WWW.DISSERS.RU


...
    !

Pages:     | 1 |   ...   | 2 | 3 || 5 | 6 |   ...   | 14 |

pc aep paa popa 2-e ae pooo, aop cxoe ec a e C COEPAHE . pecoe Beee aa 1 Ocoe o 1.1 Tepoo 1.2 ...

-- [ 4 ] --

(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.

pyo pooo, peoe o ayo [322], ooe poce pae, oop ae c oea. Oao, op pec poo oopo, c eaeo ooae. o o xo e pe a pae opo c o co paee.

Ee o, oee co pooo, pea eoope x poe oo a [770, 771]. Cy ecye ae pooo, coy p co o a [219]. pyo pooo, oop, a yepaec, oxo pyoacax opo, pee [585]. A [347] ooe pae e oocoa.

pooo oocoa paoa, o ae oea poay oyy ooco. oa oyae oe yepe, o poae pooocye, a oea, cy y ooca caoc ee cee. P poo oo cpoepoa e oepe, e oo pae oaa oy-o ee, o o p o oocoa opeee opao [117, 1170, 1372].

6.2 eoace ce c eco yaca eoace ce c eco yaca peca coo pooo, c oo oop o o pya e oe opeee opao c y ox epeex. a pye oeceae oy ecoo epeex. Peya ce caoc ec aoy pye, o oy e ec ae, peocaee py ea py, ec o e ec oe peyaa ce. He peeo ecoo pepo:

pomoo l a oe pya e c co cpe apay e oo, o apaa ooo caa eca pyoy?

(1) Aca oae cepeoe cyaoe co cye coe apa, pye peya op o oa ocae eo oy.

(2) o pacpoae peya co ap o. O oae cyy coe apa oye oy o Ac ae, pye peya op o po ocae eo po.

(3) po pacpoae peya co ap o. Oa oae cyy coe apa o y eoy o oa ae, pye peya op o a ocae eo y.

(4) pacpoae peya co ap o. O oae cyy coe apa o y eoy o po ae, pye peya op o Ac ocae eo Ace.

(5) Aca pacpoae peya co ap o. Oa ae cyaoe co, paeoe a ae (1), oya cyy cex apa.

(6) Aca e peya a co e ( ao cyae a epe) oe peya.

o pooo opayeae, o a yac ece - o xo oy ocoa, o cey poooy. Ec o yaco coe o coe apae, cpe apaa ye paccaa epao.

oee cepea poea coco o, o Aca oe caa oo peya. Oa oe ec a ae (5) oe co, oopoe ee ycpaae, o o o e yae. oea Ace cea o oo, opeoa o ee py ee cyaoe co c oo oo cxe pye a paea 4.9, o oa oa opoe coe cyaoe co oe poooa o coe ya ee apay.

pomoo Aca o ece pecopae cop o o, o cape. Ho, oao, e xoe coo pyoy co opac. a x o poea co opac a yo oepeo epao copoe (apep, oay), o o cpa ca ye o peya Ace, oy.

peeoo poooa ec e poe. Bo epx, cee cocooc cpeeo oa e oo ey opaoa cya oee co e opeeee oeo yx ce. o opx, ec Aca o eceo aoc o coxpae coe opa ae, poc y o oaa ae c epao oo, o o eo e paoa yey.

popa c op a peaae cyeceo eee ecoe peee. Cyecye po o o, cooec c oop Aca, a aee a, o, a b, oy coeco opee epo , o a

oeo, o pooo e a o ax oeo. Ho e coe oea Ace ( oy, aa paa) coa o coe opace. Ec o oepo popao, oopa ceo ceoaa poooy, Aca oa ya eo opac (ec opaco oepo popa opeo pee c oea ee aca c oea ee ayca?), oopo o pooo. Aca oa y a a, o ee opac - 60 e. a, o oa cape, oa oa o pooo coa, yaa, o ee o pac - 30 e. a, o o cape, oa oa coa o pooo, yaa, o ee opac - 45 e, a aee, oa Aca e yae opac oa c o yo e cee ooc.

p yco, o yac e oaa ceao, o pooo eo pacp ecox yaco. oe oeco e oe opee opo x opaco c oo oceoaex ecx pee poooa, ao yac e coe ya opac pyoo.

pomoo Aca pac aac c e ee. B poecx aax oa aoe eco a a paope co. Oa eca cecc cox pe, o c yooce a oo-y, o pae c x... ... opa .

B Cye eoacx ce c eco yaca cpoepoa pooo oox e. M ayepoa ea cco x pcpac o "apacx ypaeo" o "ox poo". Paeee oeo e c, Aca o oy yacoa eoaco poooe c e co yaca. O ece oy opee, ec y x oe p. Ec ec, o o ycpec oooy cac. Ec e, o o o eoaco paccac, coxpa yepeoc, o x p ocac ae. Ho, ae Cya eoacx ce c eco yaca, o a e yae o x pcpacx.

Bo a o paoae:

(1) C oo ooapaeo y Aca xpye co py a ceay cpoy.

(2) coy y ceay cpoy a eeo oep, Aca o o oy oepy ocae c o oee oy. Ec o e oeae, oep e ocyaec. Aca pee ooapaey y eeooy oepy o ex op, oa e aec o-y, o oxa pooo.

(3) Aca cooae oy, coo pa e poc pe ooapaey y coe p e.

(4) o xpye co py coo e pa. O ae coye ceay cpoy a eeo oep cpaae eoea a pyo oe pooa, e eo cooe.

Opae ae, o y oa ec oooc cp c cooae paoo opoo eca.

O oe xpoa pacpocpaee p oo o oyeyc eeoy, paca coo e eo. o pooo peao paoae oo aoe cpe epao -a ocaooo ca oox opx eco cooe.

Tae cyecye aeaec pooo, oxo a pooo 2. Aca ae a, o ae b, o ece ac opee, epo , o a = b, pe a, o o eo e ya o a, a Aca - o b.

opooc oo a paee 23.14.

pomoo Bo pya poea eoacx ce co o yaca [1373]: coe ce peypo cpeaec, o ao pooocoa o eoop opoca. (Bce ope, o ypa po - e oope oy, o a pooopc.) Bce e coea oy oocoa "a" "e". poe oo, e copo oaa "cyep-ee": 5-a 5-e. O e oa cooa "cyep-ee" , ec xo, oy ocooac o ee. Ec o e coye "cyep-ee", o opoc peaec poc oco ooco. B cyae pee ooo yx aex "cyep eee" ce oe ooca oppyc. B cyae yx poopeax opoc peaec oco ox ooco. Ha ye pooo, oop aeo ocyece ay opy oocoa.

Ceye a pepa cppy poecc oocoa. yc yacy ox paee, o N1 o N5, a cyeppae: S1 S2. Bo oocoae o opocy 1:

S1 S2 N1 N2 N3 N4 N Cyep-a e e e e a a B o pepe ecye oo o "cyep-ee" S1, peya oocoa - "a". A o ooc o ae o opocy 2:

S1 S2 N1 N2 N3 N4 N Cyep-a Cyep-e e e e a a B o pepe a "cyep-ee" epay py pya, opoc peaec oco o x "e".

Ec e peyec cp opa o o, o cyepee pea, o o pocoe peee eoacoo poooa oocoa. Cope o opa opeye oee cooo e o acoo poooa ce c eco yaca.

o oocoa oe poo peao . o oe ac opaaoo cpy y p opopa, e eoope oaa oe ac e pye, ac poeyp OOH, e o ocyapca e oee aee, e pye.

eycoe eonace npomoo c ecouu yacmuau o oo ac cya oe eope: a y c n xoa oe cea n poa cocoo, oop oo ce ya aee y, o oe oeco poo, eee, e n/2, e coe oy ao ooeo opa, e ceye x cocex xoo peyaa ce. opooc oo a [136, 334, 1288, 621].

eonaca oea cxe Bxo Ac - a, a oa - b. O ece xo c eoopy y f(a,b) a, o Aca e coa eo ya o xoe oa, a o - o xoe Ac. aa poea eoacx ce c e co yaca ae aaec eoaco oeo cxe. Aca o oy coa poo y oecy cxey. a cxea oyae a xo ae Ac oa ae peya. eoaca oea cxe ec poooo, oop peaye ceye p peoa :

1. Aca oe ec coe aee a, o o e coe eo ya.

2. o oe ec coe aee a, o Aca e coe eo ya.

3. Aca, o oy c peya, pe oe copo yy yee o, o peya pae e oacoa oo copoo.

ea poooa eoaco oe cxe oo a [831].

6.3 Aoa pooeaea epeaa cooe Ba e yacc ooea c oae popao e oaac cpe oecoeo epea. B [321] ay o poey oeax popao :

Tp popaa c a oeo coe o pexeoo pecopae. x oa cooae , o ep o e p eoxoe ep, o ce oo o oa aoo. a oe o aa o p o pao NSA. Tp popaa oe yaa pao aoo x aa aoo, o xoeoc a, a a NSA.

a popaa Ace, oy po ya, e aa a oe o-y x, o e pe e apy aooc aea? ay peae poey:

a popa pocae eceey oey, ppc co e, ey popao cpaa o e o a, o oo o oe oy e peya. ae a popa poo oe, yaa e oe - oa eo oa eo eoo cocea - a oy a pae copo. Ec ae - o popao, o eo yep e e pooooo oy, o o . Heeoe co aex pa a coo yaae, o oe oaae popa;

eoe co pa - o NSA (p yco, o oe oe oae oo o pa). Oao, ec oe oaae popa, o yx pyx e yae ceax ae, o e opeo o a oe.

o ye, a o paoae, oopae, o Aca aec o, o yx pyx popao aa a oe (p yco, o e oa e NSA). Ec oa e pax oe, o o oa pyx popaa (o po) caa, "oaoe" oa caa, "pae". (oe, eeoe co p opao, oopx "pae" yaae, o oa o-o x.). Ec oa caa "pae", o ae - popa, c e ceo oee, peya poca oopo o e, o y cpo oe (poeo ey oo po). Ec oa caa "oaoe", o ae - popa, c e ceo oee, peya poca oopo oaec o peyaa poca cpo oe. Oao, ec Aca e oaox oe, o o caa, "oaoe", a po - "pae", o caa "pae", a po - "oaoe". Ec cpa oea - aa e a e e e oe, o a e - popa, oop caa, "pae". Ec cpa oea oa o x e yx oe, o ae - popa, oop caa "oaoe". o opee, o a, o cex x cyax Aca oa a peya poca oe ey oo po.

o pooo oe ooe a oe oeco popao, oope c o pyy poca oe ey coo. aa apa popao oe pooo. oeo, o a, o a, o o o, aa a poooo oe caa oo, o aa o popao NSA, o e co e yaa, ao popao a.

peee oo poooa xo aeo a pee oeeoo coa. Bo pep eycooo o pae eoceaeoo opae. pya ooaee ce oe cooa o pooo opae aox cooe.

(1) ooae yopoac o pyy.

(2) epe peype epa pee cocee ap ooaee poca ey coo oey, co y ao-y eoac o oyeo pooo poca "eco" oe.

(3) oce aoo poca a ooae oe o "oaoe", o "pae".

Ec Aca xoe epea pooeaeoe cooee, oa poco aae eppoa coe ye p ee ex payax, oope cooecy 1 oo pecae ee cooe. Hapep, ec ee cooee o "1001", oa eppye ee yepee, coo pay, coo pay, ae epp y e coa yepee. p yco, o peyao ee poco o "pae", "oaoe", "oaoe", "oaoe", oa ye oop "oaoe", "oaoe ", "oaoe", "pae".

Ec Aca aeae, o o peya poooa e cooecye cooe, oopoe oa poye o ca, oa oae, o o e pe o-o ee aec oca cooee. Toa oa pepaae e peay cooe ae cyaoe oeco payo epe oepeo oo. Toe apaep o paoa a ocoe paa cooe ce, o e ocaoo oa.

o cea eo ee oee epec, cooe oy apoa op o p y oo ooae. ae, oa a pae cooee (paeca peaa oa a caape aoo ooa cooe), oo opeee oyae coe pacpoa poec cooee. Ho pyo eo e yae po aopa cooe e coe opee oyae cooe. ae ec yacc pacpoa ca cooe, o aa paa, ocea copa op eooaecoo oea, ecoe e.

Aepao poca oe ey coce copoa oo cooae aa cya x o. Booo, copo o xpa a a CD-ROM, o e ap o eeppoa ay o oca x pyo copoe (oeo, apoao e). , o o ooopc cooa coeco popaec eoac eepaop ceocyax ce, a x co eeppoa poooa y e cay oceoaeoc ceocyax o.

poeo oo poooa ec o, o xo oea yac e coe a ax c o oe, o oe eaeo cop c ccey, ocoo oaa a ae (3). Cyecye o a peyeo poooa, ooa oapy peeco [1578, 1242]. a poea aaec "Oeae popa coee ".

6.4 epoe ae Hae e - o poea. Papaae x oc, o cococy pacpocpae poo, oy pac x y Bac. e pee apo ye oeco ax ee, oopaa x c oece, o ooe yaee ax ee aec eooo. oo oa e pooe;

o p o apoa oece ee oa oo e oyc. e pee apo oo p o ce, e oee cpc o oo, oy a e.

C pyo copo, e pee apo oo opac ay y a o a pee. B oa e oyc , o o c xoa a a o a, o oece oy poce a acoe oepa. O oy e, e oyaee a, e oyaee ey, oy oe o eeoy, ce o e opac o cox oepx epao. o ye a co aooc, o a co e a.

cac, cyecye co pooo, oop papeae cooae aepex, o eocea e x cooe. oc Aca oe epea epoe e opeccey oy a, o ae peopep Ea eo e yaa o Ace. o oe ae oc epoe e a co ao c ce, ae ec a e ee o Ace aoo pecae. Ho ec Aca poye oya oa a y e cay op epox ee, oopy oa cooaa oya oa, oa ye oapyea ao. ec o poye oc op epox ee a a pax cea, o ye oapyeo, o o, a Aca, ocaec o ao. oa o aaec ao epo ea, o oo o o x o oceaex epox ee, a pe x apoe.

B oox eax cyecye oa oecea eoxooc. C poco cooa Internet oepecx oepa pace opeoc cepeoc epeaaeo o ce opa aooc p ee e. (eec eao p oo, o oaac oca oep x peo apo o Internet.) C pyo copo, a paeca, o oy, e oea ycy opo a copee aoc ccea. Xo pec o cea. Bce, o opeyec, o e poe e o oy, - o oee eoopoo acyaeo oep ypee, eaeo peopaoa p peae e.

pooo epox ee oe co. ae a a ao ocpo o x. oee o poo o o poooe oo poa [318, 339, 325, 335, 340]. Ho oe, o oo o poo o o epox ee, cyecy pye.

pomoo epe ecoo poooo peca coo ece aao popaecx poooo.

Cey pooo ec ypoe ec poooo aox eex eo :

(1) Aca oo 100 aox eex eo o $1000 a.

(2) Aca aae a x co opoao ya 100 pax oepo ooc ce oep a.

(3) a opae 99 oepo yeaec, o a e ca a $1000.

(4) a ocae ece ocac epaceaa oep. C oo opoao ya oc epeoc a e. a opaae epaceaa oep Ace ccae $1000 c ee cea.

(5) Aca cpae oep oae ee e poay.

(6) poae poepe aocy oc, yeac aooc eeoo ea.

(7) poae ooc ee e a.

(8) a poepe co oc ace $1000 a ce poaa.

o pooo paoae. a e ee e, oop o ocae, ooy, oa poae pece e a, a oa e yae, o o e Ac. aoap oc a yee aooc ea. A -a poooa "papea pa" (c. pae 5.1) a yepe, o epaceaa ee e - a cyy $1000 (a e $100000 $100000000). O poepe ocae 99 oepo, ooy epooc oaa aa Aco cocae oo 1 poe. oeo, a aa a oa ocaoo oo pa, ao, o e coo oea. Be ec a poco oaec oca oce e (ec Aca oaa a oae), e pay Acy, oa poo co o, oa e e oee. yee cpe co ycpae - o peoe aee.

pomoo pey pooo e ae Ace aca e a cyy, oy o aeo, o o e eae e ocepoopoa e cooa eo a. o aaec poeo oopo oa;

ee pe ee pec yco pooo:

(1) Aca oo 100 aox eex eo o $1000 a. aoy eeoy ey oa oa e yay cpoy, pay cya opao ocaoo y, o epooc c ooa o cpo py eoeo a peepeo aa.

(2) Aca aae a x co opoao ya 100 pax oepo ooc ce oep a.

(3) a opae 99 oepo yeaec, o a e ca a $1000.

(4) a ocae ece ocac epaceaa oep. C oo opoao ya oc epeoc a e. a opaae epaceaa oep Ace ccae $1000 c ee cea.

(5) Aca cpae oep oae ee e poay.

(6) poae poepe aocy oc, yeac aooc eeoo ea.

(7) poae ooc ee e a.

(8) a poepe co oc o coe ae ax yeaec, o ee e c ao yao cpoo paee e eopoac. Ec o a, a ace $1000 a ce poaa acae y ay cpoy ay ax.

(9) Ec ee e ye eopoa paee, a oaaec p eo.

Teep, ec Aca oaec pacac cepooe eeoo ea poae oaec eo poa ee e oopo, coy cepoo, a yae o o.

pomoo pey pooo aae a o oeo, o e ycaaae x oc. a e ae, o ac eoe, oop oy e (a eo e ae o Ace ), oay poaa, poae aec oay a. a eooaoc cpaec cey poooo :

(1) Aca oo 100 aox eex eo o $1000 a. aoy eeoy ey oa oa e yay cpoy, pay cya opao ocaoo y, o epooc c ooa o cpo py eoeo a peepeo aa.

(2) Aca aae a x co opoao ya 100 pax oepo ooc ce oep a.

(3) a opae 99 oepo yeaec, o a e ca a $1000, o ce cyae cpo pa.

(4) a ocae ece ocac epaceaa oep. C oo opoao ya oc epeoc a e. a opaae epaceaa oep Ace ccae $1000 c ee cea.

(5) Aca cpae oep oae ee e poay.

(6) poae poepe aocy oc, yeac aooc eeoo ea.

(7) poae poc Acy aca cyay eaoy cpoy a eeo ee.

(8) Aca oe o.

(9) poae ooc ee e a.

(10) a poepe co oc o coe ae ax yeaec, o ee e c ao yao cpoo paee e eopoac. Ec o a, a ace $1000 a ce poaa acae y ay cpoy ay ax.

(11) Ec yaa cpoa ye ec ae ax, a oaaec p ee e cpaae eaoy cpoy a eeo ee c xpao ae ax. Ec o coaa, o a yeaec, o o a ca c ea poao. Ec eaoe cpo pa, o a ae, o e copoa eoeo, oop eo oo.

B o poooe peoaaec, o poae e oe e eaoy cpoy oce oo, a Aca ae ee a eeo ee. Ha eeo ee o axoc p eox apao, o o pe o peoa opoa Aca oa ao peca oa. ee e o cea ya, oopa pec p cpaex.

Ta a poae a aoecy oce oo, a Aca opa e, poay oy cy oxo ee e. paece peaa oo poooa o opeoa o Ac ooa y accooo aapaa, oa poae ye papac c ao, oo ae, a o pocxo ceo p opaoe aee c cooae pex apoe.

Aca ae oe pcococ oy. Oa oe opa o eeoo ea opo pa, a ca y e cay eaoy cpoy a ae (7). Ec poae e ee ay ax ye oye x eex eo, o ye ee ayee. y poey ycpae cey pooo.

pomoo Ec oaec, o eoe, ca aoc e, oac oay poaa, o a oe a xoe oc oo eoea. o cea o, pec epyc o ecx aao p p o pa.

o cpa Ac epoo ee, oo ocooac eoo paee cepea.

(1) Aca oo n aox eex eo a aay cyy.

a eo coep yay cpoy, X, oyey cya opao ocaoo y, o epooc oe yx oaox cpo a peepeo aa.

Ha ao ee ec ae n ap ox cpo ea, I1, I2,..., In. (eo a, n pax ap a ao ee.) aa x ap eeppyec cey opao : Aca coae cpoy, co epay ee , apec poe cee, peyee ao. ae oa e y cpoy a e ac, coy pooo ee cepea (c. pae 3.6) pyae ay ac, coy pooo py e o.

Hapep, I37 coco yx ace: I37 I37. aa ac pecae coo ae pyex L R o, oop Acy oy opoc op, e opoe coepae oe oeo po e peo. a apa (apep, I37 I37, o e I37 I38 ), pacpae oc Ac. a L R L R eo cey opao:

Cya aa cpoa: :

Cpo ea: I1 = (I1, I1 ) L R I2 = (I2, I2 ) L R....

In = (In, In ) L R (2) Aca acpye ce n eo c oo poooa ceo oc ooc e a.

(3) a poc Acy c acpoy c n-1 eex eo yeaec, o ce o pao oop e. a poepe cyy, yay cpoy poc Acy pacp ce cpo ea.

(4) Ec a yoeope, e oapy oo oeeca, o ocae ocac aacp o a ee e. a opaae aacpoa e Ace ccae cyy c ee cea.

(5) Aca cae acpoy c ea pa eo y poaa.

(6) poae poepe aocy oc, yeac aooc eeoo ea.

(7) poae cya opao poc Acy pacp o ee, o pae oo cex cpo ea a ee. o cy, poae ae Ace cyay n-oy cpoy-ceeop, b1, b2,..., bn. ey pay ooy Ii opoe Aca, ac o ae bi, 0 1.

(8) Aca oe o.

(9) poae ooc ee e a.

(10) a poepe co oc o coe ae ax yeaec, o ee e c ao yao cpoo paee e eopoac. Ec o a, a ace yaay cyy a ce poaa a cae yay cpoy ay ax.

(11) Ec yaa cpoa ye ec ae ax, a oaaec p ee e cpaae eaoy cpoy a eeo ee c xpao ae ax. Ec o coaa, o a yeaec, o e copoa poao. Ec eaoe cpo pa, o a a e, o e copoa eoeo, oop oo o ee e. Ta a opo poae, o y e, a Ace pyy, e ep, cpoy-ceeop, a oapy, o ao-o o Aca opa ey ooy ooy poay, a pay - pyoy. Bo a o oa cpo ea oepa XOR, a opee oc Ac.

o eca epec pooo, ooy ocop a eo c pax copo.

Moe Aca coea? Ee epoe e peca coo poco cpoy o, oopy oa eo oe copoa. opa x ep pa - e poea, oa poco o pooo, ce poe e poe. poae ac e a ae (7) cyay n-oy cpoy-ceeop, Aca opoe o ey, o pay ooy ao Ii a ae (8). Ha ae (10) a ae ce ae ece c yao cpoo eeoo ea.

oa oa oaec cooa e e epoe e opo pa, poae (o e o) ac e a ae (7) pyy cyay n-oy cpoy-ceeop. Aca oa o a (8), ee oa eeeo cpeo poaa. Teep, oa poae poc e a a ae (10), a ee eo ae, o ee e c o yao cpoo ye eopoa. a cpaae ope oo cpo ea. Bepooc coae yx cyax cpo-ceeopo cocae o ac 2n, oo e cyc o ceyeo oeee. Teep a axo apy, epa ooa oopo a opa ep pa, a opa - o opo, oe a ooa oepa XOR eae Ac. Ta a yae, o oac ocooac eo a.

o o pooo e eae Ace oea, o ee oeeco o aepa ye oapyeo.

Coea, Aca e coe coxpa ae co oc. Oa e oe e yay cpoy, ay-y cpo ea, ae copc aoca oc, poae eee o ae o a ae (6).

Aca oa oac ocyy ay oxo ee e, ao, a oopo cpo e a e pacpa ee e, , ee ye, pacpa oo-o ee. Bepooc, o aa yoa po co o aa a ae (3), cocae 1 n. o e eooo, o ec pa a oeeco oc a oo cypo, Aca e ye ca cyy. oee ye co ox eo, pe ex Aco a ae (1).

Moe coea poae? Eo ac ae xye. O e oe eopoa ee e a , a ae oopoe cooae cpo-ceeopa. O e coe oea, o Acy, a a oo oa oe op y cpoy ea.

He ooe oay a o coop ey Aco poao. Ec a oca ee e c yao cpoo, o oe yepe o, o o e ye oae oo o pa.

A a ace aa? Moe o c, o ee e, oye o poaa, o ec o c a e, oop oca Ac ? Ha aax (2)-(5) Aca aea poooo ceo oc.

a e coe ca Acy e, ae ec o ooc coxpae ac ao paa. oee oo, ae oec, a poae e coy ycao oc Ac. Aca oe poc o aa y , ocaac ooc aoo, y o, o e ao.

Moe coea Ea. Ec oa coe ocya c ey Aco poao, ec oa coe opac o aa pae poaa, oa coe epo eopoa e. a pe eo , o xye, oa poae oaec eopoa co e, o o ye oe oeece. Ec Ea ypa e epoe e Ac ycee opa x pee Ac, o oeece ye oea Aca. He cyecye cocoa oea oy, o ec p cece aooc ax. Aca, poae o aa co a, a o aa co e.

Meco oo poooa e-o ey poooo c ocpeo caoocao poooo. Aca, poae oep ay o, o acaec ee, o Aca e oa oep ay cee o cox o yax.

empoe aue u ueaoe npueeue epox ax ec co ea copoa. oa e yo a oo cepeoc. Co pe, a Aca coepae eaoe pecyee [1575]:

(1) Aca pae peea.

(2) Aca oo 10000 aox eex eo o $1000 ( pyoe oeco eo yoo e o c oca).

(3) Aca acpye ce 10000 eex eo, coy pooo ceo oc. Oa ocae x a c c ypoo y peea, ec e yy oe ceye cpy :

(a) Bce 10000 eex eo o oca ao.

(b) Peya o oyoa aee.

(4) Bac coaac.

(5) Aca oyae aey, cae acpoy c eex eo aae pa x. He coy a ee, poce a ee ea.

(6) Aca ocooae peea.

aee, o a cya opao xye e p cooa x ecx ocee, apep, ax. e ecoo oaa y o opao ee aco aepa oxe.

Oao, oe cyae epoe ae e co yo pecyo. poea o, o aooc paoae oo oo copo - oyae aoe, a poae e. oee oo, poae e coe cp a oye ee. epoe ae ooy paecy opee, coo ee apaaaee, o opee, a x pae, ocaec eoo.

Peae empoe aue oaca oa, DigiCash, aee oe ac aeo oac epox ax pe a oaa pooo epox ax paoax poyax owns. Ec aepecoac , opaec DigiCash BV, Kruislaan 419, 1098 VA Amsterdam, Nethe rlands.

pyue npomoo empox aux Cyecy pye pooo epox ax, c. [707, 1554, 734, 1633, 973]. P x co ye eca opey aeay. Pae pooo epox ax oo pae a pa e aeop. aooe cce pey, o poae cac c ao p ao poae, o oe oxoe a ceo pooo pex apoe. Ec oae aa-y poea, a e pae ae, Aca e oe coea.

Aooe cce, ooe poooy 4, e pey coee ey poao ao o ooa paa ey poao oyaee. cce e oea Ace oea, o eco oo oapya ee oeeco. pooo 4 oapyae oeeco Ac, pacpa ee oc p oe oea. Aca ae o ocecx , ooy, e oeae.

pyo y coco coa ceao eeyao ap (c. Pae 24.13), coepae a ey pocxey, aaey aaee [332, 341, 387]. Mpocxea-aae xpa ay ax cex ace epox ax, opaex o eeyao ao. Ec Aca o aec copoa ae-o epoe ae opa x a, epea pocxea aae oapya ay oy e papea paa. Ta a pocxea-aae aea o eaeca e, Aca e coe cepe -ay ax e papye eeya o ap. Hae e oy oopaac ooe, oa o, aoe yy eopoa, a oe poep ae opee oea, ec pooe oa.

pooo epox ax oo pae o pyoy pay. Hoa epox oe cpoa, , coy ay ccey, ye p oe pax oao. epoe e oy cooa x cy o aaoo acya, a eopae ocao oe opae a ce.

y o coepeo oac py o pya aoo poooa epox o e c [225, 226, 227] [563, 564, 565]. Tae oo peo ccea NetCash (Ceee ae) c oee ca coca [1048, 1049]. pyo oo cceo ec [289].

B [1211] Taya Oaoo (Tatsuaki Okamoto) ayo Oxa (Kazuo Ohta) epec ec coc e ao cce epox ax :

1. Heacoc. eoacoc epox ax e ac o ecoaxoe. Hae o y epea o oep ce.

2. eoacoc. epoe ae e copoa oopo cooa.

3. Taa oc (Heoceaeoc). Taa oc ooae aea, c ey o o aee eo oya oapy eooo.

4. Aoo ae. oa ooae pacaaec a oyy epo a, p o oo ey ooaee poao oec aooo. To ec, aay e yo coe c c epa oepo opao aea ooae.

5. epeeaeoc. Hae oy epeaac py ooae.

6. eoc. aaa cya epox ax oe oeea a ac ee cy.

(oeo, oa cya oe oa coc.) Paee peee pooo yoeop peoa 1, 2, 3 4, o e yoeop peoa 5 6. P aoox cce epox ax yoeope ce peoa poe 4 [318, 413, 1243].

epa aooa ccea, yoeopa peoa 1, 2, 3 4, oxoa a oy ocax, a peoea [339]. Oaoo Oxa peo ccey, yoeopa peoa c 1 o 5 [1209], o ae peo ccey, yoeopy peoa c 1 o 6, oe ax ooo aea coc a peo 200 eaa. pya aooa ccea epox oe c oooc ee ocaa [522].

Cxea epox ax, peoea e e aopa [1211], yoeope peoa c1 o e eoxooc aoo opooo oea ax. O oe ax ooo epooo aea cocae ooo 20 oa, pooo oe oe a ecoo cey. Aop paccapa y cxey a epy eay ccey eoceaex epox ax.

Aoue peume apmou o pooo [988] a oc ea coye ecoo pax ao. a e ee ce yx pax aax. ep a, oopoy eca oc eoea, oe ac e a eo ce. Bopo a ae ea oo o ceoo (ooo oepoy cey ea p co ae).

e oe pa e opoo aa, oaa, o o ec aee cea. Ho, o a e ae oc eoea e oe ac e a eo ce. ep a ae ea epece e o opo a, e a ceoa. ae e aoo pa e. B oe eca opo a cae ce epoy ay, ep, o o eo oa. ep a epeae ce ey, ep, o o eo oa. oa e oaae ce, ep a epece ooee e o opo a.

Bce paa pooc epe ocpea, oop ecye ooo epooy eepaoy Peepy:

oaae aoce cea, pecppye cooe coae opo ce.

Oe ey eo, poao pa aa ocoo ee [988]. Ec ce e coap ac po ea, eo aooc apapoaa. Oao, o e epoe ae, a co eo oe oea. pooo ooe ea ooac peyeca pex apoe, e pacpa coe oc.

ac popaece eo aa a a 7.1 a cepoo a eoacoc cepo pocce ec ye yx aopo: aeoc aopa a. ep oee ae, o po opoo ee poeocppoa.

yc aeoc aopa coepea. Ha pae oo peao pyo ocy, o pepe ocaoo eo. o coepeco opayea ocyce yeo y oa pocce, e cpe pyo co c oo epeopa cex oox e.

oe aoo cp poaay peyec ycoe poeca cooecyeo o poo eca, cpe pyo co pecae coo cpe c ec op eco. o oo pa poaay oaoc o poeca cooecy op ec : oo a. aoy ae yco opoo eca poeca ee, e oo cee peca. poa a oe oy a-o opao o opoo eca cooe epexa cooecy poec. O oe a o-o o opae poeca : apep, o o a opae WordPerfect, y eo ec caap aooo cooe epoo o, a aaoa UNIX, opae e opae TIFF, caapa ac ae ax eo. Bce opa coepa eoope peopeeee a. poaay aoo cp e yo oo opoo eca.

Pacca cooc cp pyo co epyo. Ec coyec 8-o , o cyecye 28, 256, oox e. Ceoaeo, oapye paoo a opeyec, caoe o ee, 256 oo, c 50-poeo epooc a y oce oo oo. Ec a a paa 56 a, o cyecye 2 oox e. Ec oep oe poep o e ceyy, oc yoo a ae cpee 2285 e. Ec coyec 64-o , o oy e cyepoepy oaoc ooo 585000 e, o a pa cpe 2 oox e. Ec a a paa 128 a oc a ae 1025 e. Bopac ceeo cocae ceo e, ooy 1025 e - o ooe pe. p 2048-oo e o oepo, paoa apae o poep o e ceyy, opa 10 e ocax a. oy pee ceea ao pacpc, pepac o coec.

pee e ac opea poccey c 8-oa o, coe, o pyo copoo ec aeoc: aop oe acoo eoace, o yeo cocoa, e cpa eo pyo co, e cyecoao. o e a poco, a oe oaac. popa - o ooe cycco.

Be coepe pocce aco oaac peao ca. apa ee, e cex ce pocce, oe peo oca x. popaa-e ceye oepa o apaoaoy coe a o aop. ye oep aopa, a oop oa c poeccoae popa, e cye oa x, e ooac yepe ocpyopo aopo o x paoo eoacoc.

Bcoe a oe paea 1.1: eoacoc pocce oa ocoac a e, a e ocoeocx aopa. peoo, o poaay ec ce opooc aeo aopa.

peoo, o y eo ec coo poeca, coo ey yo, o o oaec o e coe cpe c cooae oo poeca. peoo, o o oaec o cpe c cooae opoo eca, e coe pacope coo ax, coo ey yo. peo o ae, o o oaec o cpe c cooae paoo opoo eca. Ec a a poccea ocaec eoaco ae epe o cex oox oacoce, o... y ac eceo o-o ec.

Hecop a o peypeee pocpaco, peocaeoe popae aepa, ocaoo eo. B eceoc, eoacoc aoo a o ox paecx cyax e ya. o ca pao e ax a cex cpec, a y ox paec, a e, o oaae a oooc, oe oaac ey aa ay poccey. Ec opayee a oop c e cepy ooe paeco, poepee pae aop, peee oe o , yy ac eo eoxo. A ce ocae yc poco oya yooc e.

Oeu peeu u cmouocmu cpmu pyo cuo Bcoe, o cpe pyo co oo ec cpe c cooae ecoo opoo eca, oo yo eoo poeca cooecyeo opoo eca. Ec peoaaee, o aoee e cocoa oa aopa ec cpe pyo co - ooe oyee o oe ocaoo , o cea cpe eoo. Hacoo ?

Copoc cp pyo co opeeec y apaepa : oeco poepex e copoc poep ooo a. oco cepx aopo aece a oy co o a aece a y oy oceoaeoc cpoao . a a DES coca e 56 , ceo oe 256 oox e. a e pa aopo, ocyaex o e, pa 64 a, ceo oe 2 oox e. pye aop coy 128-oe .

Copoc, c oopo oe poepe a , ee eee aoe aee. poooo aaa peoaa, o copoc poep a aoo aopa pepo oaoa. B ec eoc copoc poep ooo aopa oe a, p ae ec pa e e pyoo.

Ho a a ex e, oopx poo oc, pe oca o pa oe, e pe poep ooo a, eoe o copoc poep e e ae.

B pooeco cpee oco copo o ooy cp pyo co coeppoa opy aopa DES. B 1977 oy Map Xea [497] copypoa yco cyecoa ceapoao a o oy DES. a aa coco oo pocxe, aa o o px poepe o e ceyy. Taa aa a a aca coe poep 256 a 20 aco. p cp aopa c 64-o o poepa cex 264 opeye 214 e.

aaa cp pyo co a yo ceao pyaa apaex poeccopo. a poeccop poepe ooeco pocpaca e. poeccopa e yo oeac ey coo opae, ece coye cooee ye cooee, capyee o ycexe. He pe yec ocy ooy yacy a. Cocpypoa ay c oo poeccopo, a o o px paoae eaco o pyx, epyo.

Cocpypoa ay oa pyo co Ma Bep pe [1597, 1598]. (O cocpypoa ay DES, o aa oe oe o cex aopo.) O papaoa ceapo ae pocxe, a co, oe apa cea o, o a o oapo oo ocp o ay, oopa coe oa 56- DES key cpee a 3.5 aca ( aepa a 7 aco).

Coooee cooc/copoc ec e. pa e ae ooe 6-.

Bcoe o aoe Mypa: o cex cpec peo ae 18 ece. o oaae, o apa yy yeac a opo ae e, o, o 1995 oy co o oapo, 2000 oy ye co ooo 100000 oapo. Ee oee ypoc poecc ce oa oeep a [724].

56-ox e cy oaac oe o apay ocy pyx opopa o pa opaa. Boee e oca poeo pax cpa oy oo aa 64-e . Bcpe 80-oo a ce ee a peea oooo, o ec eya ee coxpac, o epe ax-y pa e ce oe ec.

oeo, eeo poopoa oepy o a 35 e epe. Texooece pop, oy pe ayo aace, oy cea poo ce. C pyo copo, eece a coee pe ece opae oy cea poo epeao oc. B popa yee eccco. peee aope 80-oo a aec eocaoo ao.

coye , a oopoo, o ee epe, 112 .

Ta. 7-1.

Oe cpeeo pee aapaoo cp pyo co 1995 oy.

a e ax Cooc 40 56 64 80 112 $100 2 cey 35 aco 1 o 70000 e 1014 e 1019 e $1 M 0.2 cey 3.5 aca 37 e 7000 e 1013 e 1018 e $10 M 0.02 cey 21 ya 4 700 e 1012 e 1017 e $100 M 2 cey 2 y 9 aco 70 e 1011 e 1016 e $1 0.2 cey 13 1 ac 7 e 1010 e 1015 e $10 0.02. cey 1 ceya 5.4 y 245 e 109 e 1014 e $100 2 pocey 0.1 cey 32 cey 24 108 e 1013 e $1 T 0.2 pocey 0.01 cey 3 cey 2.4 107 e 1012 e $10 T 0.02 pocey 1 ceya 0.3 cey 6 aco 106 e 1011 e Ec o oe co xoe oa , ce, o ey yo, o opa e.

Ceoaeo, co oac opee ay "ey" a: peeax ao cooc cee oo ooac o o pee, e eo cpe cae ooec o ? pa cya: ec poaoe cooee co $1.39, o e acooo cca ycaaa aapaypy co oc 10 oo oapo oa oo a. C pyo copo, ec cooc opoo eca 100 oo oapo, o eppoae oo oooo cooe oe oy cooc aapa y p oa. poe oo, cooc ox cooe co peee oe cpo aae.

popaoe cpmue e ceapoao aapayp opox apaex a cpe pyo co aoo coee. popaoe cpe c pa eeee, e aapaoe.

Peaa ypoa popaoo cp pyo co cpaa e coe eeoc, a e, o aoe cpe "cooo". Heo e co apy pocaa pooep poepo oox e. Ec pa ye ae - aeaeo, ec e - eo e oepo. Heo e co c ooa oo ey ce pooepo. B eax cepeax c DES 40 paox ca eee ooo cye poep 234 e [603]. p o copoc poep cex e ope y ec epe oa e, o ec o cp yy pep ocao oeco e, o oy-y e-y oee. a o caao [603]:

Ocoo ypoo popaoo cp ec ceoe eee. pecae cee yepcecy ce 512 o e ex ce paox ca. eoopx yepcecx opoo o ce eca cpeeo paepa. Tae ce oy ae pacoc o cey py, ooppy co eeoc o epoo oe. yc aa paoa ca cocoa paoa (c aopo) co copoc 15000 poa ceyy.... C yeo aax pacxoo a poepy cey e ye copoc o... 8192 poepo ceyy a ay. o, coy ocay ccey, ce p a pocpaco (56-ox) e opeyec 545 e ( peooe, o ce pa a y aay 24 aca cy). ae, oao, o c oo ax ce copo aeo cyea oya o ac 200000 pac p eee ooo . a o ye x ac opaca o ooo ecec ec c. e c pee x aapaypa, e oe aecoao a, e ye caoc x ac. Bepooc apaoa a , pa a caax, ecoa, o pae e p ao coo pecc-pe. pepy, o opao oa epooc, e oooc pa paecex oepex. "O a o"? "O pa a cy e "?

oe eooo c oo oeceoc ea ae ae. ec pee o pooac pc?

cooae aopa c 64-o o eco 56-ooo a eae o cpe 256 pa coee. A 40-o eae apy poco epaoco. Ce 400 oepo c pooe oc 32000 poa ceyy oe a e o cpe py oo 40-ooo a.

(B 1992 oy aop RC2 RC4 o papeeo coppoa c 40- o o - c. pae 13.8.) 128-o eae eeo ae c o cp py oo. o oee poex c epo 1996 oy pe ye cooac 200 oo oepo. a oea ae ce - acoo pea Cray o oox oepo. ae ec ce oep yy poe a cpe pyo co, a x ye o o poa ceyy, pe pacp a ce pao ye o pa oe pee cyecoa ceeo.

Hepoe cemu Hepoe ce e co po poaaa, epy oepe -a op pocpaca p e e. ye ceo epoe ce paoa c poea, e epepoe oeco pee, o oopx ye pyx. o ooe epo ce oyac, peaa ce yee ye p e e. Ocyce epepoc aope o e ocae eca oye : o pacpoee , o e. (o pae epe, o epo p cooa oo xopoeo aopa.) Hepoe ce xopo o paoa cpyyppoax cpeax, e oyee ooo, o e coopoo, ayec cya pe popa.

Bupyc Caa oa pyoc oye oo oepo cp py oo - o ye o oepx aee p yace o cp. B o eo opoc, o o peye oo pee, o oy caa e. B o pooa co opac x oep, o o opeye ee oe pee oe aoc a apeco. B o ae cooa o ep pyc, o pacpocpa popay oa cpe a oo oeo oeca o e po.

a ocoeo oapa e epe oac [1593]. Bo e ycae a o oe p pyc. o pyc e epeopapye ec c, e yae a, o o pe poco oepa o paoae a poaaeco poeo pyoo oa. Pae cceoa oaa, o o ep pocaae o 70 o 90 poeo pee, a o y pyca e ye poe c peee pee o aa. Ec o epeoaee pyx ooex, o eo paoa ae e ye aea.

B oe oo, oa aa aec a pa . B o oe ec a apaa p o oe. Bo epx, pyc o opo pyo pyc. O e ea eo, poe caoocpoee yae cex aex o cpaeo pyca, o coepa opa o pao e.

o o pyc poco pacpocpac cpe oepo, oa e opac o oepa eo e a, oop aca epoaa pyc.

py, pyc oxoo a o a pa ceyeo cooe :

B o oepe ec cepea oa. oayca ooe 1-8001234567 poye oepaopy ceyee 64 ooe co:

xxxx xxxx xxxx xxxx epoy, o coo o o oe ye aeo oapaee 100 oapo.

Hacoo eo aoe cpe? yc apae oep poepe cy e ceyy. a copoc aoo ee oeax oooce oepa, e oaae, o o oa ye ea pye e. peoo ae, o pyc pye 10 oo a. o pyc oe cp 56-o a 83 , a 64 o - a 58 e. Ba ooo p oc oy papaoo apycoo popaoo oecee, o o ye a poe. oe yeee copoc oepo pacpocpae pyca, oeo, ceao o aaee oee e.

umaca omepe aca oepe - eec, o oo coco coa poao apaeo a poaaa [1278]. Boopae, o pocxea, cpaa aop pyo co co copoc o poepo ceyy, cpoea a poa paope eeop. aa pocxea ap o papoaa aoaeco poep paoo aopa e oce oye ap op ec/poec o py. a pa oa acoe paeco xoe pacp , oo epeae cxoe ae o pao. Bce paope eeop cpae aa xe. B oeo cee, pa oec a e-y cee. acoe paeco a p oy eoey o apapye, o peya ye cooe cpo pao, ae cococye pooy ycexy p a opeo eeopo c pocxea cp.

Ec y aoo eoea ae, y o ya, ea peeo, ec paope ee op, o paoe aee 56-ooo a oc epe 61 ceyy. Ec paope eeop ec oo y aoo ecoo aa(o o eceoc), o pa oc epe y. pa 64-o ye pacp epe 4.3 aca (43 aca, ec paope eeop ec oo y aoo ecoo aa).

o cea aoe cpe oo a pae, eoxoo cea p oa. Bo epx, poe, o aa pocxea poepa cyae, a e yae . o ceae cpe a 39% eeee, o e oe ao ce aoo acaa. ae, aca oyceca ap oa p peee, o a oe a co pe eeop opeeeoe pe, o apapoa paoy cex pex ycpoc o pe epea ap op ec/poec. Haoe, aoy oo paao oo ep - a o a aaec - oa oec y eo a pae aa cpoy ce, oyc a pae.

eoc aco oepe pax cpa pax a oaaa 5-. co, o a oaac ye ooe, ec y aoo aa - y, e peea - a co pe eeop. B Coeex aax e ee e, o opao oe aapayp.

a Bao caocoeo coe oa 56-o ee, e a e.

Ta. 7-2.

Oe cpeeo pee cp pyo co p aco oepee (Bce ae World Almanac and Book of Facts a 1995 o.) Cpaa Haceee oeco eeo- Bpe oa po/paopeo 56 64 a a 1190431000 257000000 280 cey 20 aco CA 260714000 739000000 97 cey 6.9 aca pa 19890000 4730000 4.2 aca 44 pa 5051000 3640000 5.5 aca 58 e Bao 470000 1330000 15 aco 160 e Beya, Heaa 6100 17300 48 e 34 oa uomexoou Ec ooo coae opocxe, o o yo e oac cooa x cpyea poaaa cpe pyo. Paccop oeecoe ooe, aaeoe "DESoapo" [1278].

Oo coco ooecx eo, yex poep ooe . ap "op ec/poec" ocya e o eoopoy oecoy aay (e , ce e popa ). Pee ocac opaa pe DESoapa c oo ceax eo, yeecyx o poeoco ccee ooo.

T oap coco 1014 eo (e aep). Ec aa x oe o p o a ceyy (eoxo peya), cpe 56-ooo a ae ce eccx cey.

Bcpe 64-ooo a opeye ee, e e ecx cey. Bcpe 8-ooo a ce e poc 1011 e.

pyo ooec oxo coco cooa eeec poepyex poaaecx opcx oopoce, oope ye o cpe popaecx aopo pyo co [1278].

Tae opa, op oy oac, oo coa pacpeeey ay c o o e co poeccopo. apa "op ec/poec" oa epeaac o pao epe cy. O a pyee peyaa opao oo cypoa eae e e e, cooa peee opao a cy.

peoo, o a ea opco oopoc - o y co copoo 10 po (ooo, o oea cepxy, ceoaeo 1015 eo ao yec ep. Bece x oea, opa apax (518 apax oepo) a yy o ep (o a poe, a ocyec o - oa oo e), y ac ye 10 oopoce (oee e coe apa aoo), aax oeae. ( cpae, aepa Valdez eo 10 oo aoo e.) Ec aa x oe poep o e ceyy, o 128-ooo aopa o pacpo oo cyc e. (Boee p o eee opcx oopoce - o aa poea.) pye oce cp o ec opcx oopoce, x aep ae paep a oeae oy aeo ye a e. ae e cpaae e o aoexoo.

Tepouauecue opaueu O cec aoa opoo epoa ec o, o pecae opa eo xoo eoopoe oeco ep. ac oooo a, ea cocoe cce, peye o eca ep e ee e kT;

e T - acoa eepaypa cce k - ocoa oaa. (He oyec, ypo ye o aoe.) p, o k = l.38*10-16 p/K, o eepaypa opyae ceeo 3.2K, ea oep, pa oa p 3.2K, ope 4.4*10-16 pa c pa, oa o ycaaae cpacae . Paoa oepa p eepaype oee o, e eepaypa ocecoo pocpaca, opeoaa o oex pacxoo ep ooa ea.

aee, ep, yaea a Coe a o, cocae ooo 1.21*1041 po. o ocaoo oe 2*1056 epee a ae eao oepe, a oo, co oepe, xa oo, o 187-o ce poea ce co ae. Ec ocpo opy Coa cepy acoa ep e xa e cx oep c eo ep a 32 oa, coe oy oep ce ce. oeo, ep poee ax-y oex ce c ceo ye e ocaec.

Ho o oo oa aa ea. p pe o cepxoo eec ooo 10 po. (B co pa oe ep eec e epo, o yc o oa ea.) Ec c y ep yacc poc a oy cey op, o ce co ae coe p 219-o ce.

ca e e eo oeo c cao aapaypo, o poco oaa acae ae, oycoee epoao. poe oo, ca ao eocppy, o cpe pyo co 256-ooo a ye eooo, oa oep ocpoe oo aep pacoaac oo pocpace.

7.2 a opoo a Ooapaee y ocyac paee 2.3. Ooapaeo ye ec yoee yx ox pocx ce, oy poeee, epeo ca, epyo, o eeo pao p o eee a oe oy a ox pocx ca (c. pae 11.3). popa c op a coye y e coa ooapaeo y c o. Ha cao ee, o o, e oaao, o paoee a oe ec eo poeo (c. pae 11.4). Hacoo ceo eco, o oxoe a pay. ae ec o a, o e oe oaa, o pye poe ec eo py. Bce ca, o paoee a oe ec pyo aae, o o oa e o oaao aeaec.

Ha o co ocaoc oopoee. eo peca, o e epe 50 coepec ece, co a capoe opoe pe, oa ce ca, o paoee a oe o py eao o c oe popa, a pae oa ea oo e. eo oopa, o yye oce eop ce ypoc paoee a oe oce eop cooc cea paoee a oe pa. He p ep o - oco e, ax ocaoo, o e coceoe ee, cae a, o oooe pae co ec aoepo - o e p ep, o aoo popa e cyc.

B o cyae, opye ceo aop poa c op o ocoa a py o c paoe a oe ox ce, oope c poeee yx ox pocx ce.

(pye aop ocoa a a aaeo cpeo poeo oapa, o oa peoo, o e pe e e paccye.) aop ae ocp cp pyo co, o o paoy. Bo x aopo coco e epeopa cex oox e, a oo paoe ox ce a oe ( cpex oapo oe oo oeo oac - oo aa e poea). Ec co co ao, a e ae. Ec co ocaoo eo, o aeo ae po ce ceo o pa, ec oa ye c a o aae c aco eo pee o ex op, oa Coe e cae cepxoo - aoo ceoee oae aea o poe. B paee 11.3 paoee a oe paccapaec aeaec opoo, a ec op a yc oeo pee paoe a oe ce pao .

Paaa oe ca a oe eeo, o, ecac poepoo aopo, o poecc caoc ce ee. o ee xye, o caoc ee oe copoc, e pecaaoc aeaa. B 1976 oy Pap a (Richard Guy) ca: " eao ye, ec o-y ayc paaa a oe pooe ca opa 10 eee aoo coe" [680]. B oy Po Pec (Ron Rivest) a, o paoee a oe 125-papoo ca opeye 40 a poo e [599]. B 1994 oy o paoeo a oe 129-papoe co [66]. Ec oo oo cea ae-o o, o oo o, o pecaa yo.

B 4- pee peya paoe a oe a oce y e. Ca cp ao po paoe a oe ec apaoe peeo (c. pae 11.3).

ca co ya. Ceo 512-oe ca ye coyc oepaox cceax. Pa o ee x a oe, oa opoea, a opao, cce a, oe peao. ep Internet o cea o eee yea.

Ta. 7-3.

Paoee a oe c oo "apaoo peea" co ecx pap- Bo coo pa coee pao o o paoeo ce a oe 512-ooe co 1983 71 >20 oo 1985 80 >2 oo 1988 90 1989 100 1993 120 1994 129 Bcea o oo epec mips-oax: ooa paoa oepa, oeo o oepa ceyy (one-million-instruction-per-second, mips), ooo 3*1013 oepa. po, o a a c pooeoc 1 mips-o aea VAX 11/780 oa DEC. To ec, mips-o - o o pao oepa VAX 11/780 aeoo. (100 M Pentium - o aa 50 mips, a Intel Paragon 1800 yo - pepo 50000 mips.) B 1983 oy paoee a oe 71-papoo ca peoao 0.1 mips-oa, 1994 oy paoee a oe 129-papoo ca opeoao 5000 mips-e. Tao e ceo ooc o y coe, ocoo, eee pacpeeex ce, coyx pe poco ce paox ca . o oxo peoe oo Cepao ( Bob Silverman) ooc papaoa Apao e cpo (Arjen Lenstra) Mapo Maacco (Mark Manasse). B 1983 oy paoee a oe cooao 9.5 aco poeccopoo pee a eceo oepe Cray X-MP, 1994 oy paoee a o e ao 5000 mips-e cooao pe poco 1600 oepo o ce pe eee p eo oc ece. Copeee eo paoe a oe oo cooa ooe pacpeeee ce.

apa ae pooae yxyac. Ho aop paoe a oe - peeo oeo o ce - ae apaoe peeo. B 1989 oy aea caa a, o peeo oeo o ce oa e ye e paecoo ae. B 1992 oy o coo , o oo peayeo, o ae p o cpae c apa peeo oo ce co 130-150 ec papa o x. Ceo eco, o o o aop cpee, e apaoe peeo, ce aeo ex, e 116-pape [472, 635]. Peeo oeo o ce oe pao a oe 512 ooe co 10 pa cpee, e apaoe peeo. Ha 1800-yoo oepe Intel Paragon oe e oo aopa ao ee oa. B 3rd oaao oeco mips-e, oopoe peyec pao e ce pax paepo p cooa copeex peaa peea oeo o ce [1190].

Ta. 7-4.

Paoee a oe c oo peea oeo o ce oeco Coo mips-e yo paoe 512 768 2* 1024 3* 1280 1* 1536 3* 2048 3* poe oo, peeo oeo o ce caoc ce cpee cpee. Maea opea oe p, oa, eo, e p ca, o a ee oopec. aop, peeo ceaoo o ce, ye oe paaa a oe ca opeeeo ceapoao op oo e coyee popa - opao cpee, e peeo oeo o ce oe pao a oe e ca oo e paepa. Payo peoo, o peeo oeo o ce oe opoao, o oc ao e copoc [1190], ooo, o NSA ye ae, a o cea. B 2- oaao oeco mips-e, peyeoe paoe ce pao p oo peea ce aoo o ce [1190].

Ta. 7-5.

Paoee a oe c oo peea cea oo o ce oeco Coo mips-e yo paoe 512 < 768 1024 3* 1280 3* 1536 2* 2048 4* B 1991 oy yac ceapa Epoecoo cya eoacoc cce ( European Institute for System Security) coacc, o 1024-ox oye ye ocaoo eoo xpae cepeo o oa [150]. Oao, o peypea: "Xo yac oo ceapa c y ceaca cooecyx oacx, o aee (o ooy cpoa eoacoc) oo ocpo c ocopo oc." o xopo coe.

popa cepxocepae p ope opx e. o o, acoo a ye, a pec oe yy eoacoc pe a, e aa o eye coco cycca paaa a oe. o oy o e ypoe eoacoc, oop aao 512-ooe co aae ocecx, ceo a oaoc 1024-ooe co. Ec e xoe, o a ocaac eoac ae 20 e, 1024-ooe co, o oy, co opoo.

ae ec a opee cepe e co yc, yx paoe aeo oy, oee oaac oacoc. pecae cee aoaecy aocy ccey, coyy eoacoc RSA. Mop oe peca epe cyo a : "a aee a 1994 o, o RSA-129 oa, o 512-oe ca oy paoe a oe o opaae, oopa oe opa ecoo oo oapo ooa ecoo ece ? Mo a coye eoaco c 512-oe ca , ey po, ce cea e o." ae ec Mop e, cy, epoo, oe opeoa, o a o oaa.

oey e cooa 10000-oe ? oeo, oo, o e ee a , e oe cooc ce. Ba ye , oop ocaoo oecee eoacoc, o ocaoo opo, o eo oo o cooa.

Paee o paee aa pecaa yoc. Teep ca oac pecaa oe-o. B 1- pee o peoea o opy opx e acoc o oo, ao cpo eoac o c a a ye. aoo oa pee p a, oa acoo a, oa pyo opopa oa paeca ooo ocyapca.

Bo eoope coopae [66]:

M cae, o coe oy ocy 100 ca oepo e cepxeoeecx yc ex e c. To ec, e coupaec yca Internet "ep" papaaa pyc, oop peoca a cee pecypc. Bo ox opaax oe c a oe ce. ocy x oooc o peye cyco oa, o e ec eoo. p cpe pooeoc a pao 5 mips pe pao 1 o, oe ooo ocyec poe, oop peye ooa mips-e.

poe paoe a oe 129-papoo ca e aex yc co aecoa 0. poea oeoo oo ceo ooc Internet [1190]. Payo peoo, o xopoo pa peapoa poe oy a o 2 poea cepo ceo ooc.

peoo, o yee poaa coe oy coe pacopee 10000 mips-e, oa opopa - 107 mips-e, a paeco oo cpa - 109 mips-e. peoo ae, o cea o ye opaca a opo ae e. , aoe, peoo ae, o y c ex aeae paoe a oe oo a pacaa e ca co copoc, cpa o c o, oopy oeceae peeo ceaoo o ce. (o oa eooo, o pop oe cyc o oe.) 1st peoeye pax e cooa c e oecee eoac o c pae e.

Ta. 7-6.

Peoeoae opx e (ax) o acoe o opopa paeco 1995 768 1280 2000 1024 1280 2005 1280 1536 2010 1280 1536 2015 1536 2048 He aae ya aoc a. Ope aco coyc eo oece e eoacoc ao opa : a aa cce epox ax, , c oye paeco oepe acopo, poo oc ocyapceoo oap y ca. Booo, e co pa ec aoo pee a cpe aoo-o oo a, o ec o ee c oo ooo a aeaa cocee e, o e caoc eca axaae.

a 1024-ooo a ocaoa oc eo-y, o ye poepeo eee ee, ec a, ae ecox e. Ho e e xoe, peca epe cyo e 20 cyc c oca epo opao oyeo, cope, a pooooa copoa oaae, a oea oye, coy y e oc.

pecaa oee aeoe yyee ee yee. o oe a, ax ycexo 2020 oy oce cea exa, ceee ce aeaa ? Oao, ec oy o c apy, oo ae, o ao ceye ece oyae oooc paaa a oe oe oee e ca, e peye. o ooe ocpo 0-.

C pyo copo, exa paoe a oe oe oc peea cox oooce aoo o 2045. Xo ya, o o aoepoo.

He ce coacc c o peoea. NSA ycaoo coeo Caapa poo oc (Digital Signature Standard, c. pae 20.1) y e o 512 o 1024 - aoo ee, e peoe y eo eoacoc. Pretty Good Privacy ("Boe ae cepe", c. pae 24.12) ac aa a a RSA cocae 2047 . Apa ecpa, y pe pacaae a oe, eee ocex 10 e oaaec ea pecaa [949]. B -1- pee peoea Poa P eca e, oope cea 1990 oy ayc e co oc [1323]. Xo eo aa a yae xopoo, eae cop oo a pep peypo pocxox cppo. o peoxpa ce o ocec x cppo, ec cc pa c aaco.

Ta. 7-7.

oocpo poo paoe a oe o a a ( ax) 1995 2005 2015 2025 2035 2045 Mae oe peoaa e $25000, aop "apaoe peeo " copoc ex e coo popecca 20 poeo o. Cpee oe peoaa e 25 oo oapo, aop "peeo oeo o ce" copoc execoo popecca 33 poea o. Macae oe pe oaa e 25 apo oapo, aop "peeo oeo o ce", paoa co copoc peea ceaoo o ce copoc execoo popecca 45 poeo o.

Bcea ec epooc oo, o ycex paoe a oe yy opae e, o oac yec o oe cox pooax. Ho oey e yo ep? poeocppoa cocey yoc, aac pecaa.

Ta. 7-8.

Oce peoea Peca e ( ax) o Maa Cpe Macaa 1990 398 515 1995 405 542 2000 422 572 2005 439 602 2010 455 631 2015 472 661 2020 489 677 Buceue c noo H o oxoe a oeco. B 1994 oy eoap a (Leonard M. Adleman) poeocppoa eo pee aa NP-oo (c. pae 11.2) oxeco aopaop, coy oey H pecae oox pee aa [17]. aaa, peea ao, a ac cyae aa apaeoo aooa y: aa apa opoo, coeex ooapae opoa, yo a y opoa A opo Z, oop poxo epe a opo a ape oo o pa. a opo pecae coe cyao eoo H c 20 ocoa. C oo ox eoo oeyp o oo a cepoa 50 ooe (30 oo oo oey) eo H, peca e a opo. aa opoa a pecaea eoo H c 20 ocoa, o eo pac e cya opao: o yeo pac a, o "aao" eo H, pecae opoy o opoa P opoy K ("opoa PK") cpeac coec co eoo H, pecae opo P, a oe opo PK cpec coec c opoo K.

a cepoa 50 ooe H, pecax ay opoy, cea x ece c H op o a, pecae opoa, oa epe ay, oopa cae ece o oey H. pa o oopaa c ey eoa H opo eoa H opoo po oy, o aa coee eo H opo ece pa opao. To ec, "Bxo" opo PK cea ye coee co "xoo" ao-o opo, aaec opoe K, o oa c "xoo" o o po co "xoo" opo, oopa aaec e opoe K. oce aeo opaeoo pee pea aa coaa ooe oeco eoe H, pecax ooe, o ce pao cyae oee ye ap.

B o cye cyax ye a oe a ae ce - oe eceo oey - H, oopa ec oeo aa. coy oe eo oeypo oo, o ya ce eo H, pecae co opoe co e y. (co opo yo y oo pac cy opoo yc o.) ae o ya ce eo H, oope e poxo epe opo A, ae e, oope o opoa B, a aee. Moeya H, poea epe o co, pe cae coo yy oceoaeoc opo, c peee aa apaeoo aooa y.

o opeee ac cya aa NP-oo oe peopaoa a ooaoe pe acoy cya o pyo aa NP-oo, , ceoaeo, aae o apaeo aooo y. C ceecx oo poo ac cooa aa NP-oo popa c op a.

Xo ac cya, pee ao, eca poc (ce opoo a ape, poc aee a aa oe peea a ecoo y), o apaee oo aao paac, e cyecye ax pec pacpe ao eo a oee coe aa. Ta opao, paccye o eoacoc popaecx poooo, ocoax a aaax NP-oo, paccye, oope o cx op aac coa, "peoo, o y paa ec o poeccopo, a oopx oe o poepo ay ceyy ", copo, oe , yy aac coa, "peoo, y paa ec ca epex a, eoc o 20000 po aa ".

amoe uceu A eep ee oa aaca. B ocoe aox ce coyec ocea ppoa a ep ( oa, aca). oo oe oopeeo axoc oo oece coco. acc e c pepo ec o, o oo ee ce a oa, cpea aco popaoe epao. O o o peeo opaaec poxo epe epao ooo oy, a opca oa, yapc o ooo c e o oepce e, oopeeo opac o ce poe co ee. Oao, p epe oo ee ce ooo ace, oo oo cocoe oe oapyeo.

B [1443] ep op (Peter Shor) oep p ocpoe a paoe a oe, o c oao a aoax aoo exa. B oe o ooo oepa, oop oo peca a ay, eee a oe pee eceoe cpoaoe cocoe, ao oep oaae ypee ooo ye, ec cyepoe oa oox ocox c o co. Bce peopay ooy y, e ec aop coco e ece. Ta opao, ao oep ee peyeco a accec oe aoao : o coye aoe coca ca paoe a oe a ooaoe pe, eopeec oo oa pocce, ocoae a paoe a oe aae cpeoo oapa.

Oepao, o ao oep e poope yaea aoa aoo exa . Oao, eoxoe, o aoa aa paoe a oe ye ocpoea oopo y ye... ec ooe ye ocpoea. O ax pec ec poea eoepeoc, oopa ec po oep oeoc oo oa po co oepa. -a eoepeoc ao oep, paoa p 1, ye cac ay aoceyy. poe oo, ocpoe aooo ycpoca paoe a oe opeyec opooe oeco e e, a o oe e a ocpo ay. poea opa yo coepeoe ycpoco oee cee. Bypee ac e coyc, ooy paoe a oe popaec a x ce oy opeoac o , ooo, ap yax ee. Ec aa epooc oaa aoo n aox ee paa p, o cpeee oeco ca, eo xooe oce ycexa, coca (1/(1- p))n. co yx ee, o oy, pace oo ao c poco ca ( ax), ooy co peyex oo ye pac c yeee coyex ce cepxcoeao - xye e p paoe eee !

ooy, xo aooe paoee a oe ae ocxee aaeecx pyax, ao e poo, o oo ye e paecoe aee oopo yye. Ho e oope oo, o ac e peypea.

7.3 Cpaee cepx opx e Ccea aaec oo ee caee ece. Ec poepyee ccey, oopa coye cepy popa, popa c op a, o e popa aoo a o pac a, o cp o ooeo cce o oaoo pyo.

eccceo cooa cep aop co 128-o o ece c aopo c op a, coy 386-o . Too a e eccceo cooa oo ccee cep aop c 56-o o aop c op a, pe 1024-o .

B -2- epece oye opx e, pyoc paoe oopx a oe cpa a co cooc cpe pyo co coocaex oypx cepx e.

Ta. 7-9.

cepx opx e c aaoo yc ooc cp pyo co a cepoo a opoo a ( ax) a ( ax) 56 64 80 112 128 o aa oo cea o, o ec ocaoo ecooec o coe eoacoc, o pa cep aop co 112-o o, a ceye pa y oy ae a o pe c op a opa 1792 . Oao, oe cyae ceye pa y opoo a oee eoacy, e a aeo cepoo a. Ope oo coyc oe pec a oeo oeca opa.

7.4 Bcpe e poe po ooapaex x-y Cyecye a cocoa cp ooapaex x-y pyo co. ep aoee oe e: ao aee x-y cooe, H(M), pay xoeoc cye coa pyo oye, M', a o, o H(M')=H(M). Bopo coco oee oo: pay xoeoc a a cyax cooe, M M', ax, o H(M')=H(M). Tao coco aaec cooee ec oee poc, e ep, c o coo cp.

apaoc poe ec caapo caceco poeo. Coo eoe oo copa c oo oae, o c epooc 1/2 xo y oo-y x o c a e po e ? Oe - 183. Xopoo, a coo e oo copac, o c epooc 1/2 xo y ox x o e poe? Oe yee - 23. 23 eoea, axoxc oae, opay 253 pa x nap.

Ha oo-y c e e e poe - aao c ep cocoo cp, a yx eoe c poo oao e poe - aao co op cocoo. Bopo coco poo ece a cpe e poe.

peoo, o ooapaea x-y eoaca, y cocoo ee cp ec cpe pyo co. Peyao y ec m-ooe co. oc cooe, x-aee oo m poo coaae c aa, cpee opeoa xpoa 2 cyax cooe. A oapye m/ yx cooe c oao x-aee opeyec oo 2 cyax cooe. oepy, oop xpye o cooe ceyy, opeoaoc 600000 e, o a opoe cooee c e e 64-o x-aee. To e oep coe a apy cooe c o x-aee pepo a ac o a, o, ec oacaeec cp e poe, o pa y x-ae a paa ee, e a opeoaoc poo cyae. Hapep, ec xoe ye epo oc oa ae cce o 1 aca 2, coye 160-oy ooapaey x-y.

7.5 ao o a a?

Ha o opoc e eoo oea, oe o ac o cya. o o, aa cee eoac o c a ya, o aa cee ecoo opoco. Coo co aa opa? a oo oa oa eoaco xpac? ao pecypc ax pao?

Cco eo oe co $1000. acoa opa p eoao paoe oa co $10000. Peaa ae apea oo opopa o co 1 o oapo. a cce epox ax oe co ap.

B pe opo peea opee cepe o oo coxpac eee ecox y.

B aeo ece ceoe cepe - o apae aoo. opa o papaoe aoo-o p o ya, ooo, oa ye xpac cepee eee oa yx e(popa) oa a oa ocac cepeo eee oa a. ae epec CA cooec c aoo o xpac cepee eee 100 e.

Cco oce, paex a eep-cpp ec poe ae cecp, epece oo a o pocea. Topoe cepe opopa peca epec oyppyx oa. Boee cepe epec paec oe.

B x epax ae oo opee peoa eoacoc Moo. Hapep:

a a oa ao, o o, oo opa 100 oo oapo, o oa ccey eee oa c epooc e oee, e 1/2, ae c yeo copoc execoo popecca 30 poeo o.

B -3-, aco o [150], pee oe peoa eoacoc pao op a:

yyy cey o oe eeo, o o payoe pecoe pao : eoc cex cpec yaaec ae 18 ece opacae a opo ae 5 e. Ceoaeo, epe 50 e cae cpe oep yy 10 apo cpee, e ceo ! poe oo, e aa e, o ca oocc oo yepca oepa, o ae, ae ceapoae yc poca cp pocce yy papaoa ceye 50 e ?

peoaa, o popaec aop ye cooac ae 30 e, oee pe ca cee, acoo o oe eoace. Aop, coa ceo, ooo e cae poo cooac o 2000 oa, ce ee ye cooac 2025 poa cooe, oope o ocaac cepee o 2075 oa oe.

Ta. 7-10.

Tpeoa eoacoc pao opa Maa T paa Bpe a a ( ax) Taeca oea opa y/ac 56- Oe o poyax, c oa, poe - /ee x caax oopee ec-a o Topoe cepe (apep, pee oa-o) ece Cepe oopoo o >40 e oc oo >50 e e ea >50 e oaece o >65 e ae epec CA 100 e o ee epe 7.6 Caveat emptor Bc a aa - poco oo eyx. This entire chapter is a whole lot of nonsense. Ceo oop ae o cao o pecaa ceo o a 10, a e oee a 50 e epe. pace pee oo opepo, eo oe. cpaopy pooe, oyae yyee, oopoe, ooo, ye e ao oeo c pye peaoc.

ye ocepaopa. Ec a ee, e a aec eoxo, o eee oeco exooecx cppo coe ope a.

a ye ocopee oyae (a.) aa paee a Ac oa ec eoaca ccea c. O pa ce oep, oopeeo oc a opa ae e poe ae. x pooo eoac. x aop -cae ye. ecac, o oya co o "Keys-R-Us" E, e oy - "B oee oep a: eoacoc - cpeee eoea, oopoo ypcec ae ae e e cpe "Kwik-E-Mart".

Ea e yo cpa aop. E e yo oaac a oe ee poooo. Oa oe c ooa x e cex cooe Ac oa, e paa ax poaaecx yc.

B peao pe ypaee a pecae coo cay pyy ac popa. poep o a eoace popaece aop pooo e poco, o B oee ooc a oo oe aaeecx cceoa. Coxpa cepe e aoo pyee.

poaa aco cpa cepe pocce, pocce c op a epe pacpeeee e. ae Ee ecooc o poee cp popaecoo aopa eo, ec oa oe occao -a eaypaoo xpae a? ae e pa 10 oo oapo a coae aa poaaa, ec oa oe oy epa a 1000 oapo?

Mo oapo a epa c a xopoe ece oaeco ococe oe oo ceo. oep oa poaa Coea poa BMC CA. Pyooe oppae P co ee 2 oo oapo, a ey. o aoo eee, e cpo opoe a cp aa ecx poaao. Ea oe pac . Oa oe apecoa oxa oo-o, o ae . Oa oe copaa oo-o oya a opao. (Mopce exo, oxpae ococo CA Moce e yco epe ooo aao.) Haoo poe ax o ee x, e pocc eax.

Aca o o aa co , o cee pyee ae. Ec e e peypo, o oeco ax oe opoo. coae, oe oepece poy poco o "M coye DES" aa oo ce ocao. Peya e co ea.

Hapep, popaa DiskLock Macintosh (epc 2.l), poaaac oce aao p o paoo oecee, peeye a eoacoe poae DES. Oa pye a, coy DES. Pe a a DES aopa paa. Oao, DiskLock coxpae DES ece c apoa ao.

Ec aee, e ca , xoe poa a, poa DiskLock c oo DES, occa o e poaoo aa ae pacpoa a. He ee aee, o popaa co y e poae DES - peaa acoo eeoaca.

aey opa ooceo ypae a oo a [457, 98, 1273, 1225, 775, 357].

B ceyx paeax ocyac eoope opoco pee.

8.1 eepa e The security of an algorithm rests in the key. If you're using a cryptographically weak process to generate keys, then your whole system is weak. Eve need not cryptanalyze your encryption algorithm;

she can cryptanalyze your key generation algorithm.

eoacoc aopa cocpeooea e. Ec coyee popaec ca poecc eepa e, o aa ccea eo caa. Ee e yo poaapoa a aop po a , oa oe poaapoa a aop eepa e.

eee npocmpacma e DES coye 56-o c a. a pao aaa 56-oa cpoa oe o, cyecye 256 (1016) oox e. Norton Discreet for MS-DOS (epc 8.0 oee pae) pape ae ooac oo a ASCII, ea cap aoo aa oe. popaa ae peop a ye co eo pecpa epx pecp (a o aoo aa cea pooooe ecoy a) oppye aeo papa aoo aa, o po pocpacy 2 oo x e. yepe poeyp eepa e cea co peaa DES ec c pa poe cp.

7- coep co oox e pax opae a xoe cpo. B 6- peeo pe, peyeoe cepaeo epeopa cex oox e p oe oo cey y.

Moy cooa cp pyo co e ceapoae aapae apae e peaa. p poepe oa e ceyy (oo ao eco apaeo) ec ooo pacoo coo eo pecpa p coo eo pecpa o o 8 ao, aao-poe - o o 7 ao, eaaex coo ASCII-coo - o o 6 ao, 8-ox ASCII-coo - o o 5 ao.

Ta. 8-1.

oeco oox e pax pocpacax e 4 aa 5 ao 6 ao 7 ao 8 ao Cpoe y (26) 460000 1.2*107 3.1*108 8.0*109 2.1* Cpoe y p (36) 1700000 6.0*107 2.2*109 7.8*1010 2.8* Aae poe co 1.5*107 9.2*108 5.7*1010 3.5*1012 2.2* (62) eaaee co (95) 8.1*107 7.7*109 7.4*1011 7.0*1013 6.6* Co ASCII (128) 2.7*108 3.4*1010 4.4*1012 5.6*1014 7.2* 8-oe ASCII co (256) 4.3*109 1.1*1012 2.8*1014 7.2*1016 1.8* Ta. 8-2.

Bpe cepaeo oca pax pocpaca e (p oo oe poepo c e yy) 4 aa 5 ao 6 ao 7 ao 8 ao Cpoe y (26) 0.5 cey 12 cey 5 y 2.2 aca 2.4 Cpoe y p (36) 1.7 cey 1 ya 36 y 22 aca 33 Aae poe co 15 cey 15 y 16 aco 41 e 6.9 oa (62) eaaee co (95) 1.4 y 2.1 aca 8.5 2.2 oa 210 e Co ASCII (128) 4.5 y 9.5 aca 51 e 18 e 2300 e 8-oe ASCII co (256) 1.2 aca 13 e 8.9 oa 2300 e 580000 e oe, cea o yaaec ae 18 ece. Ec xoe, o a yco cp pyo co eee 10 e, o cooecy opao apoa c ooae e.

Oee op e oa ca pa , o pa yepe . O c oe epooc epy "Barney", e "*9 (hH/A". o e cea pocxo -a oxo pa, poco "Barney" ee ao e "*9 (hH/A". Ca eoac aop pe e co ooe, ec ooae o pe pa ea cox e (ye) e y co a eox coax yaax. eeyaoe cpe pyo co e epepae ce ooe coo ope, o poye caaa oee .

o aaec cpe co coape, ooy o aa coye coap ox e. e (Daniel Klein) co pacoo 40 poeo apoe a cpee oepe, coy o coco cp [847, 848]. He, o e epepa o apo a py, ac o ccey. O copoa a poa a apoe pep cpe aooo. Bo, o o pooa:

1. B aece oooo apo ooae, a, ea pyy cay c e oeo opa. B eo, a ocoe ao opa pooaoc o 130 pax apoe.

Bo eoope apoe, poepxc e ea klone ooae "Daniel V.

Klein": klone, klone0, klonel, klonel23, dvk, dvkdvk, dklein, Dklein, leinad, nielk, dvklein, danielk, DvkkvD, DANIEL-KLEIN, (klone), KleinD, a aee.

2. Coa pax a ax. cooac cc ycx ecx e (ceo ooo 16000), aa ec (a ee, ooy paccapac "spain", " Spanish", "Spaniard"), ea ecx e, y yaoe epo, aoo, epo eca o ayo aac, ece cyeca (oe Bullfinch's Mythology coape ecx ox), cop (a aa oa, poa ceae ep ), ca (acae a pa - '2001", a ya " twelve''), cpo coo ce ("a", "aa", "aaa", "aaaa" ..), ace co ( Piny in Romanization of Chinese, eyapooo ca apa ca o ac a aoo aaype), opo eca;

ooece e p , paoope yape pae (a "fuckyou", "ibmsux" "deadhead"), caap a ayp (a " werty", "asdf" "zxcvbn"), copae (a "roygbiv" - epe y aa e o pay o ac - "ooottafagvah" - eoeca cxea aoa 12 epex e p o), ea oepo (oyee /etc/hosts), epo, ec eca ec y ecpa, c a e pacpocpaee coa a , aa acepoo, cooyoc co pax e x ecx cae, oyoax paee o. oo, ooae paccapaoc oee e 60000 oex co (c opacae yao pax coapx).

3. Bapa co ya 2. o ao epeo epoo coa epx pecp eo aey ypa coo, epeo ceo coa epx pecp, epc pecpa coa (c e eyoyoo ee pecpa epo y), aey y "o" a py "0" (a, o c o o "scholar" o ae poepeo a "sch0lar"), aey y "l" a py "1" (a, o coo "scholar" o ae poepeo a "scho1ar") oee aaox ay c yo "z" po "2", a ae c yo "s" po "5". pya poepa cocoa epeoa coa o oeceoe co (eaco o oo, o coo cyece) c yeo eoxox pa, o "dress" aeoc a "dresses", "house" - a "houses", a "daisy" - a "daisies". Xo e eco pepac pa peopaoa o oeceoy cy, ooy "datum" caa "datums" (a e "data"), "sphynx" - "sphynxs" (a e "sphynges"). Aaoo, peopaoa co oac cyc "-ed", "-er" "-ing", ooo "phase" "phased," "phaser" "phasing". ooee poep oa ee 1000000 co ccy oox apoe, oope po e pc aoo ooae.

4. Pae apa peopaoa epxey pecpy co ya 2, e paccapaxc ye 3. Ca oo peopaoae epxey pecpy oox coo (a, o "michael" ae poepe a "m Ichael", "miChael", "micHael", "michAel", ..), peopaoae epxey pecpy ap coo ("MIchael", "MiChael", "MicHael",..., "mIChael", "mIcHael", ..), peopaoae epxey pecpy pex coo, .. ee oooo coa o a poepe pepo ee 400000 co, a ee ap coo - 1500000 co. e e pex coo oa o pae epe ee 3000000 co aoo ooae, ec aepe ecpoa xaao pee. poepa ee epex, ec coo a paa epao, a a x poep e xaao cex ooce.

5. 5. ocpae coa ocpax ooaee. Ceec ec, oop oe, poep apo acoo a ooaee c ac ea. acx c o o cooac caap Pinyin Romanization, co oec ece oo-, yx- pe x coe coa. Ta a e o oeo peapeo poep co a aoc, co o ac cepa epeop. Ta a ccee Pinyin cyecye 298 acx coo, o eec 158404 co c y coa, eoo oe 16000000 co c pe coa. oo coco cp o eo cooa acoo a, c yeo pa opaoa p o ocx eo e aax co.

6. ap co. Oe aoo cepaeo eca oeec. o ypoc ec, /usr/dict/words cooac oo coa o p epe coa. ae p o, co ap co coc a o peo ec oo.

Bcpe co coape aoo oee, oa oo coyec po aa e, a e po ooo a. Oo ooae oe ocaoo paye pa xopoe . Ec c e a pae coce a apo oepo cce, o ea epooc oo, o o pae epe o eoe epe , ec coape oa.

Cyae u Xopo a c cpo cyax o, coae eoop aoaec poecco.

Ec a a cocae 64 a, o ce ooe 64-oe o paoepo. e e ppye e, oyc o ae coo cyax ce (c. pae 17.14), o p o paec eoac eepaopo ceocyax o (c. a 16 17.) Ec ae aoaece poecc eocy, pocae oey oc.

o ao, o e yeaec ocyee oo, ec y yox coo oee cya, e y paoaoo pacaa. H o x coo cyaoo ya e coepee, o ce o, copee ceo, yy ocaoo xopo. eepa e ao cooa xopo eepaop cya x ce, o opao aee cooa xopoe aop poa poeyp ypae a . Ec ecooec o cyaoc ax e, coye ocay e eoy epeaa a.

Heoope aop poa e cae - ceece , eee eoace e pye . coey poep caoc a e , oapy ee, eeppoa o. DES o o 16 cax e pocpace 2, a o epooc oy o x e eepoo aa.

aoc, o poaa e ye a o o, o coyec ca , , ceoaeo, e c o e oy ao o x cyaoo cooa. Tae aoc, o opa poa a y ae coce e cooae cax e. Oao, poepa eox cax e acoo poca, o aec y peepe e.

eepa e cce popa c op a eee, ooy o aco o oaa opeee aeaec coca (ooo, o o poc ca, apa ocao, ..). Meo eepa ox cyax pocx ce paccapac pa ee 11.5. Bao o, o c o pe ypae a cyae capoe oceoaeoc ax eepaopo o eceo cya.

eepa cyaoo a ooa e cea. oa a yo o a . (epeco, co o pee a oaoc, o ao 25e8 56f2 e8ba c820?). Ec a ao eeppoa poco aoa , aacpye eo. eao ec o, o eo ao, o pyo yaa. Bo e coo peoe:

ap co, paeee coo yya, apep, " turtle*moose" "zorch!splat" Cpo y, ec apoa x pa, apep, "Mein Luftkissenfahrzeug ist voller Aale!" cy aoa a "MLivA!" ee pa y peee ec cooae eco coa eo pa peopaoae o pa .

Tae pa aac e paa. Meoa c aae epeaae a peopaye eo aoaec pa cyae . peopaoa ecoo cpo pooo cpoy ceocyax coye ooapaey x-y. Hapep, eo aoaac ecoa cpoa:

oe "epeooc" ao 64-o :

oeo, oe eeo ec oep ey pay, ec oe co e oopaac a pae. Paye peoe o pee o poe yy oee.

Ec paa ocaoo a, o oye ye cyae. Bopoc o oo cce pae "ocaoo a" ocaec op. Teop opa yepae, o opaoa aoc caapoo acoo a cocae ooo 1.3 a a co (c. pae 11.1). 64-ooo a ocaoo ye ea paa, cocoa pepo 49 coo, 10 ox acx co. B aece pecoo paa coye co ax 4 ao a. o peoee paoae c aaco, e e e yac pecp, poe a yya.

o eo ae oo cooa eepa apx e popaecx cceax c o p a: ecoa cpoa peopayec cyay capoy oceoaeoc, a a oce o aeoc oe cooaa eeppoao ccee, eeppye ap op /ap .

Bpa ey pay, coye o-y yaoe eo aoaeec. He pae pa - pep c "Ozymandias" o cce ox. eo ocy oy cooa cp co coape copae coe ecpa, ao ex o. Bepe o-y y aoe oe. He aye o yya peopaoa pecpa, ec ooo e ca ea ae co. oxo cae ac, ae o ocpa , eae ey pay oee ycoo cp co coape. O peoe ec cooae pa, oo pa ec "opcae epyo", e-o a, o p aoe p aee.

Hecop a ce acaoe ec acpoa e aee cy cyaoc. y c c y ae , oope a eo ao.

Oaac, ap ape. B, ce pa ceo, cope a o py peee.

Cmaapm eepauu e X9. Caap ANSI X9.17 opeee coco eepa e (c. 7th) [55]. O e coae eo aoa ec , oe oxo eepa ceacox e ceocyax ce ccee. eepa e coyec popaec aop DES, o o oe eo aee py aopo.

Ti poa Vi+ poa Vi poa Ri Pc. 8-1. eepa e ANSI X9. yc EK(X) - o X, apoa DES o K, cea o, peycope eep a cepex e. V0 - o cepea 64-oa capoa oceoaeoc. T - o ea pee. eepa cyaoo a Ri c:

Ri= EK(EK(Ti) Vi) eepa Vi+1, c:

Vi+1= EK(EK(Ti) Ri) pepae Ri DES, poco yae a oco . Ec a ye 64-o , coye e ee. Ec a ye 128-o , coae apy e oee x.

eepau e uucmepcme oopo CA Mcepco oopo CA eepa cyax e peoeye cooa DES pee OFB (c. pae 9.8) [1144]. Coaae DES, coy ccee eopa pepa, pecp c o co cce ccee ce. Coaae eop aa, coy ccee ac, e aop cce, c ae ay pe. opoo eca coye 64-oe e, coae e-o py, apep, 8 coo, eex cce acpaopo. coye aece coeo a peya.

8.2 Heee pocpaca e Boopae, o - o oea popaeca opaa, coaa popaec oy ax oc. B xoe cooa eoac aop, o o ye, ec aapaypa oae o p a ece py? Be e xoe, o a pop cooac a paecux cepeo.

Ec oee oec a aop ae oy, o o, o oee cea. opeye, o oy pao paoa oo c a ceao cepeo op, a co ce py a poa cooac co ocae aop. Moo cea a, o epooc oo, o o-o, e a o ceao op, cyao aec a pa , a c e ae ao.

oyeec pocpaco e aaec ee, ooy o e c oaoo c. (poooo ec eoe, ocoe, pocpaco e.) poc cocoo o c oo oo, coaa , coco yx ace: eocpeceo a eoopo cp o ao cpo, poao o. Moy pacpoae cpoy, coy . Ec pey a o oaaec cpoaa cpoa, o coyec a oo, ec e, o coyec pyo, ca aop. Ec aop ee 128-o 64-o paep oa, o a ooo a - 192 a. Ta opao, y aopa 2 ex a, o epooc cyao pa pa cocae o ac 264.

B oee cea ee xpee. Moo papaoa ao aop, o eoope yy cee pyx. aopa e ye cax e - e, oope c oeoc c eocaoo a e - e e eee y eo ye eeoe pocpaco e.

o paoae oo, ec coyec cepe aop, oop pa e oe epepoepoa, ec pae ce e ocaoo oo, o pa e co o e oaac. NSA poeao o c cepe aopa cox oyx Overtake (c. pae 25.1). ea o o e caoe c Skipjack (c.

pae 13.12)? Heeco.

8.3 epeaa e Aca o copac eoaco c cooa cep popaec aop, ye o . Aca eeppye , coy eepaop cyax e. Teep oa oa eoaco epea eo oy. Ec Aca coe e-o cpe oa (ae-y aop, oaa e oo oa y epa), o oa coe epea ey o a. B poo cyae, y x ec p o ea. popa c op a peae poey eo c yo peapex coa e , o eo e cea ocy (c. pae 3.1). Heoope cce coy aepae a a , caec eoac. Aca oa oca oy c oepe oc. Oa oa oca aao oo oo cyo oca. Oa oa ycaaa pyo aa c c oo aec, o eo o o e ocyae.

Aca oa oca oy cep o x aay c - o, oop o copac poa. Ho yo epeaa poa aaa o oy e aay opo e, o-o, ocy a aa, aepa coe pacp oa ce cooe.

Caap X9.17 [55] opeee a a e: poa e ax. a poa e p pacpeee pyc pye . ax py ca coo e . poa e o pacpeec pyy, (xo o oy eoacoc a eo o oa ycpoce, ao a pea apoa), o ocaoo peo. ax pacp e ec opao ae. opooc oo a [75]. a e yxcx e aco coyec p pacpeee e.

py peee poe pacpeee ec paee a a ecoo pax ace (c.

pae 3.6) epeaa x o pa aaa. Oa ac oe ocaa eeoo, pya - oo, pe - cyo oo oca, eepa - oo oye, a aee, (c. 6-). Ta po oe copa ce ac, poe oo, ce pao eo e yae po . o eo ye paoa o cex c y ax, poe pax. B paee 3.6 ocyac cxe pae a a ecoo ace. Aca oa ae pe cxey coeco coyeoo cepea, (c. pae 3.7), o ac oooc oy occ a aa , ec eoope ace oep p epe ae.

k ypep OTPABTE OATE k e a ac Boccaaae aaa oa k eepaa cpecc-oa k Teeo k oo oy k2 k k1 k2 k3 k4 k Pc. 8-2. Pacpeeee e o apae aaa.

Aca eoaco epeae oy poa e p o cpee, c oo oo o paccopeo eo pae. a oo y Ac, y oa ye poa e, A ca coe oca oy ax a e o oy e caoy aay c, py p o a ax o poa e. Ta a paa, pye o poa e e a ee, o o aco e e yo. Oao, a a opoea a poa e o e copoepoa ce cooe, poaoe cooa a ax, oope a poa o poa e, o oe xpac eoacoc.

Pacnpeeeue e oux cemx poa e, oe ap ooaee, xopoo cooa eox cex, o c yeee ce aa ccea cpo caoc pooo. Ta a aa apa ooaee oa oec a, oee co oeo a ce n eoe pao n(n - l)/2.

B ce c ec ooae opeyec 15 oeo a. B ce 1000 ooaee oao c ye ooo 500000 oeo a. B x cyax paoa ce opao oee ea p co o a epaoo cepepa ( cepepo) e.

poe oo, o poooo cepo popa popa c op a, peex paee 3.1, oxo eoacoo pacpeee e.

8.4 poepa e a o yae, oy , o epea Aco, a e e-o py, o ae ce a Acy? Bce poco, ec Aca epeae ey p o cpee. Ec Aca ocae co epe oepeoo ypepa, o ypepy oe oep o. Ec apoa o poa e, o o oe oep oy, o o poa e ec oo y Ac. Ec oc a Aca co ye pooo epoo oc, o p poepe oc oe oep ae ax opx e,. (Ey ae pec ca, o Aca coxpaa co eoacoc.) Ec ep pacpeee e (Key Distribution Center, KDC) ocae op Ac, o oe ca, o eo o opoo a KDC e a oeea.

Haoe, o, o ypae ce ce opy oa, oe aca eo ya ce, o ey xoec. M op oe oca poaoe ocaoe cooee, aa ce a Acy. oa o, poep o c Ac, opac ae ax opx e, Mop oe opa ey coce op . Mop oe coa co coce oe KDC oe op acoeo KDC o coeo coceoo e. o a e coe o oapy.

Heoope cooa o apye, yepa, o popa c op a ec o ea. Ta a ece coco Ace oy a aepa, o o e oa x , - o a cpea, o popa c op a oo e e oeceae eoacoc.

Pages:     | 1 |   ...   | 2 | 3 || 5 | 6 |   ...   | 14 |



2011 www.dissers.ru -

, .
, , , , 1-2 .