o x, ooopex aoo, o e oooc oy op ec oo oea opae o oeo c y ce. B acoee pe many o oe paoac, a peoae aooocy paaa o (1) ucnooam cae punmocucme - .e., pocce, oope cooecye ac (a ae o yoo!) c o y cp c oo yepex yc, (2) apaee cooam cou cepem ac. He yeo, o aa a epaa aoo cpeoa ox aepecoax paa, coaa peyae ee, o aa oc o a co a aoao eoacoc opaee aoa.

cooe pyee e ec cy poaex paeco CA popa Clipper Ca apa ycooo poa (Escrowed Encryption Standard). poea o, o oece ay o c, o e pe oo papeeoe cyo ocyae.

Escrowed Encryption Standard oeceae eoacoc c oo aeoo oopyoa. ao pocxe poa ya eao oep ( ID) cepe . o ec a e ac xpac, ece c ID, y pa opaa ycooo pye. Bc pa, oa pocxea pye a ax, oa caaa pye ceaco ya cepe o. a e oa epeae apoa ceaco co ID o aay c. oa paooxpaee opa xo pacpoa oo opa, apoao oo x pocxe, o ea ooa ID, oya cooecye opaa ycooo pye, oe x c oo oepa XOR, pacpoa ceaco ae coy eo eppoa ooa cooe. a o oeo y cxey ee ooee ycoe, opoo ocae paee 24.16.

Aaoa cxea oe peaoaa popao c cooae popa c op a [77, 1579, 1580, 1581].

Ma aae co e eco pocceo [1084,10851. (oop, o paeco CA a ao Ma $1000000 a cooae eo aeo [1086, 1087] coe caape Escrowed Encryption Standard, ae ae Ma y aoc pec.) B ax pocceax ap ec a ac pacpeeec cpe pax opaa. a cxea c coec cooae cepea, opaa oy oec occao ap . Oao, ac a oaa ooe coco - x paoc oe poepea eaco e occaoe apoo a.

Aca oe coa co coce ap pacpee eo ac cpe n oepex coceo. H o x e oe occao ap Ac. Oao a oe po e p, o eo ac - o paa ac apoo a. Aca e oe oca oy-o oepex coceo cpoy cyax o aec yy. Ec cyee ac papea ocyae, cooecye paooxpaee opa coy ocooac ocaoee cya oo, o n oepex coceo a co ac. Copa ce n ace, ac occao ap coy ocya c Ac. C pyo copo, o oy oooc occao Ac apy ee ay oc, Mop pec y cex n oepex coceo.

Bo a paoae o pooo:

(1) Aca coae apy ap /op . Oa paae ap a ecoo op x apx ace.

(2) Aca ocae opy ac cooecyy apy ac aoy oepex coc eo. cooe o apoa. Oa ae ocae op KDC.

(3) a oepex coceo eaco oe ce a co apo o po ac, o yec x paoc. a oepe coce xpa ap y ac ao-y aeo ece opae opy ac KDC.

(4) KDC oe oe cee opx ace opoo a. ec, o ce pa o, o ocae y opae eo opao Ace oeae ay-y ay ax.

p a ocaoe cya o ocya a oepex coceo epeae co ac KDC, KDC oyae oooc occao ap . o o epea KDC, o o oepex coceo e oe caocoeo occao ap , occao e a y ce oepee coce.

o aop c op a oo cea "ec" oo opao. P opex ao po paccapaec paee 23.10. B paoax Ma [1084, 1085] ocyac y oee o caoo c opooo cxeo, o occaoe apoo a peoaoc eoopoe ooeco oepex coceo (apep, poe ). O ae oaae, a oe o c pacceo epeae (c. pae 5.5) a, o oepee coce e a, e ap occaa aec.

"ece" pocce ecoepe. pecy oe cooa ay ccey, pe oco ae aa (c. pae 4.2.), o ca pyo cepe co opa. Ta opao o oe eoaco oeac opae c e-y ee, coy ocoae coe p eo e oyc o ooy papeeoo cyo ocya. aa poea peaec py poo o o, oop aaec oaoyco yco pyee e [946, 833]. o aop po oo ocaec paee 23.10.

oumua ycooo pyeu e oo paecex ao ooceo ycooo pye e pacpocpac oe p ece cce c yco pyee e. Boae oe opoc: aoe peyeco o ycooo pye e oyae ooae?

Hy, a cao ee aoo. ooae e oyae o ycooo pye e eo aoo, eo o ca e co oece. O ca oe coa peepy o e, ec axoe (c. pae 8.8).

cooe pyee e apapye, o o coe ocya eo paoop a a ax, ae oa o poa. Oo apapye, o NSA coe ocya eo eyapoe o - e coo opepa - xo o poa. Moe ey ye papeeo cooa ay p o pa c e cpaa, oopx ceac ycaoe ape, o o coeoe peyeco.

Heoca ycooo pye e eca oy. ooae pxoc ep eoacoc ec opaa, ax yco pyee e ae, a ecoc ax e. Ey pec ep, o oa cooecyx opaa ocaec eeo, paeco e oee ao, e, o ee ooo cp eo , yy ea o o aoy c oo oeceoc.

Boopae aaee eppopco a H-op, ae opae e cee oe, o ocao ocec?

Tpyo peca cee, o ycoe cxe poa, a oop x a, yy co o ac e pye e. Cey oe ao ye ape a cooae cex pyx c o coo poa. o, epoo, ece coco oc oepecoo ycexa o cce, o, opeeeo, ece coco aca exec paox pecyo eppopco cooa ee. oa e co, acoo pyo ye o e-ycoy popa e aoa, a o oe a popa a a aaeecy cy. a oy cceoa popao opepoae aop popa, e e ocya popaoy oecee ycpoc e-ycooo poa, ya e ye ceaa e?

pye aoe opoc. a ycoo pyee o a oeceoc ooaee, oa caoc eco apoaa opa ? Ec paeco CA aec a opa ycooo pye, e ye o oce ceeco oo, o ec cepe copoepoa o ooaee, o opaa ycooo pye, o oo ye pa oo ae?

o ec aa ax ao cy ycooo pye e, ce pao ocyapceo oe p eco, ye ypaea? o, ec paeco CA oaec eaoo cp o a ? co, o ce opoc o a eae ooaee ooac yco pyee e. Ec cooa e e ye opoo, o apa caao oe poc oecoo ae c e o cea c ooae oox cce opoo, o ec oe coe paa o opac.

Ee oee oac ye caa, oa cc, o oa o aee axoc oec ooe eye acpa e pooooc p cecy oecx eoc. o co acpo oeceoe ee po ycooo poa.

Ec oce yy poac e e cocoo, o poa, oy oo ee oe. oyco ace cooa oce poee oepa po oopeaeoo pecya? ye paa cyo ooc oce, ocoax a ax c yco pyee? e eceoc yy ae ooae, ec ac eceo coy x ooaee oc aoo-o eooo opaa, oep opeeex opace poeoc, poco, o ypac e ?

oaoe pacpocpaee popa poae ooee opoc. yy cxe ycooo pye e coec pax cpaax ? axo pacaoae opopa cpc c cyecoae ao cpae cox ycoo pyex e, coecx c pa ec a o oaeco? e oecee coecoc ceae oo poaapyex peyec cxe c y c o pyee e (eyapooe cooae ox cpec popa).

o ec p cpa e pe a epy aeoc opaa, cax c yco pyee e?

a yy ooae ec co ea x cpaax ? yy pa cya x epoe opa, o a, o x oce ycoo xpac CA, oo yepa e-y e a p, o o epo opa o oca o-o pyo ? e, oope ey ea oo x cpaax, yy ceae ce?

A o ea c poe oae? e apa, o cpa, aaec ceac poe oae cox aex ocyapcex pep, e ocoyc oo cc e a c yco pyee e? B cao ee, a a oa cpaa e copaec oo py cpaa ce a co paeae oepa, pacpocpaee ycooo poa ooo pee yee ocya.

ae ec cpa, oopx coac paace paa, yy cooa ycooc aoo poa oo aooo peceoa pecyo eppopco, e-y oaeo o c oyc cea cceo, aaa oecx ooeo, .. poe c peoca oooc opao oee aeo, e o o ooo aaooo pe, opop o a ec paa, x e, Digital communications offer the opportunity to do a much more thorough lob of monitoring citizens' actions, opinions, oxo oee.

He co, e ye epe 20 e poaa cce c yco pyee e Typ a ox o a poay epecx yo o Ape 1970 oy a cpoeco xecoo aoa pae 1980 oy. ae xye, eoe eaeoe ocyae c oe cyc oe p a eca, oope pae, ooo, e aac, ce a oppecoee cox paa. e apa, o epae eopa yco epe oo cyee.

aa Pae pooo 5.1 oaaeca c ye ae A o pya cop:

Aca: " a apo oepa eepao Peepo Cce, ooe cepeoo coyca Maoac oe p ae 4-o oa oaa ya".

o: "He, e ae".

Aca: "He, a".

o: "He ae".

Aca: "He, a".

o: "oa".

Aca: "Xopoo, cay ee". Oa ee oy a yxo.

o: "o epeco. Teep oe o a copac paccaa o ce Baumo ocm".

Aca: "Oooo".

ecac, oo Aca oe oaa o-y oy, oo paccaa ey ce. Ho oa o oe oy ce cee. ae o oe o oyee cee oy yoo, Aca eo e coe c oea. (B epaype oca x poooo aco coyc pae epcoa. e oo oaae, a Bop poepe. eo ea oc coyex pepax eco A c oa.) coy ooapaee y, e coe poec oaaeco c ye ae [626].

o pooo oaae Bopy, o y e eceo ec opa, o e ae Bopy e ae e oooc ya, o o a opa.

oaaeca pa opy epaoo poooa. Bop aae e p opoco. Ec e ae cepe, o oa oe a ce opoc pao. Ec cepe e eece, y ee ec eoopa epooc - 50 poeo ceyx pepax - oe pao. oce pepo 10 opoco Bop yec, o e ae cepe. Ho o opoco oeo e ac Bopy aex cee o opa e, o oae ae e o opa.

ao npomoo c ye aue a-a caep (Jean-Jac ues Quis uater) y y (Louis Guillou) oc yeoe ae cope o eepe [1281]. eep, oaao a 4-, ec cepe. To, o ae oee coa oe op o ay ep ey C D. cex ocax oa poxoa ey y.

A B C D Pc. 5-1. eepa yeoo a e ae cepe eep. Oa xoe oaa coe ae Bopy, o e xoe pacpa oex co. Bo a oa yeae eo:

(1) Bop axoc oe A.

(2) e poxo ec y o eepe, o o o C, o o o D.

(3) oce oo, a e cee eepe, Bop epexo oy B.

(4) Bop p e, cpaa ee o o:

(a) eoo poxoa (b) paoo poxoa.

(5) e coe eo pocy, p eoxooc coy oee coa, o oepe ep.

(6) e Bop oop a (1) - (5) n pa.

peoo, o y Bopa ec eoaepa, o acae ce, o . O acae, a e ceae eepe, acae, a o ca p, yaa, e e oa oc, acae a e oec. O acae ce n eco. Ec o oae y eoac po, oep oa, o e a e oee coa, opae ep ? He. A o ec e Bop apaee ooopc, o Bop ye pa, a e ye ea , o oa poa ec y. Toa oa ye a pa xo yaaoo Bopo eca, e a oex co. o o cea o pyoy. e xo o poxoo Bop cya opao pae co poc. Ec Bop yaae pao, xo poo, ec e - o pey y oy eoac. B o cyae Bop oe oy eoa c, oaay ooc y oceoaeoc, oopa oyac , ec e aa oe e coa.

o o oaae e e. Bo epx, Bop e oe ye pe copoy paoc o a aeca. o opx, a pooo ec poooo c ye ae. Ec e e ae o ex co, o oeo, o Bop e yae eo pocopa eoac. Ho a a e cocoa o peay eoac o oeao, o Bop e oe eo ya peaoo oaaeca o ec yeoe ae.

Meoa, coyea o poooe, aaec papea pa -a oo, o oa oxo a accec pooo ecoo ee eo-o :

(1) Aca e ey e ooa.

(2) o pae oy oo cee.

(3) Aca apae ocayc ooy.

B epecax Ac eco pae a ae (1), ooy o o epe a ae (2) y ooy, oopa ey oe pac. Ma Pa (Michael Rabin) ep cooa popa exy "papea pa" [1282]. o epaoo poooa yeoo a opaoa oe [626, 627].

pooo "papea pa" paoae, ooy o e e oe ecoo pa op yaa, o y a Bop opoc ee . Ec e e ae cepea, o oe oo oo poxoa, oop oa aa. B ao payepoooa ee epooc (oa aaea apeae) yaa, c ao copo Bop opoc ee , cocae 50 poeo, ooy ee epooc oay Bopa ae paa 50 poea. Bepooc oay eo yx payax coca 25 poeo, a o cex n payax o ac 2n. oce 16 payo y e 1 ac 65536 oay Bopa. Bop oe yepeo peo o, o ec ce 16 oaaec e pa, o oa eceo ae ae coa, opa e ep ey oa C D. (Aao c eepo ecoepea. e oe poco xo c oo c o po xo c pyo, pooo "papea pa" e ye. Oao, o eoxo c yeoo a c aeaeco o pe.) peoo, o e eca eoopa opa, oopa ec peee pyo poe.

ao pooo yeoo a coco ecox payo.

(1) e coye co opa cyaoe co peopaoa oo pyo poe pyy, oopy opao poee. ae oa coye co opa cyaoe co pee oo pyo poe.

(2) e pyae peee oo poe, coy cxey pye a.

(3) e pacpae Bopy o ep poe. Bop e oe cooa y oy po e y oye opa o epoaao poee ee pee.

(4) Bop poc e o (a) oaa ey, o oa capa poea oop (.e., a pax pee yx c ax poe), o (b) op peee, oyeoe a ae (2) oaa, o o peee oo poe.

(5) e coe eo pocy.

(6) e Bop oop a (1) - (5) n pa.

oe eoaepy poooe eep? ec oee cea o e caoe. Bop oe a ca oe ey e. O e coe cooa y ac yee po, o o cea o e coopc c e c e coa aop, oop oeae opa e. o apye oe cooa, o oaa, o coyec oaaeco c ye ae.

Maeaeca ocoa oaaeca oo a coa. poe cyaoe peopaoae o pac ocopoo, o Bop e oy ao opa o pee opao poe, ae oce ox oope poooa. He ce pye poe oo cooa oaaec c ye ae, o oco x.

oopu paa Ocee oo o, peeo eop pao [619, 622], oe a eoopoe pe. pa pecae coo ce ,coex pae o. Ec a paa e o ce, poe e oe, o aac oop. oe ox pao oaaeco x oopoc oe o peoa eo oepoo pee, o oa a aaex NP-ox poe, paccapaex paee 11.1.

peoo, o e ae o oopoc yx pao, G1 G2. Cey pooo oae B opy ae e:

(1) e cya opao acye G1, oya pyo pa, H, oop oope G1. Ta a e ae o oope H G1, o e ae ece oop ey H G2. oo pyoo oc o opa ey H G1 H G2 ec ao e pyo aae, a oc oopa ey G1 G2.

(2) e ocae H Bopy.

(3) Bop poc e o (a) oaa, o H G1 oop, o (b) oaa, o H G2 oop.

(4) e coe eo pocy. Oa o:

(a) oaae, o H G1 oop, e oaa, o H G2 oop, o (b) oaae, o H G2 oop, e oaa, o H G1 oop.

(5) e Bop oop a (1) - (4) n pa.

Ec e e ae o oope ey G1 G2, oa e coe coa pa H, oop oo pa a. Oa oe coa o pa, oop oope G1, o pa, oop oope G2. a pe ye pepe y ee oo 50 aco 100 yaa, aoe oaaeco opeye o ee Bop a ae (3).

o pooo e ae Bopy ao oeo opa, ooae ey oeo e yca o oop ey G1 G2. Ta a e aoo ooo paya poooa eeppye o pa H, Bop e coe oy opa eaco o oo, cox payo ye coco x pooo.

O e coe oeo e ycao oop ey G1 G2.

B ao paye Bop oyae ooe cyaoe peopaoae H, ece c oopo ey H G G2. Bop oe ae coa o-o oooe caocoeo. Ta a Bop oe coa a poooa, o eceo oaaeco c ye ae.

aumoo u Bapa oo pepa epe pecae Maye o ( Manuel Blum) [196]. e ae pyo, pooe y o paa, oop poxo epe ay oy oo o pa.

o y aaec aoo o. oc aooa a ec pyo eo aae.

e ec a opa - oa, ooo, oya ee coa pa c ope aoo o oa xoe oaa Bopy, o a opa e eca.

e ae aoo paa, G. Bopy ece G, o e eo aoo . e xoe oa a Bopy, o oa ae aoo , e pacpa caoo a. Bo a oa oa ecoa:

(1) e cya opao peopaoae G. Oa epeae o ee x e, coaa o pa, H. ocoy G H oooec oop (.e., o o o e pa), ec e ece aoo G, o oa eo oe a aoo H. Ec oa e caa coae H, opee ee oopa ey y paa ye c pyo coo poeo, peee oopo ae opeye eo oepoo pee. ae oa pye H, oya H'. (oo cooa c epoocoe poae ao cpo H, o ec, poa 0 poaa 1 ao H.) (2) e epeae Bopy o H.

(3) Bop poc e o:

(a) oaa ey, o H' - o apoaa oopa o G, o (b) oaa ey aoo H.

(4) e coe eo pocy. Oa o:

(a) oaae, o H' - o apoaa oopa o G, pacpa peopaoa pac poa ce, e oaa aoo G H, o (b) oaae aoo H, pacpoa oo e cpo, oope opay a oo , e oaa, o H G oooec oop.

(5) e Bop oop a (1) - (4) n pa.

Ec e e oaae, oa coe pe Bopy oo oaaec a ae (3). Oao, ec aoo G e eece, oa e coe coa apoa pa H', oop yoeope oo oaaeca. yee, o oa oe cea - o coa pa, oop G, pa c a e co oe pa aoo o. Xo ee ac yaa, aoe oaae co opeye Bop a ae (3), coca 50 poeo, Bop oe oop pooo ocaooe co pa, yeac, o e ae aoo G.

apaee oaamecma c ye aue B aoo poooe c ye ae coyec n oeo opae ey e Bopo.

oey e o x apaeo :

(1) e coye co opa n cyax ce peopaoa pyo poe n pa x oopx poe. ae oa c oo coe opa cyax ce peae n o x pyx poe.

(2) e pyae peee n ox pyx poe.

(3) e pacpae Bopy n ox pyx poe. Bop e oe ocooac o poea oye opa o opax poeax x pee.

(4) ao oo pyo poe Bop poc e o (a) oaa ey, o capa oa poe oop, o (b) pacp peee, pyeoe a ae (2), oaa, o oo ec peee ao oo poe.

(5) e coe eo pocy ao oo poe.

ecac, ce e a poco. o pooo, oe o peyeo, e oaae a e coc a yeoo a. Ha ae (4) Bop oe opeoa, o oaaeco o pecaeo e ae ooapaeo x-y cex ae, pyex a epo ae, ea eoo a ac poooa. o oe yeoe ae, o pyoo poa. Ha pae oo pecaec eoa c , o o e ae, a o oaa. M eceo ae oo o, o p opeeex ycox opeeee pooo opeeex poe oy oe apaeo e oep coca yeoo a [247, 106, 546, 616].

Heumepamue oaamecma c ye aue po eooo ye, ooy o oa e yacye epao poecce pooo. yee po pyx aepecoax a ye eepa pooo.

eepax oaaec c ye ae pya p poooo [477, 198, 478, 197], oope e pey eocpeceoo aoec. e oe oyoa x , a opao, o a a coe ae ce, y oo aec pe o poep ao pooo oxo a apaeoe oaaeco c ye ae, o eco Bopa aae ooapaea x-y:

(1) e coye co opa n cyax ce peopaoa pyo poe n pa x oopx poe. ae oa c oo coe opa cyax ce peae n o x pyx poe.

(2) e pyae peee n ox pyx poe.

(3) e coye ce pye aece xoa ooapaeo x-y. (B oe oo pye - e o oe, a cpo o.) ae oa coxpae epe n o oyeoo ae ooapaeo x-y.

(4) e epe n o, oyex a ae (3). o oepe ao n-o pyo poe oa epe n- (a) ec pae 0, oaae, o capa oa poe oop, o (b) ec pae 1, pacpae peee, pyeoe a ae (2), oaae, o oo ec pe e e ao oo poe.

(5) e oyoae ce pee, pyee a ae (2), ce oaaeca, oyee a ae (4).

(6) Bop, po ce ocae aepecoae a poep, o a (1)-(5) oe pa o.

o eae: e oe oyoa eoope ae, oope e coepa ao opa o ee cepee, o oy oo yoo ye cyecoa caoo cepea. o pooo oe coo a poepa opeeea a cee ooapaeo x-y epoaax cooe o caeoo cooe.

a cxea paoae, ooy o ooapaea x-y ecye a ecpcpac eepaop cyax o. o oea, e yo ye pecaa peya ooapaeo x y. (oe, ec peee pyo poe e eeco, oa oe cea a ae (4) o (a), o (b), o e oa ec oopeeo.) Ec oa a-o opao yae, oee aoo ec opeye o ee ooapaea x-y, o oa coe coea. Oao, e e coe a ca ooapaey x-y a opeee oaac, ao ye oye.

Ooapaea x-y o cy ec aeee Bopa cyao ope ooo yx oaaec a ae (4).

B eepao poooe oo opao oe epa oceoaeoc apoc/oe.

e, a e Bop, opae pye poe c oo cyax ce. Oa oe opa pae poe, ceoaeo, pae eop pye, o ex op, oa x-y e ac o-o, y oe e. B epao poooe 10 epa - epooc oeeca e coca 1 ac (1 1024) - oe ocaoo. Oao, eepax oaaec c ye ae oo e xa. oe, o Mop cea oe o a ae (4) o (a), o (b). O oe, o a (1)-(3), oac oaac, o eo opoc cea, ocope, pao eo peooee. Ec e, o opoye coa coa. Cea 1024 peooe a oepe epyo.

peopae aoo cp py oo eepax poooo yo 64 ae 128 epa.

aa e coco cooa ooapaeo x-y - e e oe pecaa xo x-y, ooy o oa e oe pecaa ee xo. Bpye, coyee a xoe, caoc ec oo oce pee ox poe.

Oue aeau (Blum) oaa, o a aeaeca eopea oe peopaoaa pa, ao, o o aaeco eope ye aeo oaaecy cyecoa aooa a oo paa.

B oe e o, o oo NP-ooo yepe ec oaaeco c ye ae, coy ee ooapaee y , ceoaeo, xopoe aop poa, oaao [620]. oe aeaecoe oaaeco oe peopaoao oaaeco c ye ae. coy y eoy, cceoae oe oaa py, o ey eco oaaeco opeo eope, e pa c pa caoo pee. o oyoa co peya, e pacpa x.

Tae cyecy oaaeca c a pacpe [590]. oaaeca c a pacpe oc ceye coca :

1. e e oe oay Bopa. Ec e e ae oaaeca, ee ac ye Bopa o, o oaaeco e eco, peepeo a.

2. Bop e oe oay e. O e oyae aeeo aea a oaaeco poe oo aa, o oaaeco eco e. B acoc, Bop e oe poeocppoa oa a eco oy pyoy, e oaa ce ca c caoo aaa.

oaaec c ye ae ec ooeoe ycoe :

3. Bop e yae o e eo aoo, eo o e co ya caocoeo poe oo a a, o oaaeco eco e.

Cyecye aea aeaeca paa ey oaaeca c a pacpe o a aeca c ye ae. o pae axoc e pao ao , o oee cyee a e oy poypoa pyy epaypy. o oe in [626, 619, 622]. aea popaoa x e, ocoaa a pax aeaecx peooex, oea [240, 319, 239].

Cyecy pae oaaec c ye ae :

Coepeoe. Cyecye aop, oop coae ceopa, ooc cooecye pea ceopaa (pep c aoo o oopo pao).

Cacecoe. Cyecye aop, oop coae ceopa, ooc cooecye p e a ceopaa, poe cpoaoo ca ce.

Bceoe. Cyecye aop, oop coae ceopa, eoe o peax.

Hecoyee. aopa oe e , o oe oaa, o Bop e yae ao opa oaaeca (apae pep) o eo pao, a eopeeco, a pao, pce oe oaaec c a pacpe ye ae. Ma epecep (Mike Burmester) o ece ope poo eaeo epaoe oaaeco, e aee cepea oe pooeaeo epeaa oo pye opoepo epaoe oaaeco c ye ae [280]. popa oaa, o ce, o oe oaao c oo epaoo oaaeca, oe oaao c oo e paoo oaaeca c ye ae [753, 137].

Xopoe oopo cae o ao ee ec [548]. ooee aeaece opooc, apa, pooo poe e [590, 619, 240, 319, 620, 113,241, 152, 8, 660, 238, 591, 617, 510, 592, 214, 104, 216, 832, 97, 939, 622, 482, 615, 618, 215, 476, 71]. Moo eo o acao o oy opocy.

5.2 cooae oaaeca c ye ae ea B peao pe oaaec ooc aco coyc ece co: acopa, o ece paa, pee apo .. co coepa o-o, caee x c ope e o eo: oo oopa oc, o c o e epooc o oe oeao aa, co cea aa peeoc co ec. a o opoo ea o-o oooe po opao?

cooa oaaeca c ye ae oaaeca eoc o epe peo e o pee ao (Uriel Feige), Aoco ao (Amos Fiat) A apo [566, 567]. ap Ac caoc ye ee "eoc". coy oaaeco c ye ae, oa oaae, o oa ae co ap , a opao, co eoc. Cooecye aop oo a paee 23.11.

o oe oooeaa e. Oa ooe eoey oaa co oc e cooa ecx coo. Oao, oa e coepea. Bo pep oox oyopee.

poea poccecmepa Bo a Aca, ae e a pa axa, oe opa poccecepa. (oa o aaec po eo poccecepa.) Oa ocae o app acapoy Aao apoy, peaa pa oo pe, oo o e ec, o paex oaax. Oa pae e po acapoa ep po apoa. H o poccecep e ae o pyo.

apo, pa e, eae co xo ep. Aca acae xo e oay acapoy. pa e, oa eae o e xo a oce acapoa. acapo eae co ep xo ep. Aca ac ae xo, e oay apoy eae o e xo. o pooaec, oa oa e pae oy ap, popa pyy, oe ap oac .

Ha cao ee acapo pae c apo, a Aca poco ocpe, oop xo ooo poc c ecepa a oce pyoo. Oao, ec apo acapo e a o pcyc py pya, a x ye opae po Ac.

o coco oeeca oe cooa po oaaeca oc c ye ae [485, 120]. oa Aca oaae co oc Mop, Mop oe oopeeo oaa oy, o o-o ec Aca.

Oa, noe aue Ocya co pooo ea c ye ae, A ap caa [1424]: " oy xo paea a aa xo o pa op, a o ce ee e coy a ce a e."

Bo a a coe o cea. Aca ec pecopae oa, paeae a. po eae oy opoo epo aae a. o po - ao, epeoapaec o oaoy p a oaay. Aca e oopea o oeece.

oa Aca oea copaac a oaa co oc oy, o oae ca po, o o pa aa. po pae pa oopoe copaec oaa co oc y. Teep, oa Aca oaae co oc oy, o oae ca po, a oe o e pooo c o. oa aae opoc o poooy, po cooae o opoc oy, a o aae eo Ace. o a Aca oeae, o epeae pa oe po. o cy, Aca poco oaae co oc y, a o po poco, axoc yp poooa, epea cooe ya-ca. oa pooo a epaec, Aca oaaa co oc y aaa a opoe pa (c oop po eep cee).

Oa, noe meppopucmau Ec Aca xoe oec c po, o o ae oy poec a. B o poooe po - eca eppopca. Aca ooae e exa cpay. - oep-opa, Aca po oa c o aoy paoaay.

oa aae po opoc cooec o poooy c ye ae, po epeae x A ce, oopa oeae a opoc. po oope oe y. Carol recites these answers to Dave. o cy, Co oc y oaae Aca, a po cyae po c. oa pooo aepa ec, cae, o po - o Aca, papeae e exa cpay. Cyc p po cae y paeceoo a ece c poaoyco, ao pao.

peaaee peeu Oa ocax oeeca oo, a a aoop coy a paoaa. O cocoo peopa oeeco ec poeee poeyp ea ee apae, o pye epoaoe yee. B pepe c eppopco o apapye, o po e oy o e o o Ac. B pepe c ae o oe ocpo ay ey apae coe pecopae, o y epa-o ea ye paoa, o po e coy oeac cooe. pee poe poccecepa Aca oa ce a coe cye o oa p.

Toac o (Thomas Both) o ece peo pyoe peee, coyee oe ac [148]. Ec a a poooa oe pocxo aaoe pe, y oeo e ocaec pee o ea opae. B cyae c poeo poccecepa o cooecye peoe opa pe o ya xoa oo yo - y Ac e ocaec pee ea oa oay. B cop c a e y o po e xa pee epeaa py pyy oe opoc.

Oa c ecouu uocmu Cyecy pye coco oyope oaaeca eoc c ye ae, ae paccapaee [485, 120]. B pe peaa poepa p pecpa eoeo coeo a e po oc. Ceoaeo, y Ac oe ecoo apx e , a opao, ecoo o ce. o oe opoo oo e, ec oa axoe oea c aoa. Aca ae oe coep pecyee cpc. B epx, oa coae ecoo oce, oa oopx e coyec. ae, oa coye y oc coepe pecye a, o cee epoa ee a y oc. ae, oa eeeo pepaae ooac o oc. Cee ae oc pecy a, o Aca oa oe e ye cooa y oc - ee eooo poce.

a o oo y exa, oeceae, o y aoo eoea a oo oa oc. B [120] aopa peaaec pya e aex o opoca ee, oope e oy opoa, y oopx ec ya oep, c ac x eeecoo oa. O ae peo pcaa aoy peey oc p poe. (eceo, poe pec ce a o, a a ae peeo oe ypae.) oe eo oyope - poe oy coa poeoc peea ecoo oce. B oe oo, yaoc oc ocoaa a oep.

poam nacnopmo Aca xoe oexa ap, o paeco o cpa e ae e . po peaae ca co oc Ace "apoa". (ep o peo o, o o p oex poe.) po poae Ace co ap Aca ee ap, aa ce a po.

po oyae e oo ay a co oc, o eaoe a. Oa coepae pecyee, oa Aca axoc ape. "po" oaaa co oc ape, a oa oa coep pecyee o a?

oeo, paa py y Ac. Oa oe coep pecyee o epe oeo, o cpay e oce opae, ooo oa po. Caaa oa oae, o oa - po (e ap po, e e coca pya cea o), ae oa coep pecyee ye. o ye ca po.

po ye yepa, o caa co oc apoa Ace, o o oep ay eepoy c o p?

poea o, o Aca oaae e co oc, a o, o e eca eoopa cepea o p a. eo c ey o opae oc cy peeo oyopee. Peee aex o opoca ee ao o aoo oeeca, a coae oecoo ocya p ca, oopo ce paae o oe aco oaa co oc ( oe , a ao yy ..). oo pe y poey oy oepece eo - oea ae, c cea aa, ac ooca ..

oaamecmo ecma Aca xoe oaa oy, o oa ec eo cyepcepeo opaa, o e xoe pacpa co oc. a poea, a poee oaaeca oc, o oaac o ee, a y ea [887, 906, 907, 1201, 1445]. P pee ca c poeo pyox oce (c. pae 4.6).

5.3 Cee oc Ba coco poooo poo oc ec ae oca coepa oc aeoo oyea. o xopoee coco, ae oa xoec opaoo.

M oe oea, o oca oye, ae e a x coepa. Cyecy co co, oa oca oe e oo, o nomu a, o o ocae. Ho ce o opy.

oocm cene nonucu o - ocyapce oapyc. Aca xoe, o o oca oye, e e aeeo pe cae o eo coepa. o e oeae a coepae oyea, o oo aepe, o oapao aceecoa eo opeeeoe pe. O copaec ecoa o ceyey ay:

(1) Aca epe oye yoae eo a cyaoe co. o cyaoe co aaec acpy oee.

(2) Aca ocae aacpoa oye oy.

(3) o ocae aacpoa oye.

(4) Aca yae acpy oe, oya opa oye, oca oo.

o pooo paoae oo, ec y oc yoee oya. Ec e, o oo yoe cyecy pye coco e oye. Hecoo oxox aopo pee paee 23.12. A ceac, poco aea ocaoc a yoe.

Moe o coea? Moe o oy ay-y opa o o, o ocae ?

Ec oe ocopooc eceo cyae eae aacpoa oye eceo c y a, o e. aacpoa oye, ocae oo a ae, (2) e e oxo a op a oye Ac. aacpoa oye c oc oa a e a ae (3) e e oxo a oca oye aa (4). ae ec o aoy oye co coe oc oce ooa p o ooa, o e coe oaa (cee oy-o pyoy), o o oca eo o opeo poooe.

O ae, o eo oc paa. O oe, a o pyo, poep co oc. Oao, y eo e ao oooc ca oca oye y opa, oyey p oe poooa. Ec o oca, coy o pooo, o oyeo, y eo e ye cocoa ya oa ao oye o oca. ooc cee oc oaa cey coca:

1. oc oa o oyeo paa cy oaaeco oo, o o oca o o ye. Oa ye oa o, o o oca o oye, oa oye ye ocec oaa oy. Oa ae oaae ce coca pox oce, ocyaex paee 2.6.

2. o e oe ca oca oye c poecco oca oyea. ae ec y eo xpac ac oo cex ceax cex ocx, o e coe opee, oa o o ca ope oye.

E, axoec ey Aco oo cee a poooo, opa ee ee, e y o a.

Cene nonucu C oo poooa ooc cex oce Aca oe aca oa oca o-y p o e: "o oe Ace o oapo", "o oe Ace coeo epoo peea", "o oe Ace ooaa". Boooc ecoe, ooy o ox poex o pooo ecoee..

Oao, cyecye coco, c oo oopoo o oe ya, o o ocae, ece c e coxp a oee coca cex oce. epa oeo oo poooa ec exa "papea pa". Paccop cey pep. Moeco e a e ea ey cpay, e apae pa xoe yocoepc, o o e o oa. Cyae oy oca aoo, o eco oo coyec epoocoe peee - ocaec a ec ea. oepa ec ocopy yeco ooo eoea ec, ocae e poycac ecpeceo. oco e opaac oce cyae pocaa eaee, o c epooc 10 poeo x o. ec cyea ccea paoae eo, aaae a ecey oy a ece pecy e oee e epeeae o e yax oo.

Ec eapae pa axoe oc epooc o opaaco, cya pec oca oe e, axoe o epooc - oo ye oca ee e. pa epooc, oo opopoa eoc poooa p oe opaaco.

pooo ceo oc paoae aao opao. o oyae oy ay pax aac poax oyeo. O opoe, apep, ce poe ooo ae oe oce.

ocope a aacpoa oye a a ea oepe. poecc acpo oyea oo paccapa a oeee oyea oep, a poecc yae oe acpo - a cpe oepa. oa oye cpa oep, o e coe eo poa. oye ocae c c oo ycoa opoao ya, oeeo oep : oa oca ca co o c a oepe, c oo ycoa opoao ya a oc cac o oyeo.

B ceye ceap ecye pya aeo oppae. x oc acepee, ae cao paee oppae e ae, o o ae. peopa pae xoe a aoy aey o ca oye ceyeo coepa : "oae oo ocaoo oyea, (cae , o o o p ecye ae), oaae oo oaeco epocoeoc ". aoo aeo ec co cco ceoo, ooy paee e oe poco paa ocae oye. Ae e xo epeaa co ceo paee, a a pa o cp oep pae. C pyo copo, paee e xoe ceo oca oye, peocaee aeo. Xp ae oe peca cooee, oooe ceyey : "Ae () e ocay, ey aaea eeoa ec o oapo. ocao, pee". B o cyae oy oe cee oc.

peoo, o y aoo aea o 10 ceoo, pax ca oe oy eec x. peoo ae, o aea ce pao, o a ee o oya oaecy epo c oeoc. Tae peoo, oep ypae aaec Agency's Large Intelligent Computing Engine (oa eeyaa Bcea Maa pae), ALICE, a a ope aeo ec Bogota Operations Branch (Ceop oepa ooe): BOB.

(1) BOB oo n oyeo, a oopx coye pa ceo, ax ey oa ecy epocoeoc.

(2) BOB acpye a oyeo o acpy oee.

(3) BOB opae n oyeo ALICE.

(4) ALICE cya opao pae n-1 oye poc BOB'a pca acpy oe aoo pax oyeo.

(5) BOB ocae ALICE cooecye acpye oe.

(6) ALICE opae (.e., yae acpy oe) n-1 oye yeaec o, o o o p pe - e c papeee a ay ec.

(7) ALICE ocae ocac oye ocae eo BOB'y.

(8) Ae yae acpy oe ae co o ceo : "Maoa ooca." oca oye ae ey oaecy epocoeoc o ee.

o pooo aeo ae o oeeca BOB'a. o coea, o oe oo yaa, ao oye ALICE e ye poep. Bepooc oo - 1 ac n - e co ea. ALICE ae o ycye ce yepeo, oca oye, oop oa e coe poep. oo oyea paccapae pooo ooc coaae c pey poooo ooc ceo oc, coxp a ce coca aooc.

Cyecye p, oop ee oe yeae epooc oeeca BOB'a. Ha ae (4) ALICE cya opao pae n/2 oyeo poep, BOB pcae e cooecy acpy e oe a ae (5). Ha ae (7) ALICE epeoae ce epoepee oye ocae oyc eaoye. Ha ae (8) BOB yae ce acpooe oe. oc ALICE ye pao, oo ec e ocao poeee n/2 ex oyeo. o coea, BOB'y yo oo yaa, aoe ooeco oyeo ye poep ALICE. Bepooc oo opao e, e epooc yaa ece oye, oop ALICE e poepa.

BOB oe coea o pyoy. O oe coa a pax oyea, o oopx ALICE coaca oca, a pyo - e. ae o oe oac a a pax acpyx oe, oope peopay yaae oye oaooy y. Ta opao, ec ALICE axoe poe p oye, BOB epeac e acpy oe, peopay oye eoy y. Ec ALICE e axoe pocope oye oe eo, o pe o acpy oe, oop peopaye aacpoa oca oye oye, c e oeeca. Xo eopeec o ooo, aeaa opex aopo eae peepeo ao epooc BOB'a a ay apy. eceo, oa oe co o, a epooc oa coa eox o y oc o poo oyeo caocoeo. o opoc ocyaec e paee 23.12.

ae. Baee aeo a p ocoeoce cex oce ec ay ( Chaum) (c. 4-).

Ta. 5-1. ae aya a cee oc aea aa Haae CA 4759063 19.07.88 Blind Signature Systems [323] (Cce cex oce) 4759064 19.07.88 Blind Unanticipated Signature Systems [324] (Cce cex eoax oce) 4914698 03.03.90 One-Show Blind Signature Systems [326] (Cce cex oce, oaaex o pa) 4949380 14.08.90 Returned-Value Blind Signature Systems [328] (Cce cex oce c opa ae aee) 4991210 05.02.91 Unpredictable Blind Signature Systems [331] (Cce epecayex cex o ce) 5.4 oca popa c op a Aca xoe opa oy eoacoe cooee. Oa e xoe oya co op c cepepa e, oa e xoe poep oc eoopo acyae oep pee copo a cepae coeo opoo a, oa ae e xoe xpa op oa coe oepe. Oa xoe po co oca ey eoacoe cooee.

y poey pea oce pocce, oa aaee ccea c Heepa pa eee e (Non-Interactive Key Sharing, NIKS) [1422]. Op oa ocoaec a eo e ceeo apece (eeoo oepe, ooo apece e-o ooo). B oo popa c o p a Ace ye oca cepa, ca oc oa eo op .

B oco popa op oa u ecm eo oc. o eceo cea e ec o coepeo ooo cce - Ec Aca ae apec oa, oa oe eoaco oca ey oy, o eae popa popao, acoo o ooe ooo.

Ccea ocoaa a ae Tpeo e ooae acoc o x oc. Ec ap Ac ye copoepoa, e pec e oo coc, opeex ee oc.

Cepeo poeo ec poepoae cce a opao, o coop eecx ooaee e o pec oee a.

p papaoe aea ax cxe, oeceee eoacoc oopx oaaoc epc co, oe oo oe pao - a opao o. Moe peoee pee coepa op Tpeo cyaoo ca aoo ooae - o oey, o ypoae cao ee ax cce. P aopo, paccapaex aax 19 20, oy oc. opooc aopo po cce oo a [191, 1422, 891, 1022, 1515, 1202, 1196, 908, 692, 674, 1131, 1023, 1516, 1536, 1544, 63, 1210, 314, 313, 1545, 1539, 1543, 933, 1517, 748, 1228]. Aop, oop e coye cyax ce, oca [1035]. Ccea, ocyaea [1546, 1547, 1507], eaea po cp c cooae paoo opoo a, o e caoe oo caa o ccee, peoeo a NIKS-TAS [1542, 1540, 1541, 993, 375, 1538]. o pae oop, cpe peoeoo e eo oopeeo paoo eoa c oo.

5.5 Paccea epeaa popa o eaeo aec pao a oe 500-ooe co n. O ae, o oo ec poeee 100-ox ce, eo oe. (Bo poea. Ec o e occao , ey pec paoa cepxypoo, o e oae a eeeey py c Aco ce oep.) o e ea? o oec Aca:

"Me ocacoc ya o oee ca ", - oop oa, - " poa eo ee a 100 oapo. o o apy a ." oaa co cepeoc, oa copaec cooa cxey pye a, pya a o eo.

o aepecoa, o oo a 50 oapo. Aca e xoe cpaca ey peaae poa oy ooy o a ooy cooc. "o aeo copa ee paoy", -.

"Ho a ya, o oe co eceo ec oee n. Ec oae e co oo e yec, o oo eceo ec oee, coayc c o yco ", - oop o.

O aoo cya. Aca e oe ye oa o, o oa ae cooe n, e pacp eo, a o e xo e oya 50 o, oope oe oy oaac ecoe.

a cop, yaea y o aa [831], o oe pacceo epea. Aca epeae oy pyy cooe. o oyae eoopoe ooeco x cooe, o Aca e ae, ae coo e o oy. Oao, o e ooc peae poey. oa o oy cyay ooy o, Ace pec yea eo, coy oaaeco c ye ae, o oa ocaa ac oe n.

B ceye poooe Aca ocae oy oo yx cooe. o oyae cooee, o aoe Aca e ae.

(1) Aca eeppye e ap op /ap , ceo epe a. Oa ocae oa o px a oy.

(2) o pae cepoo aopa (apep, DES). O pae o opx e Ac pye c eo oo co DES. O ocae poa Ace, e cooa, ao ee opx e o cooa poa.

(3) Aca a pacpoae oa, coy oa cox apx a. B oo cyae oa coye pa yceo pacpoae DES, pca oo. B pyo cyae oa coye epa oyae ecccey oceoaeoc o, oopa, e e eee, oxoa a cya DES. Ta a e eece pa op ec, oa e oe ya, ao e pae.

(4) Aca apoae aoe cox cooe a e, oyex e a peye ae (o oopx - aco, a pyo - eccce ), ocae oa cooe oy.

(5) o oyae cooe Ac, oo oopx apoao pa o DES, a pyoe - ec cce o DES. oa o pacpoae aoe x cooe co o DES, o oe poa oo x, a pyoe ye eo e oo eccce.

Teep y oa ec a cooe Ac, Aca e ae, aoe x oy yaoc yceo pacp o a. ecac, ec pooo ocaoc a o ae, Aca coe coea. Heoxo ee o a.

(6) oa pooo aepc, cay ec oa oox peyaa epea, Aca oa epe a oy co ape , o o yec ocyc oeeca. B oe oo, oa oa apoa a ae (4) oo a oo o e cooee.

B o oe, oeo e o coe ya opoe cooee.

pooo aeo ae o oa co copo Ac, ooy o y ee e oooc ya, ao yx e DES ec aco. Oa x oa coye poa cox cooe, o o oe yceo pacpoa oo oo x - o aa (6). pooo ae o oa co copo oa, ooy o o aa (6) o e coe oy ap Ac, o opee DES, o op apoao pyoe cooee. Ha o pooo oe oaac poco ycoe cocoo poca "ecy" oey o oey, o o eco coyec o ox cox poooax.

oeo e, o e oe oea Ace oca oy a coepeo ecccex cooe :

"My-y " "T ooococ". o pooo apapye, o Aca epeac oy oo yx cooe, o e ao apa, o o axoe oy oe x.

B epaype oo a pye pooo pacceo epea. Heoope x eepa, .e.

Aca yye co a cooe, a o oe poec oo oo x. O oe cea o, oa axoe, ey e yo oo cac c Aco [105].

B eceoc a pae o e coye pooo pacceo epea, o o oe ec a oo p ocpoe pyx poooo. Xo cyecye oo o pacceo epea - y e ec a cepea, a oyaee o, y e ec n cepeo, a oyaee o, y e ec o cepe, oop oyaee c epooc 1/2 a aee - ce o ae [245, 391, 395].

5.6 Paccee oc eco oop, e oy pya, eo x oo cooa, o cyecye a a paccex o ce [346]:

1. Ac ec n pax cooe. o oe pa oo x, o Aca eo ocaa, y Ac e ye cocoa ya, o e oa ocaa.

2. Ac ec eceoe cooee. o oe pa o n e, oop Aca o e cooee, Aca e coe ya, ao oa cooaa.

e a, yepe, o e-y oa ae peee.

5.7 Oopeea oc opaa onuc ompama c noo nocpeua Aca o xo a opa. O oc coac a coax, o o e xoe ca co oc, oa e ocaea oc pyoo. p o cpee o e ae apye - oa oc a ece. Ha pacco o oy opac ocpey.

(1) Aca ocae o opaa ocae ee Tpey.

(2) o ocae o opaa ocae ee Tpey.

(3) Tpe ocae cooee Ace, oy, cooaee, o pyo apep oca opa.

(4) Aca ocae e o opaa ocae x oy.

(5) o ocae oe o opaa, coxpae oy ce, ocae pyy Ace.

(6) Aca o cooa Tpey, o y aoo x ec ocaa oo apepa o opa a.

(7) Tpe yoae co e o opaa, c eceo oc o a.

o pooo paoae, ooy o Tpe aae y copo o oeeca pyo. Ec o oaec oaac o oc o opao a ae (5), Aca oe opac Tpey a oe opaa, ye ocaoo oo. Ec Aca oaec oaac o oc o opao a ae (4), o oe cea o e caoe. oa Tpe cooae, o o oy oa opaa a ae (3), Aca o ya, o pyo apep ye oca opa. Ec Tpe e oy oa opaa a aax (1) (2), o yoae eyc y eo o, oa copo e caa oee oaeca opaa.

Oopeea nonuc ompama e nocpeua (uo uy) Ec Aca o cpeac o y, o oy oca opa cey opao [1244]:

(1) Aca e epy yy coeo e epeae opa oy.

(2) o e epy yy coeo e epeae opa Ace.

(3) Aca e opy yy coeo e epeae opa oy.

(4) o e opy yy coeo e epeae opa Ace.

(5) o pooaec o ex op, oa Aca o e ay co ea ooc.

Ec peepe oeo poeo poooa ( Ac ee e oa), o o paoae oc a oo xopoo. Haca oo oy yy oc, Aca ae, o ao cy e cae aca ee o yco opaa. Ho acaa ya - o a opo o, o oeae aao ec e.

oa aa copo ae ecoo y oc, cy epoo coe yec, o oe copo oca opa. Xo, ec ec, cya eca yaa. oeo e, o, o opa e cyae cy oce aca epx y, a e oeo a o, o opa caoc ecy oce oo, a copo ay co ea. B ao ece poooa copo oaac ca opao? Haca ooy cox e? e pe? Tp eep?

Ta a Aca, o e a oo, c aoo oea aae ecoa opa, o y aoo x a poe ceo poooa ec oacee, o eo ee opa ye cy cy. He cyecye aa poooa, a oopo o co caa : "B aca epe y oc, a oo p. B ca opao, a e." oa e p pepaa oee poooa. oee oo, e oe copo o pooo, e oe epooc oo, o cy pe, o opa cy cy. coa, e p pepa pooo. B oe oo, o oa xoe oca opa, o p o co e xoe oca eo pae pyoo apepa.

Oopeea nonuc ompama e nocpeua (e uo cmpeu) B o poooe coyec aa e eopeeeoc [138]. Aca o o oepe yc ec aa oca poooa.

B o poooe Aca o oeac po ocax cooe a : " coace, o c epo oc p ca yco opaa."

oyae cooe oe pe eo cye , c epooc p, cy pae opa oca .

(1) Aca o coacoa ay ooa oca opaa.

(2) Aca o ooapac o pa epooce, oop o copac ooac. Hapep, Aca oe pe, o ee epooc cao yco opaa e oa pea e pooc oa oe, e a 2 poea. Ooa pae Ac a a, pae oa - a b.

(3) Aca ocae oy ocaoe cooee c epooc p = a.

(4) o ocae Ace ocaoe cooee c p = a + b.

(5) yc p - o epooc cooe, oyeoo Aco o oa a peye ae. Aca oc ae oy ocaoe cooee c p' = p + a 1, cop o ee.

(6) yc p - o epooc cooe, oyeoo oo o Ac a peye ae. o oca e Ace ocaoe cooee c p' = p + b 1, cop o ee.

(7) Aca o pooa o a (5) (6) o ex op, oa o oa e oya cooe c p = oa e acy coacoaa a ae (1) aa.

o epe oe poooa Aca, o coaac, o o oaac ca opao co ce oe oe epooc. Hapep, Aca oe opee coe a a 2 poea, a o coe b - a 1 poe. (ye o pa oe ppae, a o acpe a o ece.) B epo cooe Aca cooae, o oa caa opao c epooc 2 poea. o oe oe, o o ca opao c epooc 3 poea. Ceyee cooee Ac oe yepa, o oa c a a opao c epooc 5 poea a aee, oa epooc oox e ocy 100 poeo.

Ec Aca, o aep pooo ooopeo ae, o ce pepaco. B poo cyae, a copo oe pe opa cye ece c oca oce cooee pyo copo.

pee, e pocope opa, cy cya opao pae co ey 0 1. Ec o co ee epooc, ocao opo copoo, o oe copo ca opao. Ec o co oe epooc, ocao opo copoo, o oe copo e ca opao. (ae cy coxpae c ooaoe co a cya pee pyoo opoca, acaeoc oo e opaa.) eo o oaa e " ca opao c epooc p".

o ao pooo, o oy cooac ooee ycoe. Cy oe pa pe ee ocyce oo copo. Peee cy cae opao o oe copo, o oy x. He cyecye cya, oa oa copo caa opao, a pya - e. oee oo, pooo aepc, a oo oa copo axoe e xo eoo oy, e pya, epooc c ao opao.

Oopeea nonuc ompama e nocpeua (c noo punmopauu) o popaec pooo coye o e p ecx ao [529]. opeeeoc coyec DES, xo eco eo oe o cep aop.

(1) Aca, o cya opao pa 2n e DES, cpypoax oapo. B apax e eo ocoeoo, o poco coco pypo aoo poooa.

(2) Aca, o coa n ap cooe, Li Ri, apep, "o ea ooa oe i-o oc" "o paa ooa oe i-o oc". eaop, i, eec o 1 o n. B aoe cooee, e poo, ae ye xo poa oc opaa ea pee. opa caec oca , ec pya copoa oe pe oe oo, Li Ri, oo ap oce.

(3) Aca, o py co ap cooe apa e DES, eoe cooee - e o ape, a paoe - pa.

(4) Aca o oca py pyy co a 2n poax cooe, oc, ae cooe a ooa ax ap c.

(5) Aca o oca py pyy ce ap e, coy pooo pacceo epea ao ap. To ec, Aca ocae oy eaco ao n ap e o , cooa poa eoo cooe, o , cooa poa paoo cooe. o eae o e caoe. O oy oca co oo o oepe, caaa o oe oca ce 100, a oo pyo - o e ee ae. Teep y Ac, y oa ec o ooy y ao ap, o o e ae, ae ooo oy apep.

(6) Aca o, coy oyee , pacpoa e oo cooe, oope o o y pacpoa. O yeac, o pacpoae cooe pa.

(7) Aca o oca py pyy epe cex 2n e DES.

(8) Aca o oop a (7) opx o cex 2n e DES, ae pex o a aee, oa ce cex e DES e yy epea.

(9) Aca o pacpoa ocaec oo cooe, opa oca.

(10) Aca o oeac ap a, cooa poooa pacceo epea a ae (5), a x yeaec ocyc oeeca.

oey Ace oy yo o c y yy oceoaeoc ec? peoo, o Aca xoe coea, ocop, o oyc. Ha aax (4) (5) Aca oa papy poo o, oca oy eo e aae cpo. o oapy o a ae (6) p oe pacpoa oyee oo. o c oo eoacoc oe ocaoc o oo, a Aca coe pacp o a y ap cooe oa.

Ec Aca a oe xpo, oa oa papy oo ooy poooa. Oa oa o ca oy ooy ao ap pao, a eco opo opa ecccee cpo. Bepo oc oa oy pay ooy coca oo 50 poeo, ooy ooe cyae oe eco Ac yacc, o oo oo ap. Ec cooac oo e ap, o coco o eeca yacc 25 poeax cyae. Bo oey n oo eo. Ace eoxoo oo ya n a peya n poooo pacceo epea, ee epooc oc oo cocae 1 ac 2. Ec n = 10, y Ac 1 ac 1024 oay oa.

Aca ae oe opa oy cyae a ae (8). Booo, o e yae, o oa ocaa ey cyae , oa e oy ec e oaec pacpoa oo cooe. Ho co a epooc a copoe oa. O ye oy ooy e, Aca e ae ay. Ec n ocaoo eo, Aca aepa pe ey eccce a, oop y eo ye ec, o eee o yae, o oa aec eo oay.

Booo, Aca ye o a (8) o ex op, oa oa e oy ocaoo o e cp py oo, ae pepa epeay o. a a DES - 56 o. Ec oa oya 40 56 o, e ocaec epepa 216, 65536, e epo cooe, a a aaa, op e eeo, o ca copee oepa. Ho o oy poo coo e o ee e (, xy e cyae, a o ee), ceoaeo, o coe cea o e caoe. Ac e pyoo opa, poe a pooa ceoa poooy.

e o, o Ace pec pa eco, ooy o epooc oay oa co aa. B o e poooa y oex copo ec n ocax ap cooe, oe oopx ocaoo pao oc.

Ac ec oo o coco coea - oa oe oca oy oaoe cooe a ae (5). o e coe oapy oo o ooa poooa, o o coe cooa ceopay poo o a, o ye cy yoc Ac.

pooo oo a e a cax eca [138]. Bo epx, poea oae, ec cea o oo copo opao oe, e y pyo. Ec, apep, Aca oe o cpe py oo cpee oa, o oa pao pepa epeay o a ae (8) pacpoe oa caocoe o. oy, oopoy ax e ec poco e xa pee, e oee.

Bo opx, poea oae, ec oa copo pepaae pooo pae pee. Ec Aca oope oee poooa, oa coyc c oao ce poea, o y e xa pecypco aep ce yoy cpoy. poea oec, pepy, ec opa opeee, o Aca oa cea o-o epe ee, a oa pepae pooo o oe, oa oy c e ee oc opeyec e o paceo. Peaa cooc p o aaec o ae peea opaa, oopo poecc e ye aepe oo oe oca copoa.

poe cyecy ae poooo paeo 5.8 5.9.

5.8 epoa oa c oepee Tao e pooo oopeeo pacceo epea, cooa oca opaa, c e o ee coyec epoo o c oepee [529]. yc Aca xoe o ca cooee oy, o e xoe, o o poa eo, e paccac oye. B peao o oeceaec epe oo cya, o o e caoe oe ceao p oo popa. y poey ep paccope [490].

Ha ep , y poey o pe pooo oopeeoo oca opaa. Aca poco opye coe cooee o DES. Ee ooa poooa pepo a : "o ea o oa a DES: 32f5", a ooa poooa oa - a: "o ea ooa oe a." Bce oca oe e eec.

o o, oey o e paoae, coe, o pooo opaec a o, o paccea epeaa a ae (5) peoxpae o oeeca oe copo. Oa apepa a, o o oca pyo copoe pay ooy, o o e ae ay. O e oea a ae (8), ooy o epooc cyx o peao aa. Ec Aca ocae oy e cooee, a ooy a DES, o o e oe poep paoc a DES a ae (6). Aca e oe poep paoc a oa, ooy oy pec ec. Aca eo oe opa oy epa a oa o oapy o, eo a ye ye y Ac. Bo eeyxa, o.

Peee o poe opeye eoopo oppe poooa :

(1) Aca pye coe cooee cya o DES ocae eo oy.

(2) Aca coae n ap e DES. ep ao ap eeppyec cya opao, a opo pecae coo XOR epoo a a poa cooe.

(3) Aca pye cooee-ayy a cox 2n e.

(4) Aca ocae oy c ay poax cooe, poep, o o ae, ae cooe a ooa ax ap c.

(5) o coae n ap cyax e DES.

(6) o coae apy cooe, opayx pay a. Xopo apaa oy cy "o ea ooa oe a" "o ea ooa oe a" c oaee ao y cpo cyax o. O coae n ap a, yepy ay. a peye p o ooe a caec pao, ec Aca oe pe oe oo a (c o e e oepo) ce ee poa.

(7) o pye ay co apy cooe apa e DES, i-y apy cooe - i-o apo e, eoe cooee - e o ape, a paoe - pa. ape.

(8) o ocae Ace co ay poax cooe, poep, o oa ae, ae cooe a ooa ax ap c.

(9) Aca o oca py pyy ce ap e, coy pooo pacceo epea. To ec, Aca ocae oy eaco ao n ap e o , cooa po a eoo cooe, o , cooa poa paoo cooe. o eae o e caoe. O oy oca co oo o oepe, caaa o oe oca ce n, a oo pyo - o e ee ae. Teep y Ac, y oa ec o ooy y ao ap, o o e ae, ae ooo oy apep.

(10) Aca o pacpoa e oo cooe, oope oy yeac, o pacpo ae cooe pa.

(11) Aca o oca py pyy epe cex 2n e DES. (Ec o ecooc, o Ea coe poa ooe cooe, o o o poa co oe a).

(12) Aca o oop a (11) opx o cex 2n e DES, ae pex o a a ee, oa ce cex e DES e yy epea.

(13) Aca o pacpoa ocaec oo cooe. Aca oyae pay a o oa, a o oe o "caee " o ap e poy , o op apoao opaoe cooee.

(14) Aca o oeac ap a, cooa poooa pacceo epea, a x yeaec ocyc oeeca.

a (5)-(8) oa (9)-(12) oex copo e ec o cpae c poooo oca o paa. Oe - cooex-ayax Ac. O peoca oy oooc poep pa oc ee pacceo epea a ae (10), o acae ee ocaac eco a aax (11)-(13). , a poooa oopeeoo oca opaa, oe poooa peyc oe oo o oo cooe Ac.

5.9 Oopee oe cepea Aca ae cepe A, a o - cepe B. Aca copaec coo oy A, ec o paccae e B. o xo e coo Ace B, ec oa paccae ey A. Cey pooo, ocya a oo ope, paoa e ye:

(1) Aca: " cay, ec cae e ep."

(2) o: " cay, ec cae e epo."

(3) Aca: "He, ep."

(4) o: "Hy, xopoo.'' o ee Ace.

(5) Aca: "Xa, a ee e cay."

(6) o: "o e eco."

ec o oe cea popa. peye a poooa c peaa oee o e o poooa, oop oo Ace oy oopeeo oec cepea [529]. o e oop ooc ec pooo, apoca eoxoe ee poooa o c oepee.

Aca oe a (1)-(4), coy aece cooe A. o oe e ec, co y aece coeo cooe B. Aca o o paccey epeay a ae (9), pacpoa a ae (10) e oo, oope oy, o eoxoe epa a aax (11) (12). o ac o E, o o poa co cooe. Haoe, Aca, o pacpoa oca ec oo ap cooe o XOR o ap e, o oy , oop apoa opae cooe.

o pooo ooe Ace oy oopeeo oeac cepea, o e apapye aeca epeax cepeo. Aca oe ooea oy a apa Moapa pca ey cxey oco coo epo. o oy oo o cepe, oop Aca pe ey. pye pooo oca [1286, 195, 991, 1524, 705, 753, 259, 358, 415].

aa oepece pooo 6.1 eoace op oepoe oocoae oa e ye cooao ox opo, oa e oc po o o, oop oopeeo peoxpae o oeeca aae ay oc. ea pooo oe oaa, o ee epe, cey ec coca :

1. oocoa oy oo e, o ee a o pao.

2. a oe oocoa e oee ooo paa.

3. Ho e oe ya, a oo pooocoa ope pae.

4. Ho e oe pooocoa eco pyoo. (o oaaec ca e peoae.) 5. Ho e oe ao e e-o ooc.

6. a oocy oe poep, o eo ooc yac p oee oo oocoa.

poe oo, eoopx cxe oocoa oe oaoc ceyee peoae :

7. a ae, o oocoa, a o e.

pee e oca coe pooo, ee peee xapaepc, aae e a pa poooo opoe.

npoe npomoo oocoau (1) a oocy pye co ee op o epao paeo occ ().

(2) a oocy ocae co ee .

(3) pacpoae ee, oo o oyoae peya oocoa.

o pooo poco poea. e oe ya, oya oye ee, ae, p aea pcae ee paoo pae. ee e aeeo pecae o o, e oocoa paooe pae oe ooo paa. ooeo copoo ec eoo oc e ee pyoo eoea, o o e ye ac o cea, ooy o opao o ocoa oopo, oac yx peyao opo.

npoe npomoo oocoau (1) a oocy ocae co ee co ap o.

(2) a oocy pye co ee op o .

(3) a oocy ocae co ee .

(4) pacpoae ee, poepe oc, oo o oyoae peya o ocoa.

o pooo oaae coca 1 2 : Too paooe pae oy oocoa, o e oe oocoa oee ooo paa - oe aca ee, oyee a ae (3). a ee oca ap o oocyeo, ooy ae, o oocoa, a o e, , a o o coa a pae. Ec oye ee, oop e oca paoo ooaee, ee, oca paee, oop ye pooocoa, o ao ee oppyec occe. poe oo, -a poo oc o e oe e ee pyoo pae, ae ec cyee epexa eo a ae (2).

poea oo poooa o, o oc oaec ee, ae, o a oo oocoa.

poae eee op o eae ocopo oyope poooo yaa, o a oo oocoa, o a pec ooc oep o a yo ae oocoa a epe eo aae epo cy.

a ceyx pepa oaa, a pyo oece xo epe p peoa poooy eoacoo oocoa.

oocoaue co cenu nonucu Ha yo a-o oe ee o oocyeo, coxpa poeypy ea oc.

eo o oo cea c oo poooa ceo oc.

(1) a pae coae 10 aopo cooe, a aop coep pa ee aoo oooo peyaa (apep, ec eee ec o oeo "a"-"e", o a aop coco yx eee, ooo "a", a pyoo "e" ). aoe cooee coep ae cya opao coa eao oep, ocaoo oo, o ea ya c py pae.

(2) a pae o acpye ce cooe (c. pae 5.3) ocae x ece c a c py oe.

(3) o coe ae ax poepe, o ooae e pca pae oca co aa c poae ee. opae 9 aopo, poep, o o pao coppoa. ae oa yao ocae aoe cooee aopa ocae x opao pae, coxpa pae coe ae ax.

(4) pae cae acpoy c cooe oyae aop eee, ocax . ( ee oca, o e apoa, ooy pae eo y, ao eee - "a", a ao - "e". ) (5) a pae pae o eee (o, eopa!) pye eo op o .

(6) pae opae co ee.

(7) pacpoae ee, poepe oc, poepe o ae ax yaoc e aooo oepa, coxpae oceoae oep oo o. Oa oyoae pey a oocoa ece c a oceoae oepo cooecy eee.

Mop, pae-y, e oe oay y ccey. pooo ceo oc oeceae e ceoc eo ee. Ec o oaec opa o e ee a, oapy yp o ae oceoaex oepo a ae (7) e ye ya opo ee. Ec o oaec o y ecoo eee a ae (2), oapy o a ae (3). Mop e oe coa co cocee ee, ooy o o e ae apoo a occ. o o e pe o e oe epexa e ye ee.

pooo "papea pa" a ae (3) oe oece yaoc eee. e oo aa Mop o coa oo ao e, a cee eaooo oepa, aop eee aep x ce .

Moeeca e coe ya, a oocoa ope pae. Ta a pooo ceo oc acpye oceoaee oepa eee o oea oee oo, e coe yca o c ey oca e aacpoa eee ooae eee. Oy oae epe oceoaex oepo cax c eee ooe ooae ye c, o x ee pao ye.

Ho poe ce ee ocac. Ec a (6) e aoe, oe aca, o ao ee pca, o oa coe ya, o a oo oocoa. Oao, o eooo, ec occ oyae e e aeaao ype oocoa cae x oe. Xo e coe ycao c ey pae x ee, oa coe coa ooe oeco ocax pax e ee coea, pca x caa cee. ec Aca oapy, o oea ee ee, oa e coe oaa oo. Aao pooo, ac ycpa poe, oca [1195, 1370].

oocoaue c y empau ouccuu O pee ec pae ooa. H y oo x e ye ocaoo ac, o coea o coey ycope.

B ceye poooe coyec epaoe ypaee pecpa (P), aaeec poe p o ooaee, oea ocea eee [1373].

(1) a pae opae co P, apaa pecpao oep.

(2) P opaae pae cya pecpao oep. P ee cco pecpaox oepo. poe oo, P xpa cco oyaee pecpaox oepo a cya, ec o-o oaec pooocoa a.

(3) P opae cco pecpaox oepo .

(4) a pae pae cya eao oep. O coae cooee c o e po, pecpao oepo, oye P, co eee. O ocae o cooee .

(5) poepe pecpaoe oepa o ccy, oyeoy o P a ae (3). Ec pecpa o oep ec cce, epae eo (o ea oopoo oocoa). oa e eao oep ccy ex, o pooocoa a opeeeoo aaa, pae ey cooecyey oooy cy.

(6) oce oo, a ce ee yy oye, yye peya ece co cca, coep a eaoe oepa cooecye ee.

a peye poooe a pae oe ye cco eaox oepo a e co coce. Ta o oe yec, o eo ee ye. oeo, ce cooe, o op oeac yac poooa o apoa oca, o oea oy y a ce a pyoo epexa cooe.

e oe e ee, ooy o a pae ye ca co pecpao o ep. Ec pae e axo co pecpao oep axo eo ooo cce c py p e yao oocoa, o eeeo yae, o pooe oa. e oe oa ee y p y, oopa axoc o aee P. P ae, coo paee apecppoaoc, x pec paoe oepa oapy e ee.

Mop, e oaa pae paa, oe oac coea, yaa pa pecpao oep. poa oo oe poaa, ec oeco oox pecpao x oepo aoo oe, e oeco peax pecpaox oepo : 100-ooe co oa paee. oeo e, pecpaoe oepa o eeppoac cya opao.

Hecop a o, P oa acya oep opao ac - e oa oe apecp poa epaoox paee. Oa ae oe apecppoa paoox paee ecoo pa. o pc oe cee yy, ec P oyye cco apecppoaxc pa e e (o e x pecpaox oepo). Ec co paee o cce ee, e co oc ax eee, o o-o e a. Oao, ec apecppoaoc oe paee, e o pcao eee, o o, ooo, oaae, o p apecppoaxc paee e pooocoa. Moe, apecppoac, e ypyac poc ypy co ee.

o pooo eae epe coopo P. Ec o ecy ece, o oy oe co a ax ya, o a oo oocye.

oocoaue c oo empao ouccue o ea oacoc coopa ey P oo cooa oee co pooo [1373].

o pooo ee peyey c y ee :

P c eo opaae, aooo pacpeee pecpaox oepo a ae (2) coyec ANDOS (c. pae 4.13).

Ta a pooo aooo pacpeee e e ooe ya, y aoo pae ao pecpao oep, e cocoa ca pecpaoe oepa oyee ee. Ho oa ae opao, o e aa pecpaox oepo epaoo pa e . y poey ae oo pe c oo cex oce.

yeoe oocoaue c oo empao ouccue B o poooe ae coyec ANDOS [1175]. O yoeope ce ec peoa xopoeo poooa oocoa. O e yoeope ceoy peoa, o oaae y coca, oo epecee aae paea ec coc :

7. pae oe e coe ee (.e., aypoa co ee pooocoa aoo ) eee aaoo epoa pee.

8. Ec pae oapyae, o eo ee oca epao, o oe ycao c pa poey, e pcy eoacoc coeo ee.

Bo o pooo:

(1) yye cco cex paoox paee.

(2) B eee opeeeoo cpoa a pae cooae , copaec o oocoa.

(3) yye cco paee, yacyx opax.

(4) a pae oyae eao oep, I, c oo poooa ANDOS.

(5) a pae eeppye apy op /ap : k, d. If Ec v - o ee, o pae coae ocae ceyee cooee :

I,Ek(I, v) o cooee oo ocao aoo.

(6) oepae oyee ee, yy :

Ek(I, v) (7) a pae ocae :

I, d (8) pacpoae ee. B oe opo oa yye x peya , aoo apaa opa, cco cooecy a e Ek(I, v).

(9) Ec pae oapyae, o eo ee oca epao, o poecye, oca :

I, Ek(I, v), d (10) Ec pae xoe e co ee c v a v', o ocae :

I, Ek(I, v'), d pyo pooo oocoa coye eco ANDOS cee oc, o o cy ao e oaec [585]. a (1) - (3) c peape. x e coco o, o ya oyoa cex ecex paee. Xo eoope x, epoo, e py yac oocoa, o yeae oooc oa oee ee.

Ha ae (4) a pae oy oy o o e eao oep. a oooc o e poaa, ec co oox eaox oepo ye opao oe, e co peax paee. Ec a pae pca ee c oao eaopo, eeppye o eao oep, I', pae ooo paee yye :

I',Ek(I, v) Baee oo ee yae o pooee yae ocae co ee coa, oop a (5) c o eao oepo.

a (6) ae aoy pae oooc poep, o pao oya eo ee.

Ec eo ee epao oca, o oe oaa o a ae ( 9). peoaa, o ee pae a ae (6) pae, cooee, oopoe o ocae a ae (9) oaae, o eo ee epao oca.

Oo poe oo poooa ec o, o yeca coe ocooac e, o ope coo o aepe oocoa a ae (2), o e oocoa eceoc. pyo poeo ec cooc poooa ANDOS. Aop peoey paa paee a ee py, a pep paee opya.

Ee oo, oee cepeo poeo ec o, o oe e oca ao-y ee.

a poea epapea: Aca yepae, o aepeo peepe ee eee, a ye p ae, o Aca oa e oocoaa.

oocoaue e empao uupameo ouccuu B ceye poooe e coyec, pae ce py a pyo. o pooo, coa Mao Meppo [452, 1076, 453], acoo pooo, o oooc eo peaa oe e eoe coea, o ce e oaoc c ye oeo.

Aca, o, po oocy (a/e 0/1) o aoy-o opocy. yc y aoo pae ec op ap . yc ae ce ope ec ce.

(1) a oocy peae, a oocoa, eae ceyee:

(a) oae cyay cpoy coey ee.

(b) pye peya aa (a) op o a.

(c) pye peya aa (b) op o po.

(d) pye peya aa (c) op o oa.

(e) pye peya aa (d) op o Ac.

(f) oae oy cyay cpoy peyay aa ( e) pye oyeec op o a. O acae aee cyao cpo.

(g) oae oy cyay cpoy peyay aa ( f) pye oyeec op o po. O acae aee cyao cpo.

(h) oae oy cyay cpoy peyay aa ( g) pye oyeec op o oa. O acae aee cyao cpo.

(i) oae oy cyay cpoy peyay aa ( g) pye oyeec op o Ac. O acae aee cyao cpo.

Ec E - o y poa, Ri - cyaa cpoa, a V - ee, o eo cooee ye e cey opao:

EA(R5,EB(R4,EC(R3,ED(R2,EA(EB(EC(ED(V,R1 )))))))) a oocy coxpae poeyoe peya a ao ae ce. peya yy cooac a aex aax poooa oepe, o ee aoo pae ye ye.

(2) a oocy opae cooee Ace.

(3) Aca pacpoae ce ee, coy co ap , yae ce cyae cpo a o ypoe.

(4) Aca epeacoae ce ee ocae peya oy.

Teep a ee ye e c ey opao:

EB(R4,EC(R3,ED(R2,EA(EB(EC(ED(V,R1 ))))))) (5) o pacpoae ce ee, coy co ap , poepe, ec eo ee cpe pcax eee, yae ce cyae cpo a o ypoe, acye ee oc a e peya po.

Teep a ee ye e c ey opao:

EC(R3,ED(R2,EA(EB(EC(ED(V,R1 )))))) (6) po pacpoae ce ee, coy co ap , poepe, ec ee ee cpe pcax eee, yae ce cyae cpo a o ypoe, acye ee oc a e peya y.

Teep a ee ye e c ey opao:

ED(R2,EA(EB(EC(ED(V,R1 ))))) (7) pacpoae ce ee, coy co ap , poepe, ec eo ee cpe pcax eee, yae ce cyae cpo a o ypoe, acye ee oc a e peya Ace.

Teep a ee ye e c ey opao:

EA(EB(EC(ED(V,R1 )))) (8) Aca pacpoae ce ee, coy co ap , poepe, ec ee ee cpe pcax eee, ocae ce ee ocae peya oy, po y.

Teep a ee ye e c ey opao:

SA (EB(EC(ED(V,R1 )))) (9) o poepe yae oc Ac. O pacpoae ce ee, coy co ap , poepe, ec eo ee cpe pcax eee, ocae ce ee o cae peya Ace, po y.

Teep a ee ye e c ey opao:

SB(EC(ED(V,R1 ))) (10) po poepe yae oc oa. Oa pacpoae ce ee, coy co ap , poepe, ec ee ee cpe pcax eee, ocae ce ee o cae peya Ace, oy y.

Teep a ee ye e c ey opao:

SC(ED(V,R1 )) (11) poepe yae oc po. O pacpoae ce ee, coy co ap , poepe, ec eo ee cpe pcax eee, ocae ce ee o cae peya Ace, oy po.

Teep a ee ye e c ey opao:

SD(V,R1 ) (12) Bce poep ya oc a. O yeac, o x ee axoc cpe oye x (axo co cyay cpoy).

(13) Bce ya cyae cpo aoo ee cypye ee.

o pooo e oo paoae, o ca ec co appo. Aca, o, po eeeo ya, ec o-y x oaec oea. He yo ax P. o ye, a o paoae, oaec coea.

Ec o-y aec oa ee, Aca oapy y oy a ae (3), oa oa oy eee oe e oeco e, yacyx oocoa. Ec Aca oaec oa ee, o oapy o a ae (4).

oee oo ec oea ooo ee py. Ta a ee pyc pa o p a, a oe coa coo pax eee, coo yo. pooo e ppoa coco yx ace: epa ae a (3)-(7), a opa - a (8)-(11). oea ooca a pax aax oapyaec o paoy.

Ec o-y ae o ee py o opo ac, eo ec yy oapye ee eo. Ha ao ae ee ocac ocac ce pae. Ec o pae ( ecoo) oapyae, o eo ee oe e cpe aopa eee, o eeeo pe paae oee poooa. Ta a ee ocac a ao ae, a a a oe epyc o opo ac poooa a ecoo ao aa, o oapy oea, oeeo ee, eo.

aea ooo ee py epo ac poooa oee oa. Aca e oe cea aey a ae (3), ooy o o, po oapya o a aax (5), (6) (7). o oe opooa a a e (5). Ec o ae ee po a (oe, o e ae, ao ee e), po ae o a aax (6) (7). O e yy a, o oe x ee (xo o oe o-o, ye opaoa ee), o o yy a, o x ooca oee. Ec oy oeo, ey yaoc oe ee Ac, oa e ae oo o opo ac poooa. Toa oa oapy ceoee coeo ooca a ae (8), o e coe ya, o oe ee. B epo ac e e epeacoac a ao ae e ocac, ooy o e coe opaoa pooo opao opee, o oe ee.

pyo opo oeeca ec oa ya, o a oo pooocoa. -a epeaco eee epo ac o e coe opaoa pooo opao ca ee oocyx. a ee cyax cpo epo ac ae ec pea coxpae aooc. Ec cpo e yac, epeeae ooco oe eppoao p oo oopoo poa oya e x ooco op o oo, o x acoa. oa pooo ocaoc, oeaoc e ee coxpac.

oee oo, -a aao cyao cpo, R1, ae oaoe ee pyc o paoy a ao ae poooa. Ho e oe ya aee ee o aa (11).

ao poe oo poooa? Bo epx, oe poooa y paoe ce.

B peeo pepe oocoa pa yace oo eepo, o o ye coe. Tao poo o e coe paoa p peax opax c eca c oocyx. Bo opx, yae pey a opo pae ocax. Xo o e oe o a peya, o oyae opeeeoe p e yeco. C pyo copo aoe ae ooo p epaoao cxee oocoa.

Tpe poea aaec o, o Aca oe copoa ee pyoo yaca, ae e a eo coepa apaee. o o, oey o oe ca poeo, paccop op pex oocyx - Ac, oa E. Ee e a peya opo, o oa xoe a, a oocoaa Aca.

ooy oa opye ee Ac, peya opo ye cooecoa ee Ac.

pyue cxe oocoau o peoeo oo cox eoacx poooo opo. x oo pae a a a. Cye cy pooo c epeeae, a "oocoae e epao paeo occ ", oopx ce ee epeeac, o o e o ca ee p ae.

Tae cyecy pooo c paeee, oopx e ee ec ey pa ce occ a, o oa x e coe oay paee [360, 359, 118, 115]. po oo pooo aa aooc paee oo, ec pae "ac" paeca ( o e poo oocoae) e coapac po pae. (e pa epa opa a ecoo ace, oope oyc oepe, oo oa o ecy apaeo, pa [316].) O poooo c paeee peoe [1371]. Ocoa e coco o, o a p a e e co ee a ecoo ace. Hapep, ec ee coepa "a" "e", 1 oo aaa "a", a 0 - "e", pae o coa ecoo ce, oope cye aa 0 1.

o ocac ce occ, ao o oo, ae pyc coxpac. a ep cypye oyee o (cyecy pooo, oeceae paoc oa ), ooae o ec cyo cex poeyox oo. Cyecy ae pooo, apapye, o o aoo pae yy coe oye 0 1.

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