Rijndael S-box について

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Rijndael S-box ：ウィキペディア英語版

Rijndael S-box
The Rijndael S-box is a matrix (square array of numbers) used in the Rijndael cipher, which the Advanced Encryption Standard (AES) cryptographic algorithm was based on.〔(【引用サイトリンク】 title=The Rijndael Block Cipher )〕 The S-box (substitution box) serves as a lookup table.
== Forward S-box ==
The S-box is generated by determining the multiplicative inverse for a given number in , Rijndael's finite field. Zero, which has no inverse, is mapped to zero. The multiplicative inverse is then transformed using the following affine transformation:
:

\begin1&0&0&0&1&1&1&1 \\1&1&0&0&0&1&1&1 \\1&1&1&0&0&0&1&1 \\1&1&1&1&0&0&0&1 \\1&1&1&1&1&0&0&0 \\0&1&1&1&1&1&0&0 \\0&0&1&1&1&1&1&0 \\0&0&0&1&1&1&1&1\end\beginx_0\\x_1\\x_2\\x_3\\x_4\\x_5\\x_6\\x_7\end+\begin1\\1\\0\\0\\0\\1\\1\\0\end

where (..., x₇ ) is the multiplicative inverse as a vector.
This affine transformation is the sum of multiple rotations of the byte as a vector, where addition is the XOR operation.
The matrix multiplication can be calculated by the following algorithm:
# Store the multiplicative inverse of the input number in two 8-bit unsigned temporary variables: ''s'' and ''x''.
# Rotate the value ''s'' one bit to the left; if the value of ''s'' had a high bit (eighth bit from the right) of one, make the low bit of ''s'' one; otherwise the low bit of ''s'' is zero.
# XOR the value of ''x'' with the value of ''s'', storing the value in ''x''
# For three more iterations, repeat steps two and three; steps two and three are done a total of four times.
# The value of ''x'' will now have the result of the multiplication.
After the matrix multiplication is done, XOR the value by the decimal number 99 (the hexadecimal number 0x63, the binary number 1100011, and the bit string 11000110 representing the number in LSb first notation).
This will generate the following S-box, which is represented here with hexadecimal notation:


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

Here the column is determined by the least significant nibble, and the row is determined by the most significant nibble. For example, the value 0x9a is converted into 0xb8 by Rijndael's S-box. Note that the multiplicative inverse of 0x00 is defined as itself.
For C, C++ here is the initialization of the table:

unsigned char s() =
;

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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