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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

e, cea paa ay po, o o epo poo o o ax papaoax pe o pee cooaoc ea pop a paaac ae, a pye ceapoae c. B 1918 oy e ayoo oea a co aopaop Pep a ce oopa Ba . paa oaame conaeu u eo npueeu punmopauu (Index of Coincidence and Its Applications in Cryptography ) [577], oa opee x pao 20-o coe. o ecop a oe aa, o oopoy a ceaa a paoa. B o e oy ap X. Xeep Oea, aop, oy ep ae [710] a poopy ay, ycpoc o, a oopo ocoaac oea popa eee o 50 e.

oce epo poo o, oao, ce eoc. Opaa ap oa Coeex ao, ooc acepe co pao, oc yaeax ycexo popa. B eee 30 -x 40-x oo opo epaype o aoy peey oc oo oee ocoe pao oop a , o e ae, e ee o cooecoa peaoy ooe e. oy o epexo o oc aepc. Opa epaypa yepa a cee ooo aeoo ce, pao oa oa "The Communication Theory of Secrecy systems" ( Teopu cu ey cepemu cucmeau ), ae aao 1949 oy Bell System Technical Journal [1432]. a ca, a paoa paa 1918 oy, ac peyao cceoa oa o pe o. oce ooa Bopo poo o oa a paccepeea, ooo o oe.

C 1949 o 1967 epaypa o popa a eccoepaeo. B 1967 oy oa ooac paoo pyoo a, cope a aa eupouu (The Codebreakers) [794]. B o e e o ox e, o oa coepaa ocaoo oy cop peea, a yoae o eoopx eax, ce ee acepeex paeco. aee eupouo aaoc e oo aeo oxae peea, a ea ae oepec ycex oaoa c popae c e, pae e ayaxc o ee cyecoa. Toe pyeo aa oc oe pao o pop a .

o o e pe Xopca ecea, paee paoaeo a popo "co/yo" BBC, a c aey oxaa cpac popa, o epee ocoocy aopaop p IBM, pacooey opay Xac, H-op. Ta o aa papaoy oo, o ae cao caapo DES (U.S. Data Encryption Standard, Caap poa ax Coeex ao). B aae 70-x oo IBM oyoaa p execx oeo o popa, oex eceo eo oea [1482, 1484, 552].

Taoo o ooee, oa oe 1972 oa aa paoa o oac. epaypa o p o pa oo e a, o e oo o a p cepax caopoo.

B popaeco aye ec ocoeoc, ocycya ox aaeecx cax: eo xooc aoec popa poaaa. po oo ec ocyce peoa epeae peao opa, ceoaeo, epyo peo ccey, oopa aec eopeo.

Moe aaeece papao acoo co, o yy poaa e ae c eo aa. O apy p x poeax aoo coee, e papaoa x. B peyae eooo copeoae, eec o cex oo aaeecx cceoa.

oa Map Xea 1975 oy peo popa c op a [496], o ocex aceo aeo peoe o oee poe, peee oopo e aec poc.

Teep eco poepo o coa o-o - oe payy poccey, peay oee ope aa, e pocoe pepaee aoo eca eyxy. B peyae aeo opoco co e, aaxc popae, co poox cpe co oyoax cae.

B pe o ooy pcye e coeco c Mapo Xeao pe oaa E. a (pcyaeo a yy ocey ca ypae IEEE) caa, o, aca "Privacy and Authenti cation" ("Cepeoc yocoepee ooc"), oy o, oop eoe ae a x c yex, oyx pe IEEE. aca ca, oopy xoe y, oa epe cepeo aepecoac popae, oopy e co a. Ec ceo opac Copcy oey copa copeee pao o popa, , ooo, oy pecaee o peee opao pae. Ho oce 1972 oa ocy oo ecoo accecx pao p yax execx oeo.

ceoeo cceoae e ao poe. Ceo ocoa cooc coco ope, c eo aa cpe c cae eco . A ceoe popac eep, oope poco xo cooa popa? a coa opaac? o cx op eoxoo o poo oe ac, ca ayy epaypy ya ee, pee e yaaoc aa papaoy pop a ecx poe, a ao ocax oypx cax.

eo o poeyo paa ao puaa punmopau pca aepa. Haa c ee acepea epea ax eeapx pepo popa oce x ee, aep pa opaae epe a aopay peyao 20 e opx cceoa. Coepae ooc opeeec ee aae, aee e ocae pax poe, o acepea eeooo paoopa o epox ee popaecoo oecee opo.

He yoeope poc oee aopo ocae oa, aep y ocy ee pax pox opaa, cax c papaoo peee popaecx cpec, o Meyapoo accoa pooecx cceoa o NSA (National Security Agency, Aeco aoao eoacoc).

oa a pyee 70-x 80-x oo opoc oece epec popa, NSA, oa p opae opa CA, pepo p oo oa o epec. epo ao oo o co capoo copya NSA, o oy ecoaeo o coey ycope. co o ocao IEEE peypeao, o ya aepao o popa ec apyee pa ey a poo poa opy (International Traffic in Arms Regulations, ITAR). a oa pe, a oaaoc, e oepaea ca paa, o e coepa o yyex aepao, coaa eoay peay cooa popa Ceapy o eop opa 1977 oa.

oee cepea oa a pepa 1980 oy, oa NSA acpoao yee opoca A e pac coeo o opaoa c e ye opecc yao opo a ya oac popa. Peya, oaaec ae o oa NSA, pe popae opoooo p e epoa pao o popa. O cceoaee opeoa epe yae apaa ee NSA, e pece pacpe peyao cceoa pe aoa epeca.

cepee 80-x oo oco oeo a caa e eop, a paa popa. Cyec ye ao a NSA pao c oo oceapaea peypoa cop popaecoo o o pyoa. Ta a ec ce oe oe pae eyapo xapaep aepaca ac pooo pa yeaec, opacae eae cooa e poy ypeeo, e e o pa. Tae poy c cyea opo a copo, ooy NSA oyo oooc opopoa e oo coppyee popaece poy, o poaaee Coeex aax.

B o pe, oa cac cpo, oo ooe pece oeceoo cooa p opa. paeco ooo poo oyoa coye aop DES acepee aopo, peaoa pocxeax a, eace o pee. pocxe yy coepa opoa exa paeceoo opo. Opaee ace ao popa -pocoo o pocpac o oeao yeoo pacp a oc o coo co oc aapao oepa poyo, paee peaoax popao. Ta opao, peaaeoe ooeee e ao yaa oepoc poo pe, ocoeo co copo eacx p opao. P e, oao, coe yyee popapoa, a e oe yaa co yc , cpec peca py oe cpeca popa.

aeoe ocyee o oooc oo, o ao o opoe a copo oe epy o pay1, aaoc o cea 1980 oy, oa oyoae Federal Register cpae ITAR oo ceyee ooee: "...ooee o oaeo c e oaa, o peypoae copa ex e cx ax e pee oy c paa oc, opeee epo opao". Ho o, o o ey epo opao aoa o opoe a copo e papee ooaeo, oo oeo ae, ceax a oepe, pooo RSA Data Security. pecae NSA o ea opo a copo pa ee, o , yye popaece popa, ax o c " cepo oe" o ooe aoy. Ec o a, o eo y "cepy oy" eoo oceo epoe ae o . cop poe o papee c oepee oo, o oy o ae aepa e oaa o pc Coea o opo a oopyee. Oao, copp o a oyoae popa a ce o apeeo.

eee cpae NSA o oo opopoa popaece cceoa yce pey poa oac papao paepa popaecx poyo o oy oycoeo oco ae oo, o ce eae popaece pao e a ooo a opa. yy ocy CA ocae a, o o e ceae eo ooo o cpae c peecy a paoa, o cooae eo coepa a paoe ca, e ec popaec o, oe pec oy peyay.

May B, aop.

Beee popa ae yx o: popa, oopa oeae a a a ae ae c e cpe, popa, oopa oeae a a a paeca. a a o opo e popa.

Ec epy co, ay eo ce e-y H-ope, ae e Ba poa o co, o o e eoacoc. o eoo o. C pyo copo, ec epy co ay eo ce, ae epea o ce Ba ece c ea ocae, epea ae co oox ceo c x oa, o B ye "eea" pa o y ccey ao, a ce pao e coee op ce poa co - o o ec eoacoc.

B eee ox e o popa cooac ceo oex ex. Aeco a oao eoacoc Coeex ao Aep (National Security Agency, NSA) eo aao e Coeco Coe, A, pa, pae pox cpaax pa ap oapo a oe cepey py oeceee eoacoc cocex c, oopeeo ac oa ce o c ae. Oee oc, oaae aeo e cpeca oo, ecoo a co cepe o paec.

B eee ocex 20 e aeo poc oe opx aaeecx cceoa. oa oe paae cooa accecy popa, co pee Bopo poo o oepa p o pa o ce pe peac ceo oeo oac. Ceo cycco oepo p o pa paoc ce oex eoc. Hepoeccoa oy oooc cpeca, ooe oeoac ce o oyeceex poo, cpeca, oeceae ay o oex e oc.

A ya ooy eoey aa popa? a. oy apoa oecy aa, ocya ao, ec eaoe ec. O oy papaaa oe e, ocya poy oy apoa axa oyppye p. O oy cpae, oopa e coae a pea a opee y cox paa. O oy ea o-o, o e aec eao, xo ao ec. o o pa ae c o , a a p o ocopoeo ocya.

a a xo ce ecoooe pe. B 1994 oy acpa oa pa Caap y c ooo poa (Escrowed Encryption Standard), a pocxey Clipper ay Fortezza, pepa o o poo eeo ao. a ac ye oooc paeca poo epo opo.

Bcya cy eoope oacee oc Opya: paeco oyae pao pocya e epeoop, a c eoeo, ac cp co cepe o paeca, oe o-y c y c. aooaeco cea papeao cey o pee cya, o epe ca o pep a ae-o a, o ceamc ocmynu ce. a e poco peoe p a eca eo yao cepe, o ypeaa oocopo oa pco pee pa e ae paa.

aoopoe o pocxee Clipper poo eeo e cococy coxpae a, o eco eo aca e ca, o paeco yaae x a. Te e cae ac, oope eaoo aca eeo Mapa epa a, oy eo pocya eeo, ae pocxeo Clipper. B eae poo oece ac a ecax pee paaco yooo oeceoc a eaooe pocyae o ox cyax - Mpee, oeye, Bepoe, op, Mccyp Heae. e paepy exoo, oopa oe pec oe oe coo ocyapca - o oxa e.

eo o, o eocaoo a ce aoa, a yo a ce aeao. po a e ee co ooe aee, o oca ee cooae oo paeca.

a a ca Bac cpyeape, oo a a a. epeaa popa e cx poyo oe oea eaoo, epeaa opa - oa.

a a y y aca puay punmopau a oe eee popa a ceoe cp a o. ac coea aeoc eca c epeo ooc, o a a caac e a ae aeca paoa. Xo e caa opa yeo, opoc, oyca eop. epe cyxc eopeec aa pee ope cc a aaeecy epaypy.

aa 1 pecae coo eee popa, ocae oeco epo, e pao pa c capaec ooepa popa.

a co 2 o 6 (ac I) oca popaece pooo - o oy cea c oo popa - o pocx (epeaa poax cooe o ooo eoea pyoy) o cox (eae oeo o eeoy) ax (cepeoe aooe opaee epox ee ). Heoope x poooo oe, pye - ye. Moeco e e pecae oe poe, oope oe pe popa.

a c 7 o 10 (ac II) coepa ocyee eoo popa. Bce epe a a cax pacpocpaex pee popa. B aax 7 8 paccaaec o ax: aoa oa a eoacoo a, a eeppoa, xpa pacpee , .. paee a pecae coo pyey ac popa aco ec axecoo o cce, eoacx o ce ocao. B ae 9 paccapac pae coco cooa popaecx aopo, a aa 10 ocae ocoeoc e cooa x aopo - a x pa, peaoa pe.

a c 11 o 23 (ac III) oca aop. aa 11 pecae coo aeaecy ay ec oaeo oo, ec epecyeec aopa c op a. Ec copaeec cooa DES ( o-o oxoee), ee oo poyc. B ae 12 ocyaec aop DES, eo c op, eoacoc paooc. B aax 13, 14 15 paccaaec o pyx ox aopax. Ec a yo o-o oee aeoe e DES, cpay epexoe paea o IDEA poo DES. p ea ya o pye aopo, eoope oopx oy eoacee DES, poae c ay. B aax 16 17 ocyac oooe aop. B ae 18 opoo paccapac ooapaee x-y, cpe oopx ca c MDS SHA, xo ocaaac a ox pyx. B a e 19 paccapac aop poa c op o, a ae 20 - aop poo o c c op o. B ae 21 ocyac aop ea c op o, a ae 22 - aop oea c op o. Ca a c aop RSA, DSA, a-apa (Fiat-Shamir) -Xeaa (Diffie-Hellman). aa 23 coep p oepecx aopo poo o o c op o, aeaa o ae ocaoo coa, a o pcee pe.

a 24 25 (ac IV) epeoc ac pea p popa. B ae 24 ocyac eoope copeee pee aopo poooo, o pe a aa 25 acaec eoopx oecx aceo popa. Hecoeo, a e c ceoxaa.

B y ae e cxoe o 10 aopo, paccopex ac III. e co ec o, oop xoe, -a eo ooo oea, poe oo, popaece o o cyae e coppoa. (oo, o oceapae pape coppoa epoe ae o c c xo oo, o e pape coppoa oep c c e e cxo oa. Cop p cyo.) Cooecy aop co c cxo oo coep cyeceo oe cxox oo, e co y y, ooo, o caa oa oopa popaecx cxox oo, o ac a peea oex eoc. Ceac oy epeca c c cxo oo oo pa aa CA aa, y x cpaax, o, ooo, oa-y ce ec. Ec copa e ec cooa opooa aop, oye c. opooc a ocee cpae ..

eocaa o oocc o, o -a ee oeeco ppo ocpaaa aeoc . xoe aca e cpao ex, o o cpec c a-o aopo aae eco epaype p cooa aoo-o poya, apaee c epe e, o paca e yeoe ocoe. Bepe ce oeco ceaoo popa copao o oo ooo. Heco p a o, coopae oea aca e oca ooe a peea o , e e, oope e oaac a, paec epec. Ec e o ooc oxa ey, po cc a cooecye pao ca.

cea ce, o o, ac o cpa ce o e, o oe yep e, o o ce pao eooo. oeo, o opo a oo ee, e epo. epee oo oo oy y e, o ae epoec paccaec eeoepe Usenet sci.crypt. Ec o y aee oapy oy, oayca, yc coo e o o. aoy, o ep o a py ay oy e, ecao o c c cxo oo.

aoapocmu epee e, pox pyy coa o , oe oaac ecoe, o ce o o c o yoa. Me xoeoc oaoap oa Aapeca ( Don Alvarez), Pocca Aepcoa (Ross An derson), a eecoa (Dave Balenson), apa apca (Karl Barms), Ca eoa (Steve Bellovin), a epcaa (Dan Bernstein), ae (Ell Biham), oa op (Joan Boyar), ape yep (Karen Cooper), B a (Whit Diffie), oa eeay (Joan Feigenbaum), a aa (Phil Karn), Ha oa (Neal Koblitz), cyea a (Xuejia Lai), Toa epaa (Tom Leranth), Maa Mapoa (Mike Markowitz), Paa Mepa (Ralph Merkle), a aea (Bill Patten), epa pcoa (Peter Pearson), apa eepa (Charles Pfleeger), ea (Ken Pizzini), apa peea (Bart Preneel), Mapa Popaa (Mark Riordan), oaxa ypaa (Joachim Schurman) Mapa apa (Marc Schwartz) a ee peapoae ceo epoo a eo ace;

Mapa Boepa (Marc Vauclair) a epeo epoo a a payc ;

a Apa xaa (Abe Abraham), Pocca Aepcoa (Ross Anderson), a ecapa (Dave Banisar), Ca eoa (Steve Bellovin), ae (Ell Biham), Ma oa (Matt Bishop), Ma a (Matt Blaze), p apepa (Gary Carter), aa oea (Jan Comenisch), oa peo (Claude Crepeau), oa o (Joan Daemon), Xopxe aa (Jorge Davila), a oycoa (Ed Dawson), Ba (Whit Diffie), apa coa (Carl Ellison), oa eeay (Joan Feigenbaum), Hca epcoa (Niels Ferguson), Maa paa (Matt Franklin), Poapo Ceapo (Rosario Cennaro), epa oaa (Dieter Collmann), Mapa opec (Mark Goresky), Papa paa (Richard Graveman), Capa Xaepa (Stuart Haber), aa Xe (Jingman He), oa Xa (Bob Hague), eea Aepcoa (Kenneth Iversen), Mapyca eocoa (Markus Jakobsson), epa ac (Burt Kaliski), a aa (Phil Karn), oa ec (John Kelsey), oa ee (John Kennedy), apca ycea (Lars Knudsen), oa oepa (Paul Kocher), oa a (John Ladwig), cyea a (Xuejia Lai), Aea ecp (Arjen Lenstra), oa eaa (Paul Leyland), Maa Mapoa (Mike Markowitz), a Mcc (Jim Massey), pca MaHepa (Bruce McNair), Ba X Mppe (William Hugh Murray), Poepa Hx a (Roger Needham), a Heaa (Clif Neuman), ecy Haep (Kaisa Nyberg), a O'oopa (Luke O'Connor), epa pcoa (Peter Pearson), Pee epaa (Rene Peralta), apa peea (Bart Preneel), pa Paa (Yisrael Radai), Ma Pooy (Matt Robshaw), Maa Poy (Michael Roe), a Poy (Phil Rogaway), Pya (Avi Rubin), oa Pya (Paul Rubin), Cea Paccea (Selwyn Russell), aye Cao (Kazue Sako), Maxya Caacaexa (Mahmoud Salmasizadeh), Mapyca Caepa (Markus Stadler), p Toa (Dmitry Titov), Aoa (Jimmy Upton), Mapa Boepa (Marc Vauclair), Cepa Boee (Serge Vaude nay), eoa aa (Gideon Yuval), ea opa (Glen Zorn) ox ex paecex c y ax a ee peapoae ceo opoo a eo ace ;

op paya (Lawrie Brown), y (Leisa Candle), oa o (Joan Daemon), epa yaa (Peter Gutmann), Aaa c (Alan Insley), pca ocoa (Chris Johnston), oa ec (John Kelsey), cyea a (Xuejia Lai), a e epa (Bill Leininger), Maa Mapoa (Mike Markowitz), Papa Aypa (Richard Outerbridge), epa pcoa (Peter Pearson), ea (Ken Pizzini), a aa (Calm Plumb), RSA Data Security, Inc., Maa Poy (Michael Roe), Maa Bya (Michael Wood) a epaa (Phil Zimmermann) a peoca ee cxoe o;

oa MaHepaa (Paul MacNerland) a coae pcyo epoy a ;

ape yep (Karen Cooper) a peapoae opoo a;

oa paa (Both Friedman) a cepy opoo a;

po ee (po Kennedy) a paoy a pee yaaee opoo a ;

aee sci.crypt oooo cca Cypherpunks a oepoae e, oe a opoc oc oo epoo a;

P Ccc (Randy Seuss) a peocaee ocya Internet;

ea aepaa (Jeff Duntemann) oa pcoa (Jon Erickson) a o, o oo e aa;

ce Insley ( pooo ope) a c y, ooyeee, oepy, ece, pyy oe ;

AT&T Bell Labs, aee e ceae oo ce o. Bce oo coa opao yy y, e co coa ooy.

pc aep Oa ap, oc schneier@counterpane.com O aope PC HAEP - pee Counterpane Systems, Oa ap, oc, pa-ocya, cea pyac popa oepo eoacoc. pc ae aca E-Mail Security, John Wiley & Sons, 1995, (eonacocm empoo nom) Protect Your Macintosh, Peachpit Press, 1994, (aumu co Maumo). O ec aopo cae o popa ocox ypaax. O ae copeaop Dr. Dobb's Journal (ypa omopa oa), e o peapye ooy "Ae aopo", copeaop Computer and Communications Security Reviews (Oop eoacoc oepo c). pc xo coe peopo Meyapoo Accoa pooecx cceoa ( International Association for Cryptologic Research), ec eo ocyaooo coea epa Cepeoc epoo opa (Electronic Privacy Information Center ) xo oe popa Ceapa o Ho apaa eoacoc (New Security Paradigms Workshop). oy e, o axo pe acx e o p o pa, oepo eoacoc cepeoc.

aa Ocoe o 1.1 Tepoo Omnpaume u noyame peoo, o opae xoe oca cooee oyae. oee oo, o opae xoe oca coe cooee eoaco: o xoe yepe, o epexa o cooee e coe eo p o ec.

Cooeu u upoaue Cao cooee aaec op eco (oa coyec ep ep). eee a coo e a, o cpa eo cy aaec poae. poaoe cooee aaec po eco. poecc peopaoa poeca op ec aaec eppoae. a oce oaeoc oaaa a 0th.

(Ec xoe ceoa caapy ISO 7498-2, o acx ecax coye ep "enchipher" eco " encrypt" ("apoa") "dechipher" eco " decrypt" ("epoa")).

cycco aya eoacx cooe, aaea popae, ooaec popa a. poaaa aac e, o ocoo coy poaa, cycco ayy aa poec, o ec, pacpa, o axoc o aco. Opac aea, oxaaa popa poaa, aaec pooe, a , oope e aac, - pooa.

Copee pooa pxoc eoxo a aeay.

epoaa Op ec poec op ec poae eppoae Pc. 1-1. poae eppoae Ooa op ec a M (o message, cooee), P (o plaintext, op ec). o oe oo o, eco a, ooe opaee, opoa y, pooe eoopaee a o yoo. oepa M - o poco oe ae. (Bo cex ceyx aax o pa c capac oo oe ae oepa popa.) Op ec oe coa xpae epea. B o cyae, M - o cooee, oopoe oo apoao.

Ooa poec a C (o ciphertext). o oe oe ae, oa oo e paepa, o M, oa oe. (Ec poae copooaec cae, C oe ee e M. Oao, cao poae e oeceae cae opa.) y poa E ecye a M, coaa C. , a eaeco ac:

E(M) = C B opao poecce y eppoa D ecye a C, occaaa M:

D(C) = M ocoy cco poa oceyeo eppoa cooe ec occaoee e p oaaoo opoo eca, oo oc ceyee paeco :

D(E(M)) = M poepa nouocmu, eocmocm u eompuaue amopcma poe oecee oeaoc popa aco coyec pyx y :

poepa ooc. oyae cooe oe poep eo co, oye e coe aacpoac o oo-o.

eococ. oyae cooe oe poep, e o cooee eeo poecce oca, oye e coe oe paoe cooee o.

Heopae aopca. Opae e coe oo opa opay cooe.

Cyecy eo ae peoa oe p oo oepo, ae a cyecy aa oe peoa p oe o y. To, o o-o ec eo e, a oo o ce ae o -o oye - oece paa, eca cee acop - acoe o oye, o ye o oo-o, oye eo o oo eoea a pa o oecea poepa ooc, eococ eopae aopca.

Aopum u u popaec aop, ae aae po, pecae coo aeaecy y , coyey poa eppoa. (Oo o e cax y: oa poa, a pya eppoa.) Ec eoacoc aopa ocoaa a coxpae caoo aopa ae, o opae ao p. Opaee aop peca oo copec epec, o o coepeo e cooec y ceo caapa. oa eac pya ooaee e oe cooa ae aop, a a c pa, oa ooae oae pyy, ee e o epexo a pyo aop. Aop oe aee , ec o-y e cyao yae cepe.

o ee xye, opaee aop e oyca aeceoo opo caapa. a o py ooaee oe co ya aop. Tae py e oy cooa o pe aapae popae poy - oye oe y ao e poy pacp aop. pxoc papaaa peaoa cocee aop. Ec pye e xopoeo popaa, o a ee e poep, o o oyc eoac aopo?

Hecop a ocoe eoca opaee aop eoao oyp poe c ypoe eoacoc. ooae o e oa poe, cax c eoacoc cox cce, o e aoc o x.

Copeea popa peae poe c oo a K. Tao oe aee, pa ooo oeca. Moeco oox e aa pocpaco e. poae, eppoae o (o ec, o ac o a, o ooaaec e co K), eep y a:

EK(M)=C DK(C)=M p o oec ceyee paeco (c -1-):

DK(EK(M))=M eoopx aopo p poa eppoa coyc pae (c -2-).

To ec poa, 1, oaec o cooecyeo a eppoa, K2. B o cyae:

EK (M)=C DK (C)=M DK (EK (M))=M 2 eoacoc x aopo ooc ocoaa a ax, a e a eax aopo. o a, o aop oe oyoa poaapoa. poy, coye o aop, oy poo papoac. He ee ae, o oyey ece a aop, ec ey e ece o pe , o o e coe poec a cooe.

poccea pecae coo aop c ce ooe ope ec, poec .

epoaa Op ec poec op ec poae eppoae Pc. 1-2. poae eppoae c o poa eppoa epoaa Op ec poec op ec poae eppoae Pc. 1-3. poae eppoae c y pa a Cuempue aopum Cyecye a ocox a aopo, ocoax a ax: cepe c op o.

Cepe aop, oa aaee yco aopa, peca coo aop, oopx poa oe pacca o y eppoa aoopo. B oce c epx aopo poa eppoa o e e. aop, ae aaee aopa c cepe o aopa c o o, pey, o opae oyae coacoa coye epe aao eoaco epea cooe. eoacoc cepoo aopa opeeec o, pacpe a oaae, o o yoo coe poa epp o a cooe. oa epeaaee cooe o a, oe xpac cepee.

poae eppoae c cooae cepoo aopa ooaaec a :

EK(M)=C DK(C)=M Cepe aop ec a e aeop. O aop opaaa op ec oo (oa oao), o aac ooo aopa ooo pa. pye paoa c pya o opoo eca. py o aac oa, a aop - o aopa o pa. aopo, coyex oepx oeax, paep oa cocae 64 a - ocaoo ooe aee, o oea aay, ocaoo eooe yooe pao. (o oe oepo aop oo opaaa op ec ocoo. Tao apa oe paccapac a ooo aop, opaaa oo coo.) Aopum c ompm o Aop c op o (aaee acep aopa ) papaoa a opa o, o , coye poa, oaec o a eppoa. oee oo, e ppoa e oe (o pae epe eee payoo epaa pee ) pacca o y poa. Aop aac "c op o", ooy o poa oe op : o yoo oe cooa poa poa cooe, o oo ope e oe c cooecy o eppoa oe pacpoa cooee. B x cceax poa aco aaec op o, a eppoa - ap. ap o a aaec cepe o, o o e o ya c cep aopa, o ep e coyec ao e. poae c op o K ooaaec a:

EK(M)=C Xo op ap pa, eppoae c cooecy ap o o o aaec a:

DK(C)=M oa cooe pyc ap o, a eppyc op, o coyec poo oc (c. pae 2.6). Hecop a ooy yay oepa, cooeceo, ooaa c a:

EK(M)=C DK(C)=M punmoaau Cc popa - coxpae opoo eca ( a, oo, pyoo) ae o o yeo (ae aaex oa, coepa, paa, epexaa ). peoaaec, o oye ooc opopy c ey opaee oyaee.

poaa - o aya oye opoo eca, e e a. ceo poee poaa oe pacp op ec . O ae oe oapy cae eca pocceax, o oe oo pee peyey peyay. (Pacpe a e pooec cocoa a aec opoeae.) oa poaaa aaec cpe. Ocooe peooee poaaa, epe co p ypoaoe eaao ee aao A. epxoco ( Dutchman A. Kerckhoffs), icoco o, o eoacoc ooc opeeec o [794]. epxoc peoaae, o y poaaa ec o oe ocae aopa eo peaa. (oeo e, y P e oae cooa Mocca o cox p o paecx aopax, o Mocca ooo ce pao oye x.) Xo peao pe poaa e cea oaa opoo opae, aoe peooee ec xopoe paoe oeo. Ec po e coe oa aop, ae a, a o paoae, o e oee pa e coe cp a op e oo a.

Cyecye epe ocox a poaaecoo cp. aoo x, oeo, peo aaec, o poaa oaae ce ooo a o coyeo aope poa :

1. Bcpe c cooae oo poeca. poaaa ec poec eco x cooe, apoax o e e aopo poa. aaa poaaa coco pacp opoo eca a oo oeo ca cooe , o ye, oy e a (e), cooaoo poa cooe, eppoa pyx c o oe, apoax e e a.

ao: C1=Ek(P1), C2=Ek(P2),... Ci=Ek(Pi) oy: o P1, P2,... Pi;

k;

o aop, a oya Pi+1 Ci+1=Ek(Pi+1) 2. Bcpe c cooae opoo eca. poaaa ec ocy e oo p o eca ecox cooe, o opoy ecy x cooe. Eo aaa coco oy e a ( e), cooaoo poa cooe, eppoa p y x cooe, apoax e e o (a).

ao: P1, C1=Ek(P1), P2, C2=Ek(P2),... Pi, Ci=Ek(Pi) oy: o k;

o aop, a oya Pi+1 Ci+1=Ek(Pi+1) 3. Bcpe c cooae paoo opoo eca. poaaa e oo ec ocy poeca op eca ecox cooe, o oooc pa o p ec poa. o peocae oe apao e cpe c cooae opoo eca, a a poaa oe pa pyee o opoo eca, o oe a oe opa o e. Eo aaa coco oye a ( e), c ooaoo poa cooe, aopa, ooeo eppoa oe c o oe, apoae e e o ( a).

ao: P1, C1=Ek(P1), P2, C2=Ek(P2),... Pi, Ci=Ek(Pi) e poaa oe pa P1, P2,... Pi oy: o k;

o aop, a oya Pi+1 Ci+1=Ek(Pi+1) 4. Aaoe cpe c cooae opoo eca. o ac cya cp c c ooae paoo opoo eca. poaa e oo oe pa pye ec, o ae oe cpo co ocey op a ae oyex peyao poa. p cp c cooae paoo opoo eca poaa o pa poa oo o oo o opoo eca, p aao cp c c ooae paoo opoo eca o oe pa e o opoo eca, ae pa cey o, coy peya epoo opa a aee.

Cyecye o pae epe ee p a poaaeco cp.

5. Bcpe c cooae paoo poeca. poaa oe pa pa e poec eppoa ee ocy eppoa op eca. Ha pep, y poaaa ec ocy "epoy y", oop oe aoaecoe e ppoae. Eo aaa coco oye a.

ao: C1, P1=Dk(C1), C2, P2=Dk(C2),... Ci, Pi=Dk(Ci) oy: k Tao cp oo pe aopa c op o ocyaec paee 19.3. Bcpe c cooae paoo poeca oa ae eo po ce px aopo. (oa cpe c cooae paoo opoo eca cpe c cooae paoo poeca ece aa cpe c cooae paoo eca.) 6. Bcpe c cooae paoo a. Tao cp oaae e o, o po a a oe pa , a o y eo ec eoopa opa o c ey pa a. o cpa, aya e oe pa cp ocyaec paee 12.4.

7. ac poaa. poaa ypoae, aapye ae oo-y, oa e oy . Boeco oa aaec cpe c oyo a. o oe oe coco cp, aco ec ay ye oa aop.

Bcp c ec op eco c cooae paoo opoo eca cpeac ae, e oo oya. He ec eoo poaaa o op ec p o aoo cooe oy oo-y, o apye paoe cooee. Moe e opeo ac oo oya - epea co ocy, , ooo, oapye, o co ye apoao opaeo eo cpay ye. Moe cooe e caape aao ooae, o oe eco poaay. Ocoeo y poa cxo o -a acoo cooa ex co: #define, struct, else, return. Te e poe y poaoo cooo oa : y, ece cpyyp a aee. Bcp c ec op eco ( cp c pa poeco) yceo cooac ope c ea oa xoe Bopo poo o. cope ce pep cp aoo a oo a ax a aa [794,795,796].

e aae o peooe epxoca : ec o ae oo pocce opaec a o, o o e ae, a paoae aop, poa. Ec caee, o xpaee pa pao a opa cepee ye a ay poccey, e peoee aaeecoy cooecy poa a poa aop, oaeec. A ec yaee, o o-o e coe eaccepoa a cxo o occao a aop, a. (B 1994 oy aoe pooo c aopo RC4, c. pa e 17.1.) Ha y aopa c e, oope papaoa opo, oa a a c y popaa pa ce ee ecopy. (Aeco Haoao eoacoc xpa co aop cepee, o y x paoa ye popa pa, a y ac - e. poe oo, o ocy a co aop py c pyo, oaac a cocooc oapa oapy ce caoc coe p a oe.) poaao e cea ec ocy aopa (apep, cpe xoe Bopo poo o Coee aa ocoo oaecoo oa PURPLE [794]), o aco o eo oya. Ec aop coyec oepeco popae eoacoc, o o poco opoc pee ee, yac c eaccepoa popay pacp aop. Ec e aop coyec oeo ccee c, o o poco opoc pee ee y ( ypac) aapaypy peocpypoa aop.

Te, o cpec oy epacpae p, ca o p ao oo ooy, o o ca e co eo oa, o e, o ypa. ecac, ocex pe ocaoo oo. Ocepe aec e, pacxaax aeoc cox aopo, o oaaxc x oyoa. o e p a aopa e.

Xopoe popa opac a ee pyx, oe xopoe aop o oxx.

eonacocm aopumo Pae aop peoca pae cee eoacoc acoc o oo, acoo pyo oa aop. Ec cooc oa aopa e, e cooc apoax ax, , copee ceo, eoacoc. Ec pe oa aopa oe, e pe, eee oopoo a poae ae o coxpac cepee, o ae, copee ceo, eoacoc. Ec oe a x, apoax o o, ee, e oe ax, eoxo oa aopa, oa , copee ceo, eoacoc.

oop "copee ceo", ooy o cyecye epooc ox popo poaae. C pyo copo, aoc oca ax aae co peee. Bao, o aoc ax cea oc a aac ee, e cooc oa cce eoacoc, aae ae.

apc yce (Lars Knudsen) pa cp aopo o cey aeop, pee o pe ya aoc [858]:

1. ooe cpe. poaa oy , K, ao, o DK(C) = P.

2. oaa ey. poaa oy aepa aop, A, ae DK(C) e a K.

3. Meca ( oaa) ey. poaa oy op ec epexaeoo poeca.

4. opaoa ey. poaa oy eoopy opa o e op o ece. Tao opae oy ecoo a, cee o ope opoo eca a aee.

Aop ec eycoo eoac, ec, eaco o oea poeco y poaaa, opa oye opoo eca eocaoo. o cy, oo poae oopao o oa (c. pae 1.5) eooo cp p ecoex pecypcax. Bce ocae pocce o epe cp c cooae oo poeca poc epeopo oox e poe p o occeoc oyeoo opoo eca. o aaec cpe pyo co (c. pae 7.1).

popa oe epecyec poccea, oope eo oa ce cocoo.

Aop caec ceo eoac (, a oa aa, c), ec o e oe oa c cooae ocyx pecypco ceac yye. Tep "ocye pecypc" ec ocaoo paca. Cooc cp oo ep (c pae 11.1) pa coco a:

1. Cooc ax. Oe ax, coyex a xoe oepa cp.

2. Cooc opao. Bpe, yoe poee cp. aco aaec oeo pao.

3. Tpeoa a. Oe a, eoxo cp.

B aece pecoo eoa cooc cp opeeec o acaoy x pex o eo. P oepa cp peoaa aoc oeo : oee cpoe cpe ooo a ce yee peoa a.

Cooc paaec opo e. Ec cooc opao aoo aopa cocae 2128, o 2128 oepa peyec cp aopa. ( oepa oy co e.) Ta, ec peoaaec, o a cee ooc coco o o oepa c e yy, coyee pee aa o apaex poeccopo, oyee a ae y ac ce 1019 e, o ap pa peae pe cyecoa ceeo.

B o pe, a cooc cp ocaec ocoo (oa ao-y poaa e pyae yeo cocoa cp), o oepo pace. a ocee oea cee ooc e oeao poc, e ax p oopea, o a ee e ye pooea. Moe p opaece o po apaex oepo: aaa paaec a ap aex ycoo, peee oopx e peye epoeccopoo aoec. Oee aopa eoac poco ooy, o eo eeo oa, coy copeey exy, ye cyae eaeo. Xop o e pocce poepyc yco oy c yeo pa cex cpec a oo e epe.

cmopuecue mepu copec ep o oocc poccee, cao c cec ea: coa, paa, peoe a aee. Hapep, coo "OEOT" oe opoa ey pay "OBOPOT HAEBO HA 90 PACOB", coo "EEHE" - pay "OBOPOT HAPABO HA 90 PACOB", a coa "OCTAB XO" oy opoa coo "AA". o aoo a e paccapac ao e, c. [794,795]. o oe oo p opeeex ocoecax. Ec y ac e oa "MPABE", e coee epea o oe. A coy p oo caa ce.

1.2 Ceaopa Ceaopa cy epea cepeo pyx cooex, a o cpao cao cyecoae cepea. a pao opae e aoe-y epeoe cooee, a ae pe cepeoe coo ee a o e ce ya. copece pe a ee epa, ee pocoy a y oe y y, oxo aee o aca y, oe apaao aocx coo, pee, opae oy ac cooe poe ecox coo oy oooe.

e ceoey aa pa cepe paecx opaex, ae a aa opae o cooe. paecoe opaee p o eoc coce eaeo oco paecx caapo opee oe eox paa, e cocoe pa eo e ec a - cooee eaoc a pooooo oe. Ta epo-eo ape 1024x1024 cea oo cpa oo cpa cooee 64 a. Moe oeocye popa oy po e a oo oyc.

aoe y epa epa (Peter Wayner) acpy cooe. y e cooee a, o eo cacec po caoc oxo a o-y ee: pae The New York Times, a ecy ecpa eeoepe Internet [1584,1585]. o ceaopa e oypa e oea, o oe oay oo oep, y yy opa Internet.

1.3 ocaooe epecaooe p o oe oepo popa cocoa aopo a coo ocoe. Pae po paece aop o ae o co py, o epeca co. ye aop ea o, pyoe, o oo pa.

Ceo ce aeo coee, o oco ocaec pee. epoe eee aaec o, o aop ca paoa c a, a e coa. o ao xo c o pe paepa aaa c 26 eeo o yx. oco xopox popaecx aopo o cx op opye oc a o epecao.

ocmaooe up ocaoo po aaec p, oop a co opoo eca poece a ee py coo. oyae eppye ocaoy poeca, occaaa op ec.

B acceco popa cyecye epe a ocaoox po :

poco ocaoo p, ooaa p, - o p, oop a co opoo eca aee cooecy coo poeca. poc ocaoo pa c popa aeax.

Ooy ocaoo p oxo a pocy ocaooy poccey a c e e oo, o o co opoo eca oopaaec a ecoo coo poeca. Hap ep, "A" oe cooecoa 5, 13, 25 56, "B" - 7, 19, 31 42 a aee.

opa ocaoo p - o p, oop o coo pye o pya. Ha pep, "ABA" oe cooecoa "RTQ", "ABB" oe cooecoa "SLL" a aee.

oaa ocaoo p coco ecox pocx ocaoox po.

Hapep, oy cooa pax pocx ocaoox po ;

a c o opoo eca aeec c cooae ooo opeoo pa.

ae p eap, oopo a co opoo eca aeec coo, axoe o c pe coa paee o oy 26 ("A" aeec a "D," "B" - a "E",... "W" - a " Z ", "X" - a "A", "Y" - a "B", "Z" - a "C"), pecae coo poco ocaoo p. O eceo oe poc, a a aa poeca pecae coo cee, a e cyao pacpeee aa op o o eca.

ROTI3 - o poca poaa popaa, oo ocaea c ccea UNIX. Oa ae e c poc ocaoo po. B o pe "A" aeec a "N," "B" - a "O" a aee. aa ya ceaec a 13 ec. poae aa popao ROTI3 a occaaae epoaa a.

P = ROT13 (ROT13 (P)) ROTI3 e coyec eoacoc, oa aco peec oe, apa oeao ep ec, peee oooo oy oooe.

poce ocaooe p eo pacpac, a a p e pe aco cooa pa x coo opo ece. o occao op ec, xopoey poaay peye c oo a 26 coo acoo aaa [1434]. Aop cp ax po oo a [578, 587, 1600, 78, 1475, 1236, 880]. Xopo oep aop pee [703].

Ooye ocaooe p cooac ye 1401 oy epoce Maya [794]. O oee co cp, e poce ocaooe p, xo o e cpa cex cacecx coc a opoo eca. p oo cp c ec op eco p pacp a c pao. Bcpe c cooae oo poeca oee pyoeo, o oo aae a o epe ecoo cey. opooc pee [1261].

opae ocaooe p - o p, oope opy cpay py coo. p Play fair ("eca pa"), opee 1854 oy, cooac aaa epo poo oe [794]. O pye ap coo, eo poaa ocyaec [587,1475,880]. py pepo opaoo ocaoooo pa ec p Xa ( Hill) [732]. oa oo e a eco pa coye c opoae o Xaay (Huffman), o eeoac opa ocaoo p.

oaae ocaooe p opee o aco ( Lean Battista) 1568 oy [794]. O cooac ape Coeex ao xoe paaco o Aepe. Hecop a o, o o eo oy oa [819, 577, 587, 794] (ocoeo c oo oepo), oe o epece poy oepo eoacoc coy ae p [1387,1390, 1502]. (opooc oo, a cp y cxey poa, coyey popao WordPerfect, oo a [135,139].) p Beepa (Vigenere), epe oyoa 1586 oy, p oopa (Beaufort) ae c pepa oaax ocaoox po.

oaax ocaoox po oecee ooyee , a oopx c oyec poa ooo coa opoo eca. ep o pyec ep co o poo eca, op o - opo co, a aee. oce cooa cex e o oop c ec. Ec peec 20 ooyex e, o aa aaa ya pyec e e o. o apaep aaec epoo pa. B acceco popa p c epo o o pyee pacp, e p c opo epoo. cooae oepo ooe eo pacp ocaooe p c oe epoo.

p c ey o (oa aae po), coy o ec p o a pyoo eca, pecae coo pyo pep oooo pa. xo epo oo pa pae e eca, o ae oe eo oa [576,794].

epecmaooe up B epecaooo pe eec e op ec, a opo coo. B poco cooo e pecaooo pe op ec ec opoao a papaeo ce ya cpoa o p, a poec caec o epa (c. -3-). eppoae pecae coo ac poeca epao a ce papaeo ya cpoao p ae cae op oo eca opoao.

poaa x po ocyaec [587,1475]. Ta a co poeca e e, o op o ece, aco aa poeca oae, o aa ya cpeaec peo c o e acoo, o oo. o ac poaay oooc pe pae eo, opee p a opo coo oye opoo eca. peee poecy opoo epecaoo oo pa aeo oc eoacoc. Cyecy ee oee coe epecaooe p, o oep oy pacp o ce x.

Hee p ADFCVX, cooa xoe epo poo o, peca coo epecao o p coea c poco ocaoo. o coeo pee oe co aop pacp ope eo (Georges Painvin), payc poaao [794].

Xo oe copeee aop coy epecaoy, c caa poea cooa ooo oea a, a ae oa peyec paoa c cooe opeeeoo paepa. ocaoa oee oa.

Pomope au B 1920-x oax aoaa poecca poa opee pae exaece ycpo ca. oco cooao oe poopa, exaecoo oeca, coyeoo oe o cao.

Poopa aa, aa aaypy aop poopo, peaye apa pa Beepa. a poop pecae coo poooe paeee aaa, ee 26 o oe pocy oc a oy. Hapep, poop oe cooa ae "A" a " F", "B" a "U", "C'' a "I" a aee. B xoe p ooo poopa coee c xo p ceyeo poopa.

Op ec:COMPUTER GRAPHICS MAY BE SLOW BUT AT LEAST IT'S EXPENSIVE.

poec:CAELP OPSEE MHLAN PIOSS UCWTI TCBIV EMUTE RATSG YAERB TX Pc. 1-4. Coo epecaoo p.

Hapep, epexpoopo ae ep poop oe ae "A" a " F", opo - "F" a "Y", pe - "Y" a "E" eep - "E" a "C", "C" ye oe poeco. ae eoope poop cea c, cey pa ocao yy py.

eo oa ecox poopo exao, yx poopa, oeceae eoacoc a. Ta a poop paac c pao copoc, epo n-poopo a pae 26n. Heo ope poope a ae oy e pae ooe aoo poopa, o eae poa a ee oee eccce.

Ca ec poop ycpoco ec a ( Enigma). a cooaac ea o Bopo poo oe. Caa e pa ooy Apypy epycy ( Arthur Scherbius) Apy epxapy ay (Arvid Gerhard Damm) Epoe. B Coeex aax oa a aaeoaa Apypo epyco [1383]. He aeo ycoepecoa ao poe cooa o pe o.

eeo o p poopa, opoe oo o pa oox, oyaop, o o p cea acoa op ec, opaa poop, oop aca a poop opaaa o p ec aoo ca a. Hecop a cooc , oa a oaa eee Bopo poo o. Caaa pya ocx popao oaa eey y oca pacp aop aaa. B xoe o e opoa y, a aae pooa poaa ox epc. Ocee pao poopx po cocoo x pacp oo a [794, 86, 448, 498, 446, 880, 1315, 1587, 690]. B yx ceyx oeax yeaeo paccaaec o oe [735, 796].

aeeo meu aa a e ec o o acceco popa, ooy aee e yy opoo ocaa ac a x peeax. pepac a o ooepo poo c [587, 1475].

[448] coep copee poaa poax a. opo e (Dorothy Denning) pacca pae oe x po [456], a [880] coep ecpcpac co aeaec aa ex e cax po. py ocae capo popa, oca aaooy popa, e c [99]. pepac oop oe cae [579]. Beoe ae o copeco popa a aa [794, 795, 796].

1.4 pocoe XOR XOR pecae coo oepa "caee " : '^' e C Q aeaeco oa. o oa oepa a a:

0 0 = 0 1 = 1 0 = 1 1 = Tae ae, o:

a a = a b b = a aaoc , aya aop pocoo XOR o cy ec e , a oaa po Beepa. ec o yoaec oo -a pacpocpaeoc oepecx popax poyax, o pae epe pe MS-DOS Macintosh [1502, 1387]. coae, ec o popae oepo eoacoc aec, o o "aeoa" aop poa, aeo oee cp, e DES, o copee ceo coyec ao-o apa ceyeo.

o cep aop. Op ec oepaec oepa "caee " ece c e eco oye poeca. Ta a oopoe peee oepa XOR occaaae op a poa eppoa coyec oa a e popaa :

P K = C C K = P Hacoe eoacoc ec oa e o. o poa eo cpaec, ae e o epa [587, 1475]. Eo o a oepe aae ecoo cey.

peoo, o op ec coye ac . oee oo, yc a a oe e ooe co a. He ocao, a oa o p:

1. Opee y a c oo poeyp, eco a oce coae [577]. pe oepa XOR poecy, coy aece a ca poec c pa ce e , ocae coaae a. Ec ea cee paa e a, o coae ce 6 poeo ao. Ec e, o yy coaa ee e 0.4 poea (ca, o o ASCII ec opyec cya o, pyx o opx eco ca yy p y ). o aaec oaaee coae. Maoe ceee o ooo ae, pa oo e a, pyoy ec a a.

2. Cec poec a y y poee oepa XOR ceeoo opaoo poeco. Peyao oepa ye yae a oyee opoo eca, oepyoo oepa XOR c ca coo, cee a y a. Ta a aco e a o a pxoc 1.3 a eceo opa (c pae 11.1), cyecya aea ooc ooe opee coco poa.

Hecop a o, oeco ocao popaoo oecee, aax o pye a op aece "o aoo e eoacoo a DES", eae [1387]. eo o aop (c 160- oopc "o") NSA oe oo papeo cooa pox eeox coox cex ap ooca. XOR oe a a a o ae cecp, o acoeo poaaa aep a cae cey.

1.5 Oopaoe oo oepe e, o ea coco poa cyecye. O aaec oopao ooo opee 1917 oy Mopo oeo Moopo ( Major Joseph Mauborgne) epo Bepao (Gilbert Vernam) AT&T [794]. (aec oopao oo pecae coo oco cya opo o o cxe, c. pae 3.7.) B acceco oa oopao oo ec oo eoop ec oceoaeoc coo a, pacpeeex cya opao, acax a ycoax ya peex cy ooa. epoaao o a oopaoa ea eeao. Opa e cooa a co a ooa poa oo ooo coa opoo eca.

poae pecae coo coee o oy 26 coa opoo eca coa a o o paooo ooa.

a co a coyec oo eo eceoo cooe. Opae py e cooe yoae cooae cpa ooa cooay ac e. oyae, co oepe, coy oo ao e oo, eppye a co poeca. Pacpoa cooee, oyae yoae cooecye cpa ooa ac e. Hooe cooee oe co a. Hapep, ec cooee ec:

ONETIMEPAD a ea oceoaeoc ooe:

TBFRGFARFM o poec ye e a:

IPKLPSFHGQ a a Q T mod 26 = I N B mod 26 = P E F mod 26 = K ..

B peooe, o oye e coe oy ocy oopaooy ooy, cooa oy poa cooe, a cxea coepeo eoaca. aoe poaoe cooee a cooecye oy opoy cooe oo e paepa.

Ta a ce ee oceoaeoc coepeo oao (oe, co a eeppyc cya opao), y poa ocycye opa, ooa oepy poec poa a y. ycoe poeca oe oxo a :

POYYAEAAZX o eppyec a:

SALMONEGGS a:

BXEGBMTMXM o eppyec a:

GREENFLUID oop ee pa: a a ce ope ec paoepo, y poaaa e oooc ope e , ao opx eco ec pa. Cyaa ea oceoaeoc, coea c ecya op eco, ae coepeo cya poec, ae cee o o c e coy o e.

Heoxoo ao, o co a o eeppoac cya opao. e o cp ay cxey caac co cocoo, oop coaec oceoaeoc coo a. c ooae eepaopo ceocyax ce e caec, y x cea ecyae coca. Ec coyee eceo cya co - o aoo pyee, e aec a ep , c. pa e 17.14 - o coepeo eoaco.

pyo a oe: ey oceoaeoc oa e cooa opo pa. ae ec coyee oo paepo ecoo aa, o ec poaa oy ecoo eco c epepac a, o coe occao op ec. O ce ay apy poeco ooceo py pya ocae co coae ao o. Ec poec cee p a o, coooee coae peo opace - ooe aee ac o a opoo eca. C o o pe poaa e pecae pya. o oxoe a oaae coae, o cpaac a pax "epoa" [904]. He coye ey oceoaeoc oopo.

e oopaooo ooa eo pacpec a oe ae. Beco oopaooo ooa, c o coeo y, coyec oopao oo o. Beco coe opoo eca c o oopaooo ooa coye XOR. eppoa pee XOR poecy c e e oo pao ooo. Bce ocaoe e eec, eoacoc ocaec ao e coepeo.

Bce o xopoo, o cyecye ecoo poe. Ta a ee o cya e oy cooac coa, a eo oceoaeoc oa pac e cooe. Oopa o oo yoe ecox eox cooe, o eo e cooa pao o aay c c poyco cocooc 1.544 M/c. B oee xpa 650 Ma cyax ax a CD-ROM, o y ec poe. Bo epx, a yo oo e o cyax o, o CD-ROM oo oo p ox paax. o opx, a yo yoa cooae . CD-ROM e pyo oooc ya opa poe a ec papy ec c. opao oe oxo poa ea.

ae ec poe pacpeee xpae e pee, a pec oo cxpopoa p a oy opae oyae. Ec oyae poyc ( ecoo poay p epeae ), cooee oepe c cc. C pyo copo, ec ecoo ec p epeae ( o e ye yae oae - o opao oe oxoe a e cyaoo ya ), o yy pacpoa epao. Ho oopao oo e oeceae poepy ooc.

Oopaoe oo coyc ceo, a opao cepxcepex aao c c o poyco cocooc. o cyxa "opa " ey Coee aa Coe c Coo (a ecye oa ceac?) pyec c oo oopaooo ooa. Moe cooe coecx oo apoa c cooae oopaox ooo. cooe epacp ceo acea ocayc epacp. Ha o a e oe pe pao cyepoepo a o poeo. ae oa pa coe Apoe pe co ee opa c oepa e co ooc, o e coy poec cooe coecx oo, apoae c oo o opaox (ec, oeo, o e coy epyc pooe o ye oopaoe oo ).

1.6 oepe aop Cyecye oeco oepx aopo. Ceye p coyc ae ceo :

DES (Data Encryption Standard, caap poa ax) - ca oyp oep a o p poa, ec aepac eyapo caapo. o cep aop, o o e coyec poa eppoa.

RSA (aa ec coaee - Peca (Rivest), apa (Sharnir) aa (Adleman)) - ca o yp aop c op o. coyec poa, poo oc.

DSA (Digital Signature Algorithm, aop poo oc, coyec a ac caapa p o o oc, Digital Signature Standard) - pyo aop c op o. coyec oo poo oc, e oe cooa poa.

eo ooe aop ocac o e.

1.7 oe ca Ha poe ce coy pae oe ca oca pax ee p o pa. Ta a eo ayc x cax x aex, ece aao eoopx ce p e e 0-.

ca oeac o opy e oopa pax coo. Moe acpo ece ae occ paoe paa acoa ( Freeman Dyson), "Bpe e oa: a o o opo Bceeo" ("Time Without End: Physics and Biology in an Open Universe") Reviews of Modem Physics, v. 52, n. 3, July 1979, pp. 447-460. Cepoc peyae aoaacpo paccaa c oo ca c Mcepca pacopa (163 cep o eoe 1993 oy cpee pooeoc 69.7 oa.

Ta. 1-1. oe ca ec aao co Bepooc y oe ( eee ) 1 9 apo (233) Bepooc pa a p ocyapceo oepee CA 1 4000000 (222) Bepooc pa a p ocyapceo oepee CA 1 y oe eee oo e Bepooc yoy ( CA eee oa) 1 59000 (216) Bepooc oy aoaacpoe ( CA oy) 1 6100 (213) Bepooc oy aoaacpoe ( CA eee pee ) 1 88 (27) Bpe o ceyeo oeee 14000 (214) e Bpe o pepae Coa cepxoy ey 109 (230) e Bopac ae 109 (230) e Bopac Bceeo 1010 (234) e co aoo ae 1051 (2170) co aoo Coa 1057 (2190) co aoo aa 1067 (2223) co aoo Bceeo 1077 (2265) Oe Bceeo 1084 (2280) c Ec Bceea oea:

ooe pe ceeo 1011 (237) e 1018 (261) cey Ec Bceea ecoea:

Bpe o oca ex e 1014 (247) e Bpe o opa ae o e 1015 (250) e Bpe o opa e o aa 1019 (264) e Bpe o papye op paaoo paae 1020 (267) e Bpe o papye epx p poecca Xoa 1064 (2213) e Bpe o pepae aep oc p yeo eepaype 1065 (2216) e Bpe o pepae aep epoe eo 1010 e Bpe o pepae aep epy py 1010 e ac PTOPAECE POTOO aa ee poooo 2.1 Beee pooo Cc popa - pee poe. (o cy, o coco cc cooa oepo, o e oe ac a.) popa peae poe cepeoc, poep ooc, eoc o c eoeeco eecoc. B oee y ce o popaecx aopax eoax, o o peca oo aaeec epec, ec e coyc pee ao-y poe.

eo ooy copaec caaa y a pooo.

pooo - o opo ec, pepaex y oee copoa, peaae p e e opeeeo aa. o aoe opeeee. "opo ec" oaae, pooo oec opeeeo oceoaeoc, c aaa o oa. aoe ece oo oc co oepe oo oce ooa peyeo. "pepaex y oee copoa " oaae, o pea a poooa peyec o pae epe a eoea, o eoe e coe peaoa pooo. e oe ooy oe o eoope ec, pea aay (apep, oya op), o o e p o oo. ( oo, o oyc aco pooo, o-o oe cec op.) Haoe, "peaae pee opeeeo aa " oaae, o pooo oe po aoy-o peyay. o-o, oxoee a pooo, o e peaee ao aa - o e pooo, o oep pee. poooo ec ae pye xapaepc :

a yac poooa oe a pooo oceoaeoc cocax eo ec.

a yac poooa oe coacc ceoa poooy.

pooo oe epoope, aoe ece oo opeeeo a, o e o oooc eoa.

pooo oe o, ao ooo cya oo cooecoa opeeeoe e ce.

B o e a pooo opaoa a eoop opo ec. Boee poooa poc xo o ec, eo, oa e ye oa epe ceyey ec. aoe ece ae o pae epe oo yx : ce, oee oo eco copoa, cooe, oop oeac copo.

popaec pooo - o pooo, coy popa. Copo oy py ceo oep py pyy paa e ep py pyy ae p cooe pee cyo. p opaec pooo ae eoop popaec aop, o, ooe oop, peaaee poooa xo a pa poco eoacoc. ac poooa oy axoe oec cepeo py c pyo, coeco eeppoa cyay oceoaeoc, oep py pyy co o oc oca opa o o e oe pee. Cc cooa popa poo o e - peopae oapye peeca oeeca. Ec oa e caac c oo poooa, o oy paao e ae pecaee o o, o eoepe py pyy copo oy o, coy oepy ce. Oee pao oo copypoa c e y opao:

Heooo cea ya oe, e opeeeo poooe.

o opao coee, e aec. B ceyx ecox aax paccapa oeco poooo.

B eoopx x o yaco oe oay pyoo. B pyx, oye oe oa pooo ya cepey opa. P poooo poaac, a a x papao eoc a oo aeo opee peoa. pye poaac -a oo, o x papao eocaoo aeo aapoa co pooo. a aopo, opao ee oaa ooy ee o acoc poooa, e eo oy eoacoc.

Cc npomooo B oceeo o ceo cyecy eopae pooo : aa oapo o eeoy, pa oep, oocoae a opax. Ho e ayaec o x poooax, o paaac e e e eoo pee, ce a, a ooac o paoa ocaoo xopoo.

Ceo ce oe oe e oac e o, a coy oepy ce. ex e e e, oope ea e ayac, oepa y opae pooo. oa epeeae e ocyapca ocyapco oapyaee ay, coepeo oayc o o, oopo p , eo aapyeec. oep aeo e a .

ecoc eoacoc ox poooo eoeecoo oe ocoa a o pcyc. Pa e ae eaoy yy ee, o o y ac o-y aaee ? Cee pa oep c e, o yae, caa ap? oee co pae ee paecy, e yy yepe aoc aoo oocoa?

Hao ca, o ooae oepx cee cea ec. Tae ao ca, o cea e c papao oepx cee. oca x o eo a, o ae ecoo yo oy pec oo pea. opapy pooo, oo poep coco, coyee ya oa poooo. Ta oe papaoa pooo, ycoe oy.

poe opaa ec, pooo oo acpapoac p pee aa o cocoa p e e. pooo c o o e a PC, a VAX. Moo poep pooo, e aac ea eo peaa. oa yec aeoc poooa, eo oo ye peaoa e yoo o o e po o eeoo eeyax ocepo.

pou eocpa pao poooo coy ecoo poo (c. 1-). epe oe - o Aca o. O yacy o cex ycopox poooax. a pao, Aca (Alice) aae ce pooo, a o (Bob) oeae. Ec poooa ya pe eepa copoa, py cya po () (Dave). pye po pa ceae cooaee po, o yy pecae o e.

pomoo c nocpeuo ocpe - o eaepecoaa pe copoa, oopo oepeo aepee poooa (c. 1- (a)).

Heaepecoaoc oaae, o y ocpea e aepecoaoc peyae pao poooa cooc oo copo. "oepeo" oaae, o ce yac poooa pa ce, o cae ocpe a cy, ce eo ec - a pae, yepe o, o ocpe o co ac poooa. ocpe ooa peaoa paoy poooo aoec eoepx py pyy copo.

B peao pe aece ocpeo aco cya pc. Hapep, Aca poae eaooy e oy ay. o xoe aa eo, o y Ac e cocoa poep, ecee e. Aca xoe, o pace o ey poee pee, e pao coceoc epee oy. o, oop ep Ace e oe, e oa ey, e xoe epeaa e, e oy paa coceoc.

Ta. 2-1. ecye a Aca ep yac cex poooo o Bopo yac cex poooo po Tpe yac poooax c yace pex epex copo eep yac poooax c yace pex epex copo Ea oye (eavesdropper) Mop Bo poooo Tpe acya oep ocpe oep opoep, aae Acy oa pe poooo e Cee Bop poepe ooc Tpe o Aca (a) pooo c ocpeo Aca o Tpe oce cyeoc oaaeco oaaeco () appa pooo o Aca () caoocao pooo Pc. 2-1. T poooo ocpeeco pca ycpo oox. C eo oo Aca o oy o cey pooo, o a ce o oaa:

(1) Aca epeae pao coceoc pcy.

(2) o epeae e pcy.

(3) Aca eopye e.

(4) oac oa ea pc epeae pao coceoc oy. Ec e e oae eee op e eeoo pee, Aca oaae o a pcy, o opaae pao coceoc Ace.

B o poooe Aca ep, o pc e epeac oy pao coceoc o ex op, oa e e y e oae, epe pao coceoc Ace, ec e oae e ye. o ep, o pc ye oa a pao coceoc o ex op, oa e e ye oae, epeac pao coceoc oy cpay e oce oa ea. pc e aoc o oae ea. O o cyae o co ac poooa, e ey aa o cyae.

B o pepe pc pae po ocpea. pc aco cya po ocpeo p ae a x oa p epeoopax o opae. Pae p cya aece ocpeo ey o y ae poaa.

B aece ocpea oe cy a - oy a :

(1) o aoe e epeae eo a.

(2) Ec a cey oa ocaoo ee op ea, a aepe e opaae eo oy.

(3) Aca epeae oy pao coceoc, a o epeae Ace aepe e.

(4) Aca eopye e.

o pooo paoae, ooy o Aca ep aocoy ceecy. Aca ep, o a coxpa e oa ee e coye x acpoa coex oepa c eoc aaox pecyax.

py oep ocpeo ec oapyc. oa o oyae o Ac aepe oap y co oye, o yee, o Aca ocaa oye o coey ea coceopyo. p eoxo oc oapyc oe cy cye aceecoa o a.

oe ocpea capo a p. Bcea cyecoa opeeee - o, pe oy oo oe - oaae e, oo ecoa cpaeo. ocpe pa opeeey po ae oece, oa oep oopa aaeoe ooee. pc-ocpe, apy ae paa pa, oepac aaa - apep, ce oe aoao. o ea a apa, peao pe ooee, coae, oe oac o ee.

o ea oo epeec a p oepo, o c oep ocpea cyecye p p o e:

eo a epay pe copoy, oopo oo oep, ec aee ocpea oee o ye eo. e copo, oocec py pyy c oopee, c e e oopee oecy c eoy ocpey, aepoy e-o ce.

oepa ce oa oece oepy ocpea. aoc pco oeeca, a oo ce y ooee aae pacxo ?

Cyecye aepa, pcya ce poooa c ocpeo.

ocpe oe pa yace ao paa, c y eco pyoacax peaax oo poooa. Poc ca ocpeo c y poey, o pace ea o ycy.

Ta a a ce oe oep ocpey, o ocpe pecae coo caoe eco ce p oe ee oa.

Hecop a o ocpeeco ce ee ao coyec. B poooax c cooae ocpea y po ye pa Tpe.

Apumpae npomoo coye -a coo cooc aa ocpeo appae pooo oe pa a a opoooa eo ypo. ep pecae coo pooo e ocpea, coye p ea copo o pooo. pyo pecae coo pooo c ocpeo, paae cex ocoecax - p a paoac ey copoa. Cooecy cea ocpe aaec appo (c. 1-()).

App, a ocpe, pecae coo eaepecoaoo yaca poooa, oopoy oep oe copo. B oe o ocpea o eocpeceo e pae yac ao oeo pea a poooa paaec oo poep ecoc oe poooa copoa.

poeccoa appa c cy. B oe o oapyco cy opaac oo p oe paoac. Aca o oy a opa e yac cy. Cy oa e yae o opae, ec oa copo e oac a pyy cy. pooo oca opaa oo opa o a cey opao:

opooo e ocpea (oec cea) :

(1) Aca o ooapac o ycox opaa.

(2) Aca ocae opa.

(3) o ocae opa.

opooo c cooae appa (oec p a paoac) :

(4) Aca o peca epe cye.

(5) Aca peocae co oaaeca.

(6) o peocae co oaaeca.

(7) Cy pae peee a ocoa oaaec.

Pae coyex o e o ocpea appa coco o, o yace appa p o cxo e cea. Copo opaac cye oo p paoacx. Ec paoac e, cy e y e.

Cyecy appae oepe pooo. O peoaa, o yacye copo ec, o p oope o ooo oeece o cyecyey aopy ax pe copoa, oopo oep yac, coe oapy a oeeca. Xopo appa pooo ooe a p py ycao oc oea. Appae pooo oapya, a e peypea oe eco. Heopaoc oapye cyae aece peypeeo ep, peopaa oe eco.

Caoocmamoe npomoo Caoocao pooo ec y o poooa. O ooc oeceae ecoc copo (c. 1-()). oe poooa e ye ocpe, e pea cop app. Cao o cpoee poooa oeceae ocyce copo. Ec oa copo oaec coea, oe eco ye eeeo oapyeo pyo copoo, pooo pepa oc. eo e aac oc oeaa copoa, oy e cyeo cyc.

B ye pe o pooo oe caoocao, o, ecac, e cyecye caooc a ox poooo ao cya.

onmu cpmu npomooo popaece o oa oy apae po popaecx aopo, c oyex poooax, po popaecx eoo, coyex peaa aopo poooo eocpeceo po poooo. ocoy o paee ocyac eo p o oo, peoaa, o popaece aop eo eoac, paccapa oo o cp poooo.

oy cooa oeco cocoo oa pooo. Heoope, e c yaca p o ooa, oy "ocya" ay-o ac ec pooo. o aaec acc cpe, a a o e oecye a pooo. Bce, o o oe cea - o poce a poooo o ac o opa. o cp cooecye cp c cooae oo poeca, ocyaeyc paee 1.1. Ta a acce cp pyo oapy, pooo cpec peo paa, a e oapya x. B x poooax po oyea ye pa Ea.

B pyo cyae o oe oac e pooo coceo o. O oe a ce a pyoo, ec oe cooe pooo, ae oo cooee py, oopo epea c a pe cooe, paopa aa c e xpayc oepe opa. Tae ec aac a cpe, a a o pey aoo eaeca. op cp ac o a ce.

acce o capac oy opa o yacax poooa. O copa cooe , epeae pa copoa, ac poaapoa x. o aoo cp, c pyo copo, pecey oee po aop ee. Bo oe aepecoa oye opa, yxye pao cce oye ecaopoaoo ocya pecypca.

Ae cp oee cepe, ocoeo ooe poooo, oopx copo e oaeo oep py pyy. Bo e oaeo o-o coce ocopo, o oe apecppoa ooaee cce ae cce acpaopo. Moe ae ecoo ax o o, paoax ece. B o e po oaepeoo aoo oa ye pa M op.

Boo oe o yaco poooa. O oe oaa, o pooo, oce e ceoa paa poooa. Tao o aaec oeo. acce oe o paa poooa, o capac oy oe opa, e peycopeo poooo.

Ae oe apya paoy poooa, ac coea.

Oe pyo oepa eoacoc poooa, ec oco eo yaco - ae oe , o oa aoe oeeco oe oapyeo ao yaca. oeo, pooo o ae o accoo oeeca.

2.2 epeaa opa c cooae cepo popa a y copoa eoaco oeac opae? oeo e, py co cooe. oco p, o oo poo, oa Aca ocae poaoe cooee oy (o pooo opao coee).

(1) Aca o pa ccey poa.

(2) Aca o pa .

(3) Aca pye op ec coeo cooe c cooae aopa poa a, o ya poaoe cooee.

(4) Aca ocae poaoe cooee oy.

(5) o eppye poec cooe c cooae aopa poa a, oya o p ec cooe.

o oe Ea, axoc ey Aco oo, ya, ocya o pooo ? Ec oa oe o cya oo epeay a ae (4), e pec oepy poec poaay. o accoe cpe pecae coo cpe c cooae oo poeca, peee aop yco (acoo a eco) o ooe ce ooc, oop oe ao y Ea pee poe.

Ea, oao, e ya. Oa oe ae ocya a (1) (2). Toa e cay ec aop - ae a oy. oa oa epexa cooee a ae (4), o e ocaec oo epoa eo caocoeo.

B xopoe poccee eoacoc ooc ac o a a acoo e ac o a aopa. eo ooy ypaee a a ao popa. coy cep aop, Aca o oy opo o a (1), o a (2) o o coxpa ae. oe ocaac cepee epe, oce eee pao poooa - o ex op, oa oo ocaac ae epeaaeoe cooee - poo cyae cooee y e ye pacpo. (O popa c o p a, peae y poey ae, paccaaec paee 2.5.) Mop, a o, oe cea oe-o pyoe. O oe oac apy c e ae (4), cea a, o Aca ooe e coe epeaa opa oy. Mop ae oe e pexa cooee Ac ae eo co coce. Ec ey yaoc ya (epexa oe opae a ae (2) oa poccey), o coe apoa coe cooee op a eo oy eco epexaeoo, o e coe ya, o cooee opaeo e Aco. Ec M op e ae a, o oe oo coa cooee, pepaaeec p epoe ecccy.

o, ca, o cooee opaeo Aco, oe pe, o o y Ac, o ce o cepe e poe.

A Aca? o oa oe cea, o cop pooo? Oa oe epea o a Ee, oa Ea coe a ce, o oop o, aeaa eo coa H-op Tac. o cepeo, o poea e poooe. Aca a oe epeaa Ee e ope ec, epeaaee c cooae poooa. oeo, o e caoe oe cea o. pooo peoaae, o Aca o oep py pyy. a, cep poccea pcy ceye poe :

Pacpeeee e oo pooc cepee. co e a, a ce cooe, a poae a, a a ae a ooe pacp ce cooe. pacpo cpaex cce poa aaa pacpeee e - cepeea aaa. aco ypep o oca o aae.

Ec copoepoa (ypae, paaa, a, oye a y .. ), o Ea coe pacpoa ce cooe, apoae o. Oa coe ae cy aece oo copo coaa oe cooe, ypaa pyy copoy.

B peooe, o aa apa ooaee ce coye oe , oee co e cpo opacae c poco ca ooaee. Ce n ooaee peye n{n - l)/2 e. Ha pep, oe 10 ooaee ey coo yo 45 pax e, 100 ooaee opeyec 4950 e. Peee poe - yee ca ooaee, o o e cea o oo.

2.3 Ooapaee y oe ooapaeo y ec epa popa c op a. He c poooa eocpeceo ooapaee y peca coo paeyo ae oca poooo, ocyaex o e.

Ooapaee y ooceo eo cc, o eppyc c o pyo. To ec, a x poco pacca f(x), o o ecoy f(x) eeo c x. ec, "eeo" oaae, o ce x o f(x) oy opeoac o e, ae ec a o poeo yy c ce o ep pa.

Xopo pepo ooapaeo y cy paa apea. eo pa apey a cy poex ycoo.. Oao, eeo coa co apey x ycoo.

o y paco, o yao eoo. Maeaec cpooo oaaeca cyecoa o o apaex y e, e peax ceec oooc x ocpoe [230, 530, 600, 661]. He cop a o, oe y ooc a ooapaee : oe pacca x , o cx op, e ae pocoo cocoa eppoa x. Hapep, opaeo opecoc eo c x2, o aoo coee x1/2. B ocaec ac paea copac popc, o ooapaee y cyecy. M ooop o o ee paee 1 1.2.

a, o e xopoeo ooapaex yx ? Heocpeceo x e cooa poa. Cooee, apoaoe ooapaeo ye ecoeo - eo eooo epoa.

(paee: ae a apee o-y, paee apey a poee oco ae oae x pe. opoce eo poa cooee. ocope, a o ye oaae ooapaeo y e.) popa c op a a yo o-o pyoe (xo cyecy eocpecee popaece pee ooapaex y - c. pae 3.2).

Ooapaea y c o - o oco ooapaeo y, c cepeo aeo.

Ee eo c oo apae pyo - opao. Ho ec a ece cepe, oee eo pacca opay y. To ec, eo c f(x) o aaoy x, o pyo o ecoy f(x) c x. Oao, cyecye eoa cepea opa, y, ooa, p a f(x) y, eo c x.

B aece xopoeo pepa ooapaeo y c o paccop ac. eo paopa ac a co acex ycoo pyo coa copa x eae paoae ac. Ho, c cepeo opae - cpye o cope - aoo ee pe y aay.

2.4 Ooapaee x-y ooapaeo x-y oe oeco e: y ca, y copae contraction function, paoe oee, xapaep pa, popaeca opoa cya, o e ococ cooe (message integrity check, MIC) o oapye ay (manipulation detection code, MDC). a oa e aaac a y ec epao copeeo popa. Oo apaee x-y - o pya ac yaea ox poooo.

X-y, ooe pe coyec oepx ayax, peca coo y, ae aece e, oope oya a xo cpoy epeeo (aaey poopao) peo pay ee cpoy cpoao, oo ee, (aaey aee x -y). B aece poco x-y oo paccapa y, oopa oyae poopa opaae a, peca coo XOR cex xox ao.

Cc x-y coco oye xapaepoo paa poopaa - ae, o oopoy aa pyc pae poopa p pee opao aa. Ta a oo x-y pecae co o coooee "oe ooy", eooo co ce opeeeoc caa, o e cpo coaa, o x oo cooa, oya peey oey ooc.

Ooapaea x-y - o x-y, oopa paoae oo oo apae : eo c aee x-y o poopay, o pyo coa poopa, aee x -y oopoo pao aao ee. oaec paee x-y, ooe oop, e c ooapae : aa ope a, e pecae pya coa cpoy ao, XOR oopx ae aaoe aee.

C ooapaeo x-ye aoo e e. Xopoe ooapaeo x-ye ec x-y e cooe - pyo coa a poopaa c oao aee x -y.

X-y ec opo, a ee pacea e cyecye. eoacoc ooapaeo x-ye aaec eo ee ooapaeoc. xoa e o acoc o xoa. eee ooo a poopaa po ee, cpee, oo o ae x -y. B ceo eooo a poopa, cooecy aaoy ae x -y.

ocope a o a a coco oy xapaepe pa ao. Ec xoe poep, o y oo-o ec o e a, o y ac, o e xoe, o o a epea a, opoce oca a aee x-y. Ec pcaoe aee x-y coae c pacca a, o o a epa yo a coaae c a. o ocoeo oeo p acox paax, oa e xo e e-o ce pepa ce co cea $100 ce $1000. B ox ycox oee cooa ooapaey x-y e a, a o o yoo oe poep aee x -y. Ec yo, o poep aee x-y o oo o oyae, poe cey pae.

o npoepu nouocmu cooeu o poep ooc cooe (message authentication code, MAC), ec ae a o po ep ooc ax (data authentication code, DAG), pecae coo ooapaey x-y c oaee cepeoo a (c. pae 18.14). aee x-y ec ye poopaa, a. Teop ocaec o e, o x -y, o oo o, o ae , oe poep a e e x-y. MAC oo coa c oo x-y ooo aopa poa, cyec y ae ceapoae MAC.

2.5 epeaa opa c cooae popa c op a Be a cep aop a a ce. ec oae. a oa e oe oe op ce, oo eo oye coa ap. o-o pyo p oo o e o a oe op ce apa oye. Te, o e ae oa, pec ayc a a ce.

B 1976 oy Map Xea acea e y apay popa [496].

(NSA ao, o ao o ao oooc ee 1966 oy, o oaaec e pecao.) O oca popa c op a, coy a pax a - o op o ap.

Opeeee apoo a o opoy peye opox cex apa. o yoo, coy op oe apoa cooee, o e pacpoa eo. Pacpoa cooee oe oo aee apoo a. o oxoe a pepaee popaecoo cea oo .

poae c op o aaoo oyca ca oo , o oe cea o, oyc co pope oooo a. eppoae c ap o aoae eee o oooo a. Oo o opao coee - a oe oaoc capo apea. Oao, ec aee cepe (y ac ec o oooo a ), e pya ocaee ay oy.

Maeaeco ocoo poecca c paee ocyaec ooapaee x-y c o. poae oec po apae. aa o poa op, a oe apoa cooee. eppoae oec opao apae. Oo acoo pyoeo, o, e a cepea, ae a oepax Cray a c ( o) e eooo pacpoa coo ee. Cepeo, o, cy ap , o eae eppoae a e poc, a poae. Bo a, coy popa c op a, Aca oe oca cooee oy :

(1) Aca o coacoa poccey c op a.

(2) o ocae Ace co op .

(3) Aca pye coe cooee opae eo oy.

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

Opae ae, o popa c op a ycpae poey pacpeee e, pcyy cep poccea. Pae Aca o o ao ooopc o e.

Aca oa pa o , o e yo o epea eo oy. Oa oa cea o apaee, o o peye o ee opeeeo peycopeoc. Oa oa oca c cepe ypepo, o oo yo pe. popa c op a ce ypoae. Aca oe opa oy cepeoe cooee e ax-o peapex ec. E, ocyae acoo ce, ec op oa cooee, apoaoe o, o oa e coe oy ap oa, ec cooe.

Oo ea ce ooaee coacoae coyey poccey. aoo x ec o p ap , ope oeac oeocyo ae ax. Teep pooo ee poe:

(1) Aca eae op oa a ax.

(2) Aca pye coe cooee c oo opoo a oa ocae eo oy.

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

B epo poooe o oe oca Ace ee op pee, e oa oa opa ey cooee. Bopo pooo oe oxo a oy oy. o e yacye poooe o ex op, oa o e ae a cooee.

Ceae punmocucme epe aop c op o ca ec o e pe, oa poxoo DES ocyee a peoaaeoo caapa. o peo eco apae popaeco cooece. a o oca [494]:

pepace pocce c op o, ocyaee oypo ayo ea, e e eee, e a cooecyeo oa cpe popaecx oo. B o e oy, oa a opa popa c op a, Aeco aoao eoacoc ( NSA) peoo yoy popaecy ccey, papao ay po IBM, aece eepaoo Cmaapma upoau ax (Data Encryption Standard, DES). Map Xea poa o peoee -a eocaoo a, o pooe oooc oepa caap, aa pa a ocpa o a oa oea ee caapa pa poe ae coceo pao. popa c op o, co oepe, ae oepaac pe oypo ep a ype [1125] execx cax [849, 1159], coo o oyppy poy, a e eaee ayoe ope.

o, oao, e oeao NSA o o cox acyax o oac. Eo peop oo cae Encyclopedia Bri tannica [1461] yaa, o "yxea popa a opa Aece a ec e pae ", xo oaaeca oo yepe e yo pecae.

B peao pe aop c op a e ae cepe aop coyc e poa cooe, a poa e o cey y pa :

1. Aop c op a paoa eeo. Cepe aop o pae epe 1000 pa cpee, e aop c op a. a, oep caoc ce cpee cpee e epe 15 popa c op a oce copoce, cpax c ce o e copoc cepo popa. Ho peoa oey epeaaeo opa ae opaca, cea ye peoac poa ae cpee, e o coe cea popa c op a.

2. pocce c op a y o ooe cp c pa op eco. Ec C = E(P), e P - op ec n oox opx eco, o poaa y yo oo apoa ce n oox opx eco cpa peya c C (oe, poa oeocye). O e coe pacp eppoa, o o coe opee P.

Bcpe c pa op eco oe ocoeo e, ec co oox poax cooe ooceo ao. Hapep, ec P - o eea cya oapax, ea e $1000000, o aoe cpe cpaoae, poaa epeepe ec o ae. (a poea pe aec c oo epoocoo poa, c. pae 23.15.) ae ec P e a xopoo opeeeo, a oe cpe oe oe eo. oe oe pocoe ae, o poec e coo ecye opeoy opoy ecy. Cepe pocce e yce cp aoo a, a a poaa e oe o ecox epoo c eec o.

B oce peaa popa c op a coyec acepea pacp o cpae ceacox e, oope coyc cep aopa ap ooa coo e [879]. oa ae peaa aac cea (p) poccea (1) o ocae Ace co op (2) Aca coae cya ceaco , pye eo c oo opoo a oa epeae eo oy.

EB(K) (3) o pacpoae cooee Ac, coy co ap , oye ceacooo a.

DB(EB(K))=K (4) Oa yaca py co cooe c oo ooo ceacooo a.

cooae popa c op a pacpeee e peae oe ay p o ey pacpeee e. B cepo popa poa ax, ec o e co y ec, aec e ea. Ec Ea aoy eo, oa coe pacpoa ce ape o coo e . C oo peeoo poooa p eoxooc apoa cooe coaec ceaco , oop yoaec o ooa ceaca c. o aeo yeae pc opoea c e acooo a. oeo, opoea ycee ap , o pca aeo ee, a a eee ceaca o coyec oo o pa poa ceacooo a. opoo c ae c opoc ocyac paee 3.1.

oooou Mepa Pa Mep (Ralph Merkle) ope epy cxey popa c op a. B 1974 oy o a cac a ypc o oepo eoacoc aopco yepcee, ep, oop e ac Xoa (Lance Hoffman). Teo eo ypcoo pao, oao pae cpoa, a "eoaca epeaa ax o eeoac aaa" [1064]. Xoa e o peoe Mepa, oe oo Mep pepa a. O pooa paoa a poeo ecop a pooaeec eoae eo p e yao.

Texa Mepa ocoaac a ooooax ( "puzzle"), oope opae oyae pe e e e oyey. Bo a Aca oe oca poaoe cooee oy, e oeac c o o oo.

(1) o coae 220 (py coa, oe oa) cooe a: "o ooooa oep x. o cepe oep y.", e x - cyaoe co, a y - cya cepe . x, y oac ao cooe. coy cep aop, o pye aoe cooee co 20 o ce x opae Ace.

(2) Aca pae oo cooee pcyae cp pyo co, ac oy op ec. a paoa ec oeo, o e eooo.

(3) Aca pye coe cepeoe cooee p oo eoopoo cepoo aopa oye e o ocae o cooee oy ece c x.

(4) o ae, ao cepe y o cooa cooe x, ceoaeo o oe pacpoa cooee Ac.

Ea oe oa y ccey, o e pec o opao oe pao e Ace oy. pacp cooe a ae (3) oa oa ye cp pyo co aoe 2 cooe, opa ex oo a ae (1). Cooc oo cp coca 2. ae x ae e ooy Ee, e o a ae (1) pcoe cya opao. B oe cyae, cee apa E yy pa o e e apa ce apaa Ac.

o p (n o ooe n2) ee o popaec caapa, o p opeeex yc o x oe ocaoe. Ec Aca o oy poep ec c e ceyy, aoy x opeyec ya oe cox ec ee oa ya epea ooooo o oa Ace o c 1.544 M/c. Ec cee oooc E cpa c pee, e opeyec ooo oa oa cce. pye aop ee oee yco cp.

2.6 poe oc Pyoce oc aa coyc a oaaeco aopca oyea , o pae epe, coac c . o e a paeo oc [1392]?

1. oc ocoepa. Oa yeae oyae oyea o, o oca coaeo o ca oye.

2. oc eoea. Oa oaae, o eo oca, o o, coaeo oca oye.

3. oc e oe cooaa oopo. Oa ec ac oyea, y e coe epeec oc a pyo oye.

4. oca oye e e. oce oo, a oye oca, eo eooo e .

5. O oc e ooo opec. oc oye aepa. oca e coe o cec yepa, o o e oca oye.

B eceoc, oo x yepe e ec ooc cpae. oc oo oea, cec c ooo ca ya a pyo, oye oy ee oce oca. Oao, pc c poea -a oo, o oeeco apyeo oe oap yeo.

Xoeoc peaoa o-y oooe a oepax, o ec p poe. Bo epx, o epe a copoa e poco, a oe poco. ae ec oc eoea pyo oea (apep, paecoe opaee pyoco oc), oo eo pea pay oc ooo oye a ca pyo. pocoe ae ao oc eo e oaae. Bo opx, oepe a oe eo oo e oce oo, a o oca, e oca aeeo cea ee.

onuc oyema c noo cuempux punmocucme u nocpeua Aca xoe oca pooe cooee opa eo oy. Oa oe o cea c oo Tpe a cepo pocce.

Tpe - o oaa ac ocpe, oopoy oep. O oe cac c Aco, c o o ( co ce py ea oca poe oye ). O ae cepe , KA, A ce pyo cepe , KB, - oy. opeec aoo o aaa ec poooa oy cooa oopao ox oce.

(1) Aca pye coe cooee oy o KA ocae eo Tpey.

(2) Tpe, a KA, pacpoae cooee.

(3) Tpe oae pacpoaoy cooe yepee, o o oy o cooee o Ac, pye o ooe cooee o KB.

(4) Tpe ocae ooe cooee oy.

(5) o pacpoae cooee o KB. O oe poa cooee Ac, oepee Tpea, o cooee opaeo eo Aco.

Oya Tpe yae, o cooee po eo o Ac, a e o aoo-o caoaa ? O eae o o poa cooe.

Tae o xopoo, a oc a yae? ocop a peyee coca:

1. a oc ocoepa. Tpe - o acya oep ocpe, Tpe ae, o coo e e oyeo o Ac. oepee Tpea cy oaaeco oa.

2. a oc eoea. Too Aca ( Tpe, o ey ce ep) ae KA, ooy oo Aca oa oca Tpey cooee, apoaoe o KA. Ec o-y oaec a c e a Acy, Tpe cpay ae o a ae (2) e aep ooc.

3. y oc e cooa oopo. Ec o oaec oepee Tpea p coe eo pyoy cooe, Aca ap "apay!" ocpe (Tpe o-o coce pyo, e ocy o e opa) opoc oa pe eo cooee p o aoe cooee Ac. ae ocpe apye cooee o KA y, o oo e co oecye poaoy cooe, epeaoy oo. o, oeo e, e coe coa pa oe poaoe cooee, ooy o o e ae a KA.

4. oca oye e e. Ec o oaec, oy oye, e eo, Tpe oapy oeeco ye oca cocoo.

5. O oc eooo oaac. Ec ocec Aca a, o oa oa e ocaa cooee, oepee Tpea oae opaoe. oe, ce oep Tpey, ce, caaoe - ca.

Ec o axoe oaa po oye, oca Aco, o e coe pacp e co cepe . Ey pec coa opac Tpey:

(1) o epe cooee yepee Tpea, o cooee oyeo o Ac, pye x o KB ocae opao Tpey.

(2) Tpe pacpoae oye ae c oo a KB.

(3) Tpe poepe co ay ax oepae, o opaee opaoo cooe a Aca.

(4) Tpe pye oye o oa ae o KC, oop o e po, ocae po poa ae.

(5) Tpe pacpoae oye ae c oo a KC. Teep oa oe poa coo e e, oepee Tpea, o cooee opaeo Aco.

pooo paoa, o o pey o Tpea eax apa pee. O oe e pacpoa poa cooe, ocpea ey ao apo e, oope xo oe ac oca oyea. O oe xpa cooe ae ax (xo oo oo ea, oca oyae o poaoo cooe opae ). O ye y eco o cce c, ae ec o - poco ecycea oepa popaa..

Taoo ocpea a Tpe, oopoy yy oep ce oppecoe, eo a eo coxp a . Tpe oe eope, ec o ceae xo oy oy a o oce, o e ye ep ey. Tpe oe acoo eoace. Ec eo aa ax c cepe a oa y pacpoec, o-y coe epepopapoa eo, ce oc cay ecoe. o c oye yo ocae o aa. o pee xaocy. paeca ay, cae pa aapx. Taa cxea eopeec oe paoa, o oa eocaoo xopoa paecoo p ee.

epe upox nonuce Pa Mep peo ccey pox oce, ocoay a popa c cepe o, coae ecoeoe oeco oopaox oce, coy peoy cpyypy [1067,1068]. Oc oo ee o cxe ec oec ope epea e op a, yocoep eo a o pao. ope ocae oo cooee yocoepe oy epea. a x yo ocae oo cooee yocoepe co oy, a aee.

onuc oyema c noo punmopauu c ompmu au Cyecy aop c op a, oope oo cooa pox oce. B e oopx aopax - pepo ec RSA (c. pae 19.3) - poa oe cooa op, ap . apye oye co ap o, oye aey poy oc. B pyx cyax - pepo ec DSA (c. pae 20.1) - pox oce co yec oe aop, oop eooo cooa poa. a e epe a o peea Xeao [496] aee a pacpea yyea pyx paoax [1282, 1328, 1024, 1283, 426]. Xopo oop o oac pee [1099]. Ocoo pooo poc:

(1) Aca pye oye co ap o, a opao oca eo.

(2) Aca ocae oca oye oy.

(3) o pacpoae oye, coy op Ac, a opao poep oc.

o pooo opao ye peyeo. Tpe e ye oc oyeo, ee poep.

(O ye oepe, o op pae eo Ace.) Tpe e ye copoa ae papee copo: Ec o e co ocyec a (3), o o ae, o oc epaa. Taa oc cooecye ce peoa :

1. a oc ocoepa. oa o pacpoae cooee c oo opoo a Ac, o ae o oa ocaa o cooee.

2. a oc eoea. Too Aca ae co ap .

3. y oc e cooa oopo. oc ec ye oyea e oe epeecea a pyo oye.

4. oca oye e e. oce oo ee oyea oc e coe oe oepac op o Ac.

5. O oc eooo oaac. oy e peyec oo Ac p poepe ee oc.

onuc oyema u emu peeu Ha cao ee, p opeeex ycox o coe coea. O oe oopo cooa oye oc coeco. o e ee ae, ec Aca ocaa opa (oo oe o caoo opaa oe, oo ee ), o o ec Aca ocaa poy oc o eo?

peoo, o Aca ocaa oy oca e a $100. o oec e a, oop poep oc epee e c ooo cea a pyo. o, cya po ya, coxpa o e pooo ea. Ha ceye eee o coa oec eo o pyo a. a oep oc e pee e c ooo cea a pyo. Ec Aca e poepe co eoy y, o coe poe a o oa.

ooy poe oc aco a e pee. aa pe oca oyea oa c oyey ocac ece co ce coepae cooe. a coxpae y ey pee ae ax. Teep, ec o oaec oy ae o ey Ac o opo pa, a poep ey pee o coe ae ax. Ta a a ye oa e Ac c o e eo pee, o ye aa o. ae o poee e 15 pe eop, ya popaece pooo.

onuc oyema c noo punmopauu c ompmu au u ooanpaex x yu Ha pae aop c op a aco eocaoo e oc ox o y eo. oo pee pooo poo oc epeo coy ece c ooapae x-y [432, 433]. Aca ocae e oye, a aee x-y aoo oyea. B o poooe ooapaea x-y aop poo oc coacoac apaee.

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

(2) Aca pye o aee co ap o, a opao oca oye.

(3) Aca ocae oy oye ocaoe aee x-y.

(4) o oyae aee ooapaeo x-y oyea, pcaoo Aco. ae, c oy aop poo oc, o pacpoae ocaoe aee x-y c oo opoo a Ac. Ec ocaoe aee x-y coaae c pacca, oc paa.

Copoc aeo opacae , a a epooc oy yx pax oyeo oaooe 160-oe aee x-y coca e oo o ac 2160, oo eoaco ppa oc ae x-y oc oyea. oa cooac oo ooapaea x-y, ae coa pae oye c o e e aee x-y epyo, oc ooo o y ea pee ooo oc cpay ox oyeo.

poooa ec pye o. Bo epx, oc oe oeea o oyea. Bo opx, a eo yeac peoa oey a oyae, oopo xpac oye oc. Ap xa ccea oe cooa o pooo oepe cyecoa oyeo, e xpa x coepa. B epao ae ax oy xpac ae x-y ao. Boce e yo pocapa a, ooae oea co ae x-y ay ax, a aa a x xpa ae, oea x peee oye oyea. Ec yye oe aoe-y paoace o ooy aopa pee coa oyea, aa ax coe pape eo p oo xpaeoc e ae x-y. ooa ccea ee ooe aee p xpae cepeo opa: Aca oe oca oye coxpa eo cepee. E oaoc oyoa oy e, oo ec oa axoe oaa coe aopco. (C. pae 4.1).

Aopum u mepuoou Cyecye oeco aopo poo oc. Bce o peca coo aop c op a c apo ac oc oyeo c opo - poep oc. oa poecc oc aa poae c ap o, a poecc poep oc - eppoae c op o. o oe ec ayee, c cpae oo ooo aopa, RSA. pyx aopo - pye peaa. Hapep, cooae ooapaex x -y eo pee oa po oe ooex ao p oca poepe oc.

Moe aop oo cooa poo oc, o e poa.

B oe cyae yy ccac a poecc oc poep, e aac opooc aopo.

oc cooe c ap o K ye ooaac a:

SK(M) a poepa oc c oo cooecyeo opoo a a :

VK(M) Cpoy o, pcoeey oyey oce eo oca ( peye pepe, aee o o apaeo x-y oyea, apoaoe ap o ), ye aa poo o c poco oc. Bec pooo, c oo oopoo oyae cooe poepe oc o pae eococ cooe, aaec yocoepee ooc. oee opoo pooo paccapac paee 3.2.

Hecoo nonuce a Ace oy oopeeo oca o o e oye? B ocyce ooapaex x-y cyecye e oooc. Aca o oy oca pae o ooo oo e oyea. oyeoe cooee ye a paa ee epoaaoo oyea. Aca oc ae oye, a ae o ocae oc Ac. o coco paoae, o poep oc Ac, e poep p o oc oa, eooo.

C oo ooapaex peaoa ecoo oce poco :

(1) Aca ocae aee x-y oyea.

(2) o ocae aee x-y oyea.

(3) o ocae co oc Ace.

(4) Aca ocae po oye, co oc oc oa.

(5) po poepe oc Ac oa.

Aca o oy o aa (1) (2) apaeo, oceoaeo. Ha ae (5) po o e poep y oc eaco o pyo.

Heooocm omaamc om upoo nonucu Aca oe coea c po oc, c eo e oea. Oa oe o ca oye ae yepa, o oa oo e eaa. Caaa oa, a oo, ocae co. a e oa aoo pacpae co ap epe o ece. Teep Aca yepae, o ee oc a copoepoaa cooaa e-o py, a ce a ee. Oa eaypye co oc o ce oyea, oca c oo oo apoo a. o aaec oa o oc.

Me pee oy c e aoo oeeca, o Aca cea oe a, o ee copoepoa pae. Ec Aca pao paccae pe, oa coe oca oye ae yceo a, o oa oo e eaa. ooy a oo oopc o xpae apx e aex ecax - o Aca e oa opac o coeo oyope .

Xo c oo oyopeee eo e cea, oo pep eoope ec, apa pye o, o cape oc e yy pa eocoep -a paoac o o oc.

(Hapep, Aca oe "oep" co , o e a oy a oepay ay, oopy o epa e poa , peyae, ceae eece co aoc ce.) oyae yo poca e pee oyex oyeo [453]. Oa cxea poooa peea [2, 8]:

(1) Aca ocae cooee.

(2) Aca coae aooo, coepa eoopy eaoy opa. Oa pcoee aooy ocaoe cooee, ocae ce ece ocae Tpey.

(3) Tpe poepe e oc oepae eaoy opa. O oae e y pee ocaoy cooe Ac eaoo opa. ae o ocae ce ece ocae ae Ace oy.

(4) o poepe oc Tpea, eaoy opa oc Ac.

(5) Aca poepe cooee, oopoe Tpe oca oy. Ec oa e pae coe aopco, oa cpo ae o o.

B pyo cxee Tpe coyec aece appa [209]. oy ocaoe cooee, o oc a e o Tpey poep. Tpe oe oep oc Ac.

cnooaue upox nonuce O cax pax peoex pee pox oce o ypoee poep co e ooopo o epx cax [1454, 1467]. Coeee a Coec Co (o-y o Coec Co?) pape py pyy paec a yo eppop cecopa cee a ep ca. poea a o, o aa copo oa a yepea o, o pya copoa e oeaa ae x cecopao. Oopeeo, pya copoa oa a yepea, o a oca oo y opa, oopa ya cee a ep ca.

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