Vazirligi mirzo ulug„bek nomidagi

Shifrlash:

1. 
   BESH so‗zini ASCII jadvali yordamida bit ko‗rinishga o‗tkazamiz: 01000010 01000101 01010011 01001000.
   
2. 
   Bitlardan iborat matnni 8 bitdan bloklarga ajratamiz va har bir blokni o‗nlik sanoq sistemasiga o‗tkazamiz: M₁=66, M₂=69, M₃=83, M₄=72.
   

3. 
   C
   

= M^e modn
formula yordamida shifrlanadi:

i i

= M^e modn = 66¹¹ mod1517 =

66 ⋅ ₍66⁵ mod1517₎2

C

mod1517 =
^{1 1} ( )
= ₍66 ⋅ 532² mod1517₎mod1517 = ₍66 ⋅ 862₎mod1517 = 763,


C = M^e modn = 69¹¹ mod1517 =1441, C = M^e modn = 83¹¹ mod1517 = 821,
2 2 3 3


C = M^e modn = 72¹¹ mod1517 =1097.

4 4


Hosil bo‗lgan shifrtekst quyidagicha:

Shifrni ochish:

C =_{763,1441,821,1097_}.

Modul son n = p ⋅q =1517,
(^{p −1})^⋅(^{q −1})
ko‗paytma bilan o‗zaro tub

bo‗lgan e=11 ochiq kalit, matn uzunligi L=8 bit va bizga ma‘lum.
C =_{763,1441,821,1097_}

1. 
   ^{e sonining} (^{p −1})^⋅(^{q −1})
   

modul bo‗yicha teskarisini topamiz:

d = e⁻¹ mod₍₍p −1₎⋅₍q −1₎₎ =11⁻¹ mod1440 =11³⁸³ mod1440 =131

2. 
   
   i i
   M
   

= C^d modn
formula yordamida shifrni ochamiz:

M = C^d modn = 763¹³¹ mod1517 = 66, M = C^d modn =1441¹³¹ mod1517 = 69,
1 1 2 2


M = C^d modn = 821¹³¹ mod1517 = 83, M = C^d modn =1097¹³¹ mod1517 = 72,
3 3 4 4

3. 
   M_i larni o‗nlikdan ikkilikka o‗tkazib, ASCII jadval yordamida harflarga o‗tamiz va natijada M=BESH so‗zi paydo bo‗ladi.
   

Mustaqil ish uchun misollar.

1. 
   n=1517, e=11, C={ 413, 665, 620, 30 }, L=8 bit, M=?
   
2. 
   n=1517, e=11, C={ 593, 27, 763, 30 } L=8 bit, M=?
   
3. 
   n=1517, e=11, C={ 763, 30, 593, 27 }, L=8 bit, M=?
   
4. 
   n=1517, e=11, C={ 1270, 1408, 902, 665 }, L=8 bit, M=?
   
5. 
   n=1517, e=11, C={ 902, 1408, 620, 30 }, L=8 bit, M=?
   
6. 
   n=1517, e=11, C={ 13, 665, 1408, 1390 }, L=8 bit, M=?
   
7. 
   n=1517, e=11, C={ 1437, 1408, 902, 285 }, L=8 bit, M=?
   
8. 
   n=1147, e=11, C={162,881,767,753,162,516,881,753,139,881,894,
   

162,1109,894,229,881,162,894,890,162,1109}, L=8 bit, M=?

9. 
   n=1147, e=11, C={778,890,753,890,946,778,881,946,1109,139,881,
   

231,881,778,516,162,881,778}, L=8 bit, M=?

10. 
    n=1189, e=11,C={1071,416,529,50,368,1096,801,55,368,368,1096,
    

148,55,575,646,628,1096,495,50,529,352}, L=8 bit, M=?

11. 
    n=1189, e=11,C={220,1096,451,416,529,352,416,801,449,86,1096,
    

575,416,628,575,50,801,220,1096,451,368,50}, L=8 bit, M=?

12. 
    n=341, e=13, L=6 bit, C={ 335, 161, 130, 276} M=?
    
13. 
    n=407, e=13, L=6 bit, C={ 280, 334, 235, 315} M=?
    
14. 
    n=341, e=13, L=6 bit, C={ 335, 232, 282, 226} M=?
    
15. 
    n=407, e=13, L=6 bit, C={ 280, 165, 261, 348} M=?
    
16. 
    n=341, e=13, L=6 bit, C={ 246, 112, 1, 293} M=?
    
17. 
    n=407, e=13, L=6 bit, C={ 280, 23, 185, 94} M=?
    
18. 
    n=341, e=13, L=6 bit, C={ 246, 198, 1, 226} M=?
    
19. 
    n=407, e=13, L=6 bit, C={ 288, 334, 235, 310} M=?
    
20. 
    n=341, e=13, L=6 bit, C={ 246, 161, 168, 130} M=?
    
21. 
    n=407, e=13, L=6 bit, C={ 280, 165, 312, 310} M=?
    

22. 
    n=341, e=13, L=6 bit, C={ 178, 161, 191, 151 } M=?
    
23. 
    n=407, e=13, L=6 bit, C={ 174, 23, 258, 382 } M=?
    
24. 
    n=341, e=13, L=6 bit, C={ 208, 208, 80, 132 } M=?
    
25. 
    n=187, e=13, L=6 bit, C={ 21, 21, 25, 33 } M=?
    
26. 
    n=209, e=13, L=6 bit, C={ 98, 98, 25, 154 } M=?
    
27. 
    n=209, e=7, L=6 bit, C={ 36, 19, 4, 2 } M=?
    
28. 
    n=209, e=13, L=6 bit, C={ 81, 98, 25, 204 } M=?
    
29. 
    n=187, e=13, L=6 bit, C={ 169, 21, 25, 6 } M=?
    
30. 
    n=341, e=7, L=6 bit, C={ 181, 145, 192, 271 } M=?
    
31. 
    n=187, e=7, L=6 bit, C={ 104, 47, 181, 7 } M=?
    

5.