Сборник трудов III международной научно практической конференции
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Table 1. The first S–box encryption algorithm AES–IDEA16–2 0x0 0x1 0x2 0x3 0x4 0x5 0x6 0x7 0x8 0x9 0xA 0xB 0xC 0xD 0xE 0xF 0x 0 0x0 1 0x4 B 0x0 4 0xF D 0x9 A 0xA 9 0xF 8 0x5 2 0xA 7 0x9 C 0x5 0 0xB C 0x6 3 0xA 4 0x3 6 0x4 1 0x 1 0x4 C 0xF 1 0xA B 0x0 E 0x3 2 0x7 5 0x7 A 0x3 8 0xC 5 0x4 3 0xD B 0x6 7 0xF E 0x2 8 0x1 0 0x4 6 0x 2 0x9 B 0x8 4 0xE 0 0x0 0 0x5 4 0xB 9 0x8 E 0xB F 0xF 6 0x6 D 0x7 8 0x7 D 0xF 7 0xB A 0xE 2 0x9 9 0x 3 0x8 8 0xF 0 0x1 4 0xA 1 0x2 5 0xF 4 0xC D 0x0 D 0x6 F 0x2 F 0x5 3 0xC E 0x2 3 0x4 5 0x8 F 0xA 6 0x 0x3 0xB 0x0 0x8 0xC 0xB 0x9 0x7 0x3 0xE 0xE 0xC 0x1 0x8 0xE 0x0 46 4 4 4 A 7 2 D 2 9 A 8 1 A E B D 2 0x 5 0x7 F 0x5 7 0xD 9 0xD 0 0xF 3 0xC 1 0x6 8 0xD 7 0xE C 0x0 9 0x7 6 0x4 A 0xC 6 0x3 5 0x3 0 0x5 8 0x 6 0x1 2 0x7 2 0x7 3 0x7 7 0x2 B 0x7 0 0x4 0 0x4 7 0xD 8 0xD 5 0x7 B 0xA C 0x9 8 0x5 E 0x1 9 0xD 1 0x 7 0xD D 0x9 E 0xC C 0x4 D 0xA 5 0xB B 0x0 F 0x2 C 0xD 4 0xD E 0x1 8 0xB 6 0x8 D 0x2 6 0xD F 0xB 0 0x 8 0xF A 0x2 0 0x6 A 0x9 5 0x8 6 0xB 1 0x9 D 0x3 B 0x1 7 0xC F 0xE 9 0x1 B 0xB 7 0x2 4 0x6 0 0x5 5 0x 9 0xE 6 0x1 6 0xD 2 0xE B 0x5 1 0xF 9 0x0 7 0xF B 0x3 F 0x3 7 0x8 5 0xD C 0x4 9 0xC 3 0x9 6 0x5 D 0x A 0x6 C 0x0 5 0xA D 0xD 3 0x2 1 0x2 A 0xA 2 0x6 1 0xE 4 0xF 5 0x8 0 0x4 4 0x4 2 0x1 3 0x3 D 0x5 F 0x B 0xD A 0xE E 0x1 1 0x5 A 0xE F 0x0 6 0x9 7 0x9 4 0x1 F 0x6 B 0x6 9 0x6 6 0xF 2 0xB 8 0x2 2 0x7 1 0x C 0x2 7 0x1 A 0xE 7 0xA 8 0x7 4 0x8 A 0x7 C 0xB 5 0xC 4 0xA E 0xE 3 0x9 3 0x8 3 0x9 1 0x1 C 0x5 9 0x D 0xB 2 0xF C 0x3 9 0x1 5 0x6 4 0x3 E 0xC B 0x8 2 0xA 3 0xB 3 0x2 E 0xC 0 0xA 0 0x0 3 0x3 1 0x5 C 0x E 0x2 9 0x9 0 0xA F 0xC 8 0x0 B 0xF F 0x0 8 0x5 6 0x4 8 0xD 6 0xE 5 0x8 1 0x1 D 0x8 C 0x5 B 0x0 C 0x F 0xA A 0x3 C 0xB E 0x6 5 0x3 3 0x9 F 0x6 E 0x4 E 0x8 9 0xE A 0x4 F 0xC 7 0x2 D 0xC 9 0x6 2 0x7 E Table 2. The second S–box encryption algorithm AES–IDEA16–2 0x0 0x1 0x2 0x3 0x4 0x5 0x6 0x7 0x8 0x9 0xA 0xB 0xC 0xD 0xE 0xF 0x 0 0xF 8 0xD 0 0xE 3 0x0 1 0x9 5 0x5 7 0x1 A 0xB 1 0x6 B 0x8 8 0xB 5 0x0 E 0x7 7 0x6 D 0x2 3 0xF 5 0x 0xC 0x3 0x5 0xC 0x3 0x2 0x1 0x1 0xE 0xF 0x9 0x6 0x0 0x5 0xB 0xE 47 1 F 9 3 6 A 8 6 F 4 1 A E 7 D 8 A 0x 2 0x9 7 0xE B 0x7 9 0xF A 0xA C 0x1 5 0xC E 0x0 8 0x2 6 0x4 B 0x1 2 0x0 9 0x2 4 0x1 3 0x7 D 0x9 3 0x 3 0xD 3 0x3 B 0xA 1 0x7 6 0x6 7 0x2 2 0xC 5 0xC 0 0x4 F 0x4 2 0xB 3 0xC 3 0x7 A 0xE C 0xC C 0x6 9 0x 4 0x2 7 0x2 F 0xD F 0xE D 0xF B 0x0 C 0xB 4 0x1 0 0x1 B 0x5 8 0x7 B 0xD A 0x8 4 0xD 5 0x4 3 0xF E 0x 5 0x0 D 0xA A 0x9 E 0xB D 0x3 D 0xF D 0x5 0 0xA 2 0x4 1 0xD 9 0x2 E 0xD 2 0xE 2 0x2 5 0x3 E 0x9 4 0x 6 0xB C 0x3 7 0x3 5 0x2 C 0x5 B 0x3 3 0xF 7 0xE 8 0x9 C 0xA 6 0x1 4 0x4 C 0x9 1 0x8 9 0x9 B 0xB F 0x 7 0x8 7 0x8 C 0xC 7 0xC D 0x6 F 0x1 1 0xC 4 0x4 4 0xA 4 0x8 1 0x9 9 0x2 B 0xC 8 0x6 1 0x8 3 0x3 6 0x 8 0x1 E 0x7 C 0x5 4 0xA B 0xE F 0x3 4 0x8 A 0x1 9 0xA 7 0xC 1 0x5 A 0x9 F 0x2 9 0x6 5 0x7 1 0xA E 0x 9 0x6 4 0xA 5 0xB 9 0x5 E 0xB 7 0x1 8 0xE 5 0x1 C 0x0 0 0x2 1 0xE 9 0x8 5 0xD 4 0xF 9 0xA D 0x8 F 0x A 0x4 9 0xE 1 0x4 E 0xB B 0x7 E 0x5 9 0x7 0 0x7 3 0x6 0 0x2 0 0xF 2 0xE E 0xF 3 0xB E 0x0 4 0x8 B 0x B 0x9 8 0x4 5 0xB A 0x9 0 0x4 7 0xE 7 0xA F 0xA 9 0x8 6 0x5 6 0x5 2 0x6 C 0x3 F 0x1 7 0x7 8 0x3 1 0x C 0x6 3 0x9 D 0x6 6 0x5 5 0x2 A 0xD 7 0x0 B 0x2 D 0xE 6 0x4 8 0x7 F 0xB 6 0xF 4 0xB 2 0x8 0 0x9 6 0x D 0x3 2 0x0 3 0x1 D 0xA 3 0x6 8 0x0 2 0xD 8 0xF 6 0x7 2 0x3 0 0x4 0 0xF F 0x7 4 0xF C 0x3 C 0x8 D 0x E 0x5 F 0xB 0 0x4 A 0xD E 0xD D 0x0 5 0xD B 0xA 8 0xD 6 0xA 0 0x6 2 0xF 0 0x8 2 0xC A 0x9 2 0xC 2 0x F 0x5 1 0x0 6 0x0 A 0x6 A 0x3 8 0x8 E 0x4 D 0xC B 0xD 1 0x5 C 0xC 9 0xE 0 0x4 6 0xD C 0x7 5 0x0 F 48 Consider encryption process of encryption algorithm AES–IDEA16–2. First, 512–bit block of plaintext X is partitioned into 32–bit subblocks 0 0 X , 1 0 X , …, 1 5 0 X and the following steps are performed: 1. subblocks 0 0 X , 1 0 X , …, 1 5 0 X are summed to XOR with the corresponding round keys 16 18 n K , 17 18 n K , ..., 31 18 n K : i n i i K X X 16 18 0 0 , 15 ... 0 i . 2. subblocks 0 0 X , 1 0 X , …, 1 5 0 X multiplied and summarized to the same round keys ) 1 ( 1 8 i K , 1 ) 1 ( 18 i K , ..., 15 ) 1 ( 18 i K and calculated 0 T , 1 T , ..., 1 5 T as follows ) ( ) ( 8 ) 1 ( 18 8 1 ) 1 ( 18 0 1 0 i i i i K X K X T , ) ( ) ( 9 ) 1 ( 18 9 1 1 ) 1 ( 18 1 1 1 i i i i K X K X T , ) ( ) ( 10 ) 1 ( 18 10 1 2 ) 1 ( 18 2 1 2 i i i i K X K X T , ) ( ) ( 11 ) 1 ( 18 11 1 3 ) 1 ( 18 3 1 3 i i i i K X K X T , ) ( ) ( 12 ) 1 ( 18 12 1 4 ) 1 ( 18 4 1 4 i i i i K X K X T , ) ( ) ( 13 ) 1 ( 18 13 1 5 ) 1 ( 18 5 1 5 i i i i K X K X T , ) ( ) ( 14 ) 1 ( 18 14 1 6 ) 1 ( 18 6 1 6 i i i i K X K X T , ) ( ) ( 15 ) 1 ( 18 15 1 7 ) 1 ( 18 7 1 7 i i i i K X K X T , 1 i . 3. subblocks 0 T , 1 T , ..., 1 5 T written in two arrays State and performed SubBytes(), ShiftRows(), MixColumns(), AddRoundKey() transformation. After the transformation 32 bit subblocks 0 Y , 1 Y , ..., 7 Y is obtained 4. subblocks 0 Y , 1 Y , ..., 7 Y are summed to XOR with the corresponding subblocks j i X 1 i.e. j j i j i Y X X 7 1 1 , j j i j i Y X X 7 8 1 8 1 , 7 ... 0 j , 1 i . 5. at the end of round except subblocks 0 i X and 1 6 1 i X all subblocks will be swapped 15 1 j i j i X X , 14 ... 1 j , 1 i . 6. repeating steps 2–5 n times, i.e., n i ... 2 , the 32bit subblocks 0 n X , 1 n X , …, 3 1 n X is obtained 7. in the output transformation round keys n K 18 , 1 18 n K , ..., 15 18 n K are multiplied and summed with the corresponding subblocks n n n K X X 18 0 0 1 , 1 18 14 1 1 n n n K X X , 2 18 13 2 1 n n n K X X , 3 18 12 3 1 n n n K X X , 4 18 11 4 1 n n n K X X , 5 18 10 5 1 n n n K X X , 6 18 9 6 1 n n n K X X , 7 18 8 7 1 n n n K X X , 8 18 7 8 1 n n n K X X , 9 18 6 9 1 n n n K X X , 10 18 5 10 1 n n n K X X , 11 18 4 11 1 n n n K X X , 12 18 3 12 1 n n n K X X , 13 18 2 13 1 n n n K X X , 14 18 1 14 1 n n n K X X , 15 18 15 15 1 n n n K X X . 49 8. subblocks 0 1 n X , 1 1 n X , …, 1 5 1 n X are summed to XOR with the corresponding round keys 32 18 n K , 33 18 n K , ..., 47 18 n K : j n j n j n K X X 32 18 1 1 , 15 ... 0 j . As ciphertext plaintext X are accepted combining 32bit sub–blocks 15 1 1 1 0 1 | | ... | | | | n n n X X X . Key generation encryption algorithm AES–IDEA16–2 In the n–round encryption algorithm AES–IDEA16–2 each round are applied 16 round keys length of 32 bits, two key length of 128 bits and in output transformation 16 round keys length of 32 bits. Besides, before the first round and after output transformation applied 16 round keys length of 32 bits. Total number of 32–bit round keys equal to 16n+48 and 128–bit round key equal to 2n. If 128–bit round keys convert to four 32–bit key, the total number of 32 bit keys equal to 24n+48. When encryption in Figure 5 instead i K used encryption round keys c i K , when decryption decryption round keys d i K . When generating round key like encryption algorithm AES are used array Rcon: Rcon=[0x00000001, 0x00000002, 0x00000004, 0x00000008, 0x00000010, 0x00000020, 0x00000040, 0x00000080, 0x00000100, 0x00000200, 0x00000400, 0x00000800, 0x00001000, 0x00002000, 0x00004000, 0x00008000, 0x00010000, 0x00020000, 0x00040000, 0x00080000, 0x00100000, 0x00200000, 0x00400000, 0x00800000, 0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000, 0x20000000, 0x40000000, 0x80000000]. The key of encryption algorithm K length l ( 1024 256 l ) bit is divided into 32– bit round keys ' 0 c K , ' 1 c K ,..., ' 1 c Lenght K , 32 / l Lenght , здесь } ,..., , { 1 1 0 l k k k K , } ,..., , { 31 1 0 ' 0 k k k K c , } ,..., , { 63 33 32 ' 1 k k k K c ,..., } ,..., , { 1 31 32 ' 1 l l l c Lenght k k k K and ' 1 ' 1 ' 0 || ... || || c Lenght c c K K K K . Then calculated ' 1 ' 1 ' 0 ... c Lenght c c L K K K K . If 0 L K then as L K selected 0xC5C31537, i.е. 0xC5C31537 L K . When generating a round keys ' c i K , 47 24 ... n Lenght i used SubBytes32() and RotWord32() transformation, here SubBytes32()–transformation 32–bit subblock in the S–block, i.e. )) ( ( || )) ( ( || )) ( ( || )) ( ( ) ( 32 1 1 0 0 1 1 0 0 X sb S X sb S X sb S X sb S X SubBytes , RotWord32() – 50 cyclic shift 32–bit subblock left by 1 bit. Here 0 S and 1 S – the S–boxes, given in the table 1 and 2. If the conditions 1 3 mod i , then round keys calculated as L c Lenght i c Lenght i c i K i Rcon K RotWord SubBytes K SubBytes K ] 32 mod [ )) ( 32 ( 32 ) ( 32 ' ' 1 ' , otherwise L c Lenght i c Lenght i c i K K SubBytes K SubBytes K ) ( 32 ) ( 32 ' 1 ' ' . After every generation of round keys value L K rotated to the left by 1 bit. Decryption round keys are computed based on encryption round keys and decryption keys output transformation associated with encryption keys as follows: ) , ) ( , , ) ( , , ) ( , , ) ( , ) ( , , ) ( , , ) ( , , ) ( , ( ) , , , , , , , , , , , , , , , ( ' 15 1 ' 14 ' 13 1 ' 12 ' 11 1 ' 10 ' 9 1 ' 8 1 ' 7 ' 6 1 ' 5 ' 4 1 ' 3 ' 2 1 ' 1 ' 0 ' 15 24 ' 14 24 ' 13 24 ' 12 24 ' 11 24 ' 10 24 ' 9 24 ' 8 24 ' 7 24 ' 6 24 ' 5 24 ' 4 24 ' 3 24 ' 2 24 ' 1 24 ' 24 c c c c c c c c c c c c c c c c d n d n d n d n d n d n d n d n d n d n d n d n d n d n d n d n K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K In the same manner, decryption keys second, third, and n–round associated with the encryption keys following: n i K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K c i n c i n c i n c i n c i n c i n c i n c i n c i n c i n c i n c i n c i n c i n c i n c i n d i d i d i d i d i d i d i d i d i d i d i d i d i d i d i d i ... 2 ), , ) ( , , ) ( , , ) ( , , ) ( , ) ( , , ) ( , , ) ( , , ) ( , ( ) , , , , , , , , , , , , , , , ( ' 1 5 ) 1 ( 2 4 1 ' 1 ) 1 ( 2 4 ' 2 ) 1 ( 2 4 1 ' 3 ) 1 ( 2 4 ' 4 ) 1 ( 2 4 1 ' 5 ) 1 ( 2 4 ' 6 ) 1 ( 2 4 1 ' 7 ) 1 ( 2 4 1 ' 8 ) 1 ( 2 4 ' 9 ) 1 ( 2 4 1 ' 1 0 ) 1 ( 2 4 ' 1 1 ) 1 ( 2 4 1 ' 1 2 ) 1 ( 2 4 ' 1 3 ) 1 ( 2 4 1 ' 1 4 ) 1 ( 2 4 ' ) 1 ( 2 4 ' 1 5 ) 1 ( 2 4 ' 1 4 ) 1 ( 2 4 ' 1 3 ) 1 ( 2 4 ' 1 2 ) 1 ( 2 4 ' 1 1 ) 1 ( 2 4 ' 1 0 ) 1 ( 2 4 ' 9 ) 1 ( 2 4 ' 8 ) 1 ( 2 4 ' 7 ) 1 ( 2 4 ' 6 ) 1 ( 2 4 ' 5 ) 1 ( 2 4 ' 4 ) 1 ( 2 4 ' 3 ) 1 ( 2 4 ' 2 ) 1 ( 2 4 ' 1 ) 1 ( 2 4 ' ) 1 ( 2 4 ' 16 ) ( 24 ' 16 ) 1 ( 24 c j i n d j i K K , 7 ... 0 j , n i ... 2 Decryption of round key first round associated a encryption round key as follows: ) , , , ) ( , , ) ( , , ) ( , , ) ( , ) ( , , ) ( , , ) ( , , ) ( , ( ) , , , , , , , , , , , , , , , , , ( ' 17 ) 1 ( 24 ' 16 ) 1 ( 24 ' 15 24 1 ' 14 24 ' 13 24 1 ' 12 24 ' 11 24 1 ' 10 24 ' 9 24 1 ' 8 24 1 ' 7 24 ' 6 24 1 ' 5 24 ' 4 24 1 ' 3 24 ' 2 24 1 ' 1 24 ' 24 ' 17 ' 16 ' 15 ' 14 ' 13 ' 12 ' 11 ' 10 ' 9 ' 8 ' 7 ' 6 ' 5 ' 4 ' 3 ' 2 ' 1 ' 0 c n c n c n c n c n c n c n c n c n c n c n c n c n c n c n c n c n c n d d d d d d d d d d d d d d d d d d K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K Decryption round key, applied to the first round and after output transformation associated with encryption keys as follows: ' 32 24 ' 16 24 c j n d j n K K , ' 16 24 ' 32 24 c j n d j n K K , 15 ... 0 j Encryption round keys c i K associated with the keys ' c i K are as follows: ' 24 18 c j i c j i K K , 15 ... 0 j , ' 19 24 ' 18 24 ' 17 24 ' 16 24 16 18 | | | | | | c i c i c i c i c i K K K K K , ' 23 24 ' 22 24 ' 21 24 ' 20 24 17 18 | | | | | | c i c i c i c i c i K K K K K . In the same manner, decryption round keys d i K associated with the keys ' d i K as follows: ' 24 18 d j i d j i K K , 15 ... 0 j , ' 19 24 ' 18 24 ' 17 24 ' 16 24 16 18 | | | | | | d i d i d i d i d i K K K K K , ' 23 24 ' 22 24 ' 21 24 ' 20 24 17 18 | | | | | | d i d i d i d i d i K K K K K . жүктеу/скачать 7,09 Mb. Достарыңызбен бөлісу:
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