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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 ...

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oee coe nopooe cxe B peyx pepax oaa oo pocee opooe cxe : cepe ec a n ee a, o , oe e m x, oo o pacp cepe. Ha ae x aopo oo coa aoo oee coe cxe. B ceyx pepax ye cooac aop apa, xo yy paoa ce ocae.

o coa cxey, oopo o yaco aee pyx, ey aec oe ee. Ec occaoe cepea yo ee, y oo-o ec p e, a y cex ocax - o oo, o eoe ece c y py oe occao cepe. e eo yac occaoe cepea op e yec eoe.

o ecoo ee oy oy a eoea oee. aoy eoey oe ao ooe co ee. Heaco o oo, coo ee o poao, occaoe cepea opeyec e m x. H o eoe, ea pya e coy occao cepe, oaa oo m-1 e.

pyx cxe peca ceap c y pae eea. Moo pacpee cepe a, o eo occaoe opeoaoc oe 7 yaco eea A poe 12 yaco eea B. Coaec ooe cee 3, oop ec poeee eoo apaoo pae.

aoy yacy eea A aec e, oopa ec aee eoo pae, a yac a eea B ac ae apaoo pae.

occaoe eoo pae ocao e e e yaco eea A, o ea co o oo, coo pyx ee ec y eea, ee yac e coy eo ya o cepee. Aao o eea B: ee yac oy co p e, occaaa apaoe paee, o pyy opa, eoxoy occaoe cepea eo, o oy e coy. Too epeo co pae, yac yx eea coy occao cepe.

B oe cyae, oe peaoaa a ca cxea paee cepea. opeyec oo aca ccey ypae, cooecyx opeo ccee. Bo ecoo pepacx cae a ey ooex cxe paee cepea [1462, 1463, 1464].

Paeeue cepema c oeuau o aop ee caapy opooy cxey (m, n) oapye oeo [1529]. oa y eo cooae a ae cxe apaa, o aop paoae c py cxea. Bpaec pocoe co p, oee n oee (s - 1)(m - 1)/e m e s - o ca oo oo cepe, a e - epooc ycexa oeeca. e oo cea a coo a, acoo o eoxoo, o poco yco ce. ocpoe e a pae, o eco cooa 1, 2, 3,..., n xi, epe cya opao ca aaoa o 1 o p-1.

Teep, ec Mop p occaoe cepea ae co ac oeo, eo e c coo epo oc oaec eooo. Heoo cepe, oeo e, oaec oea cepeo. Maea a o cxe peea [1529].

coae, xo oeeco Mop ye opo, ey yacc ya cepe (p yco, o ce ocae ye e pa ). O oo aae pyo pooo, oca [1529, 975]. Oco o ee ec cooae aopa k cepeo, a o o yaco apaee e a, ao x pa. a cepe, a cee acoeo, oe peyeo. ac oe co e, oya o cepe a py, oa o e oya aeee aee cepea. o cepe ye pa.

B o cxee oe eo c ee o oye oeoo cepea. Cyecye opeeee cooc, ec yac pe co e o oepe, opooc oo a epaype. B ce yx paoax ae paccapac oapyee peopaee oeeca opoox cxeax [355, 114, 270].

23.3 ocoae aa Ong-Schnorr-Shamir o ocoae aa (c. pae 4.2), papaoa ycayco Coco (Gustavus Simmons) [1458, 1459, 1460], coye cxey ea Ong-Schnorr-Shamir (c. pae 20.5). a opa o cxee opae (Aca) pae oeocy oy n ap k a, o n k ao poc ca. B o o opao cxe k coyec coeco Aco oo, o yaee ocoaeo aae. Op cec cey opao :

h = -k2 mod n Ec Ace yo opa ocoaeoe cooee M eoo cooe M', oa caaa po epe, o ap M' n, a ae M n c ao poc ca. Aca ce S1 = 1/2*((M'/M M)) mod n S2 = 1/2*((M'/M - M)) mod n apa ce S1 S2 pecae coo oc paoo cxee Ong-Schnortr-Shamir oopeeo ec ocee ocoaeoo cooe.

Tpe oep (oe aoo?) oe poep ooc cooe, a o po Ong Schnorr-Shamir, o o oe cea ee oe-o. O oe poep ooc cooe (Bcea o oo, o oep oaec ey ocyy oeoe cooee ). O poepe, o S12 - S22 M' (mod n) Ec ooc cooe oaaa, oyae oe e ocoaeoe cooee, coy ceyy opyy:

M=M'/(S1+ S2k-1) mod n o paoae, o e aae, o caa cxea Ong-Schnorr-Shamir a oaa.

ElGamal pyo peoe Coco ocoae aa [1459], oca [1407, 1473], ocoa a cxee oc ElGamal c. pae 19.6).

eepa a oec ae, a ocoo cxee oc ElGamal. Caaa paec pocoe co p a cyax ca, g r, ee p. ae cec K = gr mod p Op o cya K, g p. ap o ec r. oo Ac r eco oy, o co coyec e oo oc eooo cooe, o aece a opa e ocoaeoo cooe.

o oca ocoaeoe cooee M eoo cooe, M', M p o oapo ao poc, poe oo, ao poc o M p-1. Aca ce X = gM mod p peae ceyee ypaee Y (c oo pacpeoo aopa a ):

M' = rX+ MY mod (p-1) a aoo cxee ElGamal, oc ec apa ce: X Y. oep oe poep oc El Gamal. O yeaec, o KXXY gM' (mod p) o oe occao ocoaeoe cooee. Caaa o yeaec, o (gr)XXY gM' (mod p) Ec o a, o cae cooee o (e oea oepo). ae occaoe M o ce M = (Y-1 (M' - rX)) mod (p - 1) Hapep, yc p = 11, a g = 2. ap r paec pa 8. o oaae, o op o, oop oep oe cooa poep oc, ye gr mod p = 28 mod 11 = 3.

o opa ocoaeoe cooee M = 9, coy eooe cooee M' = 5, Aca poe pe, o 9 11, a ae 5 11 oapo ao poc. Oa ae yeaec, o ao poc 9 11-1=10. o a, ooy oa ce X = gM' (mod p) = 29 mod 11 = ae oa peae ceyee ypaee Y:

5 = 8 6 9 Y mod Y= 3, ooy oc cy apa ce 6 3 ( X Y). o yeaec, o (gr)XXY gM' (mod p) (28)663 25 (mod 11) o a (oe apeece ec caocoeo, ec e e epe ), ooy o oe pacp ocoaeoe cooee, c M = (Y-1 (M' - rX)) mod (p - 1)= 3-1(5 - 8*6) mod 10 = 7(7) mod 10 = 49 mod 10 = ESIGN ocoae aa oo oa ESIGN [1460] (c. pae 20.6). B ESIGN cepe ec apo ox pocx ce p q, a op o cy n = p2q. cooa ocoaeoo aaa ap o c p pocx ca p, q r, a op o - n, aoe o n = p2qr epeea r - o ooee ae, ye oy poe ocoaeoo cooe.

o oca ooe cooee, Aca caaa pae cyaoe co x, eee pqr, ce:

w, aeee eoe, oopoe oe pao (H(m) - xk mod n)/pq s = x ((w/kxk-1 mod p) pq H(m) - o x-aee cooe, a k - apaep eoacoc. oc ec aee s.

poep oc o ce sk mod n. poe oo, o ce a, aeee eoe, oopoe oe pao yoeoy cy o n, eeoy a 3. Ec H(m) ee paa sk mod n, ec sk mod n ee H(m) 2a, o oc caec pao.

opa ocoaeoo cooe M c oo eooo cooe M' Aca ce s, c oy M eco of H(m). o oaae, o cooee oo ee, e p2qr. ae oa pae cyaoe co u ce x' = M' ur ae o aee x' coyec aece "cyaoo ca" x p oc M'. Cooecyee a ee s ocaec aece oc.

oep oe poep, o s (opoe s) ec pao oc M' Too ae poep o oc cooe oe o. Ho, a a ey eco r, o oe c s = x' ypqr = M ur ypqr M (mod r) a peaa ocoaeoo aaa aoo ye yx peyx. B apaax Ong-Schnorr Shamir ElGamal y oa oe ap Ac. o coe e oo a ocoaee cooe Ac, o aa ce a Acy, oca oe oye. Aca eo c e co e oea, ycaaa ao ocoae aa, e pec oepc oy.

Cxea ESICN cpaae o o poe. ap o Ac cy aop pex pocx ce: p, q r. Cepe o oa ec oo r. O ae n = p2qr, o, o pacp p q, ey oaoc pao a oe o co. Ec poce ca ocaoo e, oy ye a e pyo a ce a Acy, a oepy oy-y ee.

DSA ocoae aa cyecye DSA (c. pae 20.1) [1468, 1469, 1473]. Ha cao ee x ae oe ecoo. poce ocoae aa ae op k. peoaaec, o o ye 160-ooe co. Oao, ec Aca pae opeoe k, o o, a ap Ac, coe pacp o k. Aca oca oy 160-ooe ocoaeoe cooee ao oc DSA, a ce ocae yy oo poep oc Ac. ooeoe ycoee: Ta a k oo cy a, Aca o o cooa o oopao oo poa ocoaeoe coo ee c oo oo ooa, eeppy k.

B DSA ec ocoaee aa, e peye epeaa oy ap Ac. O ae opayea op opex ae k, o e oy epeaa o 160 o opa. Ceya cxea, pecaea [1468, 1469], ooe Ace oy oeac ao oc o o ocoaeo opa.

(1) Aca o pa cyaoe pocoe co P (oaeec o apaepa p cxee oc). o cepe ocoaeoo aaa.

(2) Aca ocae eooe cooee M. Ec oa xoe opa oy ocoae 1, oa yeaec, o apaep r oc ec apa ocao o oy P. Ec oa xoe opa ey 0, oa poepe, o apaep r oc e ec apa ocao o oy P. Oa oaec oo, oca cooee c oo cyax ae k, oa oa e oy oc c y e coco r. Ta a ca, ec apa ocaa e ec , paoepo, o o e oo co coo.

(3) Aca ocae oy ocaoe cooee.

(4) o poepe oc, yeac ooc cooe. ae o poepe, ec r apa ocao o oy P occaaae ocoae .

epeaa a opao ecox o opayeae oop aoo r, oopoe ec e ec apa ocao o eco oy. opooc pee [1468, 1469].

a cxea oe eo pacpea epea ecox ocoaex o a oc. Ec Aca o pa a cyax ca P Q, o Aca oe oca a a, pa cyaoe k a, o r oc e oc apa ocao mod P, a ae oc e oc ap a ocao mod Q. Cyaoe aee k c epooc 25 poeo oo oy r c y coca.

Bo a Mop, eec peaaop DSA, oe coa aop, ea o 10 o apoo a Ac ao ee oc.

(1) Mop cpo co peaa DSA ae ycoo oy CC, o o e co poep, a oa paoae. O coae 14 ocoaex aao coe peaa DSA. To ec, o pae 14 cyax pocx ce coye pocxey, oopa pae aee k a, o r oc e oc apa ocao o oy aoo x 14 pocx ce, acoc o ocoaeoo cooe.

(2) Mop ae pocxe Ace, oy oca ea.

(3) Aca o opao ocae cooee, coy co ap 160-o x.

(4) Mpocxea cya opao pae 10-o o x: epe 10 o, ope 10 o, ..

Ta a cyecye 16 oox 10-ox oo, o oep oa paaec 4-o co.

o 4-o eaop 10 o a yy 14-o ocoae cooee.

(5) Mpocxea epepae cyae ae k, oa e yacc a o, oopoe oaae pa apa ocaa, y epea ocoaeoo. Bepooc cyaoo k oaa pao opo paa 1/16384. Ec pocxea oe poep 10000 ae k ceyy, y oe aee ye aeo ee, e a apy cey. ce e ac o cooe oy ce apaee, o oo, a Aca axoe oca cooee.

(6) Mpocxea o opao ocae cooee, coy paoe a ae (5) aee k.

(7) Aca ocae poy oc oy, oyoae ee ce, ee o-y eae.

(8) Mop pacpae r , a a o ae 14 pocx ce, pacpoae ocoaeoe cooee.

Cpaee ceo, o, ae ec Aca ae, o pocxo, oa eo e coe oaa. oa 14 po cx ce xpac cepee, Mop eoacoc.

umoeue nocoameoo aaa DSA ocoae aa opaec a o, o Aca oe pa k epea ocoaeo opa. o cea ocoae aa eoo, Ace e oo ooeo pa k.

Oao, op k oe apee cex pyx. Ec oy-o pyoy ye ooeo pa k, o o eoe oy oooc oea oc Ac. Ece peee Ac ec poeee eepa k ece c pyo copoo, oo, a, o Aca e oa opopoa o k, a o e o opee o k. Ha pyo copoe poooa y oa oa oooc poep, o Aca cooaa eo coeco coaoe k.

Bo o pooo [1470, 1472, 1473] (1) Aca pae k' ocae oy u = gk' mod p (2) o pae k" ocae eo Ace.

(3) Aca ce k = k'k" mod (p - 1). Oa coye k, o oca coe cooee M, coy DSA, ocae oy co oc: r s.

(4) o poepe, o ((u = gk' mod p) mod q) = r Ec o a, o o ae, o oc M cooaoc k. oce aa (4) o ae, o r e o eo ao ocoaeo opa. Ec o ec oepeo copoo, o oe poep, o oc Ac e ocoaeo opa. py pec oep eo ae, o e c o e oaa o a pee copoe, ocpoe pooo.

eo o, o o, ec axoe, oe cooa o pooo coa coceoo o coaeoo aaa. o oe ocoaey opa oy oce Ac, pa k" c opeee xapaepca. oa Coc op ay oooc, o aa ee "aao y y". opooc pao aaa yy, ea oy pexpoxo pooo eepa k, pac capac [1471, 1473].

pyue cxe ocoae aa oo opaoa o cxe oc [1458, 1460, 1406]. Ocae poo oa cpaa ocoaeoo aaa cxe Fiat-Shamir Feige-Fiat-Shamir ece c oo o yopee oo a [485].

23.4 Heopaee poe oc Aopo oo aopa eopaeo oc (c. pae 4.3) ec ay (David Chaum) [343,327]. Caaa oyoac ooe pocoe co p p ee g, oope yy co eco cooac pyo ocax. Ac ec ap x op gx mod p.

o oca cooee, Aca ce z = mx mod p. o ce, o e yo cea. poepa o c eoo coee.

(1) o pae a cyax ca, a b, ee p, opae Ace:

c = za(gx)b mod p (2) Aca ce t=x-1 mod (p-1), opae oy:

d = ct mod p (3) o poepe, o d magb (mod p) Ec o a, o cae oc co.

peca, o Aca o o o pooo, o eep cae, o Aca ocaa cooe e. o xoe ye o po, ooy o oaae e ac poooa. , oao, xoe ye po, o oye oca e-o py. O coae oey ac poooa. Caaa o eeppye cooee a ae (1). ae a ae (3) o eeppye d oy epeay o pyoo eoea a ae (2).

Haoe, o coae cooee aa (2). po ac oa a oao. Ee eooo ye paoc oc, oa oa e o pooo caocoeo.

oeo, ec oa cea -a ea oa a e, a o oe pooo, oa a yeea.

po yo ye oee ao o opy, a, a o ea o.

coy y cxey oc, oo coyc c poeo, o e a opooce. pee, e ocooac o cxeo, pocope epaypy.

pyo pooo ae e oo pooo oepe - Aca oe ye oa paoc coe oc - o pooo opa. Aca oe c oo epaoo poooa c ye a e ye oa, o ee oc epaa, ec o a [329].

a pey pooo pya ocax coye oeocyoe ooe pocoe co p p ee g. Ac ec ap x op gx mod p. o oca cooe e, Aca ce z = mx mod p. o poep oc:

(1) o pae a cyax ca, a b, ee p, opae Ace:

c = magb mod p (2) Aca pae cyaoe co q, eee p, a ae ce opae oy:

s1 = cgq mod p, s2 = (cgq)x mod p (3) o ocae Ace a b, o Aca oa yec, o o e oea a ae (1).

(4) Aca ocae oy q, o o o ocooac mx occao s1 s2. Ec s1 cgq mod p s2 (gx)b qza (mod p) o oc paa.

Aca oe ae oaac o oc z o cooee m. opooc pee [329]. oo ee pooo eopaex oce oo a [584, 344]. e Xap (Lein Harn) yao (Shoubao Yang) peo cxey pyox eopaex oce [700].

peopayee eompuaee nonucu Aop peopayex eopaex oce, oope oo poep, oe peopa o a oe eopaee oc, pee [213]. O ocoa a aope pox oce El Gamal.

a ElGamal, caaa pac a pocx ca, p q, a, o q o eee p-1. Teep yo coa co g, eee q. B aaoe o 2 o p-1 paec cyaoe co h cec g=h(p-1)/q mod p Ec g pao 1, paec pyoe cyaoe h. Ec e, coyec oyeoe aee g.

ap a cya a pax cyax ca, x z, ee q. Op a c p, q, g, y u, e y = gx mod p u=g mod p ce peopayeo eopaeo oc cooe m (oopoe eceoc ec x-aee cooe), caaa aaoe o 1 o q-1 paec cyaoe co t. ae cec T = gr mod p m' = Ttzm mod q.

Teep cec oa oc ElGamal m'. Bpaec cyaoe co R, eee p-1 ao pocoe c . ae cec r = gR mod p , c oo pacpeoo aopa a, cec s, oopoo m' rx Rs (mod q) oc cya oc ElGamal (r, s) T. Bo a Aca oepae co oc oy:

(1) o eeppye a cyax ca, a b, ce c = TTmagb mod p ocae peya Ace.

(2) Aca eeppye cyaoe co k ce h1 = cgk mod p h2 = h1z mod p, a ae ocae oa ca oy.

(3) o ocae Ace a b.

(4) Aca poepe, o c = TTmagb mod p. Oa ocae k oy.

(5) o poepe, o h1 = TTmagb k mod p, o h2 = yrarsaub k mod p.

Aca oe peopaoa ce co eopaee oc oe, oyoa z. Teep o o e poep ee oc e ee oo.

Cxe eopaex oce oo oe co cxea paee cepea, coa pacpeeee peopayee eopaee oc [1235]. o-y oe oca cooee, a ae pacpee oooc oepe paoc oc. O oe, apep, opeoa, o poooe ye e oa paoc oc yacoa poe oaaee oooc oepe p a oc. B [700, 1369] peoe yye, ooe oaac o eoxooc oepeoo a - pacpeee.

23.5 oc, oepaee oepe o Bo a Aca oe oca cooee, a o poep eo a, o po eoo oe oa oaa y paoc oc Ac (c. pae 4.4) [333].

Caaa oyoac ooe pocoe co p p ee g, oope yy coeco cooac pyo ooaee. Tae oyoaec n, poeee yx pocx ce. po ec ap z op h = gx mod p.

B o poooe Aca oe oca m a, o o o poep paoc ee oc, o e o ye o pe copoy.

(1) Aca pae cyaoe x ce a = gx mod p b = hx mod p Oa ce x-aee m, H(m), x-aee oee a b, H(a,b), a ae j = (H(m) H(a,b))1/3 mod n ocae a, b j oy.

(2) o pae a cyax ca, s t, ex p, ocae Ace c = gsht mod p (3) Aca pae cyaoe q, eee p, ocae oy d = gq mod p e = (cd)x mod p (4) o ocae Ace s t.

(5) Aca poepe, o gsht c (mod p) ae oa ocae oy q.

(6) o poepe d gq mod p e/aq asbt (mod p) (H(m) H(a,b)) = j1/3 mod n Ec ce oeca oc, o o cae oc co.

o e oe cooa ac oo oaaeca yee a coc oc, o oe o pooo c oepe o Ac, po. Bo a po yeae a o, o a b opay pay oc.

(1) pae cyae u v, ee p, ocae po k = guav mod p (2) po pae cyaoe w,, eee p, ocae y l = gw mod p y = (kl)z mod p (3) ocae po u v.

(4) po poepe, o guav k (mod p) ae oa ocae y w.

(5) poepe, o gw l (mod p) y/hw hubv (mod p) Ec ce oeca oc, o cae oc co.

B pyo poooe po oe peopaoa pooo oepeoo a oy poy oc.

opooc [333].

23.6 Bce c apoa a poea ucpemoo oapua Cyecye ooe pocoe co p eepaop g. Aca xoe opeoo x a aoe e, oo poo ge x (mod p) o pya poea, Ace e xaae cex ooce ce peyaa. oa ec ae oooc - o pecae paeco, o ce ep, ee ay y ey opaa. Bo a Aca oe oy oo oa, e pacp ey x [547, 4]:

(1) Aca pae cyaoe co r, eee p.

(2) Aca ce x' = xgr mod p (3) Aca poc oa pe ge' x' (mod p) (4) o ce e' ocae eo Ace.

(5) Aca occaaae e, c e = (e' - r) mod (p - 1) Aaoe pooo poe apax ocao px ope pee [3, 4].

(C. ae pae 4.8.) 23.7 pocae "eco" oe Ceye pooo oo Ace oy poca ecy oey ce epea ax (c. pae 4.9) [194]. o pep poca oe ooe (c. pae 4.10). Caaa oo o yae peya po ca cooae eo Ace. ae Aca oe poep, o o coo pa peya poca.

pocaue "ecmo" oem c noo apamx ope opooo poca eco oe :

(1) Aca pae a ox pocx ca, p q, ocae x poeee n oy.

(2) o pae cyaoe ooeoe eoe co r, eee n/2. o ce z = r2 mod n ocae z Ace.

(3) Aca ce epe apax op z (mod n). Oa oe cea o, a a oa ae pao e e n a oe. Haoe x +x, -x, y -y. Ooa a x' eee ceyx yx ce:

x mod n -x mod n Aaoo, ooa a y' eee ceyx yx ce:

y mod n -y mod n Opae ae, o r pao o x', o y'.

(4) Aca eae aec yaa, aoe ae pao r - x' y', ocae co oay oy.

(5) Ec oaa Ac paa, peyao poca oe ec "ope", a ec epaa "pea". o oe peya poca oe.

opooo poep:

(6) Aca ocae p q oy.

(7) o ce x' y' ocae x Ace.

(8) Aca ce r.

Ac e oooc ya r, ooy oa eceo yaae. Oa a ae (4) cooae oy oo o coe oa, e aa oy oy x', y'. Ec o oy oa x ca, o coe e r oce aa (4).

pocaue "ecmo" oem c noo oeeu cmene no oy F B o poooe aece ooapaeo y coyec oeee cee o oy p o coo ca p [1306]:

opooo poca eco oe :

(1) Aca pae pocoe co p a, o oe p-1 ec, cpe x o o pae epe oo ooe pocoe co.

(2) o pae a px eea, h t, GF(p). O ocae x Ace.

(3) Aca yeaec, o h t c p eea, ae pae cyaoe co x, ao pocoe c p-1. ae oa ce oo yx ae :

y = hx mod p, y = tx mod p Oa ocae y oy.

(4) o aec yaa, ca Aca y a y h a y t, ocae coe peoo ee Ace.

(5) Ec oaa oa paa, peyao poca oe ec "ope", poo cyae "pea". Aca oe peya poca oe.

opooo poep:

(6) Aca pacpae oy aee x. o ce hx mod p tx mod p, yeac, o Aca paa ec o poep peya poca. O ae poepe, o x p-1 - ao poce ca.

o Aca oa coea, oa oa a a ex ca, x x', oopx oec hxtx' mod p. oo, o ya ae, e yo c :

logth =x'x-1 mod p-1 logth =xx'-1 mod p-1.

o pye poe.

Aca coa cea o, ec oa aa logth, o o pae h t a ae (2). Ac e py oo cocoa poe, a oac c cpe oap. Aca oe ae oac coe a, pa x, oopoe e ec ao poc c p-1, o o oapy o a ae (6).

o oe coea, ec h t e c p eea oe in GF(p), o Aca co e eo poep o oce aa (2), a a e eco paoee p-1 a poce oe.

a o poooe ec o, o ec Aca o axo poc ecoo oe, o7 coy cooa o e e ae p, h t. Aca poco eeppye ooe x, pooo pooaec c aa (3).

pocaue "ecmo" oem c noo ex uce a B poooe poca oe oo cooa ee ca a.

(1) Aca eeppye eoe co a n, cyaoe x, ao pocoe c n, x0 = x2 mod n x1 = x02 mod n.

Oa ocae oy n x1.

(2) o yaae, e ee ec x0.

(3) Aca ocae x oy.

(4) o poepe, o n ec e co a (Aca yo epea oy oe n oaa eca oo, o o c poc, o eoop pooo c ye ae, ye a oa, o n - o eoe co a), o x0 = x2 mod n x1 = x02 mod n. Ec ce poep oc, o yaa pao, o pae poco.

o ao, o n o co a. ae Aca coe a aoe x', o x' mod n = x02 mod n=x1, 0 e x' ae ec apa ocao. Ec x0 e, a x' - ee ( aoopo), Aca 0 oa oea.

23.8 Ooapaee cyaop Cyecye poca y ooapaeoo cyaop [116] (c. pae 4.12.):

A(xi, y) = xi-1y mod n ca n (eec poeee yx pocx ce ) x0 o apaee coacoa. Toa cypoae y1, y2 y3 ye y2 ((x0 yq mod n) mod n)y mod n o cee e ac o opa y1, y2 y3.

23.9 Pacpe cepeo "ce eo" o pooo ooe eco copoa ( pao poooa yo e ee yx yaco ) oya pae cepe y ooo poaa (c. pae 4.13) [1374, 1175]. Hae c opeee. Boe e cpo o, x y. cpoa o eco ( fixed bit index, FBI) x y aaec oceoa eoc oepo coaax o x cpo.

Hapep:

x = y = FBI(x, y) = {1, 4, 5, 11} (M ae cpaa aeo, ca ye pa pa .) Teep o a pooo. Aca ye poao. o po - oyae. Ac ec k n ox cepeo: S1, S2,... Sk. o xoe y cepe Sb, po - cepe Sc.

(1) Aca eeppye apy "op /ap " cooae oy (o e po) op .

Oa eeppye pyy apy "op /ap " cooae po (o e oy) op .

(2) o eeppye k n-ox cyax ce, B1, B2,... Bk, cooae x po. po eeppye k n ox cyax ce, C1, C2,... Ck, cooae x oy.

(3) o pye Cb (ao, o xoe y cepe Sb) op o, oye o Ac. O ce FBI Cb oo o apoaoo peyaa. O ocae o FBI po.

po pye Bc (ao, oa xoe y cepe Sc) op o, oye o Ac. Oa ce FBI Bc oo o apoaoo peyaa. Oa ocae o FBI oy.

(4) o epe aoe n-ox ce B1, B2,... Bk aee a , oepa oopoo e FBI, oyeo o po, eo ooee. O ocae o o cco n-ox ce B', B',... B' 1 2 k Ace.

po epe aoe n-ox ce C1, C2,... Ck aee a , oepa oopoo e FBI, oyeo o oa, eo ooee. Oa ocae o o cco n-ox ce C', C',... C' 1 2 k Ace.

(5) Aca pacpoae ce C' ap o oa, oya k n-ox ce C", C",... C". Oa i 1 2 k ce Si C" i = 1,... k, ocae peya oy.

i Aca pacpoae ce B' ap o po, oya k n-ox ce B", B",... B". Oa i 1 2 k ce Si B" i = 1,... k, ocae peya po.

i (6) o ce Sb, o XOR Cb b-o ca, oyeoo o Ac.

po ce Sc, o XOR Bc c-o ca, oyeoo o Ac..

Bce a coo. oc oe ec a pepe.

Ac ec poa oce 12-ox cepeo : S1 = 1990, S2 = 471, S3 = 3860, S4 = 1487, S5 = 2235, S6 = 3751, S7 = 2546 S8 = 4043. o xoe y S7, a po - S2.

(1) Aca coye aop RSA. B aoe c oo oa coye ceyy apy e : n = 7387, e = 5145 d = 777, a aoe c po - n = 2747, e = 1421 d = 2261. Oa cooae oy po x o pe .

(2) o eeppye oce 12-ox ce, B1= 743, B2= 1988, B3= 4001, B4= 2942, B5= 3421, B6= 2210, B7=2306 B8= 222, cooae x po. po eeppye oce 12-ox ce, C1= 1708, C2 = 711, C3= 1969, C4 = 3112, C5 = 4014, C6 = 2308, C7 = 2212 C8 = 222, cooae x oy.

(3) o xoe y S7, ooy o op o, a Aco, pye C7.

22125145 mod 7387 = Teep:

2212 = 5928 = Ceoaeo, FBI x yx ce pae {0, 1, 4, 5, 6}. O ocae eo po.

po xoe y S2, ooy oa op o, a Aco, pye B2 ce FBI B2 peyaa poa. Oa ocae oy {0, 1, 2, 6, 9, 10}.

(4) o epe B1, B2,... B8 aee a , ec oopoo ocycye aope {0, 1, 2, 6, 9, 10} eo ooee. Hapep:

B2= 111111000100 = B' = 011001111100 = O ocae B', B',... B' Ace.

1 2 po epe C1, C2,... C8 aee a , ec oopoo ocycye aope {0, 1, 4, 5, 6}eo ooee. Hapep:

C7 = 0100010100100 = C' = 1011100101000 = Oa ocae C', C',... C' Ace.

1 2 (5) Aca pacpoae ce C' ap o oa oe XOR peyao c Si. Hapep, i i = 7:

5928777 mod 7387 = 2212;

2546 2212 = Oa ocae peya oy.

Aca pacpoae ce B' ap o po oe XOR peyao c Si. Hapep, i i = 2:

16602261 (mod 2747) = 1988;

471 1988 = Oa ocae peya po.

(6) o ce S7, o XOR C7 ceoo ca, oyeoo o Ac :

2212 342= po ce S, o XOR B2 opoo ca, oyeoo e o Ac.

1988 1555 = pooo paoae oo oeca oyaee. Ec o, po xo y cepe, A ca ae aoy oyae a opx a, o ooy a aoo pyoo oyae. a oy ae oyae aop ce o aoo pyoo oyae. ae o o pooo c Aco a oo cox aopo oepo o XOR cex oyex o Ac peyao, oya co cep e . oee opoo o ocao [1374, 1175].

coae, apa eecx yaco oy coea. Aca po, ecy a apy, oy e o o, ao cepe oy o: ec o a FBI Cb aop poa oa, o oy oca aoe b, o y Cb ye pa FBI. A o po, ecy ece, oy eo aoy ce cepe Ac.

Ec caee, o yac ec, oo cooa pooo opoe [389].

(1) Aca pye ce cepe RSA ocae x oy:

Ci = Sie mod n (2) o pae co cepe Cb, eeppye cyaoe co r ocae Ace.

C' = Cbre mod n (3) Aca ocae oy^ P' = C'd mod n (4) o ce P' Sb = P'r-1 mod n Ec yac oy ya, o oe oaa c ye ae, o o ae eoopoe r, aoe o C' = Cbre mod n, xpa b cepee, oa Aca e epeac ey a ae (3) P' [246).

23.10 ece oaoycoe pocce ecma cxea Diffie-Hellman ece pocce peca coo popa coco ycooo pye oyeo (c. pa e 4.14). o pep pao C Ma ( Silvia Micali) [1084, 1085]. O aaeoa [1086, 1087].

B aoo cxee Diffie-Hellman pya ooaee coye oee pocoe co p eepaop g. a p o Ac ec s, a ee op o t = gs mod p. Bo a cea cxey Diffie-Hellman eco ( o pepe coyec oepex ).

(1) Aca pae ex ce, s1, s2, s3, s4, s5, ex p-1. ap o Ac ec s = (s1 s2 s3 s4 s5) mod p- a ee op o t = gs mod p Aca ae ce i ti = mod p, i = 1,... 5.

gs Op ac Ac c ti, a ap - si.

(2) Aca ocae apy cooecyy opy ac aoy oepeoy y. Hapep, oa ocae s1 t2 oepeoy y 1. Oa ocae t KDC.

(3) aoe oepeoe o poepe, o i ti = mod p gs Ec o a, oepeoe o ocae ti ocae eo KDC. oepeoe o coxpae si eo aco ece.

(4) oy ce opx ace, KDC poepe, o t=(t1* t2* t3* t4* t5) mod p Ec o a, KDC pae op .

B o oe KDC ae, o y aoo oepeoo a ec paa ac, o o p eoxo oc coy occao ap . Oao KDC, e epe oepex a e oy oc cao ap Ac.

Pao Ma [1084, 1085] ae coepa oceoaeoc ec coa ecoo RSA oee opooo cxe c eco pocceo, ooe m oepe a n occao ap .

Omaoycmoua cxea Diffie-Hellman a peye poooe y py ooaee ec oe pocoe co p eepaop g. ap o Ac ec s, a ee op o t = gs mod p.

(1) KDC pae cyaoe co B aaoa o 0 o p-2 pyae B c oo poooa pye o (c. pae 4.9).

Aca pae cyaoe co A aaoa o 0 o p-2. Oa ocae KDC gA mod p.

(2) ooae "paee" A c a oepe o, coy cxey oepaeoo coecoo cooa cepea (c. pae 3.7).

(3) KDC pacpae B Ace.

(4) Aca poepe pyee aa (1). ae oa ycaaae co op pa t = gA gB mod p a ap pa s = (A B) mod (p-1) oepee a oy occao A. Ta a KDC ae B, oo ocaoo occaoe s. Aca e coe cooa ax ocoaex aao epea ecaopoao op a. o pooo, paccope [946, 833] acoee pe aeyec.

23.11 ZERO-KNOWLEDGE PROOFS OF KNOWLEDGE oaamecmo c ye aue ucpemoo oapua e xoe oaa Bopy, o e eco x, eec peee Ax B (mod p) e p - pocoe co, a x - poooe co, ao pocoe c p-1. ca A, B p oeocy, a x xpac cepee. Bo a e, e pacpa ae x, oe oaa, o oo e eco (c. pae 5.1) [338, 337].

(1) e eeppye t cyax ce, rl, r2,... rt, pe ce ri ee p-1.

i (2) e ce hi = Ar mod p cex ae i ocae x Bopy.

(3) e Bop, ocooac poooo poca oe eeppy t o: b1, b2,... bt.

(4) cex t o e oe oy ceyx oepa :

a) Ec bi = 0, oa ocae Bopy ri b) Ec bi = 1, oa ocae Bopy si = (ri - rj) mod (p-1), e j - aeee aee eca, p o o po bj = (5) cex t o Bop poepe oo ceyx yco :

i a) p bi = 0 o Ar hi (mod p) i b) p bi = 1 o As hihj-1 (mod p) (6) e ocae Bopy Z, e Z = (x - rj) mod (p-1) (7) Bop poepe, o AZ Bhj-1 (mod p) t Bepooc yaoo oeeca e paa 1/2.

oaamecmo c ye aue ooocmu cpm RSA Aca ae ap po. Moe oa oaa RSA, a oe oa oaa ep app po paa . Aca xoe ye oa, o e ece po. Oao oa e xoe coo a oy , ae pacpoa oa oo cooe po. aee pee pooo c ye ae, c oo oopoo Aca yeae oa, o oa ae ap po [888]. yc o p po - e, ee ap - d, a oy RSA - n.

(1) Aca o pa cyaoe k m, oopx km e (mod n) ca o o pa cya opao, coy eepa k pooo poca oe, a ae c m. Ec k, m oe 3, pooo pooaec. B poo cyae ca pa c aoo.

(2) Aca o eeppy cya poec C. coa o o ocooac poooo p o ca oe.

(3) Aca, coy ap po, ce M = Cd mod n ae oa ce X = Mk mod n ocae X oy.

(4) o poepe, o Xm mod n = C. Ec o a, o o yeaec paoc ae Ac.

Aao pooo oo cooa eocpa oooc cp poe cpe o o oapa [888].

oaamecmo c ye aue moo, mo n emc uco a oa eeco ax eceo pax oaaec oo, o n =pq, e p q - poce c a, opye 3 o oy 4. Oao ec n ee opy prqs, e r s ee, o y ca n coxpac coca, oope ea ca a oe popa. oa cyecye oaaeco c ye ae oo, o n ee ay opy.

peoo, o Ace eco paoee a oe ca a n, e n oaae paccopeo e opo. Bo a oa oe oaa oy, o n ee ay opy [660].

(1) Aca ocae oy co u, e co o pae -1 o oy n.

(2) Aca o coeco pa cyae : b1, b2,... bk.

(3) Aca o coeco pa cyae ca : x1, x2,... xk.

(4) aoo i = 1, 2,... k Aca ocae oy apa ope o oy n ooo epex ce: xi, -xi, uxi, - uxi. Co o apaoo op oe pae bi.

Bepooc yaoo oeeca Ac paa 1/2k.

23.12 Cee oc oe cex oce (c. pae 5.3) o pyao o ayo (David Chaum) [317, 323], o op ae peo epy peaa oo o [318]. Oa coye aop RSA.

oa ec op e, ap d op oy n. Aca xoe, o o cey, e a, oca cooee m.

(1) Aca pae cyaoe co k aaoa o 1 o n. ae oa acpye m, c t = mke mod n (2) o ocae t td = (mke)d mod n (3) Aca cae acpoy c td, c s = td/k mod n (4) Peyao ec s = md mod n o oo eo oaa td (mke)d mdk (mod n), ooy td/k = mdk/k md (mod n).

ay pya eoe ceeco oee cox aopo ceo oc [320, 324], aaex eo a ce oc. Cxe x oce coee, o o a oe oooce.

23.13 epeaa c aae B o poooe, peoeo Mao Pao ( Michael Rabin) [1286], Aca c epooc 50 po eo yaec epea oy a pocx ca, p q. Aca e ae, yceo poa epeaa (C. pa e 5.5.) (o pooo oo cooa epea oy oo cooe c 50-poeo epoo c yceo epea, ec p q pacpa ap RSA.) (1) Aca ocae oy poeee yx pocx ce : n = pq.

(2) o pae cyaoe co x, eee n ao pocoe c n. O ocae Ace:

a = x2 mod n (3) Aca, a p q, ce epe apax op a: x, n-x, y n-y. Oa cya opao pae o x ope ocae eo oy.

(4) Ec o oyae y n-y, o oe c ao o ee x y n, oop ye o p, o q. ae, oeo e, n/p = q. Ec o oyae x n-x, o e oe eo c.

oo poooa oe caoe eco : ooa cya, oa o oe c aoe co a, o p eco apao ope a o coe ce pe pacaa n a oe.

23.14 eoace ce c eco yaca o pooo [1373]. Aca ae eoe co i, a o - eoe co j. Aca o ece xo y a, o pao - ij i>j, o Aca, o e xoe pacp coe co apepy. o oco cy a eoacx ce c eco yaca (c. pae 6.2) oa aa poeo oepa o [162, 7].

B poo pepe peoaaec, o i j pac aaoa o 1 o 100. oa ec op ap .

(1) Aca pae ooe cyaoe co x pye eo op o oa.

c = EB(x) (2) Aca ce c-j ocae peya oy.

(3) o ce ceye 100 ce:

yu = DB(c-i u), 1u DB ooaae eppoae ap o oa.

O pae ooe cyaoe co p. (Paep p oe eoo ee x. o e ae x, o Aca oe eo coo ey paep x.) o ce ceye 100 ce:

zu = (yu mod p), 1u aee o poepe, o cex uv |zu - z| o cex u 0 < zu < p- Ec o e a, o o pae pyoe pocoe co poye coa.

(4) o ocae Ace y oceoaeoc ce, coa x o opo:

zl, z2,... zj, zj 1 1, zj 2 1,... z100 1, p (5) Aca poepe, opye i- e oceoaeoc x mod p. Ec o a, oa eae o, o ij. B poo cyae oa peae, o i> j.

(6) Aca cooae oy co o.

poepa, oopy o oe a ae (3), oa apapoa, o oo co e oc a oceoaeoc, eeppoao a ae (4). B poo cyae, ec za = zb, Aca yae, o a j < b.

Heocao oo poooa ec o, o Aca yae peya ce pae oa. Ho e oeae e aep pooo a ae (5), oaac cooa oy peya. Oa ae oe coa oy a ae (6).

puep npomooa yc o coy RSA. Op o oa ec 7, a ap - 23. n = 55. Cepeoe co Ac, i, pao 4, cepeoe co oa, j - 2. (peoo, o ca i j oy pa oo ae 1, 2, 3 4.) (1) Aca pae x = 39 c = EB(39) = 19.

(2) Aca ce c-i=19-4=15. Oa ocae 15 oy.

(3) o ce ceye epe ca:

y1 = DB{15 l) = y2 = DB{15 2) = y3 = DB{15 3) = y4 = DB{15 4) = O pae p = 31 ce:

z1 = (26 mod 31) = z2 = (18 mod 31) = z3 = (2 mod 31) = z4 = (39 mod 31) = O oe ce poep yeaec, o oceoaeoc paa.

(4) o ocae Ace y oceoaeoc ce, coa x opo :

26, 18, 2 1, 8 1, 31, .e., 26, 18, 3, 9, (5) Aca poepe, opyo eepoe co X mod p. Ta a 9 39 (mod 31 ), o i > j.

(6) Aca cooae o o oy.

o pooo oo cooa coa aoo oee cox poooo. pya e oe poo cepe ayo o ce. O oec yopoa ce o pyy , c oo oapx cpae, opee, o peo oy ey. o oea ye e ceae pe oe cepee ayoa oe cooac ao-o pooo pye o. Ec ayo poo c o oaco ccee, o peo acy ey oyae pee a peoey ey.

Ec ayo pooc o aco ccee, o o oyae pee a opy cy ey. (o oe ceo o pe opoo pya oapx cpae.) Aaoe e pe p ae ceo, epeoopax appae.

23.15 Bepoocoe poae oe epoocoo poa o opeeo a oaccepo (Shafi Goldwasser) C e Ma [624]. Xo x eop ooe coa cay eoacy opeex pocce, pa peaa a eeo [625]. Ho oee oe peaa ce e.

ee epoocoo poa ec ycpaee ye opa popa c op a. Ta a poaa cea oe pacpoa cyae cooe op o, o oe oy eoopy opa. p yco, o y eo ec poec C = EK(M), o aec oy op ec M, o oe pa cyaoe cooee M' apoa eo: C' = EK(M'). Ec C' = C, o o yaa pa op ec. B poo cyae o eae ceyy oy.

poe oo, epoocoe poae ooe ea ae aco ye opa o op ao cooe. p cooa popa c op a poaa oa oe ya oe-o o ax: XOR 5-o, 17-o 39-o o pao 1, ... p epooco poa ocaec cpo aa opa.

Ta cocoo oo e e oo opa, o oeao oooc poaaa pacpoa cyae cooe a op o oe coa opeeee poe. a pa, py cooee, poaa oe e eoo opa. Ho e ae, acoo aea a opa.

Bepoocoe poae aec ycpa y yey. e oo eoa coco o, o ce, pooe a poeco, poepa x pyx opx eco e co a p oaay ao opa o cooecye op o ece.

p epooco poa aop poa ec epooc, a e eeppoa.

py coa, oe poec p pacpoe a a op ec, ope po ec, coye o opeo poa, paec cya opao.

C1 = EK(M), C2 = EK(M), C3 = EK(M),... Ci = EK(M) M = DK(C1) = DK(C2) = DK(C3) =... = DK(Ci) p epooco poa poaay oe e yacc poa pooe ope ec ocax paoo poeca. cpa yc y poaaa ec poec Ci = EK(M). ae ec o pao yaae M, oye p poa EK(M) peya ye coepeo py poeco C: Cj. Cpaa Ci Cj, o e oe o x coae opee paoc coe o a.

o opaeo. ae ec y poaaa ec op poa, op ec poec, o e oe e apoo a eppoa oaa, o poec ec peyao poa opeoo opoo eca. ae o cepa oc, o oe oaa oo, o a oo op ec ec oo op eco.

B o cxee poec cea ye oe opoo eca. oo eooo ea, o ec peyao oo, o oe poec pacpoac o o e op ec. B epo cxee epoocoo poa [625] poec oyac acoo oe opoo eca, o o e c oe.

Oao May (Manual Blum) oaccep (Goldwasser) oy ey peaa ep o ocoo poa c oo eepaopa ceocyax o Blum Blum Shub (BBS), ocaoo paee 17.9 [199].

eepaop BBS ocoa a eop apax ocao. Cyecy a pocx ca, p q, opy x 3 o oy 4. o ap . x poeee, pq = n, ec op o. (aoe co p q, eoacoc cxe opaec a cooc paoe n a oe.) poa cooe M caaa paec cyaoe x, ao pocoe c n. ae cec x0 = x2 mod n x0 cy capoo oceoaeoc eepaopa ceocyax o BBS, a xo eepaopa coyec aece ooooo pa. oo oec XOR M c xoo eepaopa. eepaop ae bi (a aa xi, e xi = xi-12 mod n), ooy M=M1, M2, M3,... Mt c = M1 b1, M2 b2, M3 b3,... Mt bt e t - o a opoo eca oae oceee ceoe aee, xt, oy cooe, eo ceao.

Pacpoa o cooee oo oo o cocoo - oy x0 c o capoo oceoa eoc ayc eepaop BBS, o XOR xoa c poeco. Ta a eepaop BBS eoace eo, aee xt ecoeo poaaa. Too o, oy ec p q, oe pacpoa co oee. Bo a a e C aop oye x0 xt:

p a x0 eppoae ecoo. poco aae capoy oceoaeoc eepaopa BBS oe XOR peyaa c poeco.

y cxey oo cea ee cpee, coy ce ece eoace xi, a e oo a aa . C a yyee epoocoe poae Blum-Goldwasser oaaec cpee RSA e oycae ye opa o opo ece. poe oo, oo oaa, o cooc cp o cxe paa cooc paoe n a oe.

C pyo copo, a cxea coepeo eeoaca o ooe cp c pa poe co. o a aa a pax apax ocao oo c apa ope oo apaoo ocaa. Ec o yacc, o yacc paoee a oe. opooc oo a [1570, 1571, 35, 36].

23.16 aoa popa aoa popa o ececey eopeeeoc aooo pa. C ee oo oo coaa c, oope eooo ocya, e oc oex epeay. ao aeo aa ao ao aa, ae ec ocya oe pepa e ec, ae ec o ee ocy eopaeo ceo ooc, ae ec P = NP. ap ee (Charles Bennett), paccap (Gilles Brassard), o peo (Claude Crepeau) pye pacp y e, oca aooe pacpeeee e, aooe pocae oe, aooe pyee a, aoy epeay c aae aoe ce c eco yaca. Ocae x peyao oo a [128, 129, 123, 124, 125, 133, 126, 394, 134, 392, 243, 517, 132, 130, 244, 393, 396]. y oopo o ao o popa ec [131]. py xopo eexec oopo oe cy [1651]. oy opa o aoo popa oo a [237].

e a ocac peeo ocye aao popa, o ee paccap papaoa ecyy oe [127, 121, 122]. Teep y ac ec cnepuemaa aoa popa.

a ycpoec oyoee, aee cee eo-y paccaec. opoy oc a, o o aoe.

B cooec c aoa aoo exa ac a cao ee e axoc oo ece, a c o peeeo epooc cyecy cpay o ox ecax. Oao o a oo o ex op, oa e p xo ye e oepe acy, "oaayc" ao opeo ece. Ho ep ce apaep ac (apep, oopa copoc) oopeeo eooo. Ec ep oy x yx e , ca a epe yoae cy oooc ep pyy ey. Heopeeeoc e c yaea coco aooo pa, ya o oo e eec.

y eopeeeoc oo cooa eepa cepeoo a. yeecy, oo oe c opeeeo apae, epx-, eo-pao, , o oee epoo, o a-o yo.

O coe ce eopoa, oo oec o cex oox apaex. oa apa ee oea ox ooo coaae, o c opoa. opaoe p poyca oo e oo, oope opoa opeeeo apae, a ocae opyc.

Hapep, opoa opao p poycae oo oo c opoao opa e. oepe o p a 90 payco, eep co eo yy poxo oo epao op o ae oo.

yc y ac ec yc opoao opoax ooo. Ec o opoy po epe op oa p, o y x y cex pepaco oyc. Ec eeo oopaa p a 90 payco, oeco poycaex ooo ye caoc ce ee ee, aoe o oo e po e epe p. o poope paoy ccy. aec, o ae eae oopo pa oe ocao ce oo, a a o opoao opoa. Ho aoo exae aa ac a c opeeeo epooc oe e co opa poco epe p. Ec yo ooe pa ee, a epooc coa, a ec o pae 90 payca, o epooc paa y.

A ec yo oopoa pa pae 45 payca, epooc ooa po p paa 50 poea.

opa oo ep o ccee oopa: yx apaex, pacxoxc o p yo. pepa cce oopa c poyoa - opoaoe epaoe apae - aoaa - ea paa aoa. Ec yc ooo opoa aao ccee oopa, o p epe o e ccee oopa yaee opa. p epe epao ccee oopa, oye cya peya. M copaec cooa o coco eepa cepe oo a:

(1) Aca ocae oy oceoaeoc oox yco. a yco cya op a o opoa oo epex apae: opoao, epao, eo- paoa o ao.

Hapep, Aca ocae oy:

| | / \ | / (2) oa ec eeop opa. O oe acpo co eeop a epee poyoo aoao opa. Oopeeo ep y, pyy y eo e oyc, ey e oo aoa exaa. epee oo opa e ac ep pyy. a, o ycaaae co eeop poo opao:

X X X X X Teep, ec o pao acpo co eeop, o apecppye pay opa. Ec o acpo eeop a epee poyoo opa, yc ye opoa poyoo, o yae, ay opa ooo paa Aca. Ec o acpo eeop a epee a o ao opa, a yc ye opoa poyoo, o peya epe ye cya . o e coe opee pay. B peeo pepe o oe oy cey pey a:

/ | \ / \ / | (3) o cooae Ace o eaeoy aay, ae acpo o cooa.

(4) Aca cooae oy, ae acpo pa. B ae pepe eeop pao yc aoe yco 2, 6, 7 9.

(5) Aca o oca oo pao epee opa. B ae pepe o oca:

* | * * * \ * * C oo apaee pooeoo oa Aca o peopay peya epe opa. Hapep, opoaa eoaoaa oy oaa ey, a epaa paoaoaa - o. B ae pepe o oa oya:

0 0 1 a, Aca o oy epe a. C oo o cce o oy eeppoa coo o, coo yo. B cpee o pao yaae 50 poeax cyae, ooy eepa n o Ace pec oca 2n oox yco. O oy cooa a cepe c epoo aopa oece acoy eoacoc, oy ocaoo o cooa aece oopaooo ooa.

aeae ec o, o Ea e coe ocya. a oy, e yo yaa epeo opa, , a y oa, ooa ee oao ye epao. Ta a epae epe e opa ooo, o p ocya oa eyeo oc o epeay. Ec o a, Aca o oya pae oe oceoaeoc. a, Aca o aaa pooo oo ec:

(6) Aca o cpaa ecoo o cox cpo. o a pacxoe o ya o oc y a. Ec cpo e oac, o o opaca cooae cpae c oy ocaec.

ye oo poooa oo Ace o cooa co ae pcyc E [133, 134, 192]. O oy cpaa oo eoc ox ooec. Toa, ec e oapyeo pacxo e , pec opoc oo o ooeca. o oapyae ocyae c epooc 50 poeo, o ec o cep a opao n pax ox ooec, epooc E oc y n a ocac eaeeo ye paa 1/2.

B aoo pe e ae accoo ocya. Ec Ea oaec pacp ce , oa o aeo papy aa c.

ee paccap ocpo paoay oe aooo pacpeee e oec eoa c a a oeco cae. oceee, o ca, o cooee o o, o British Telecom o ca o 10-oepooy ooooy [276, 1245, 1533]. O ca, o oco paccoe 50 oepo. o opaae oopaee.

ac IV Pea p aa pep peaa Oo eo papaaa pooo aop, coce pyoe eo cpaa x oepaoe c c e. B eop paa eop e o, o a pae ey opoe pa. aco e aeaeo a yae, o e paoa peao . Moe co e peoa copoc aaa, oe pooo co eee. Heoope opoco cooa pop a paccapac ae 10, o ae ocyac pep oo, a popaece aop peayc a pae.

24.1 pooo ypae cepe a oa IBM B oe 70-x oo IBM, coy oo cepy popa, papaoaa aoey ccey ypae a epea ax eoacoc ao oepx cex [515, 1027]. He a a peae exa poooa, a eo oa oco : a ce aoaa eepa, pacpe e e, ycao, xpae, ee papye e o pooo aeo poyc, oecea eoacoc eax eo ocoe popaecx aopo.

o pooo oeceae p e: eoacy c ey cepepo pa epaa, eo acoe xpaee ao a cepepe eoacy c ey cepepa. pooo e oeceae acoeo poo coee epa-epa, xo eo oa oe peaoa ay oooc.

a cepep ce oe popaeco aapaype, oopa oe ce poae e ppoae. aoo cepepa ec a (Master Key), KM0, a apaa, KM1 KM2, oo pe c ypoe apaa KM0. coyc poa pyx e eepa ox e. aoo epaa ec a epaa (Master Terminal Key), KMT, oop coyec oea a c py ep aa.

KMT xpac a cepepax, apoae o KM1. Bce ocae , apep, coyee poa ao e (o aac KNF), xpac apoao ope, ape o KM2. a KM0 xpac epoeaco oye eoacoc. Ceo o oe o , o aa apoa, oe oc ooaee c aayp (ooo a ecoa cpoa, peopayea ). KM1 KM2 e xpac e-y ccee, a, oa oaoc, cc o KM0. Ceacoe c ey cepepa eeppyc a cepepe c oo ce ocyaoo poecca. Aao opao eeppyc poa xpax ao (KNF).

Cepe poooa cy yco cp oy, aae popaeco aapay po (cryptographic facility). a cepepe, a epae ce poae eppoae pocxo eo o oye. B o oye xpac cae ae , coyee eepa ecex e poa. oce oo, a aca, ca x caoc eoo. poe oo, o oee opeoo cooa : , peaae pee oo aa, e oe cyao cooa pee pyo. a oe eopo ypae a ooo ec ca ae ocee o cce. oa c (Donald Davies) B pac (William Price) opoo paccapa o pooo ypae a [435].

Mouuau Moa o cxe aoo ceacox e oo a [1478]. Oa ocpoea a ae cee x yo c aapaypo poep ooc e, oopa ocyae oae epa. a o a a papaoaa, o :

Oeoac yec aa ey y ooaec epaa.

Oeoac c c oo poao o.

Oece ay x ao.

Oece oooc poo oc.

c epea ao ey ooae o cxee coyc , eeppoae aapaype poep ooc e, opaee ooae oce poa c oo a o o a. opa o oc ooae cpaaec , peoca oaaeco oo, o ceaco coyec opeo apo ooaee. Boooc poep ooc e ec ao o ccee. Xo ccee e coyec popa c op a, oa o epae oooc, oxoy a poy oc : oe pca oo opeoo c oa poa oo opeo ece aae.

24.2 MITRENET Oo cax pax peaa popa c op a a cepeaa ccea MEMO (MITRE Encrypted Mail Office, poaoe oooe oeee). MITRE - o a oaa yx ape, paoaa o aay Mcepca oopo. MEMO cya cceo eoaco epoo o ooaee ce MITRENET cooaa popa c op a oea a DES poa ao.

B ccee MEMO ce ope xpac epe pacpeee opx e (Public Key Dis tribution Center), oop ec oe yo ce. xpac cpaeo epepopapyeo , o e a e x. ape eeppyc ooae cce.

o ooae o opa eoace cooe, ccea caaa ycaaae eoacoe c o eee c epo pacpeee opx e. ooae apaae epe a cex opx e. Ec ooae poxo ea c cooae eo apoo a, ep epec a e apoe cco a paoy ca ooae. oecee eococ cco pyec c oo DES.

poa cooe coyec DES. poa ao ccea eeppye cya DES, ooae pye a o DES, a DES - op o oyae. apo a a opac oyae.

MEMO e peycapae ep peocopooc po oep e. Cyecy eoope cpeca poep eococ cooe c cooae opox cy. B ccey e cpoe cpeca po ep ooc.

pee, e ccea a peaoaa, a oaaa eeoacoc opeo peaa cce o px e MEMO - oea a o cxee Diffie-Hellman a GF(2127) (c. pae 11.6), xo e pyo e ccey, o oo o cooa oe ca. MEMO a opeea a opao cepeax ee oa e cooaac peao ccee MITRENET.

24.3 ISDN Bell-Northern Research papaoaa poo eoacoo eeooo epaa ISDN (Integrated Services Digital Network, poa ce c eppoae ycy) [499, 1192, 493, 500]. a eeo aapa, ep a ocac a ypoe pooa. B peyae oc poe eoacoc aeo ax ( Packet Data Security Overlay). Tepa coye cxey oea a Diffie-Hellman, poe oc RSA DES poa ax. O oe epeaa pa pe ae co c opoc 64 /c.

u B eeo cpoea apa "op /ap " eoo cooa. ap xpac ycoo o cp oye eeoa. Op cy ea eeoa.

c ac caoo eeooo aapaa e oy ee.

poe oo, eeoe xpac ee a opx a. O x ec op ae a aapaa. o coyec poep ooc oa aea, o oe ee o oae, ocao aee. Ta ooae oe epea oy-o pyoy pao ae aap a o.

B eeoe ae xpac op ce. O coyec poep ooc oa a a payp ypae ce poep ooc oo o pyx ooaee ce. o ae oo e oao, ocao aee. o ooe aey e ce, oopo o e eo aapa.

paccapac a eoo ooa - o ec peo, ec ooe e c. B eeoe ae xpac apa "op /ap " paocpooo cooa.

O cpoe cepa, oca epo ypae a. a eeoa oeac cep aa p ycaoe coee. ooc x cepao yocoepec op o ce.

Oe cepaa x poepa oc oo p ycaoe eoacoo coee ey aapaa. ycaoe eoacoo coee ey pooo coep ooe ooe. B aapao e aa, oop caec eeo aee, xpac ap aea, apoa cepe apoe, ec oo aey (eo e ae eeo aapa, ep ypae ce, ee o-y). aa ae coep cepa, o ca epo ypae ce, oop e op aea eoopa ea oa opa (, oa, ceaoc, cee oyca, e copa , cecyaa ope a poee). Bce o ae apoao. eppoa o opa oa ee eeo ooae o co cepe apo c aayp aapaa. Teeo aapa coye y opa coee, o oa yaec oce oo, a ooae ee co aa.

B eeoe ae xpac aop cepao, ax epo ypae ce. cepa yocoep pao opex ooaee ooac ope eeo aapaa.

Bo Bo oa Aco pocxo cey opao.

(1) Aca cae eeo co aa o co apo.

(2) Teeo opaae aa, o opee oc Ac a e ca " co oa".

(3) Teeo poepe co aop cepao, poep, o Aca ee pao cooa o aapa.

(4) Aca apae oep, eeo opeee apecaa oa.

(5) a eeoa coy pooo oea a a ae popa c op a, o eeppoa ya cya ceaco . Bce oceye a poooa pyc c oo oo a.

(6) Teeo Ac epeae co cepa eaop ooae.

(7) Teeo oa poepe oc cepaa eaopa ooae, coy op ce.

(8) Teeo oa pye oceoaeoc apoco/oeo. oo eoxoo peao pe e (e oee aao aep) opa ocae oe a apoc. (o oeae o yey cooa cepa, copoae peyeo oea.) O oe oe oca ap o eeoa Ac, a pyo - ap o Ac.

(9) Ec oa e y eeoa, o eo eeo o.

(10) Ec o oa, o cae eeo co aa. Eo eeo opaae aa poepe cepa oa, a a aax (2) (3).

(11) o epeae co cepa eaop ooae.

(12) Teeo Ac poepe oc oa, a a ae (7) pye oceoaeoc apo co/oeo, a a ae (8).

(13) Oa eeoa o a co pa oc oep eeoa pyoo ooae.

(14) Haaec eoac paoop.

(15) oa oa copo eae pyy, yac ceaco , a ae cepa, oope eeo oa oy o eeoa Ac, cepa, oope eeo Ac oy o eeoa oa.

a DES yae aoo oa. O cyecye oo yp yx eeox aapao oo eee paoopa, a oce eo ooa eeeo yoaec. Ec oye oye o oa yacoax paoope aapaa, o e coe pacpoa o peecy pa oop, oopo yacoa a aapaa.

24.4 STU-III STU ooaae "Secure Telephone Unit" (eoac eeo oy), papaoa NSA eoac eeo. o paepa ope o oy o ao e, a o eeo, oe co oa ae, a o eeo. Aapa yco oy, e a o paoa a ecepee.

O ae a op epea ax oo epea pe oy cooa eoaco epea ax o oeoy aay [1133].

oca STU-III [494]:

o oo, coy STU-III, o caaa o opao o a pyo STU-III, ae cae o xoee a ycpoco, coepaee popaecy epeey, aae oy "cepee epeoop" ( "go se cure"). Cyc pepo 15 cey aep, yo popaeco acpo, a eeo o a pa opa o oc oyce pyo copo, paoop oe aac.

ecpeee ao oee oepa (Walter Deeley), aece peopa NSA o eoacoc oya, o STU-III yye ccee eoaco oocoo c co ep, ao The New York Times [282]. ao e oo cce o peoca Mcepcy oopo CA eo opa cpeca eoaco epea pe eoaco ocopoco epea ax. B ep e o oo caao o paoe c c e, o oceeo opa aaa oc. B oo ccee coyc ope .

O oo oxoe pacpeee e o paccaao [68], oo cae oopoc o eeoax, "epepopapyex pa o o eoacoy eeooy aay ", o eca epoo peoaae cooae poooa poep cepao, aaooo ocaoy [ paee 24.3], oop pye eeoo eox o oc oac c epo ypae a. ocee ec oee opa, x paccaaoc o ccee ypae a, aao FIREFLY, oopa [1341] "papaoaa a ae exoo opx e c oyec pacpeee e poa oapoo paa". o ocae, ceece oaa, ae opeccy CA Hpo (Lee Neuwirth) Cylink [1164] peoaa cooae oa oea a cepaa, aaooo coyeoy eoacx eeoax ISDN. Beca epoo, o FIREFLY ae ocoaa a oee cee.

STU-III pooc AT&T GE. a 1994 o o yeo 300000-400000 y. Hoa epc, Secure Terminal E uipment (STE, eoac epa), ye paoa o ISDN.

24.5 KERBEROS Kerberos pecae coo papaoa cee TCP/IP pooo poep ooc c oepeo pee copoo. Cya Kerberos, paoaa ce, ecye a oepe ocpe, oecea eoacy ceey poepy ooc, ay ooae oooc paoa a ecox a ax ce. Kerberos a cepo popa (peaoa DES, o eco eo oo cooa p y e aop). p oe c a oeo ce Kerberos coye o o cepe , ae oo cepeoo a paoco ea oea.

Kerberos epoaao papaoa MT poea Aa. Moe Kerberos ocoaa a poooe Needham-Schroeder c oepeo pee copoo (c. pae 3.3) [1159]. Opaa epc Kerberos, Bep c 4, opeeea [1094, 1499]. (Bepc c 1 o 3 ype pao epc.) Bepc 5, oa Bepc 4, opeeea [876, 877, 878]. y oopo o Kerberos ec [1163]. pye oope ca - [1384, 1493], cooae Kerberos peao pe xopoo ocao [781, 782].

Moe Kerberos ao pooo Kerberos cxeao oca paee 3.3. B oe Kerberos cyecy pacoo ee ce oe - e cepep. ea oy ooae, o oy eace p o pa, oe ceye ec : apyy ao, epeay cooe, ocy aa ax, ocy pepa, oyee acpax pe, ..

Kerberos xpa ay ax eo x cepex e. ooaee-e cepe ec apoa apoe. Ceee cy, peye poep ooc, e, oope xo cooa cy, pecppy Kerberos co cepee .

Ta a Kerberos ae ce cepee , o oe coaa cooe, yeae o oe ooc pyoo. Kerberos ae coae ceacoe , oope ac ey cepepy ( y ea) oy oe. Ceaco coyec poa cooe, oop oe a c e copo, yoaec oce ooa ceaca.

poa Kerberos coye DES. Kerberos epc 4 oecea ecaap, ca pe poep ooc - o e o opee opeee ee poeca (c. pae 9.10). Kerberos epc 5 coye pe CBC.

1. apoc aaa a eee aaa 2. Maa ee aaa 3. apoc aaa cepepa Kerberos TGS 4. Maa cepepa 5. apoc ycy 2 e Cepep Pc. 24-1. a poep ooc Kerberos a paomaem Kerberos B o paee paccapaec Kerberos epc 5. He opcy pa ey epc 4 5. poo o Kerberos poc (c. 23rd). e apaae y Kerberos aa a opaee Cye ee a ao (Ticket-Granting Service, TGS). o aa, apoa cepe o ea, ocaec ey. cooa opeoo cepepa e apaae y TGS aa a opaee cepepy.

Ec ce ope, TGS ocae aa ey. ae e pee cepepy o aa ece c y o coepee. coa, ec apy ea pa, cepep peocae ey ocy ycye.

Ta. 24-1.

Taa copae Kerberos c = e s = cepep a = ceeo apec ea v = aao ooae pee ec aaa t = ea pee Kx = cepe x Kx,y = ceaco x y (m)Kx = m, poaoe cepe o x Tx,y = aa x a cooae y Ax,y = yocoepee x y Ampuym Kerberos coye a a apyo: aa yocoepe. (B aee o paee ye cooac oa, coyea oyeax Kerberos - c. 23-.) Maa coyec eoaco epea cepepy oc ea, oopoy a o aa. B e ae coepc opa, o o py cepep oe cooa poep oo, o e, coy aa, - o eo o e, oopoy o aa a. ocoepee - o ooe apy, pee ece c a ao. Maa Kerberos ee ceyy opy:

Tc,s = s, {c, a, v, Kc,s}Ks.

Maa xopo ooo cepepa ooo ea. O coep ea, eo ceeo apec, ce p epa, ey pee ceaco . a opa pyec cepe o cepepa. Ec e oy aa, o oe cooa eo ocya cepepy oo pa - oa e cee cpo ec aaa. He oe pacpoa aa (o e ae cepeoo a cepepa ), o o oe pe eo cepepy apoao ope. poa e aa p epeae eo o ce eooo. o coepee Kerberos ee ceyy opy:

Ac,s = {c, t, }Kc,s e coae eo a pa, oa ey yo ocooac ycya cepepa. ocoepee coep ea, ey pee eoae ooe ceaco , ce ae py c ceaco o, o ea cepepa. B oe o aaa yocoepee coyec oo o pa. Oao o e poea, a a e oe eeppoa yocoepe o epe aooc (ey ece o cepee ).

cooae yocoepe peceye e e. Bo epx, oo coep eoop op ec, apoa ceaco o. o oaae, o ey ece . o e eee ao, a poa op ec ae ey pee. oye, oopoy yaoc aca aa, yocoepee, e coe cooa x cyc a .

Cooeu Kerberos epcuu B Kerberos epc 5 coyec cooe (c. 23-):

1. e-Kerberos: c,tgs 2. Kerberos-e: {Kc,tgs}Kc, {Tc,tgs}Ktgs 3. e-TGS: {Ac,s}Kc,tgs{Tc,tgs} Ktgs,s 4. TGS-e: {Kc,s}Kc,tgs{Tc,s}Ks 5. e-cepep: {Ac,s}Kc,s {Tc,s}Ks Teep paccop cooae x cooe opoo.

oyeue nepoaaoo aama ea ec ac opa, oaae eo oc - eo apo. oo, o e xoec a ca ea epeaa apo o ce. pooo Kerberos pye epooc opoea a po, o p o e ooe ooae pao epoa ce, ec o e ae apo.

e ocae cooee, coepaee eo eo cepepa TGS a cepep poep ooc Kerberos. (oe ecoo cepepo TGS.) Ha pae ooae, copee ceo, poco o coe popaa xoa ccey ocae apoc.

Cepep poep ooc Kerberos e ae o ee coe ae ax. Ec opa o ee ec ae ax, Kerberos eeppye ceaco , oop ye cooac oea a ey eo TGS. O aaec Maao a eee aaa (Ticket Granting Ticket, TGT). Kerberos pye o ceaco cepe o ea. ae o coae ea TGT, oaa ooc ea TGS, pye eo cepe o TGS. Cepep poep oo c ocae a apoax cooe ey.

Teep e pacpoae epoe cooee oyae ceaco . Cepe ec ooapaeo x-ye ecoo apo, ooy y aooo ooae e ye ax p o e. Caoae e ae paoo apo , ceoaeo, e oe pacpoa oe cepepa p o ep ooc. ocy apeaec, caoa e e oe oy aa ceaco .

e coxpae TGT ceaco , cpa apo x-aee. a opa yoaec yee epooc opoea. Ec pa oaec copoa a ea, o oy oo TGT ceaco . ae a, o oo a pe TGT. oa cpo ec TGT cee, cee cay eccce. Teep eee pee TGT e oe oaa TGS co ooc.

oyeue cepepx aamo ey peyec oy oe aa ao yo ey ycy. TGS ee aa oex cepepo.

oa ey ye aa, oopoo y eo oa e, o ocae apoc TGS. (Ha pae popaa, copee ceo, eae o aoaec eaeo ooae.) TGS, oy apoc, pacpoae TGT co cepe o. ae TGS coye e TGT ceaco , o pacpoa yocoepee. Haoe TGS cpaae opa yocoepe c opae aaa, ceeo apec ea c apeco opae apoca ey pee c ey peee. Ec ce coaae, TGS papeae oee apoca.

poepa eo pee peoaae, o ac cex oepo cxpopoa, o pae epe c ooc o ecox y. Ec pe, yaaoe apoce, oco o eyeo oea co a e o pooe yyee, TGS cae apoc oo oope peyeo apoca. TGS oa a e ocea paoc cpoo ec yocoepe, a a ycy cepepa oy apaac e coo pa oceoaeo c o aao, o pa yocoepe. pyo apoc c e e aa o ye cooao eo pee yocoep e ye oepy.

B oe a pa apoc TGS opaae pa aa, oop e oe pe ce p epy. TGS ae coae o ceaco ea cepepa, apoa ceaco o, o ea TGS. Oa x cooe opac ey. e pacpoae cooee eae ceaco .

anpoc ycyu Teep e oe oaa co ooc cepepy. O coae cooee, oe oxoee a o, o o poe ocaoc TGS ( o oo, a a TGS - oe ycya).

e coae yocoepee, cocoee eo e, ceeoo apeca e pee, apoaoe ceaco o, oop eeppoa TGS ceaca ea cepepa. apoc coco aaa, oyeoo o Kerberos (ye apoaoo cepe o cepepa ) apoaoo eaopa.

Cepep pacpoae poepe aa yocoepee, a ye ocyaoc, a ae poepe apec ea ey pee. Ec ce ope, o cepep yepe, o, coaco Kerberos, e - eo o, a oo o ce ae.

Ec poee peye ao poep ooc, cepep ocae ey cooee, cocoee e pee, apoao ceaco o. o oaae, o cepepy ece pa ce pe , o oe pacpoa aa yocoepee.

p eoxooc e cepep oy poa aee cooe o o. Ta a o ece oo , o oa oy yepe, o oceee cooee, apoaoe o, opaeo pyo copoo.

Kerberos epcuu B peyx paeax paccapac Kerberos epc 5. Bepc 4 eoo oaec cooe ocpye aao yocoepe. B Kerberos epc 4 coyc ceye cooe :

1. e-Kerberos: c,tgs 2. Kerberos-e: {Kc,tgs{Tc,tgs}Ktgs}Kc, 3. e-TGS: {Ac,s}Kc,tgs{Tc,tgs} Ktgs,s 4. TGS-e: {Kc,s{Tc,s}Ks}Kc,tgs 5. e-cepep: {Ac,s}Kc,s {Tc,s}Ks Tc,s = {s, c, a, v, l, Kc,s}Ks Ac,s = {c, a, t} Kc,s Cooe 1,3 5 e ec. ooe poae aaa a aax 2 4 epc 5 o ycpaeo.

Maa epc 5 ooeo a oooc cooa ecoo apeco, a oe "pe ", l, aeeo peee aaa ooa. B yocoepee epc oaea oooc e ooeoo a.

eonacocm Kerberos C eo (Steve Bellovin) Ma Mepp (Michael Merritt) poaapoa eoope oe ae ye eca Kerberos [108]. Xo a paoa a acaa po pooo epc 4, oe ee a ea pe epc 5.

Booo poae oopoe cooae capx yocoepe. Xo e o peopa ay oooc, yocoepe oy cooac oopo eee pee aaa.

peoaaec, o cepep xpa ce pae aa, o oapy oop, o o e cea ooo. poe oo, pe ae ocaoo o, aco o oc aco.

cooae yocoepe ocoa a o, o ce ac ce oee eee cxpopoa. Ec pe oepa ye ycaoeo epao, o capoe yocoepee oe cooao e p o e. oco ceex poooo oep eoo pee eeoac, ooy aa oooc pecae coo cepey poey.

Kerberos ae ycee cp c yaae apo. oye oe aca aa ae oac x pacpoa. He aye, o cpe ooae peo pae xopo apo.

Ec Mop oye ocaoo aao, y eo oc eoxe ac pacp apo.

Booo ca oac ec cpe, coyee ceaoe popaoe oeceee. po oo Kerberos opayea, o popaoy oecee oo oep. He cocoa oea M op coa ae ce ecoe popaoe oeceee Kerberos ao epce, oopa oo oe poooo Kerberos acae apo. o ec poeo oo popaecoo popaoo aea, paoaeo a eeoaco oepe, o poo pacpocpaeoe cooae Kerberos oox cpeax eae eo ocoeo peaeo e.

Beyc pao a yyee Kerberos, a oepa ypae a c oo p o pa c op a epeca eeyax apoe.

ueuu Kerberos e ec oeocy, o o MT ocye cooo. ecea peaa pao ax cceax UNIX - o coce pya cop. P oa poae epc Kerberos, o oo oy xopoy epc ecao o Cygnus Support, 814 University Ave., Pale Alto, CA, 94301;

(415) 32,2.-3811;

fax: (415) 32.2.-3270.

24.6 KRYPTOKNIGHT KryptoKnight (poPap) ec cceo poep ooc pacpeee e, papa o ao IBM. o pooo c cepe o, coy o DES pee CBC (c. pae 9.3) opoay epc MD5 (c. pae 18.5). KryptoKnight oepae epe cepca eoacoc :

poepa ooc ooae (aaea eceo oc - single sign-on) ycopo poepa ooc Pacpeeee e poepa ooc coepa pocxoe ax C o pe ooae, KryptoKnight oxo a Kerberos. Bo eoope o:

poep ooc poa aao KryptoKnight coye x-y.

KryptoKnight e coye cxpopoax aco, coyc oo eye apoc (c. pa e 3.3).

Ec Ace yo cac c oo, oa o KryptoKnight ooe Ace oca cooee oy, a ae ooe oy aa pooo oea a.

KryptoKnight, a Kerberos, coye aa yocoepe. O coep TGS, o KryptoKnight aac cepepa poep ooc. Papao KryptoKnight opa eao yc, py oeco cooe, x paep oe poa. O KryptoKnight ae [1110, 173, 174, 175].

24.7 SESAME SESAME oaae Secure European System for Applications in a Multivendor Environment - eoaca epo eca ccea poe eoopox cpeax. o poe Epoecoo cooeca, a 50 poe o acpye RACE (c. pae 25.7), ao e oopo ec papaoa exoo p o ep ooc ooae p pacpeeeo opoe ocya. y ccey oo paccapa a epoec apa Kerberos. poe coco yx ace: a epo ca papaaaec aoa apx eypa, a opa ca pecae coo p oepecx poeo. Ceye p oa pa aoee yace papaoe cce - ICL Beopa, Siemens epa Bull o pa.

SESAME pecae coo ccey poep ooc oea a [361, 1248, 797, 1043]. Oa coye pooo Needham-Schroeder, pe popa c op a c ey pa eoac oea. B ccee ec p cepex o. Beco cooa acoeo aopa poa o ccee peec XOR c 64-o o. o ee xye, SESAME c oyec XOR pee CBC, oop ocae eapoa ooy opoo eca. B ay papaoo ao caa, o o copac cooa DES, o paycoe paeco pao eyooce o oy ooy. O yep o c DES, o ae ypa eo. a ccea e e ea a.

Ooecee SESAME ec ye epoo oa, a e ceo cooe. B peyae oo o eceoc cooe ye poepea o coa "Dear Sir'', a e o cey coepa cooe. eepa e coco yx oo y rand oepaoo cce UNIX, oopa coce e cyaa. B aece ooapaex x-y SESAME coye crc32 MD5. oeo, SESAME ooo Kerberos ycea yaa apoe.

24.8 Oa popaeca apxeypa IBM Oa popaeca apxeypa ( Common Cryptographic Architecture, CCA) a papaoaa o ae IBM, o oece popaece p oeaoc, eococ, ypa e a opao epcoaoo eaooo oa (PIN) [751, 784, 1025, 1026, 940, 752].

paee a pocxo c oo eopo ypae ( control vector, CV) (c. pae 8.5). ao y y cooecye CV, c oop oee oepae XOR. CV paec oo eoaco aapao oye. CV pecae coo cpyypy ax, oeceay yoe o ae pe, cax c ope o.

Oee CV oaa ope cco p cooa aoo a, peeoo CGA. CV epeac ece c apoa o cpyypax ax, aaex e ap e pa (key token). Bypee ee apep coyc oao coepa , poae o a a o (master key, MK). Bee ee apep coyc poa a ey ccea. o ex ex apepax apoa a poa e (key-encrypting key, KEK). paee KEK ocyecec c oo ypex ex apepo.

paec a py cooec c x cooae.

a a ae aaec p oo o CV. oapo - 56-oe - coyc ax y, a oeceee oeaoc cooe. oo - 112-oe pec ypae a, y PIN pyx ceax ee. oy DOU BLE-ONLY (oo oe), pae ee oo oopx o pa, DOUBLE (oe) oo oopx oy cyao coac, SINGLE-REPLICATED (oape-oopee), oopx p a e ee oo pa, SINGLE (oape), coepae oo 56 o. CGA opeee aa pay peaa opeeex o e, coyex eoopx oepa.

CV poepec eoaco aapao oye : ao y CGA eop oe cooecoa opeee paa. Ec CV yceo poxo poepy, o p oo XOR KEK MK c CV oy aec apa KEK MK, ee eppoa opoo eca cooe co y ec oo p oe y CGA. p eepa ox e CV aae coco cooa co aoo a. oa o e, oope oy cooa cp cce, e co ac CGA-coecx cceax e opp yc x.

pacpeee e CGA pee oa popa c op a pop a c cepe a. KDC pye ceaco ooae cepe a o, pa ee c ooaee. Pacpeeee ax e pocxo c oo popa c o p a.

Papao cce pa ao p oxo o y pa. epo x ec e oc. popa c op a peye ox cex pecypco, ec ceacoe pacpeec c oo popa c op a, ccea oe ocy. Bopo po ec opaa coecoc, ccea oe c a ocec ycaoea oepx cyecyx cxe c cepe a.

CGA-cce poepoac a, o o o aoecoa c pa py ccea.

p oae c ecoec ccea y pac eopa ypae (Control Vector Translate, CVXLT) ooe ccea oeac a. aa y CVXLT peye opo c oe x copo. aa x oa eaco ycao ye a pac. Tao oo opo oeceae coy cee aeoc, acaec eococ pocxoe e, oppyex ccey.

T a DATA oepaec coecoc c py ccea. a DATA xpac ece c cooecy CV, yaa, o o a DATA. a DATA oy coo ac ocaoo poo, ooy yo oocc c oopee cooa x c ocopo o c. a DATA e cooa ax y ypae a.

Aapaypa ap oepecx ax (Commercial Data Masking Facility, CDMF) pecae coo coppyey epc CGA. Ee ocoeoc ec yeee eo e DES o pa peex copy 40 o (c. pae 15.5) [785].

24.9 Cxea poep ooc ISO cooa cxee poep ooc ISO, ae eco a pooo X.509, peoeye c popa c op a [304]. a cxea oeceae poepy ooc o ce. Xo ope aop e opeee oecee eoacoc, poep ooc, ce a peoeye cooa RSA. Oao ooo cooae ecox aopo x-y.

epoaa apa X.509 ye 1988 . oce opoo ye oepoa o epecope 1993 oy, o cpa eoope eoacoc [1100, 750].

Bepc oceoae oep eaop aopa - Aop - apaep Baa opaa Bpe ec - aao ec - oe ec Cye Op cyea - Aop - apaep - Op oc Pc. 24-2. Cepa X.509.

Cepmuuam Haoee ao ac X.509 coyea cpyypa cepao opx e. ea cex ooaee pa. oepe Opa cepa (Certification Authority, CA) pcaae aoy ooae yaoe ae oca cepa, coepa op oo a e. Cpyypa cepaa X.509 oaaa a 22- [304].

oe epc opeee opa cepaa. oceoae oep yae opeoo CA. Ce yee oe opeee aop, cooa oc cepaa, ece co ce eoxo apaepa. Bae opaae ec CA. Cpo ec pecae coo apy a, cepa ecee poeye ey y aa. Cye - o ooae. opa o o po e ae aae aopa, ce eoxoe apaep op . oce oe ec oc CA.

Ec Aca xoe cac c oo, oa caaa eae a ax eo cepa poepe eo ocoepoc. Ec y x o CA, o ce poco. Aca poepe oc CA a cepae oa.

Ec o oyc pa CA, o ce opao coee. pecae cee peoy cpyypy, oopo o CA ceppy pye CA ooaee. Ha cao epxy axoc a CA. ao o CA ec cepa, ocae eco CA eco CA. p poepe cepaa oa Aca coye cepa.

Taa cxea poeocppoaa a 21-. Cepa Ac aepe CAA, cepa oa aepe CAB.

Aca ae op CAA. CAC ec cepa, oca CAA, ooy Aca oe poep o. CAC ec cepa, oca CAD. cepa oa oca CAD. oac o epey cep a o oe o, ao cyae CAD, Aca oe poep cepa oa.

CAE CAD CAC CAB CAA o Aca Pc. 24-3. pep epapx cepa.

Cepa oy xpac aax ax a pax yax ce. ooae oy oca x py pyy. cee cpoa ec cepaa o oe yae cex oeocyx aaoo.

Oao CA, a cepa, oe pooa xpa eo o, oopa oe opeoac p papee oox copo.

Cepa ae oy ooa, o -a opoea a ooae, o -a oo, o CA oe e xoe oepa cepa aoo ooae. a CA oe oepa cco cex ooax cepao, cpo ec oopx ee e aoc. oa Aca oyae o cepa, oa oa poep, e o ooa. Oa oe poep ay ax ooax e o ce, o cope ceo oa poep oao pye epee ooax cepao. B ao ccee opeeeo epo oyopee, o cepao ooo ec cao cao ac o cxe.

pomoo npoepu nouocmu Ace yo cac c oo. Caaa oa eae a ax oceoaeoc cepa o Ac o oa op oa. B o oe Aca oe poa oopoxo, yxpoxo pexpoxo pooo poep ooc.

Oopoxo pooo pecae coo pocy epeay ax oy Aco. pooo ycaa ae oc Ac, oa, a ae eococ opa, epeaaeo oy Aco. poe oo, o oeceae ay o cp c c oo oopa.

B yxpoxoo poooe oae oe oa. pooo ycaaae, o eo o, a e ao-o caoae, ocae oe. O ae oeceae eoacoc oex epea aae o cp o opo.

oopoxox, yxpoxox aopax coyc e pee. B pexpoxoo poo oe oaec ee oo cooee Ac oy ooe ea eo pee (, ceoaeo, p a oo eoo pee).

Oopoxo pooo:

(1) Aca eeppye cyaoe co RA.

(2) Aca coae cooee, M = (TA, RA, IB, d), e TA - ea pee Ac, IB - eaop oa, d pooe ae. eoacoc ae oy apoa op o oa EB.

(3) Aca ocae oy (CA, DA(M)). (CA - o cepa Ac, DA - o o ye epea cepa.) (4) o poepe CA oyae EA. O poepe, o cpo ec x e ee e ce. (EA - o o p Ac.) (5) o coye EA eppoa DA(M). ece o poepe oc Ac, eoc oc ocao opa.

(6) o ooc poepe IB M.

(7) o poepe TA M yeaec, o cooee ec ey.

(8) ooeo o oe poep RA M o ae ax capx oepo, o yec, o coo ee e ec oope cap cooee.

yxpoxo pooo coco oopoxooo poooa oceyeo aaooo oopoxo oo poooa o oa Ace. oce oe ao (1)-(8) oopoxooo poooa yxpoxo pooo pooaec cey opao :

(9) o eeppye cyaoe co RB.

(10) o coae cooee M' = (TB, RB, IA, RA, d), e TB - ea pee oa, IA- eaop Ac, a d - pooe ae. eoacoc ae oy apoa op o Ac EA. RA - cyaoe co Ac, coaoe a ae (1).

(11) o ocae Ace sends DB(M').

(12) Aca coye EB, o pacpoa DB(M'). Ta opao oopeeo poepc oc oa eococ ocao opa.

(13) Aca ooc poepe IA M'.

(14) Aca poepe TB M' yeaec, o cooee ec ey.

(15) ooeo Aca oe poep RB M', o yec, o cooee e ec oop e cap cooee.

Tpexpoxo pooo peae y e cay aay, o e eo pee. a (1) - (15) ae e, a yxpoxoo aope, o TA = TB = 0.

(16) Aca cepe oyey epc RA c RA, oopoe o opaeo oy a ae ( 3).

(17) Aca ocae oy DA(RB).

(18) o coye EA, o pacpoa DA(RB). Ta opao oopeeo poepc oc Ac eococ ocao opa.

(19) Aca cepe oyey epc RB c RB, oopoe o opaeo Ace a ae (10 ).

24.10 oa c oeo cepeoc PRIVACY-ENHANCED MAIL (PEM) oa c oeo cepeoc (Privacy-Enhanced Mail, PEM) pecae coo caap Internet o c oeo cepeoc, oope Coeo o apxeype Internet (Internet Architecture Board, IAB) oecee eoacoc epoo o Internet. epoaa apa papaoa pyo cepeoc eoacoc (Privacy and Security Research Group, PSRG) Internet Resources Task Force (IRTF), a ae x papaoa a epeaa Paoy pyy PEM Internet Engineering Task Force (IETF) PEM Working Group. pooo PEM peaae poa, poep ooc, poep e o coc cooe ypae a.

ooc pooo PEM caaa eao oca pe RFC (Re uests for Comment, apoc oeape) [977] ae epecope [978]. Tpe epa poooo [979, 827, 980] ceea [177, 178]. pooo ee yye, ooaee pooo eao ocac p y o aope RFC [981, 825, 76, 802]. B pyo cae M oa (Matthew Bishop) [179] opoo oca ce ee. o peaa PEM paccapac [602, 1505, 1522, 74, 351, 1366, 1367]. C. ae [1394].

PEM ec pacpe caapo. poeyp pooo PEM papaoa a, o co ec co oeco oxoo ypae a, a cepy cxey cooae opx e poa e poa ax. Cepa popa peec poa eca cooe. opo eococ cooe coyc popaece coc o xpoa. pye oye oepa exa ypae a c oo cepao opx e, aopo, peo cax eaopo, a ae epoe opooc, pacpyypy poeyp ypae a.

PEM oepae oo opeeee aop, o ooe oa oee oe aop.

Cooe pyc aopo DES pee CBC. poepa ooc, oeceaea cpeco poep eococ cooe (Message Integrity Check, MIC), coye MD2 MD5. Cepoe ypaee a oe pe o DES pee, o poo DES c y a (a aae pe EDE). ypae a PEM ae oepae cepa opx e, co y RSA (a a o 1024 o) caap X.509 cpyyp cepao.

PEM oeceae p cepca oe cepeoc: oeaoc, poepa ooc o po eococ cooe. epoo ocoo ccee e peec ax ceax pe o a. PEM oe cpoe opoo, opeeee y y opeeex ooaee, e a paoy ocao ce.

oyem PEM PEM opeeec ceyx epex oyeax :

RFC 1421: ac I, poeyp poa poep ooc cooe. B o oyee ope ec poeyp poa poep ooc cooe, oope o oece y o c oeo cepeoc epea epoo o Internet.

RFC 1422: ac II, paee a c oo cepao. B o oyee opeeec ap xeypa pacpyypa ypae a, oope ocoa a eoe cepao opx e, peocax opa o ax opae oyae cooe.

RFC 1423: ac III, Aop, pe eaop. o oye coep opeee, opa, cc a popaecx aopo, peo cooa cax eaopo apaepo.

RFC 1424: ac IV, Cepa e pocee y. B o oyee ocac p a y, oepaex PEM: cepa e, xpaee eee cca ooax cepao (certificate revocation list, CRL).

Cepmuuam PEM coec co cxeo poep ooc, ocao [304], c. ae [826]. PEM pecae co o aoeco X.509, opee poeyp coae pacpyyp ypae a, c oyeo c PEM yye py poooa (a ce TCP/IP OSI).

pacpyypa ypae a coye o ope ce cepa Internet. ep pe cpaoo o (Internet Policy Registration Authority, IPRA) opeee oay cpae, p e y o ce epapx. He op - IPRA - axoc ep cepaoo o ( Policy Certifica tion Authorities, PCA), a oopx opeee oyoae co cpae pecpa oo a ee opaa. a PCA ceppoa IPRA. Ceo a PCA y CA, ceppye oo aee ypae opaao opaee (eapaea, oca, oep o a ). epoaao peoaaoc, o oco ooaee ye pecppoac aece eo opaa.

a oaec, p PCA ye oecea cepa ooaee, e xox oy opa a . peoaaec e o ecoo PCA pecpa ooaee, eax oco o ac peyeca cepeoc PEM coxpa aooc. Cpae x PCA ye oo pe cppoa ooaee, e eax pacpa co oc.

Cooeu PEM Cepe PEM ec opa cooe. Ha 20- oaao apoaoe cooee p cepo ypae a. Ha 19- oaao ocaoe apoaoe cooee p ypae a a ae opx e, a Figure 24.6 oaao ocaoe (o eapoaoe) cooee p ypa e a a ae opx e.

Pc. 24-4. pep cpoeoo cooe (cep cya) Pc. 24-5. pep cpoeoo poaoo (ENCRYPTED) cooe (acep cya).

ep oe ec "Proc-Type", eaop a opao, oopo oepoc cooee. Cy ecye p oox a cooe. Ceaop "ENCRYPTED" ooaae, o cooee apo ao ocao. Ceaop "MIC-ONLY" "MIC-CLEAR" yaa, o cooee ocao, o e apoao. Cooe MIC-CLEAR e opyc oy poa c oo pyoo, e xo eo PEM popaoo oecee. peopaoa cooe MIC-ONLY yooaey opy eoxoo popaoe oeceee PEM. Cooee PEM ocaec cea, a poae e ec oae.

Ceyee oe, "Content-Domain", aae oooo cooe. Oo e e a eoacoc. oe "DEK-Info" coep opa o e oea a (Data Exchange Key, DEK), aope, co yeo poa eca, apaepax, cax c aopo poa. B acoee pe ope ee ece aop - DES pee CBC, "DES-CBC" Bopoe ooe coep IV. B yye PEM oy opeee pye aop, x cooae ye apooopoao oe DEK-Info pyx ox, opeex aop.

B cooex c cep ypaee a (c. 20th) cey oe ye "Originator-ID Symmetric" c pe oo. epoe ooe c oo yaoo apeca epoo o opeee opae. Bopoe oe e ec oae opeee opa, a aee . Tpe ec eoaeoe ooe Bepc/Ooae cpoa.

aee, p cooa cepoo ypae a, y aoo oyae ec a o :

"Recipient-ID-Symmetric" "Key-Info." oe "Recipient-ID-Symmetric" coep p oo, oope ope e oyae ae, a oo o "Originator- ID-Symmetric" opee opae.

oe "Key-Info" aae apaep ypae a. oo o epe oo. epoe opeee aop, cooa poa DEK. Ta a paccapaeo cooe peec ce poe ypaee a, o opae oyae coy o . O aaec aee o (Interchange Key, IK) coyec poa DEK. DEK oe apoa o c oo DES pee ECB (o coco ooaaec "DES-ECB"), o po DES ("DES-EDE"). Bopoe ooe opeee aop MIC. Moe cooac MD2 (ooaaec "RSA-MD2") MD5 ("RSA MD5"). Tpee ooe, DEK, eepoe ooe, MIC, pyc c oo IK.

Ha 19- 18- oaa cooe, oopx coyec ypaee a c oo opx e ( epee PEM ao coco aaec acep ). aoo ec. B cooex EN CRYPTED oce o "DEK-Info" e oe "Originator-Certificate". opa cepaa cooecye caa p y X.509 (c. pae 24.9). Cey oe ec "Key-Info" c y oo. epoe ooe opee e aop c op o, cooa poa DEK, acoee pe oepaec oo RSA. Ceyee ooe - DEK, apoa op o opae. o eoaeoe oe, oopoe ooe opae pacpoa coe coceoe cooee, opaeoe ooo c c eo. Cey oe ec "Issuer-Certificate", cepa opaa, ocae cepa o pae ("Originator-Certificate").

aee p acepo ypae a ceye oe "MIC-Info". epoe ooe aae aop ce MIC, a opoe - aop, cooa oc MIC. Tpee ooe coep MIC, o ca ap o opae.

Pc. 24-6. pep cpoeoo MIC-ONLY cooe (acep cya).

Ceye o ca c oyae. aoy oyae cooecy a o : "Recipient-ID Asymmetric" "Key-Info". o"Recipient-ID-Asymmetric" a oo. epoe opeee opa, a op oyae, a op ec eoaeoe ooe Bepc/Ooae cpoa. oe "Key Info'' aae apaep ypae a : epoe ooe opeee aop, cooa poa cooe, a op ooe cy DEK, apoa op o oyae.

eonacocm PEM a e RSA, coyex PEM, oe ec aaoe o 508 o 1024 o. oo oca oo paec oo ypo eoacoc. oee epoo, o cpe ye apaeo po poooo ypae a. Mop oe ypac a ap - e acae eo e - oac ocyy a a op . poeyp cepa e PEM ea o eoo, ec ce ooae cpoo cey cooecy poeypa, o, a eco, aco eaypa.

Mop oe ocy xpee opoa peaa PEM, paoay ae ccee. a eea epc oe ao epeca Mop c ay oy, apoa ee eo op o.

Ey oe ocaa ae o aeo apoo a. Ec eea peaa ye paoa x o poo, o oa e yaee, o cyoc.

Peaoo cocoa peopa aoe cpe e cyecye. B oee cooa ooapae y x-y oy opoy cyy coeoo oa PEM. ae, p ao ayce po paoo oecee oee poep opoy cyy, o ope oapy ee. Ho Mop oo ae oe e o opoo cy p ee oa PEM. Moo coxpa opoy cyy opoo cy, o Mop oe e ee. Ec y Mop ec ocy a ey oepy, o oe papy eoacoc PEM.

Mopa o, o e o oep aoy eey popaoo oecee, ec e o e e oep aapaype, a oopo paoae o popaoe oeceee. oca ae oace oayc eoocoa. Ho eoopx e o oe pea.

TIS/PEM oepee opaoe cce ( TIS, Trusted Information Systems), aco oepaee paee o epeo ay poea paeca Coeex ao, a peaa PEM (TIS/PEM). Papaoae aop UNIX, o ae epeece a VMS, DOS Windows.

Xo cea PEM opee Internet o a cepao ep, TIS/PEM o epae cyecoae ecox epapx cepa. oy opee aop cepao, oope yy cac ece, a ce cepa, ae ya. oo, o o oac TIS/PEM yy e yo pcoec epapx Internet.

Bce opaa paae CA aa p ea oy oy ocy TIS/PEM, oopa pacpocpaec e cxooo oa. aepecoae a o opaac o ceyey apecy :

Privacy-Enhanced Mail, Trusted Information Systems, Inc., 3060 Washington Road IRte. 97), Glenwood, MD 2,1738;

(301) 854-6889;

fax: (301) 854-5363;

Inte rnet: pern-info@tis.com.

RIPEM RIPEM - o popaa, acaa Mapo Popao ( Mark Riordan) peaya pooo PEM.

Xo a popaa e ec cooo ocyo, e oo ocooac ecao acoo, e oepecoo cooa. e a ee cooae xo oyea.

o e oe coppoa. oeo, ao paeca CA e ecy a peea Coe ex ao, p e oppye cope opae. o RIPEM ocye o cey py a e pox ocax oe. Papeea copa epc, aaea RIPEM/SIC, peaya oo poe oc.

oey aca x cpo RIPEM e ooc peaoaa pooo PEM, e e oooc cooa cepa poep ooc e.

o RIPEM Popa aca oxoy popay RPEM. opayeaoc, o o ye oeocya popaa epoo o. ac oo aee poe, Popa cooa aop Rabin (c.

pae 19.5). Public Key Partners aa, o x ae pacpocpac a c popa c op a. o ypoo cyeoo poecca Popa pepa pacpocpaee popa.

Ceac RPEM e coyec. Oa e coeca c RIPEM. Ta a oo cooa RIPEM, e cpe a pec co copo Public Key Partners, e ooa opaac RPEM.

24.11 pooo eoacoc cooe pooo eoacoc cooe (Message Security Protocol, MSP) - o oe ae PEM. O papaoa NSA oe 80-x oo p paoe o popae coa eoaco cce epea ax o ce (Secure Data Network System, SDNS) program. o coec c X.400 pooo ypo poe ap epoo o. MSP apyec cooa papaaaeo ce oopox cooe (Defense Message System, DMS) Mcepca oopo.

peape pooo eoacoc cooe (Preliminary Message Security Protocol, PMSP), oop peoaaec cooa "ecepex, o ax" cooe, pecae coo aapoay cooa c X.400 TCP/IP epc MSP. o pooo ae aa Mosaic.

a PEM, popae peaa MSP PMSP ocaoo , x ocpy ooe ocp o c o cooae pax aopo ocyece y eoacoc, ax a oc, xpoae poae. PSMP ye paoa c pocxeo Capstone (c. pae 24.17).

24.12 PRETTY GOOD PRIVACY (PGP) Pretty Good Privacy (PGP, eca xopoa cepeoc) - o cooo pacpocpaea popaa eoa c o epoo o, papaoaa o epao ( Philip Zimmermann) [1652]. poa ax oa coye IDEA, ypae a poo oc - RSA (a a o 2047 o), a ooapaeoo xpoa - MD5.

oye cyax opx e PGP coye epoocy poepy ce a pocoy, coy oye capox oceoaeoce epa ey aa ooaee a a aaype. PGP eeppye cyae IDEA c oo eoa, ANSI X9.17, Appendix C (c. pa e 8.1) [55], coy eco DES aece cepoo aopa IDEA. PGP ae pye ap ooae c oo xpoao apoo pa, a e apo eocpeceo.

Cooe, apoae PGP, e ecoo ypoe eoacoc. Ecea e, eca poaay o apoao cooe, - o oyae cooe p yco, o poaay ece ID a oyae. Too pacpoa cooee, oyae yae, e oo ocao, ec oo ocao. o peo oaec o cooe PEM, aooe oopoo eao opa o opa ee, oyaee cao cooe xpac eapoao e.

Cao epeco ocoeoc PGP ec pacpeee oxo ypae a (c. pae 8.12). epo cepa e e, eco oo PGP oepaec "ce oep". a oo ae ca coae pacpocpae co op . ooae oca py pya, co aa aocaoe cooeco ooaee PGP.

Hapep, Aca oe ec epea oy co op . o o ae Acy, ooy o ocae ee op . Oy ocay o o opaae Ace, a pyy ocae. oa Ace yo cac c po, oa ocae po ocay o o a. po, y oopo a o opao ye ec oa (oa oya eo pae), oopa oepe oy aep pyoo e oea, poepe eo oc o o Ac yeaec, o oa paa. Ta opao, o ao Acy po.

PGP e opeee cpae ycao oepex ce, ooae ca pea, oy ep, a oy e. PGP oeceae exa oep accoaoo oep op a c ooa oep. a ooae xpa aop ocax opx e e aa oa opx e (public-key ring). a oa oaae oe aooc a, opee ypoe oep y opeoo ooae. e oe ypoe oep, e oe ooae yepe aooc a. oe oep oc epe, acoo ooae ep oy, o o ca ope pyx ooaee. aoe oe oep aey a aae ypoe, ope e , acoo ope ooae ep aey a, ocaey pye ope .

o oe pyy ycaaaec ooaee. PGP epepo ooe o o epe oe o o opa.

Ha 17- oaao, a a oe opeoo ooae, Ac. Ac axoc cao epxy epapx, aee a acoo aee. Aca ocae oa, po, a, e pa. Oa oepe oy po oca ope pyx e, poe oo, oa a c o oepe y e oca ope pyx e. oa oepe e oca ope pyx e, xo caa e ocaa e.

yx aco oepex oce oe oaac ocao cepa a. Aca ca e, o ypa aoe, a a e oca eo. poe oep ycaaaec PGP py y, Aca oe pa ycpaay ee cee apao.

Aca e oa aoaec oep a pyx e oo ooy, o o oca o, oop oa cae pa. Aca Oa e oepe py Oa oca pye , xo oa coceopyo ocaa eo . poe oo, oa e oepe oc aa o o Mapa oc ypa o o.

Oya ooe a xo ce, oe , Aca oya eo o cepepa. PGP e cae a oaec pa, Aca oa o o o paoc a, o pec oep ooy ex, o oca .

oeo, o e eae Ace cooa , oop oa e oepe. aaa PGP - peype Acy o oopeoc a, a e oea e ycaaa coee.

Ca ca eo o cce ec o e : apapoa, o o-y e ocoye c copoepoa o, eooo. Ec ap Ac ypae, oa oe oca e cepa oa a (key revocation certificate), o, a a eoe pacpeeee e ye pooo, e apapoa, o o cooee ye oyeo ce, coy ee op coe oe e. a a Aca oa ye oca co cepa oa a co ap o, o ec oa oepe , oa e coe ooa eo.

Aca oepe aey a x pao oca pye x ocae y Aca aco oepe aey y a pao oca pye Aca cae ao Aca cae eao Aca ?

?

p o po e ?

?

e a eep yp a ? ?

Map Hc Oy Pc. 24-7. Moe oep PGP.

Teye epce PGP ec 2.6.2. oee oo epc, PGP 3.0, oaec oy 1995 oa. B 3. e o pooo DES, SHA, pye aop c op a, paeee ap "op /ap " poa oc, pacpee poeyp oa e, yyee y ypae oo e, API eppoa PGP pye popa ooc epe cae coee oy.

PGP ocya MS-DOS, UNIX, Macintosh, Amiga Atari. B x, eoepecx ex ee oo cooa cooo, caa co ox yo ftp Internet. o copoa PGP c ya MIT c oo telnet oec net-dist.mit.edu, oe ccey a getpgp, oee a opoc, ae coye ftp coee c net-dist.mit.edu epee aao, yaa cecc telnet. y popay ae oo oy ftp.ox.ac.uk, ftp.dsi.unimi.it, ftp.funet.fi, ftp.demon.co.uk, CompuServe, AOL, .. oepecoo cooa CA PGP oo popec - ooc, ece c e - pepo a 100 oapo oa ViaCrypt, 9033 N 24th Ave., Phoenix, AZ, 85021;

(602) 944-0773;

viacrypt@acm.org. Cyecy pa e cpeca, ooae eppoa PGP MS-DOS, Microsoft Windows, Macintosh UNIX.

O PGP acao ecoo [601,1394,1495]. cxo o ae oyoa eao e [1653] p oe oo oceapae CA, oop pooae ca, o cxo o oo c oppoa oo yao, a e epoo e. Ec oepee IDEA, PGP oo a p c oeoy ypo poa.

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