Al-xorazmiy nomidagi tоshkеnt aхbоrоt

ij
^sij
^s 1 ^ 1 mod (x⁸+x⁴+x³+x+1);

2. 
   
   ij
   
   s
   har bir s_ij ni teskarisi bo‘lgan
   

• 
  ¹ ni b =
  

s ^1 , deb belgilab olib, bir baytdan iborat

ij
bo‘lgan b sonini uning bitlari orqali b  b₀ , b₁ ,… , b₇  ko‘rinishda tasvirlab, uning ustida quyidagi afin akslatirishi bajariladi
Cb +c (mod x⁸ +1) =b^’

Bu yerda C =

^{1 0}

1

_1
^1 1

_1 1
^1 1

_0 1
^0 0

0



^{0 0 1 1 1 1}

1


0 0 0 1 1 ^
1 0 0 0 1 1^

1 1 0 0 0 1_
1 1 1 0 0 0 ^

1 1 1 1 0 0 _
1 1 1 1 1 0 ^


-matritsa va c  c

, c₁ ,… , c₇
 =1,1,0,0,0,1,1,0 
–vector

_^{0 0
0 1 1 1 1 1}_

algoritmda berilgan o‘zgarmas ifodaga ega bo‘lib, keltirilgan afin akslantirishi

^b 

^b ^{' }

^{1 0 0}
0 1 1
^{1 1} ₀
¹  _{ }

  ^
  
^b ' 

_1 1 0 0
0 1 1 1_
^b1 
¹  ¹

^1 1 1 0 0 0 1 1^{ b 
}0 ^
_b ' ^

2
  ^{ }  
 ² 

1 1 1 1 0 0 0 1 ^b 0
_b ^' 

  ^{ 3 } _ 
^ mod
257    ³ 

^1 1 1 1 1 0
0 0 ^
_b 
₀ 
^b ' 

  ^{ 4 }   ⁴

_0 1
1 1 1 1 0 0 _
^b 
¹ 
 _' 

5
  ^{ }  
^b5 

_0 0
1 1 1 1 1 0 _
^{b 6}  ¹
_b ^' 

  _ 6 _

_^{0 0 0 1 1 1
1 1}_
^^b 7 ^
_⁰ _
_b ^' 

ko‘rinishda amalga oshiriladi.

 7 

Natijaviy b ^/  b ^/ , b ^/ ,… , b ^/  vektorning koordinatalari

0

i

b

i
^/  b  b
( i  4 ) mod 8
1 7
^{ b}( i  5 ) mod 8


^{ b}( i  6 ) mod 8


^{ b}( i  7 ) mod 8

 c_i

, i=0,1,2,…,7 ;

ifoda bilan rasional hisoblanadi.

Yuqoridagi a) va b) qismlarda berilgan barcha mantiqiy va arifmetik amallarni bajarish bilan amalga oshiriladigan o‘rniga qo‘yish akslatirishi
4 - jadvaldagi S -blok akslantirishlariga (almashtirishlariga) keltirilgan. Bu esa algoritmning dasturiy ta'minoti va apparat qurilmasini yaratishda qulaylik tug‘diradi.