Advanced Encryption Standard symmetric block cipher

What is this article about

Good day, reader. In this article I would like to talk about one of the most common symmetric encryption algorithms - the AES algorithm.

---

Introduction

80- DES (Data Encryption Standard). 90- . , 56 . , .

1997 NIST (National Institute of Standards and Technology,) . :

• 128- ;

  
  
  
  
  

• 3 (128, 192, 256 ), ;

  
  
  
  
  

• , , ;

  
  
  
  
  

• , ;

  
  
  
  
  

, AES – Advanced Encryption Standard, Rijndael ( AES). , . , , , .

, .

, AES , F(2⁸). , , , . :

• xor. , P = { p_7, p₆, p₅, p₄, p₃, p₂, p₁, p₀ } Q = { q₇, q₆, q₅, q₄, q₃, q₂, q₁, q₀ } R = { r₇, r₆, r₅ , r₄, r₃, r₂, r₁, r₀ }, r_i = p_i xor r_i .

  
  
  
  
  

• . : p(x) = p₇x⁷ + p₆x⁶ + p₅x⁵ + p₄x⁴ + p₃x³ + p₂x² + p₁x + p₀ , F(2⁸) m(x) = x⁸ + x⁴ + x³ + x + 1. , , F(2⁸), p(x) q(x), m(x) p(x) q(x), r(x) = p(x)q(x) mod (m(x)), r(x), 8- F(2⁸).

  
  
  
  
  

AES c 128 .

16 , 16 , , 16 . 4x4 — state. state 2-4. , :

1. - KeyExpansion;

   
   
   
   
   

2. - state ;

   
   
   
   
   

3. 9 , :

   
   
   
   
   

   · SubBytes

   
   
   
   
   

   · ShiftRows

   
   
   
   
   

   · MixColumns

   
   
   
   
   

   · AddRoundKey

   
   
   
   
   

4. , :

   
   
   
   
   

   · SubBytes

   
   
   
   
   

   · ShiftRows

   
   
   
   
   

   · AddRoundKey

   
   
   
   
   

:

• SubBytes - state S-box. b = (x, y), x 4 b, y — 4 . S-box 16x16 : b' x y S-box b.

  
  
  
  
  

• ShiftRows — state. , 1 , 2 3 .

  
  
  
  
  

• MixColumns — state . state. , .

  
  
  
  
  

• AddRoundKey — state XOR.

  
  
  
  
  

• KeyExpansion — , . 44 (w_i): 4 4 10 . , 1408 .

  
  
  
  
  

  Rcon :

  
  
  
  
  

  • .

    
    
    
    
    

  • i 4, w_i =SubBytes(RotByte(w_i-1 )) xor Rcon_i/4 .

    
    
    
    
    

  • : w_i = w_i-4 xor w_i-1 .

    
    
    
    
    

RotByte : { x₀, x₁, x₂, x₃ } → { x₃ , x₀ , x₁ , x₂ }.

, 2 .

, , . , :

1. - KeyExpansion;

   
   
   
   
   

2. 9 , :

   
   
   
   
   

   · AddRoundKey — state ;

   
   
   
   
   

   · InverseMixColumns — state;

   
   
   
   
   

   · InverseShiftRows — state;

   
   
   
   
   

   · SubBytes — state InverseS- box;

   
   
   
   
   

3. :

   
   
   
   
   

   · AddRoundKey

   
   
   
   
   

   · InverseShiftRows

   
   
   
   
   

   · InverseSubBytes

   
   
   
   
   

AES

state— 128 3 AES. : AES-192 192 — 12 , AES-256 — 256 14 .

. , AES-256 . , , .

, , N_k - , N_b - N_r - .

AES

. 2 .

1. .

   
   
   
   
   

   , . , , .

   
   
   
   
   

   , ( ), AES , , .

   
   
   
   
   

   :

   
   
   
   
   

   · , . , , , .

   
   
   
   
   

   · , .

   
   
   
   
   

2. .

   
   
   
   
   

   . , , .

   
   
   
   
   

   :

   
   
   
   
   

   · — .

   
   
   
   
   

   · .

   
   
   
   
   

, - ?

, .

32- : w₀, w₁, w₂, w₃, …, w₄₀, w₄₁, w₄₂, w₄₃, w₀, w₁, w₂, w₃ - 128- AES, w₄₀, w₄₁, w₄₂, w₄₃ - . w_i = w_i-4 xor F_i(w_i-1), F_i - , KeyExpansion. w₀, w₁, w₂, w₃ .

, AES-128. : w_j = w_j+4 xor F_j+4(w_j+3). j = i - 4 . , , w₄₀, w₄₁, w₄₂, w₄₃ ,c w₀ .

AES-192 AES-256. , 256- AES, AES 2²⁵⁶ 2¹²⁸, .

AES

:

• — .

  
  
  
  
  

• — .

  
  
  
  
  

• , : , , square — .

  
  
  
  
  

• Byte-oriented structure, which gives good prospects for implementing the algorithm in future processors.

  
  
  
  
  

• High performance across multiple platforms.

  
  
  
  
  

Conclusion

In this article, I tried to describe in detail the principle of the AES algorithm. I would like to note once again that the algorithm really deservedly won the competition for a new standard due to the large number of its advantages. Thank you for your attention.