Rijndael S-box - Inverse S-box

Inverse S-box

The inverse S-box is simply the S-box run in reverse. For example, the inverse S-box of 0xdb is 0x9f. It is calculated by first calculating the inverse affine transformation of the input value, followed by the multiplicative inverse. The inverse affine transformation is as follows:

The following table represents Rijndael's inverse S-box:

| 0 1 2 3 4 5 6 7 8 9 a b c d e f ---|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--| 00 |52 09 6a d5 30 36 a5 38 bf 40 a3 9e 81 f3 d7 fb 10 |7c e3 39 82 9b 2f ff 87 34 8e 43 44 c4 de e9 cb 20 |54 7b 94 32 a6 c2 23 3d ee 4c 95 0b 42 fa c3 4e 30 |08 2e a1 66 28 d9 24 b2 76 5b a2 49 6d 8b d1 25 40 |72 f8 f6 64 86 68 98 16 d4 a4 5c cc 5d 65 b6 92 50 |6c 70 48 50 fd ed b9 da 5e 15 46 57 a7 8d 9d 84 60 |90 d8 ab 00 8c bc d3 0a f7 e4 58 05 b8 b3 45 06 70 |d0 2c 1e 8f ca 3f 0f 02 c1 af bd 03 01 13 8a 6b 80 |3a 91 11 41 4f 67 dc ea 97 f2 cf ce f0 b4 e6 73 90 |96 ac 74 22 e7 ad 35 85 e2 f9 37 e8 1c 75 df 6e a0 |47 f1 1a 71 1d 29 c5 89 6f b7 62 0e aa 18 be 1b b0 |fc 56 3e 4b c6 d2 79 20 9a db c0 fe 78 cd 5a f4 c0 |1f dd a8 33 88 07 c7 31 b1 12 10 59 27 80 ec 5f d0 |60 51 7f a9 19 b5 4a 0d 2d e5 7a 9f 93 c9 9c ef e0 |a0 e0 3b 4d ae 2a f5 b0 c8 eb bb 3c 83 53 99 61 f0 |17 2b 04 7e ba 77 d6 26 e1 69 14 63 55 21 0c 7d

For C, C++ implementation, here is the initialization of the table:

unsigned char inv_s = { 0x52, 0x09, 0x6A, 0xD5, 0x30, 0x36, 0xA5, 0x38, 0xBF, 0x40, 0xA3, 0x9E, 0x81, 0xF3, 0xD7, 0xFB, 0x7C, 0xE3, 0x39, 0x82, 0x9B, 0x2F, 0xFF, 0x87, 0x34, 0x8E, 0x43, 0x44, 0xC4, 0xDE, 0xE9, 0xCB, 0x54, 0x7B, 0x94, 0x32, 0xA6, 0xC2, 0x23, 0x3D, 0xEE, 0x4C, 0x95, 0x0B, 0x42, 0xFA, 0xC3, 0x4E, 0x08, 0x2E, 0xA1, 0x66, 0x28, 0xD9, 0x24, 0xB2, 0x76, 0x5B, 0xA2, 0x49, 0x6D, 0x8B, 0xD1, 0x25, 0x72, 0xF8, 0xF6, 0x64, 0x86, 0x68, 0x98, 0x16, 0xD4, 0xA4, 0x5C, 0xCC, 0x5D, 0x65, 0xB6, 0x92, 0x6C, 0x70, 0x48, 0x50, 0xFD, 0xED, 0xB9, 0xDA, 0x5E, 0x15, 0x46, 0x57, 0xA7, 0x8D, 0x9D, 0x84, 0x90, 0xD8, 0xAB, 0x00, 0x8C, 0xBC, 0xD3, 0x0A, 0xF7, 0xE4, 0x58, 0x05, 0xB8, 0xB3, 0x45, 0x06, 0xD0, 0x2C, 0x1E, 0x8F, 0xCA, 0x3F, 0x0F, 0x02, 0xC1, 0xAF, 0xBD, 0x03, 0x01, 0x13, 0x8A, 0x6B, 0x3A, 0x91, 0x11, 0x41, 0x4F, 0x67, 0xDC, 0xEA, 0x97, 0xF2, 0xCF, 0xCE, 0xF0, 0xB4, 0xE6, 0x73, 0x96, 0xAC, 0x74, 0x22, 0xE7, 0xAD, 0x35, 0x85, 0xE2, 0xF9, 0x37, 0xE8, 0x1C, 0x75, 0xDF, 0x6E, 0x47, 0xF1, 0x1A, 0x71, 0x1D, 0x29, 0xC5, 0x89, 0x6F, 0xB7, 0x62, 0x0E, 0xAA, 0x18, 0xBE, 0x1B, 0xFC, 0x56, 0x3E, 0x4B, 0xC6, 0xD2, 0x79, 0x20, 0x9A, 0xDB, 0xC0, 0xFE, 0x78, 0xCD, 0x5A, 0xF4, 0x1F, 0xDD, 0xA8, 0x33, 0x88, 0x07, 0xC7, 0x31, 0xB1, 0x12, 0x10, 0x59, 0x27, 0x80, 0xEC, 0x5F, 0x60, 0x51, 0x7F, 0xA9, 0x19, 0xB5, 0x4A, 0x0D, 0x2D, 0xE5, 0x7A, 0x9F, 0x93, 0xC9, 0x9C, 0xEF, 0xA0, 0xE0, 0x3B, 0x4D, 0xAE, 0x2A, 0xF5, 0xB0, 0xC8, 0xEB, 0xBB, 0x3C, 0x83, 0x53, 0x99, 0x61, 0x17, 0x2B, 0x04, 0x7E, 0xBA, 0x77, 0xD6, 0x26, 0xE1, 0x69, 0x14, 0x63, 0x55, 0x21, 0x0C, 0x7D };