Deskripsi dasar-dasar konversi AES crypto

• simetris
• asimetris

• gumpal
• Streaming

• publikKey
• privateKey

• sistem bilangan biner
• sistem angka desimal
• bit
• byte
• XOR (^)

Konsep matematika dalam rijndael:

• GF bidang (2⁸) adalah sejumlah elemen hingga, yang hasilnya adalah tingkat alami ke-n dari bilangan prima. Dalam kerangka kerja GF (2⁸), operasi penambahan, pengurangan, produk, divisi yang dilakukan secara sewenang-wenang. Bidang GF (2⁸) pasti.
• . Rijndael [00000000₂; 11111111₂]. , x. , , :
  
  a(x)=a₇x⁷ +a₆x⁶ +a₅x⁵ +a₄x⁴ +a₃x³ +a₂x² +a₁x +a₀x;
  
  , a₇, a₆, a₅, a₄, a₃, a₂, a₁, a₀ {0, 1}, :
  87 = 01010111 ( );
  : x⁶ + x⁴ + x² + x + 1;
• . , , 1 . rijndael m(x):
  m(x)= x⁸ + x⁴ + x³ + x + 1;
• . XOR, : 1 ^ 1 = 0 ^ 0 = 0; 1 ^ 0 = 0 ^ 1 = 1, :
  
  , a₇, a₆, a₅, a₄, a₃, a₂, a₁, a₀;
  B, b₇, b₆, b₅, b₄, b₃, b₂, b₁, b₀;
  
  A = 87 = 01010111; B = 131 = 10000011;
  A ^ B = a₇, a₆, a₅, a₄, a₃, a₂, a₁, a₀ ^ b₇, b₆, b₅, b₄, b₃, b₂, b₁, b₀ = 11010100;
• . GF(2⁸) ( | -x | = x ) 8, :
  
  87 x 131 :
  (x⁶ + x⁴ + x² + x + 1)(x⁷ + x + 1) = x¹³ + x¹¹ + x⁹ + x⁸ + x⁷ + x⁷ + x⁵ + x³ + x² + x + x⁶ + x⁴ + x² + x + 1.
  . (.4):
  
  x⁷ + x⁷ = x⁷(1 + 1) = x⁷(1 ^ 1) = x⁷0 = 0;
  (x⁶ + x⁴ + x² + x + 1)(x⁷ + x + 1) = x¹³ + x¹¹ + x⁹ + x⁸ + x⁶ + x⁵ + x⁴ + x³ + 1.
  
  m(x) = x⁸ + x⁴ + x³ + x + 1 ( ), rijndael , 8, . . , . :
  
  (x⁶ + x⁴ + x² + x + 1)(x⁷ + x + 1)/(x⁸ + x⁴ + x³ + x + 1) =
  (x¹³ + x¹¹ + x⁹ + x⁸ + x⁶ + x⁵ + x⁴ + x³ + 1)/(x⁸ + x⁴ + x³ + x + 1) = |Result| = x⁷ + x⁶ + 1

:

1. keyExpansion() — ;
2. addRoundKey() — ;
3. subBytes() — state;
4. shiftRows() — state;
5. mixColumns() — state;
6. invMixColumns() — mixColumns;
7. invShiftRows() — shiftRows;
8. invSubBytes() — subBytes;

AES :

1. state
   - . [0; 255] ( ASCII Unicode). n- 16 . state ( 4 = [ [], [], [], [] ] ), 16 , 16 :
   
   
2. keyExpansion();
   AES, state. . XOR Rcon.
   
   Rcon — XOR. keyExpansion() XOR’ Rcon . — 11. 10 .
   
   

   let rCon = [
     [ 0x00, 0x00, 0x00, 0x00 ],
     [ 0x01, 0x00, 0x00, 0x00 ],
     [ 0x02, 0x00, 0x00, 0x00 ],
     [ 0x04, 0x00, 0x00, 0x00 ],
     [ 0x08, 0x00, 0x00, 0x00 ],
     [ 0x10, 0x00, 0x00, 0x00 ],
     [ 0x20, 0x00, 0x00, 0x00 ],
     [ 0x40, 0x00, 0x00, 0x00 ],
     [ 0x80, 0x00, 0x00, 0x00 ],
     [ 0x1b, 0x00, 0x00, 0x00 ],
     [ 0x36, 0x00, 0x00, 0x00 ],
   ];
   

3. addRoundKey();
   
   state , . addRoundKey XOR’ state, . ’XOR’ state , :
   
   
   
4. 
   
   10 , 10 . 9 4 :
   
   
   • subBytes();
   • shiftRows();
   • mixColumns();
   • addRoundKey();
   
   10- :
   
   
   • subBytes();
   • shiftRows();
   • addRoundKey();
   
   
5. subBytes();
   
   state S-box:
   
   
   
   State hex , : 01010011 -> 0101 | 0011 -> 53h
   
   
   
   53h edh
   
   
   S-box

   const sBox = [
     0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76,
     0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0,
     0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15,
     0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75,
     0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84,
     0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf,
     0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8,
     0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2,
     0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73,
     0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb,
     0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79,
     0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08,
     0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a,
     0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e,
     0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf,
     0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16,
   ];
   

   
   
   
   
6. shiftRows();
   
   3- :
   
   
   
7. mixColumns();
   
   . a(x) = {03}x³ + {01}x² + {01}x + {02}. state a(x). :
   
   
   
   
   
   
   

AES :

1. keyExpansion();
2. 
   
   10 , .
   
   9 4 , , :
   
   
   • addRoundKey();
   • invMixColumns();
   • invShiftRows();
   • invSubBytes();
   
   10-:
   
   
   • addRoundKey();
   • invShiftRows();
   • invSubBytes();
   
   
3. addRoundKey();
   
   , Rcon
   
4. invMixColumns ();
   
   Fungsi invMixColumns melakukan operasi multiplikasi terbalik terbalik sesuai dengan aturan mengalikan algoritma dengan fungsi konstan a⁻¹ (x) dari kolom state tertentu:
   
   
   
   
   
5. invShiftRows ();
   
   Inverse transformation shiftRows () - perubahan siklik ke kanan:
   
   
   
6. invSubBytes ();
   
   SubBytes inversi () - penggantian kebalikan byte negara, yang jelas diwakili dalam hex menurut tabel S-box invers tetap:
   
   
   

1. Spesifikasi untuk AES
2. Standar Enkripsi Lanjut (AES)
3. Tiang Galois
4. Kode siklus
5. Buku teks untuk sekolah menengah A.N. Stepanov - Kursus Ilmu Komputer - Keamanan Data Informasi
6. Cuplikan