Kriptografija i Enkripcija Vladimir Apostolov

 Kriptografija i enkripcija PROJEKAT IZ PREDMETA PREDM ETA IS360 Reviija i kontro!a

Mentor" Prof%Dr%Ta Prof%Dr%Tatjana tjana &i'a!ija

St#$ent" (!a$i)ir Apo*to!ov +,,-

.i/ +0%0+%10+6

Sadržaj APSTRAKT.....................................................................................................2 1. UPOZNAVA UPOZNAVANJE NJE I TERMINOLOGIJA....................... TERMINOLOGIJA............................................. ................................. .................... ......... 2 RIPTOGRAFIJA .............................................................................................................2 1.1 K RIPTOGRAFIJA 1.2 ENKRIPCIJA ILI ŠIFROVANJE ...............................................................................................2 1.3 ŠIFRA.........................................................................................................................3  TVORENI  TEKST VS ŠIFRAT.............................................................................................3 1.4 O TVORENI TEKST RIPTOANALIZA............................................................................................................4 1.5 K RIPTOANALIZA

2.KRIPTOGRAFIJA KROZ ISTORIJU...................................................................5

2.1 S TARI EGIPAT...............................................................................................................5 2.2 GRČKA........................................................................................................................6 2.3 RIM............................................................................................................................6 2.4 ALBERT-VINŽEROVA ŠIFRA ALBERTI!VIGENERE CIP"ER#......................................................$ 2.5 %ŽEFERSONOV ŠIFRARNI  TOČAK     JEFFERSON &"EEL CIP"ER#...............................................' 3. KRIPTOGRAFIJA U I SVETSKOM RATU................... RATU......................................................... ......................................10 10 IMERMANOV  TELEGRAM#...........................................................1( 3.1 ZIMMERMAN TELEGRAM  CIMERMANOV TELEGRAM O%E  TALKERS ERS.............................................................................................11 3.2 C"OCTA& CO%E TALK 4. KRIPTOGRAFIJA U II SVETSKOM RATU............... RATU..................................... ................................. ................... ........11 11

4.1 ENIGMA....................................................................................................................11 4.1.1 Princip rada enigme........................................................................................12 4.1.2 Princip napada na enigmu...............................................................................13 4.2 P)RPLE.....................................................................................................................14 5. SAVREMENA SAVREMENA ENKRIPIJA ! I "EO...................................... "EO................................................... ........................ ........... 15

5.1 ONE-TIME PA%............................................................................................................15 5.2 PSE)%O-RAN%OM N)MBER GENERATOR  PRNG#..............................................................16 E* ENCRIPTION  PRIVATE-K E* E*#- PRIVATNI KLJ)Č.............................................16 5.2 S *MMETRIC K E* #. SAVREMENA ENKRIPIJA ! II "EO..............................................................1$ E* ENCR*PTION   P)BLIC-K E* E*#............ 6.1 AS*MMETRIC K E* #................... .............. ............... ........................................1$ ................................1$ E* E+C"ANGE.............. 6.2 %IFFIE-"ELLMAN K E* ..................... ............... ............... .............. ............... ........................................1$ ................................1$ 6.3 RSA ENKRIPCIJA.........................................................................................................1, $. STEGANOGRAFIJA........ STEGANOGRAFIJA.............................. ............................................ ............................................ ................................. ...........1% 1%  TEGANOGRAP"IC EMBE%%ING#..............................................1' $.1 )GRA%NJA STEGANOGRAFIJE S TEGANOGRAP"IC

%. METO"E ENKRIPIJE U &U"U'NOSTI.........................................................20 (.ZAKLJU)AK...............................................................................................22 LITERATURA................................................................................................23

1

A*+,ra-, K/0  78/9  :;<8 # => 7:?8 @ =>8> 7>879> @> >D D D8. K@ =0> <8 7>879   8<? >09 8 :;8  8/D7 =0. P0 D = @D 798  /<08 7>879 =>  /D<8 8;98 D 7  /H 1',(-. MD I8080  I@>8 7=8 1'6(.  8 =07 <8 9 =< D7 8 @:8 &D &D & 1','. &D &D &  708=7 /07 7 D@<< >D D 7>89> />0  D 8;9 7@ D08 D. O< 8< 0D @ @8> 8;9 @@<  8> /0> D = @D 8;9. T8 @><8 87/9  87/9 ? /? >D D @<>  8H8 @:00 <8 8;9 77 08 /=0   7=8.

1. U*/aaj  ,r6ja 1.1 Kr*,6ra7ja K/0  8>7  >H8 087 08 =7<8# /=8  =7<8 />7. K/0  :7 7  ;8 8<=07 7 00 @8H8 H D 8 7 8> ;8 088 0. 8 /@8>   D<8. T7  =/9H8 7 D8 87/9 0 7 = 7=0 D =>> 08=79  7>879> /7 D08 . K/0 /D=0<  7 0D > 7  87 /7>:< D =7 == />7  @H8 =0.

1.2 E-r*8ja  9:raj E87/9  :;<8  D8 =/9H8 80 7/0 7 7 /D07  8;9> 08=;:>? > 7D 7 8  D = :;>. E87/9 0:H8 >@ =/9H8 /0  7>H D @<: 08=;9> /D07. N7 87/9=7 0 @0<> D 7>H >D =0 D>8 7  />7 D   D = D:;> /7 D> 87/9=7 0 > D0 = 8 8 7>H< > D8=> 2

8 />7>. %7/9  D:;<8 # = H=0 7=7> 7 87/9 7  08. E87/9 = 7=0 =<7D8<8 > D8 <0>. E87/9 = 8H:? 7=0 7D 08=79 /7 8=>8 78 7>879 7 :0  8080. E87/9 = 07 7=0 D @:00 /D07 7 = @8>> @> > 7 :0 => 870 8 0;8  8 D>. E87/9 =  7=00 D = 7 D08 /0/= 7 >?< />9 D >D >0807<8  <8 #. KD = /<8 =/<D D08 /0/= D /9> />7 @ D <> D  />7> /<0 /:9.

1.3 ;:ra Š;  0 /9=  0D @ <8 87/9  D7/9. Š;  =0 D D8=8 77 7 > 0 /?8 @ 87/9>  D7/9> />7. RD :; > <7  @<= D >/0 7>H @ 87/9>. K>H  0  7 D /?8 8;9 DD0 :; D /@<D D8 @>00.

1.4 O,r ,-+, + 9:ra, O0<8 07=0  :;0 => H=0 =>/08=0 D8 D D>. O0<8 07=0    7 8;9 / 8 :0  87/0<8. Š;0  @@8 8;9 87/9 D8 :;. M8 ==0 @ 87/9> =D 8 =< 87/9 > 7 :;0 8 @@> /=0 0<8 07=0 8 >@> > D> = 87/9. P9= D7/9 >@ :;0  08=;:  > 88 0<8 07=0.

3

1.5 Kr*,aa/a ) 8=08> D =08> @D8 <D => @/:< = @ />H<8 87/9  8< @8. K/08@  /9D> /9=  0D 7 = 7=0 D = /<D  /7> 08 @/=  7>879 7 7D  :; @ 7>  7>H 8/@80. I7  9  =0 0D  087 7/08@ => = /8 D=0H8 7@ <. O< /8 /@@ => @ /7>: D = /D =0>? 7/7=8=0 7/0. )=D 8 /D8=0 /@8<8 8/0=7 8 0  <8 /70H7 =8 @ 7/08@>. K@ =0> 8 <D @/:< => D<@ D8 @ 7/08@> @ < 0. T7 /: <7 <D => @/:< =08 D<@ > 0> =<>.

4

2.Kr*,6ra7ja -r/ +,rj< 2.1 S,ar E6*a, N8 /@80 07=0 7 =D 7/880 7/0 /0H @ /0=7 D M80 K>;> 8 > /? K8>0/- II / =7 4.((( D8. O7 1'(( D8 / 8<  K8>0/< /=  =90 8 > <0 =< =/D. K :0  890 ; 07  7=0  <7  8H8 = D /7 @8H8 80/=. O< 0D 87/9  / @8 :; 7 =<7> :;> > ==0> @8> =  770 @ D>>.

Slika 1. Simboli uzeti sa groba Khnumhotepa II

K7 = /0=7 7>0> @< @8<8 ; /=0 =< H:?. O< 0D 7/9   0<8 7 070 @ 8 7 => > D H0>  /:>. P=0 877 >?8=0 @:0 => E/?8 7=0 ==0 87/9. N<<08 =>  D @:00 8;9  =< =7 0> D H8 >D. %> 80/09 /0=7 7/0  D => 78<89  D D> ;8 @D =< =/=. O< @D < =H8 ;8 7/7<8 @7> 7 = 7=0 >  7 =<8 8 D7>80> /<8 70>#. E/0=7 7/0  07  0 8H8 D 78<89 /=8> D> /7@>>?  D =>  D /:> 8 <: 8<> D D>.

5

2.2 Gr=-a O7 5(( D8 / 8<  S/089 => @< > / 8> S90 7 = 7=0 @ =8  /8 08 />7. O< =/<>  /= H7 =0H>0 P>0. P9  /:9 />7  => 0 =0 98D  S90 # = =0 /H87. T8=/@9  /:08 770 0<8 07=0 => =08 .

Slika 2. Primer šifrovane poruke

S90  / 08=/@98 :; D = =<7 :; ==0 8 D=D @87< >=0 D 8 = @87<.

2.3 R N8 @/=8 <8 >/0 7/0 D@ D J> C@ / 7 2(((( D8. C@   78D80 =7 <=7 7  : / @ =>8> 7>879> = =< 0>/. P   0 D => =89 08 <8 />7 H=0  @<8 D =08 8/0. C@  @< 0D> @8 :; 7   D @8 =< D> =<. JD8 8 7 => @8 @8>  => D D:;>> 08 />7  = 0 08 />7 8=>  @8 8/0>. O<  D =7 <=9 <7> /D8=0 07 0.

6

Slika 3. Primer šiforvane poruke

2.4 A>r,?Vžra 9:ra @A>r,V6r *BrC SD8 14(( D8 H<7 / 8> L8 B00=0 A0 @=  ==0 87/9 7=0? :;8 D=7 @ @8> :;=7 ;0.  T7 15(( D8 B= % V8 /0? A0< =0 /;0=7 :; 7  :;87 7 ? 0 /@80 7 V8-< :;. O< :; D =7 7 C@< :;87 = :0 8 7>H 07 /9= 87/9. O< :07  8@<8 V8-< 0. T = ==0 D 26 770 = @H0 /9.

Slika 4. Šifrarni disk 

N / ATTACKAT%A&N O= 7 87/0> />7> D 7>H8> H  /8<  =< D7 = D>8 8 /7/ = 0<8 07=0. N / LEMON 7

LE!"LE!"LE

O0<8 07=0 ATTACKAT%A&N K>H8 H LEMONLEMONLE Š;<8 07=0 L+FOPVEFRN"R

N / K>H8 H C"IFFRE E87/9 VIGENERE /=0 +POJSVGG K70 0<8 07=0 V  @88 = 770 > D<>? D>  > 78 = /< 7>H8 H 770 C. SD? 0<8 07=0 I   @88 = 770  D<>? D>  78 = =D? 7>H8 H 770 "  07 D. A7 = =< 770 7>H8 H =7=0 8D =D? 770 7>H8 H   /< 7>H8 770.

8

Slika 5. Primer poruke u Vignere-ovoj tablii

2.5 "ž:r+ 9:rar ,=a- @ JDr+ B *BrC  T7 1$(( D8 H7 D<87 T= %;=8  @> 0H7 @ :;<8 7  8@<8 %;=8< 0H7. TH7 = ==0 D D<8 98D = >/ > =D8 7@ 7> /@ @D8 9<. C8D   /D8 8 26 8 98D D87 :8. N 0H7> = 8@ 26 =< 8=7 ;0  8 =<7 =08 D=7 8@ = 26 D87 7<D0?.

9

Slika #. $%e&ersono' to(ak 

P:9  /9 />7 =>  0 =0 0H7< D   D D:;>> />7>. B7 = :;> 07 :0 = D=7< 0> > D8 D >? 26 D  D = 0<8 07=0. P9 />7 D:;> />7> 07 :0 0 D=7 > D8 D> D D :;0  878 0 = 0 > =0 25 D 87 07=0 7  ==  8 /D=0< 0<8 07=0. AH7 <=7  < 0H7 /H D 7=0 07 7 1'22-1'23 D 1'42 D8.

3. Kr*,6ra7ja < I +,+- ra,< 3.1 Zra T6ra @ ra ,6raC C8< 0 =>  @ 08> 7>879> @> =70 NH7 / A0> C8  8H7 =D > M7=7> "8 <8 E7D. T  =D /8>D> D M7=7 /<0 =< 10

00 N< M7=7 A@8>  T7== >77 = /D> NH7. M7=7  @7>H D 0 8   >?  H7 /8 D />@ =< <: 00.NH7  /70H8 @0< D M7=7 D < 0 SD88 AH7 %<. ) < 7D  0 /=0 /< =<0=7 0  <?  8 <>89>. S< D 0 08>07 SA%  =0 8>08. T => D:;< B08=7 8>H89 @ 07@<8 = 4(. B089 => /= SA%-> D7D8 0 24 ;> 1'1$  <? 6 / =0 D8 SA%  < 0 NH7  88 =<@89.

Slika !. "odirani i dešifrovani #imermanov telegram

3.2 B8,a d ,a-r+ K7 = /< =<0=7 0 8=0< < => = / > 7>879. S7 =<7 0;8=7 /@< 7  8/<8 >=/:8  /=08 D =08 NH7 7 => @8 =<7 77.

11

K8D80  7/08 L>= ==  /8 7 ? 0 =7:?8  @7 H7 8D89. P8:  , H<7 7 => 7>89 /7 D 8 0 @7> 07 D 8H7 => 8=>  D D7D> 0  @7. ) 07> 24 77 => 7=0 < @7 7 87/9> /D8=0   8 =08 SA%-. ) 7> D $2 N9 => = /<>7  8< =<@89 =>  8/D8>0.

4. Kr*,6ra7ja < II +,+- ra,< 4.1 E6a E8  78=0>=8 1'23 D8 D =08 8H7 /8@H A0> Š>=. E8  => @ :;<8 D 0;=7 />7  7=0 = 07 D> =<0=7 0. E8   0=00>> D 26 =<  26 =9 7 => /D=0< 1 D =<. E8 = ==0 D <: <7 0H8 3  4  D 0=00>. Z / <7 /=0 => 6 >?8=0 D = 3 <7 D<D> > @H0 / :0 @8H D /=0 H7 1(5456 789 :;. S<7 <7   D = /D= 8 D8> D 26 /H08 / > @<=8=0 D />7 :0 /@<D 1$5$6 @H0 /. K80708 0  /@<D 7 164(3,,$5 @H0 789.

Slika $. %nigma

12

4.1.1 P89/ D 8

Slika &. Prinip rada enigme

S<7 D> 8 0=00> /<@8  = 0 >@ /? 7. N >@ > 0> = / >@8 =<  7 @@ = D =< =7<8 /?> 09 /=7<8.

Slika '(. )otiranje i promena tablie preslikavanja

P< >=/:8 8/D 8 8> @<:  /=7 7/0; M8 R<=7  8< 0 1'32 D8 = :8 /D 8@< 7/0-. N<> :8>  >=<: 08=7 7/0;  00H A8 T>8. RD< 8 =< :8 A8  D< > /7> BH = =< 0 7/0; / => 1'3' >=/ D @> :;<8 />7. P9= D B = @ 8 09 D 8. P<  /D 8@< V90 8/<8  1'4( D8  @  7 1$, />7. N9 => 7>H< @ D:;<8 8 8 =<7 24 = 0 N9 => DD : 2 0 @ :;<8.

13

4.1.2 P89/ 8/D 8 8> V: 8 3 8H8  0  1. N/D 0D D<=0>7 7>H- @=8< = 8 /9D>8 :9 8H7 <8 =8 H => D/0 :; D< />0 /8<8 7>H 2. %708 8@ :;0- 0D 0  /8 @ C==>= @ 8/D 8 :;> F= 3. N/D 0D /D/=0<8 07=0- C= P 7:8 C= RH &00<= =7 P0/=0< = D  D < 07=0 >9 > :;8 8@ 7 :0  QFZ WRW IVT YRE SXB FOG KUH QBA ISE

 T  >D0 = 7 8 D D /7/8 770. R&I VT* RES +BF OGK )" BAI SE &ET TER VOR "ER SAG EBI SKA *A SD 0 >0<D0 D  /=0 08=;9 7 /=7< D8 @87 > D> @87  7 => 88 /0. 123 456 $,' (12 345 6$, '(1 23 R&I VT* RES +BF OGK )" BAI SE &ET TER VOR "ER SAG EBI SKA *A

14

N78 0 7=0 /H> GD8 &98-.

Slika 11. )i&rarnik upari'an*a1

4.2 P/  :8 7> => 78=0>= J/89 > D> =<0=7 0> > /7>:> D 7/> 8> D N9. P>/  8/<8 /?> /7DH 7 => = 8H:? 7=0 @ >08 0;8=7 =8.  T7 D> =<0=7 0 J/89 =>  8>=/:8 > >8:0<8> =< :8 @ 87/9>. T8>08 8 D8 7/08 />/ :8 8 /88.

1 http://www.ellsbury.com/bombe1.htm 15

Slika '2. Purple mašina *a enkripiju

K/0; @ SA%- 8=>  87 < D D7/0>> />7  J/89. & FD8  78=0>= :8> 87 />/-> @0 :0 8 @8 77 />/ D   8 7> 8< 0 >=/ D =@8 0D> 7>  7=0 />/  8/< => D>H> :8> @ D7/9>. O<  / SA%-> D D /=0>/ /8=7 D/0=7 08 > D> =<0=7 0>.

5. Sara -r*8ja ! I d 5.1 O?T *ad O8-T /D 0 @ 87/9>  /88 8 1'(( D 7  8>7 /7@ 7 8=<>. O< 0  8@<8 G0 V8. Z:00 8-0 /D =8 = 8 D<8> 7>H 1((Q =>8. O< 0  /808 7:?8 D>8 DD07 +OR# D 78> 80 =8<8 07=0 = 80 7>H. K>H 7 = 7=0 @ 87/9> 07 = 7=0  @ D7/9>. P 16

Slika 13. !ne+,ime pad implementaci*a kori-en*em modularnog dodatka

5.2 P+r Gra,r @PRNGC P=>D-R8D 8> 80  0 @ 8=8 8@ < H =8 /< =<=0< =7<89 8=>H8 <. Č7  /D =>8=0 PRNG 8 1((Q 8=< D 8  D @D D<8> =>8=0 7D = 0H8 /80>. PRNG 7 => @8H8 D @:00 7/0> 8@<> = C/0/ S9> P=>D-R8D N> G80 CSPRNG=#. CSPRNG= > 7<00 7 PRNG= 8>. O8 > D /> =D?-0 0=0 7 > D0 /< k  0 8 /=0 /8-< 0 7  D /D<D 71#0 0 = <<08? >=/ <? D 5(Q.

5.2 S,r8 K E8r*, @ Pra,?KC? Pra, -j<= S<7 0D 87/9 @0< =/98 08 7>H 7 / 0  0 =>8 =8<8. O<  /D =0H8 7>H 87/9. S0H8 7>H 87/9=7 :;87   7 0 > 7  7>H @ 87/9> 0<8 /<@8 = 7>H 7 = 7=0 > D7/9. %  = @:00 8:0 <D8 @ < 7>H =  D0 =<7 H8> @D8. 17

Slika 14. /ra'a ko*a se otkl*u(a'a i diza*nirana samo za *edan kl*u( 

 J: D8 0D 87/9 =0H8 7>H  7 :; 7 <: /9> 8D 7=8 0<. B7 :; >@ =0 0< 0<8 07=0  @@ D<>? =0 <H8 12,0# 7 :;87. P/>8 7 :; >7>H>> B= T=%ES  AES.

#. Sara -r*8ja ! II d #.1 A+,r8 K E8r*, @ P<>8?KC K/0; > <   1'$( # =<0 => D > 9> =8 />7 @D8 @ /0D8 ==087 = /9 D  0 ==0 7 7=0 @H0 7>H< @ 87/9>  D7/9>. ) /8> = =0H8 87/9 7>H ==0  >/< < 7  D8 7>H @ 07>H<8  D> 7>H @ @7>H<8.

18

Slika 10. /ra'a ko*a se otkl*u(a'a i zakl*u(a'a sa razli(itim kl*u(e'ima

#.2 "H?a K E8Ba6 O< 7/0;=7 /07 7 D@<< D D< =087 @ D8 @88 D8  D> >=/=0< =>8=0 7>H @ D8 7 = 0/H8 7=0 7 =0H8 7>H :;. O< /07 = @=8< 8 7=/8898 ;>879 H>88 8  8 7D D=708 0.

Slika 1#. $ie+ellmano' kl*u( razmene protokola

N < =9 => /7@8 79 @ >=/=0<8 7>H 7@ %U"8< @8 7>H. A9  D >=/=0< 7>H = B /< 77  /D:<8 <   /. B = D>H> @ . N78 =8 <8 7>H < =<7 =087  7>890 7@ K 7 87D 8 /=@ 7@ D>  8 /0D8 D08=8.

19

#.3 RSA E-r*8ja RSA  0 @ =0H8> 7/0> 7  8=0 1'$$ D8. ) < 0> <8> >> <D <7 /=0 <. S>8=0 < ==0 @=8< = 8 =8=0 ;70@9 <7 <. OD<8 88 />7 8 =8<> :;0  7>H 7<<808  ;70@9 /@<D D< <7 /=0 . K>H = 8: 07 :0 = 7 @ D< <7 /=0  A  B /< /8 0 D<  C @0 H>8 % 7 = D % C-1# W B-1#  @0  =>H8  E 7  D <8 7>H @0 H>8 /:8 E>7D<  0. 08 7>H. S 0 <8 7>H< => C  E.

$. S,6a6ra7ja S08  ; 7/0 7 >> /D07 > D> D> 8 8/08 8H8 >=0 >/:<8 87/9. V /=0 /809 =08  0 8<D< =0 >/=8 @> <D< 8 07=0 > 87 D7>80>. V7 =7 =08 @<:8 = H>8 0/H8  @8 8 >D=7 8DD< <.

$.1 U6radja +,6a6ra7j @S,6a6ra*B8 E>dd6C

20

Slika '!. +ajni dokument ugra,en u sliku desno slika levo je pre ugradnje dokumenta

N =9 = <D D7>80 7  D =7. S7 <  88 =7 =7 D=8 /7@> @D =7 /= >D8 D7>80 > =0>. R@7>  /00 >77 >/D 88 7D<  =7.

21

%. M,d -r*8j < >8=0< K<808 H>88 = 7=0 /?> 7<808 H>8 OD8=8 7<808 /9=# 7 7=0 ;88 7<808 87 7 :0  7<808 =>//@9  7<808 >:<8. MD8 H>8 H><> /D07 > 88 7> D8=8 =7>/> 8>   D890@<. B0# RH>88 > < ==0 = @<< 0 / 0. K<808 H>8 H><> /D07 >@ /? 7<808 =>//@9 > <: =08. O< =08 = H><> > K<808 0  0@<. 0-<. Z<=8 D 7<808 D@8 =<7 0  =H><0 =0 8>H7 <D8=0 DD8 O< >?< H>88 < 877 D< <H8  D 0D988 88 /9== 8 08 08@=0

Slika 1. Pr'i komerci*alni dostupni k'antni procesor $+5a'e S6stems7

S7 1,. P7@> /< 798 7<808 H>8 8 =<0>. N< >?8=0 => 7 1((( />0 8 D D8 /9= = 08@=0. K<808 /9= /@<D8 D8= => <   8> 8> H>8=7> <H8> 7> /9= = 08@=0 >. K/0 = <8 7>H = =8 8 0 D => 7/>0 =/ D @H>8> D=708 0  /8 ;70@9.

22

P< D8H8 /7@> < 7  /08 D = /78  /@80 0 @ @H>8<8 /8 ;70@9 8 88 ;08 /9=>.  JD8H8 D< /7@> 0 07<8 D =08 P0 S 7 @H>8< /8> ;70@9> > 7<808 H>8>. )  =>H     0< > >. %  =<0 =8> 00=7 7<808 H>8 >@ RSA < /DD8 /8>0. RSA-64(  = 1'3 9;  ;70=8 = ,( 2.2G"@ 07 /D D 5 =9. A7 < RSA  >D /88 8 7<808 H>8> D87 <H8 S< 0 /7@> D   ;70=8 @ 8 D 1$ =7>8D. B< @ 7   /08 D D8 D = @H>8>   D = @H>8> > 7> D 877 =0  8>0 = /0/>8 @<8 7<80 H>8.

23

(.Za-j<=a-  P=0 =0=7 :8 7 /7@> D @ = 8H 87/9  D > <8 =8@. S0>D8 7/0  87/9 @  D H =<> D8>  D  8/D8 =D=0< D /< > 8/0=7 8=08 =<0>. R@><8 87/9 07  /?  8D<D> 7D @<8 /<08 /D07  8;9. Č7  7  < 8-0H7 8: 7>879 >=8 = 78=080 /0. O= 7 /0 8:> 7>879> > D >7>H>> <D 8080 /<D 7 7D<9 D8000  D>. O>7 7:?8 7/0 @ @D8> 7>879>  D = =H>< D 8/DH 7 > D 8 >7D> 8;9. K/0  8 > 8 @ @0 :0 78 <D  D > >?8=0 /=0>/ 8: /=0 />7. M8 :/7>> D SD88 AH7 %< 8=> /08 < @78 @0 :0 NSA  @< 0D 7/08@ 7 @> =< 0D 87/9.

24

L,ra,D8D8>80 X3Y 00/=8.7/D.7E8>=9/90# X4Y 00/.8.>0.D>[89D8T>0=E89/08R=9R<./ D;  X5Y 00/=8.7/D.7C/0/ X6Y 00/=8.7/D.7RSA9/0==0# X$Y

00/=.9<.2((1111612223300/0.9=.0.D>[<=0= //./D;  X,Y 00/=.9/0.=901/=8008=C/TP=80088./D; 

25