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aa 18 Ooapaee x-y 18.1 Oco Ooapaea y H(M) peec cooe pooo M opaae aee cpoao h. ...

-- [ 2 ] --

(10) Ec p < 2L-1, o epee a a (13).

(11) poep, ec p poc co.

(12) Ec p - pocoe, epee ay (15).

(13) yc C=C 1 N=N n l.

(14) Ec C = 4096, epec ay (1). B poo cyae epee a a (7).

(15) Coxpa ae S C, cooae eepa p q.

B [1154] epeea S aaec capoo, epeea C - ceo, a N - ceee.

Cc oo ypae o, o oo ec oyoa cocoo eepa p q. cex pa ecx pee o eo ooe ea cax ae p q. Ec o-o py a ae-o p q, ac oe aepecoa, a oye ca. Oao, ec oye ae S C, cooa e p eepa cyax p q, coee oop c poeypy caocoeo. cooae o oapaeo x-y ( caape coyec SHA) e ooe oy S C o ae p q.

a eoacoc ye, e oeceaea RSA. B RSA poce ca xpac cepee. o oe eeppoa aoe pocoe co co, opa oopoo ypoae paoee a oe. He a apoo a, o oa e poep. B DSA, ae ec ap eece, oo y e c, o p q eeppoac cya opao.

upoaue ElGamal c DSA epaoc, o DSA a pac paecy, ooy o eo e cooa aece a o pa poa. Oao oo cooa o y DSA poa EIGamal. yc ao p peaoa a o oo y aa xoe ae p, q, g, k, x h, oo oy apaep oc: r s.

poa cooe m aopo EIGamal c oo opoo a y epe cyaoe c o k oe Bopaeoe aee r ye a cxe EIGamal. Opoc s. ae oe, call epeeye aee r u, opoc s. Boe Opoc r. Bopaeoe aee s ye b cxee EIGamal. Teep y ac ec poec, a b. e ppoae ae poco. coy ap x poec cooe, a b, oe aee r - o ax mod p. Haoe eo e. ae oe aee s ye op eco cooe, m.

o coco paoae e co ce peaa DSA - eoopx x oy acpoa a e p q eoopx pyx apaepo. Te e eee, ec peaa ec ocaoo o e, o oo poa cooee, e coy eo, poe y poo oc.

upoaue RSA c DSA poae RSA ee poe. coy oy n, cooee m op e, oe Bopaeoe aee r ec poec. eppoae RSA ec oo a e. Ec d - a p , o opaae op ec a aee r.

eonacocm DSA C 512 a DSA eocaoo aee eo eoacoc, o o oe aee p 1024 ax. B coe epo ae a y ey NSA a oepoao yepee o epe ( Joe Aber nathy) The Houston Chronicle o ooy ae DSS [363]:

o acaec peoaaeo ae DSS. M cae, o ep "aea" o ayee, a o peo a ae, o epe aey oo a-o pacpoa (poa) apoae cooe, ocaee c oo DSS, e papee opae.

DSS e pye ax ax. o cy opoco ec, e oe o-o p oo DSS oea oc, , a opao, cpepoa c ccey. M aeopec ae, o epooc, o o-y - a NSA coe oea oc DSS, p pao cooa caapa ecoeo aa.

oee oo, peooee o yceoc aee cpaeo o cce poep ooc c o p a, a RSA. epee, o o e oo a DSS (apye, oyp pecce), ooc eepo. Bopoc peaa cocoe opa pocx ce. M pae ac ye ae eae oepe EUROCRYPT, e "a py coo" ocyac opoc aee DSS. O yaco ocye o c ceoaee Bellcore, yepa o oooc ae, o aey oa yac cycc - a oo cceoae Bellcore - p oy, o opoc o aee DSS e pecae poe. oee oo, ce o pao, o opoc o aee ec pa pay pecco. Oao, ac o poce NIST oe a oee o aee, papaoa poecc eepa pocx ce, oo ea opa ooo ooc eo eooo ca cax pocx ce, cooae oopx ocae DSS. poe oo, NIST acaae a c ooa oye oe , o o 1024, o ooe e ooac papaoa poecco eepa pocx ce, ea cax pocx ce. Oe a ooe oeo, a oop aco e opaa ae, ec o, o p cooa DSS poce ca oeocmyn , ceoaeo, oy peeo opoo ye. He ce cce c op a coco po ooy poepy.

eococ o cce a opa peye opa ae a peaa. a yoc c c e c oa paopax ooaee, NSA o pa acaae a cooa epaoax oepe x epo a a cocoe poa pc ccee. Xo o poce NIST papaoa p execx o a DSS, oox peaoa eee epaoa oxo, ce e yo e y ac oe o DSS Federal Register, oopo oopc:

"Xo o caap oe oece oe peoa eoacoc eepa pox oce, cooece caapy e oeceae eoacoc opeo peaa. Oeceoe o ao eapaee ypa e oo apapoa, o oa peaa apapye pee ypoe eoacoc. NIST poo paoy c paece ooae, oecea paoc pea a."

Haoe y ce yepe o eeoacoc DSS, o ac e ye. DSS aeo ye NSA, o ooo aey peopy o eoacoc opaox cce pape cooa o caap o c ecepex ax, opaaaex opeeex paeaex cceax, ae oc cepex a x pe cce. M cae, o oooe pae ceecye o eoooc aoo-o epooo cp eoacoc, oeceaeo DSS p eo pax peaa cooa. Ocoac a peoax pa eca CA exe eoacoc pox oce, cae, o DSS ec y opo. B ec eoc, DSS cyae aece ooo poea Cce a cooe (Defense Message System), paoo apapoa ooc epox cooe eo ax oa opoo opa. a aa a eocpa ae yace oea aao ao, oex cy oopox eoc pooc ooepa c NIST.

e copac oepoa coc ae NSA. pa eo a py e - ac o a eo ey ooe.

Bcpmu k ao oc yo ooe aee k, oopoe oo pac cya opao. Ec Ea y ae k, oopoe Aca cooaa oc cooe, oe ocooac eoop co ca eepaopa cyax ce, oop ae k, oa coe pacp ap Ac, x. Ec Ea oye a cooe, ocax c oo ooo oo e k, o, ae e a aee k, oa co e pacp x. A c oo x Ea coe ao oea oc Ac. B o peaa DSA eoacoc cce oe ae xopo eepaop cyax ce [1468].

Onacocmu oeo oy Xo DSS e opeee peee ooae oeo oy, pae peaa oy oco oac ao oooc. Hapep, Haoooe ypaee paccapae cooae DSS e poo aoo. o ec a opaa opeye, o ce aooae cpa cooa o e p q? O oy co eo caoc e poaaa. oa co pao ocy a pae peaa DSS, o p ecooca ec.

ocoame aa DSA yc Coc (Gus Simmons) op DSA ocoae aa [1468, 1469] (c. pae 23.3). o o coae aa ooe cpaa oc aoe cooee, oopoe oe poao oo e, y oo ec . Coaco Cocy, o "aeaeoe coaee", o "ce oee eoca ocoaex aao, coyx cxey ElGamal, oy ycpae" DSS, o DSS "a ceo oeceae aoee oxoy cpey ocoaex oya ". NIST NSA e oepo a o ocoae aa, o ae e ae, oaac o o ao oooc. Ta a o ocoae aa ooe p eopocoeco peaa DSS epeaa c ao oc ac apoo a. Hoa a oyec peaae DSS, ec e oepee papaoy pea a.

amem pa (David Kravitz), paee paoa NSA, aee aeo DSA [897]. Coaco NIST [538]:

NIST epecax oeca cpec cea exoo DSS ocyo ecao o cey py. M cae, o a exoo oe aaeoaa, o ae pye ae e pe DSS, o e oe a epx a pa oo o oye aea.

Hecop a o, p aea aeo yepa, o DSA apyae x ae: Diffie-Hellman (c.

pae 2.2.1) [718], Merkle-Hellman (c. pae 19.2.) [720] Schnorr (c. pae 21.3) [1398]. ae Schnorr ec coo aox cooce. Cpo ec yx pyx aeo ceae 1997 oy, a ae Schnorr ecee o 2008 oa. Aop Schnorr papaoa e a paecee e. B o e o aeo PKP y paeca CA e pa a ae Schnorr, opp aaeoa co aop o cey py. ae ec cy CA ecy peee oy DSA, eco, aoe peee py cy p y x cpaax. Coe eyapoa opopa p caap, oop aoe ox cpaax a pyae aeoe aooaeco pyx ? Hyo pe, o pe y poey, oey aca o o opoc e pee ae Coeex aax.

B e 1993 oa NIST peo a PKP cey aey e a DSA [541]. Co aee poaoc oce poeco oeceoc caap e ce e cx coae. NIST a [542]:

.. NIST paccope ae o ooo apye aeo cea o, o ae ecpae.

a caap oao p, oyxe axe cye poecca, o e ae, o ea.

NIST a, o o ooe ac , oe apye aeoo aooaeca p cooa DSA paoe o paeceoy opay. Ocae, o oy, o aoc o cee ca. poe aocoo caapa, coyeo DSA, y ANSI [60]. NIST paoae a ee e caapa DSA paeceo aapae. Shell Oil ceaa DSA co eyapo caapo.

O pyx peoex caapax DSA e eeco.

20.2 Bapa DSA o apa eae poe ce, eoxoe oc, e aca c k-1 [1135]. Bce coyee apaep - ae e, a DSA. oc cooe m Aca eeppye a cyax ca, k d, ee q. poeypa oc a r = (gk mod p) mod q s = (H(m) xr) * d mod q t = kd mod q o poepe oc, c w = t/s mod q u1 = (H(m) * w) mod q u2 = (rw) mod q 1 Ec r = (( gu * yu ) mod p) mod q, o oc paa.

Cey apa ypoae ce p poepe oc [1040, 1629]. Bce coyee apae p - ae e, a DSA. oc cooe m Aca eeppye cyaoe co k, eee q. poey pa oc a r = (gk mod p) mod q s = k (H(m) xr)-1 mod q o poepe oc, c u1 = (H(m) *s) mod q u2 = (sr) mod q 1 Ec r = (( gu * yu ) mod p) mod q, o oc paa.

Ee o apa DSA papeae aey poepy, o oe poep oc aea [1135]. Ec ce oc pa, o paoa oa aoea. Ec oa x epaa, o ey ee yo o, aa. ecac, o eeoaco. o oca, o poep oe eo coa aop ax oce, oop yoeope pep poep aea oce [974].

Cyecye ae apa eepa pocx ce DSA, oop ae q coyee e epa pocx ce apaep yp p. Be a cxea a eoacoc DSA, ce ee eeco.

(1) Bepe pooy oceoaeoc, o pae epe, 160 o aoe ee S. yc g - o a S ax.

(2) Bc U = SHA(S) SHA((S 1) mod 2g), e SHA oca paee 18.7.

(3) Opaye q, ycao ao ae aae U 1.

(4) poep, ec q poc.

(5) yc p - o oeee q, S, C SHA(S ). C pecae coo 32 yex a.

(6) p=p-(p mod q) l.

(7) p=p+q.

(8) Ec C p pao 0x7fffffff, epec a a (1).

(9) poep, ec p poc.

(10) Ec p - cocaoe, epec a a (7).

peyeco oo apaa ec o, o a e yo xpa ae C S, cooae eepa p q. O e coca p. poe, paoax ycox exa a, ap ep, eeyax apoe, o oe ao.

20.3 Aop poo oc OCT o pycc caap poo oc, Oao aae OCT P 34.10-94 [656]. Aop oe oxo a DSA, coye ceye apaep p = pocoe co, a oopoo o ey 509 512 a, o ey 1020 1024 a.

q = pocoe co - oe p-1, o o 254 o 256 o.

a = oe co, eee p-1, oopoo aq mod p = 1.

x = co, eee q.

y = ax mod p.

o aop ae coye ooapaey x-y : H(x). Caap opeee cooa e x-y OCT P 34.1 1-94 (c. pae 18.1 1), ocoao a cepo aope OCT (c.

pae 14.1) [657].

epe p apaepa, p, q a, op oy cooac coeco ooae ce. ap o cy x, a op - y. o oca cooee m (1) Aca eeppye cyaoe co k, eee q (2) Aca eeppye I = (a* mod p) mod q s = (ct k(H(m))) mod q r = (ak mod p) mod q s = (xr k(H(m))) mod q Ec H(m) mod q =0, o aee x-y ycaaaec pa 1. Ec r =0, o epe pyoe aee k ae coa. oc cya a ca: r mod 2256 s mod 2256, Aca ocae x oy.

(3) o poepe oc, c v = H(m)q-2 mod q z1 = (sv) mod q z2 = ((q-r)*v) mod q 1 u = (( az * yz ) mod p) mod q Ec u = r, o oc paa.

Pae ey o cxeo DSA o, o DSA s = (k-1 (H(m) xr)) mod q, o ae pyoe ypae e poep. oo, oao, o a q paa 256 a. ocy aax popao aec ocao q pepo 160 o o. Moe o poco cece pycco p pa cepxeoacoc.

Caap coyec c aaa 1995 oa e ap po " cyeoo ooa", o o e ao.

20.4 Cxe poo oc c cooae cpex oapo Cxe oc ElGamal, Schnorr (c. pae 21.3) DSA oe oxo. o cy, ce o c pe pepa oe cxe poo oc, coye poey cpex oapo. Bece c c a pyx cxe oce o c ac ooo oo e ceeca [740, 741, 699, 1184].

Bepe p, ooe pocoe co, q, paoe o p-1, o ooy pocoy oe p-1. ae epe g, co ey 1 p, oopoo gq 1 (mod p). Bce ca op, oy coeco c ooa pyo ooaee. ap o ec x, eee q. Op o cy y =gx mod q.

o oca cooee m, caaa epe cyaoe aee k, eee q ao pocoe c .

Ec q oe pocoe co, o ye paoa oe k, eee q. Caaa c r = gk mod p Ooeoe ypaee oc pe ak = b cx mod q oe a, b c oy pa pae ae. aa cpoa 16th peocae ec o ooce. poep oc, oyae oe yec, o ra = gbyc mod p o ypaee aaec ypaee poep.

Ta. 20-4.

Booe epecao a, b c (r'= r mod q) r' s m r' m s r' m ms m r' r' s ms r' s B 15th epece ooe apa oc poep, oyee oo epo cpo o ox ae a, b c e yea eo .

Ta. 20-5.

Cxe poo oc c cooae cpex oapo paee oc paee poep (1) r'k=s+mx mod q rr'=gsym mod p (2) r'k=m+sx mod q rr'=gmys mod p (3) sk= r'+mx mod q rs=gr'ym mod p (4) sk= m+ r'x mod q rs=gmyr' mod p (5) mk= s+ r'x mod q rm=gsyr' mod p (6) mk= r'+sx mod q rm=gr'ys mod p o ec pax cxe pox oce. oaee yca yeae x oeco o 24. p cooa cex oox ae a, b c co cxe oxo 120.

EIGamal [518, 519] DSA [1154] o cyecy ocoa a ypae (4). pye cxe - a ypae (2) [24, 1629]. Schnorr [1396, 1397], a pya cxea [1183], eco ca c ypaee (5). A ypaee (1) o o e a, o oy cxey, peoey [1630]. Ocaec ypae - oe.

aee. y x cxe oo cea oee DSA-ooo, opee r a r = (gk mod p) mod q coye o e ypaee oc ceae ypaee poep u1 = a-1b mod q u2 = a-1c mod q 1 v = (( gu * yu ) mod p) mod q (r mod q)a = gbyc mod p Cyecy e pye oooc oox peopaoa [740, 741]. Tae oepa oo poe a c ao 120 cxe, oe oee co cxe poo oc, coyx cpee oap, o 480.

Ho o ee e ce. ooee ooe ee po oee, e 13000 apaa (e ce x ocaoo e) [740, 741].

Oo px copo cooa RSA poo oc ec coco, aaeoe oc caoee cooe. oa poepee oc RSA, cee m. ae ceoe m cpa aec c cooee poepec, paa oc cooe. B peyx cxeax occao m p ce oc eooo, a opeyec epooe m, oopoe coyec ypae po ep. Ho, oaaec, oo ocpo apa c occaoee cooe cex epeex cxe. oc caaa c r = mgk mod p ae m ee ypae oc. ae oo occao ypaee poep a, o m oo ceo eocpeceo. To e caoe oo pep DSA-oox cxe:

r = (mgk mod p) mod q eoacoc cex apao oaoa, ooy ee cc pa cxey o cooc ce.

oco cxe aee eoxooc c opae ae. a oaaec, oa x cxe ooe c ypaee oc, ypaee poep e cooa opax ae, p o ee occaaa cooee. Oa aaec cxeo p-NEW [1184].

r = mg-k mod p s = k - r'x mod q m occaaaec ( poepec oc) c oo ce m = gsyr'r mod p B pe apao oopeeo ocaec o a-p oa cooe [740], pye apa oo cooa cex oce [741].

o aea oac ye. Bce pae cxe poo oc c cooae c pex oapo oee oec apaco. o ca, o o ooaeo oo oe copa ey Schnorr [1398] DSA [897]: DSA e ec pooo Schnorr, pao a EIGa mal. Bce p aopa c ac cya ocao oe cxe, a oa cxea eaae o aa.

20.5 ONG-SCHNORR-SHAMIR a cxea oc coye ooe o oy n [1219, 1220]. Bpaec ooe eoe co (a paoee n a oe e oaeo). ae paec cyaoe co k, ao pocoe c n, cec h, paoe h = -k-2 mod n = -(k-1)2 mod n Op o cya h n;

a ap - k.

o oca cooee M, caaa eeppyec cyaoe co r, ao pocoe c n. ae c ec:

S1 = 1/2 (M/r r) mod n S2 = 1/2 (M/r -r) mod n apa ce S1 S2 npecae coo oc. poep oc, yeac, o S12 h*S22 M (mod n) Oca ec apa cxe ocoa a apax ooeax. p eo oyoa [1217] a yce poaa o peoeo oapaee $100. Heeoacoc cxe a oaaa [1255, 18], o o e ocaoo ee aopo. O peo oa aopa, ocoay a yecx ooeax, ae oaayc eeoaco [1255]. Aop peo epc a ae ooeo e epo cee, o a oaa oa [524, 1255]. Bapa, pea poe, oca [1134].

20.6 ESIGN ESICN -o cxea poo oc, papaoaa NTT Japan [1205, 583]. epaoc, o oa e eee eoaca, e RSA DSA, aoo cpee p ex e paepax a oc. ap o cy apa ox pocx ce p q. Op o ec n, oopoo n = p2*q H - o x-y, peea cooe m, pe aee H(m) axoc peeax o 0 o n-1.

coyec ae apaep eoacoc k, oop ye pae paccope.

(1) Aca pae cyaoe co x, eee pq.

(2) Aca ce:

w, aeee eoe, oopoe oe pao (H(m) - xk mod n)/pq s = x ((w/kxk-1 mod p) pq (3) Aca ocae s oy.

(4) 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.

Bo p peapex ce, o aop oo ycop. ce oy oe poo oe pee a e ca c ocae cooee. Bpa x, Aca oe pa a (2) a a oaa. Caaa.

(2a) Aca ce:

u = xk mod n v = l/(kxk-1) mod p (2b) Aca ce:

w= aeee eoe, oopoe oe pao (H(m) - u)/pq s = x ((wv mod p) pq oo coyex paepo ce peapee ce ycop poecc oc a o po. o c pya paoa oec eo a ca peapex ce. Ocyee ec oyo ape, oex p ycope ESIGN, oo a [1625, 1624]. o ao p oo pacp pao c ec p [1206].

eonacocm ESIGN oa o aop epe peoe, k o pao pa 2 [1215]. Taa cxea cpo a oaa p peo (Ernie Brickell) oo eaypeco [261], oope pacpocpa coe cpe a cya k = 3. Mopoaa epc oo aopa [1203] a oaa apo [1204].

Bapa, peoe [1204], oa [1553]. ESIGN - o ceo peapa aopo oo ceeca. oa cp ESIGN [963] oaaac epeyao.

B acoee pe aop peoey cooa ceye ae k: 8, 16, 32, 64, 128, 256, 512 1024. O ae peoey, o p q e ee 192 o aoe, opay n e eee, e 576 o y. ( ya, o n oo ee a paa oe.) Aop ca, o c a ae apaepo, eoacoc ESIGN paa eoacoc RSA Rabin. oe aa oaae, o copoc ESIGN aoo e, e y RSA, EIGamal DSA [582].

amem ESICN aaeoa Coeex aax [1208], aae, A, pa, epa a. o, o xoe oy e a aop, oe opac Oe eeyao coceoc NTT (Intellectual Property Department, NTT, 1-6Uchisaiwai-cho, 1-chome, Chiyada-ku, 100 Japan).

20.7 eoe aoa Coepeo oa e, yea aya yao ( Papua Guam) [665], coco cooa poc ceax c op a eox aoao. a ccea ce ee co oa e poa epe a eoe yee, o peapeoe cceoae oaao, o y ee oe aoe e popaec caoe eco, a y pyx cce [562]. Te e eee, o oooeaa oac cceoa. Coc o eox aoao ec o, o ae ec o eppye, eooo c pea po ooo coco, eppoa pao axoe ooa. o oe oxoe a ooapa ey x-y c aeo.

20.8 pye aop c op o a o o peoeo cpo oeco pyx aopo c op a. Aop Matsumoto-lmai [1021] cp [450]. Aop Cade epe peoe 1985 oy, oa [774], ae opaoa o e oy [286]. oo x cp, cyecy oe cp, paca ae ooe a oe o [605]. oy aopy, eoacoc oopoo opeeec ooe ooeo a oe o, yo oocc co ceo, ec e c opoe oopee.

Aop Yagisawa oee oeee cee mod p c apeo mod p-1 [1623], o oa [256]. pyo aop c op o, Tsujii-Kurosawa-Itoh-Fujioka-Matsumoto [1548], ae oaac eeoac [948]. Heeoaco [717] a pe ccea, Luccio-Mazzone [993]. Cxea oc a ae birational epecaoo [1425] a oaa a cey e oce ee pecae [381]. Hecoo cxe oce peo Taya Oaoo ( Tatsuaki Okamoto): o oaao, o oa x a e eoaca, a poea cpeoo oapa, a pya - a poea cpeoo oapa u poea paoe a oe [1206]. Aaoe cxe pecae [709].

ycayc Coc (Gustavus Simmons) peo cooa aece oco aopo c op a J-aepy [1455, 145]. O o e poc oaac oce opee ex eoo paoe ooeo a oe [951]. Tae ye ceae oypy ooeo [1619, 962], o o eo e ao. Xapa Heppeep (Harald Niederreiter) peo aop c op o a ae oceoaeoce cox pecpo [1166]. pyo aop cooa coa oa (Lyndon) [1476], a pe - prepositional ccee [817]. eoacoc ooo eax aop o c op a ocoaac a poee matrix cover [82]. Taya Oaoo ayo Oa (Kazuo Ohta) poe cpaee pa cxe poo oc [1212].

epce coa paao ox pax aopo c op a ec. B oy oe, o oco aopo c op a ocoa a oo pex pyx poe [492, 494]:

1. Pa: ao oeco yax ce, a ooeco, cya oopoo paa N.

2. cpe oap: Ec p - pocoe co, a g M - ee, a x, oopoo oec gxM (mod p).

3. Paoee a oe: Ec N - poeee yx pocx ce, o o (a) pao N a oe, (b) aax ex ce M C a d, oopoo Md C (mod N), (c) aax ex ce e C a M, oopoo Me C (mod N), (d) aaoo eoo ca x opee, cyecye eoe co y, oopoo x y2 (mod N).

Coaco [492, 494], poea cpex oapo a peoea . o ( J. Gill), po ea paoe a oe - yo, a poea paa - ca .

a yoc aeaecx oco popa c op a eoo ecoo. pop pee o poe cpex oapo, o poe paoe a oe ceae eeoac ee acc aopo c op a. oaa [492, 494], o oo pc caec y aopa:

1. Bce oepa, a oope ceac opaec popa c op a - yoee, oeee cee paoee a oe - peca coo yaeae apeece e. Bea o peeo ecoo aeaecoo ye, poc a , a peee pocceax c op a, ye, a e ye ae oepe.

2. Haa oooc o oe apeece ce pace paoepo ceac ooe a pea oa cce c ca aoo paepa, o cce yce oo eceo paa popa paoe a oe, cpex oapax ee ope.

a ye e, e ce aop c op a, ocoae a x poeax, eoac.

Ca oo aopa c op o ac e oo o ceo cooc poe, e a e ocoe aopa. Tpya poea eoaeo peayec co aope. A ap o ce o pe pa [1415]:

1. Teop cooc oo caa c oe ac cya poe. poaa e aco oyae oo aop cacec cax poe - pae poec, a poae o e e o.

2. Bcea cooc poe oo epec xyeo cpeeo cyae. o eo aece cocoa poa, poea oa pyo pee o o cex cyax.

3. pooy coy poey eoaeo oo peopaoa poccey, oy e poea oa oo cpo ee aey, ae oopo oo oo eae oo pocoe peee poe.

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