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Updated SM4 with AESENCLAST (markdown)

Sun Yimin 2023-10-10 11:02:10 +08:00
parent 8113171e73
commit a83c7d6e3e
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SM4-with-AESENCLAST.md

@ -142,6 +142,17 @@ sm4_box_aesbox_4
}
```
## How to calculate lookup table from M, C?
$\{ M\times i + C \mid i \in [0,255] \}$
这个查找表有256个元素，考虑到寄存器的使用，需要换个形式。
$M\times i + C = M\times i_{4highbits} + (M\times i_{4lowbits} + C) \mid i \in [0,255]$
我们可以看到
$M\times i_{4highbits} \mid i \in [0,255]$
的每一列（16个字节）都是相同的。而
$M\times i_{4lowbits} + C \mid i \in [0,255]$
的每一行（16个字节）都是相同的。
这样，我们去除重复，只用16*2个字节就可以存储这个查找表。
```golang
// {Mi+C | i>=0 && i<256}
@ -192,14 +203,101 @@ def gen_lookup(m, c):
table.append(matrix_col_byte(tmp.GetColumn(0)) ^ c)
return table
def gen_lookup_low(m, c):
Mmatrix = to_matrix(m)
table = []
for i in range(256):
Imatrix = genericmatrix.GenericMatrix(size=(8, 1), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
for j in range (8):
if j < 4:
Imatrix.SetRow(j, [0])
else:
Imatrix.SetRow(j, [(i >> (7 - j)) & 1])
tmp = Mmatrix * Imatrix
table.append(matrix_col_byte(tmp.GetColumn(0)) ^ c)
return table
def gen_lookup_high(m, c):
Mmatrix = to_matrix(m)
table = []
for i in range(256):
Imatrix = genericmatrix.GenericMatrix(size=(8, 1), zeroElement=0, identityElement=1, add=XOR, mul=AND, sub=XOR, div=DIV)
for j in range (8):
if j < 4:
Imatrix.SetRow(j, [(i >> (7 - j)) & 1])
else:
Imatrix.SetRow(j, [0])
tmp = Mmatrix * Imatrix
table.append(matrix_col_byte(tmp.GetColumn(0)))
return table
def print_table(table):
for i, s in enumerate(table):
print(f'0x%02X'%s,',', end='')
if (i+1) % 16 == 0:
print()
print_table(gen_lookup_low([0xfe, 0x54, 0xaf, 0xdd, 0xf7, 0xf9, 0xac, 0xe2], 0x34))
print()
print_table(gen_lookup_high([0xfe, 0x54, 0xaf, 0xdd, 0xf7, 0xf9, 0xac, 0xe2], 0x34))
print()
print_table(gen_lookup([0xfe, 0x54, 0xaf, 0xdd, 0xf7, 0xf9, 0xac, 0xe2], 0x34))
print()
```
示例结果：
```
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,0x00 ,
0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,0xDC ,
0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,0xAF ,
0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,0x73 ,
0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,0xDD ,
0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,0x01 ,
0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,0x72 ,
0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,0xAE ,
0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,0xBF ,
0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,0x63 ,
0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,0x10 ,
0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,0xCC ,
0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,0x62 ,
0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,0xBE ,
0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,0xCD ,
0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,0x11 ,
0x34 ,0x08 ,0x9D ,0xA1 ,0xCE ,0xF2 ,0x67 ,0x5B ,0x82 ,0xBE ,0x2B ,0x17 ,0x78 ,0x44 ,0xD1 ,0xED ,
0xE8 ,0xD4 ,0x41 ,0x7D ,0x12 ,0x2E ,0xBB ,0x87 ,0x5E ,0x62 ,0xF7 ,0xCB ,0xA4 ,0x98 ,0x0D ,0x31 ,
0x9B ,0xA7 ,0x32 ,0x0E ,0x61 ,0x5D ,0xC8 ,0xF4 ,0x2D ,0x11 ,0x84 ,0xB8 ,0xD7 ,0xEB ,0x7E ,0x42 ,
0x47 ,0x7B ,0xEE ,0xD2 ,0xBD ,0x81 ,0x14 ,0x28 ,0xF1 ,0xCD ,0x58 ,0x64 ,0x0B ,0x37 ,0xA2 ,0x9E ,
0xE9 ,0xD5 ,0x40 ,0x7C ,0x13 ,0x2F ,0xBA ,0x86 ,0x5F ,0x63 ,0xF6 ,0xCA ,0xA5 ,0x99 ,0x0C ,0x30 ,
0x35 ,0x09 ,0x9C ,0xA0 ,0xCF ,0xF3 ,0x66 ,0x5A ,0x83 ,0xBF ,0x2A ,0x16 ,0x79 ,0x45 ,0xD0 ,0xEC ,
0x46 ,0x7A ,0xEF ,0xD3 ,0xBC ,0x80 ,0x15 ,0x29 ,0xF0 ,0xCC ,0x59 ,0x65 ,0x0A ,0x36 ,0xA3 ,0x9F ,
0x9A ,0xA6 ,0x33 ,0x0F ,0x60 ,0x5C ,0xC9 ,0xF5 ,0x2C ,0x10 ,0x85 ,0xB9 ,0xD6 ,0xEA ,0x7F ,0x43 ,
0x8B ,0xB7 ,0x22 ,0x1E ,0x71 ,0x4D ,0xD8 ,0xE4 ,0x3D ,0x01 ,0x94 ,0xA8 ,0xC7 ,0xFB ,0x6E ,0x52 ,
0x57 ,0x6B ,0xFE ,0xC2 ,0xAD ,0x91 ,0x04 ,0x38 ,0xE1 ,0xDD ,0x48 ,0x74 ,0x1B ,0x27 ,0xB2 ,0x8E ,
0x24 ,0x18 ,0x8D ,0xB1 ,0xDE ,0xE2 ,0x77 ,0x4B ,0x92 ,0xAE ,0x3B ,0x07 ,0x68 ,0x54 ,0xC1 ,0xFD ,
0xF8 ,0xC4 ,0x51 ,0x6D ,0x02 ,0x3E ,0xAB ,0x97 ,0x4E ,0x72 ,0xE7 ,0xDB ,0xB4 ,0x88 ,0x1D ,0x21 ,
0x56 ,0x6A ,0xFF ,0xC3 ,0xAC ,0x90 ,0x05 ,0x39 ,0xE0 ,0xDC ,0x49 ,0x75 ,0x1A ,0x26 ,0xB3 ,0x8F ,
0x8A ,0xB6 ,0x23 ,0x1F ,0x70 ,0x4C ,0xD9 ,0xE5 ,0x3C ,0x00 ,0x95 ,0xA9 ,0xC6 ,0xFA ,0x6F ,0x53 ,
0xF9 ,0xC5 ,0x50 ,0x6C ,0x03 ,0x3F ,0xAA ,0x96 ,0x4F ,0x73 ,0xE6 ,0xDA ,0xB5 ,0x89 ,0x1C ,0x20 ,
0x25 ,0x19 ,0x8C ,0xB0 ,0xDF ,0xE3 ,0x76 ,0x4A ,0x93 ,0xAF ,0x3A ,0x06 ,0x69 ,0x55 ,0xC0 ,0xFC ,
```
## How to calculate M, C from lookup table?