Vazirligi mirzo ulug„bek nomidagi

Affin tizimi

Affin tizimidagi Sеzar usulida har bir harfga almashtiriluvchi harflar maxsus formula bo‗yicha aniqlanadi: (a·t+b) mod m, bu yerda a, b - butun sonlar, 0≤a, b

m=26, a=3, b=5 bo‗lganda, quyidagi jadval hosil qilinadi:
Shunga mos ravishda harflar quyidagicha almashadi:

Natijada yuqorida kеltirilgan matn quyidagicha shifrlanadi: C=PFXJDZSR

Shifrni ochish formulasi quyidagicha: 𝑀 = (𝑎⁻¹⁽𝐶 − 𝑏⁾)𝑚𝑜𝑑 𝑚. Bu yerda a^-1 qiymat a sonining mod m bo‗yicha teskarisi, C – shifrtekst.

Nazorat uchun savollar:

1. 
   Affin usulida kalit nimadan iborat?
   
2. 
   Kalit qaysi sondan qaysi songacha oraliqda bo‗ladi?
   
3. 
   Shifrlanadigan matn harflari nomerlanish tartibi qanday?
   
4. 
   Shifrlangan matnni ochishda modulda manfiy son chiqsa nima qilinadi?
   
5. 
   Kalit har ikkala tomonda ham bo‗lishi shartmi?
   
6. 
   Kalitsiz qanday ochish mumkin?
   

Mustaqil ish uchun misollar.

1. 
   a=5, b=11, n=26: C= zxuyzyptlnxlaz, M=?
   
2. 
   a=5, b=12, n=26: C= jakdeqtmuumeczm, M=?
   
3. 
   a=7, b=12, n=26: C= smimlmlmbnmzolq, M=?
   
4. 
   a=9, b=11, n=26: C= frwrahgfthigfz, M=?
   
5. 
   a=11, b=11, n=26: C= clcflulgabuly, M=?
   
6. 
   a=17, b=11, n=26: C= rfayryjhluhnyr, M=?
   
7. 
   a=19, b=11, n=26: C= mlerwlirwhzl, M=?
   
8. 
   a=21, b=11, n=26: C= olonlctzxijxixzc, M=?
   
9. 
   a=23, b=11, n=26: C= plrglgnheljq, M=?
   
10. 
    a=3, b=11, n=26: C= zjyubznvtgjqjul, M=?
    
11. 
    a=3, b=14, n=26: C= ehanoqmebtmlmygo, M=?
    
12. 
    a=5, b=17, n=26: C= wjdatryfdaoreluf, M=?
    
13. 
    a=7, b=19, n=26: C= otpwdistijtlxixpq, M=?
    
14. 
    a=19, b=17, n=26: C= rlrssrcnenkrgrcnvu, M=?
    
15. 
    a=25, b=11, n=26: C= slqtdnlhsdalid, M=?
    
16. 
    a=23, b=12, n=26: C= swpcmrokwjwh, M=?
    
17. 
    a=15, b=14, n=26: C= wijobwxwmwbnxoje, M=?
    
18. 
    a=17, b=8, n=26: C= zyliamtgivwmlciteinil, M=?
    
19. 
    a=19, b=17, n=26: C= krgrcnvuzrknsrc, M=?
    

7.