伽罗华乘法原理与C语言实现

た入场券 2022-01-17 08:29 189阅读 0赞

![Center][]![Center 1][]![Center 2][]![Center 3][]

**       2.2 算法实现**

接受两个unsigned char类型（1B）变量left和right,返回unsigned char类型结果，其为left和right的伽罗华乘法结果。

unsigned char find\_result(unsigned char left,unsigned char right)

//poly数组存储是码字

unsignedchar  poly\[8\] = \{0x1d, 0x3a, 0x74, 0xe8,0xcd, 0x87, 0x13, 0x26\};

unsignedchar  i, bit;

unsignedshort temp = 0;//16位变量，存储中间结果，必须初始化为0

unsignedchar h\_temp, l\_temp;//用来存储temp的高8位和低8位

//本位相乘

for(i = 0; i < 8; i += 1)

bit= (right >> i) & 1; //以上例来说，从右到左获取01111001的第i+1位

if(bit)//如果第i+1位不为0

temp^= (left << i); //11010101左移i位和temp异或并存储到temp

//“溢出位”处理（高8位对于一字节变量\[8bit\]来说可称做溢出位）

h\_temp =(temp & 0xff00) >> 8;//获取temp高8位

l\_temp =temp & 0x00ff;//获取temp低8位

for(i =0;i < 8;i += 1)

bit= (h\_temp >>i) & 1;

if(bit)//对于非0位进行多项式的替换并伽罗华加（^）

l\_temp^= poly\[i\];

returnl\_temp;

**2.3 二位乘法和四位乘法**

**      **  思想：二（四）位伽罗华乘法思想和一位是一样的。只是对应的乘法由一位一位乘变成两（四）位和两（四）位乘。为了减少重复计算，可以事前得出对应数相乘的结果。

//二位乘法

unsigned short find\_result2(unsigned char left,unsigned char right)

//“溢出位”替换码字

unsignedchar shift\[4\]\[4\] = \{ \{0x0, 0x1d, 0x3a, 0x27\},

\{0x0,0x74, 0xe8, 0x9c\},

\{0x0,0xcd, 0x87, 0x4a\},

\{0x0,0x13, 0x26, 0x35\}\};

//乘法表

unsignedchar list\[4\]\[4\] = \{ \{0x0, 0x0, 0x0, 0x0\},

\{0x0,0x01, 0x02, 0x03\},

\{0x0,0x02, 0x04, 0x06\},

\{0x0,0x03, 0x06, 0x05\}\};

unsignedchar i, j;

unsignedshort temp = 0;

unsignedchar h\_temp, l\_temp;

for(i =0; i < 8; i += 2)

for(j= 0; j < 8; j += 2)

temp^= (list\[(left >> j) & 3\]\[(right >> i) & 3\] << (i +j));

h\_temp =(temp & 0xff00) >> 8;

l\_temp =temp & 0x00ff;

for(j =0; j < 8; j += 2)

l\_temp^= shift\[j >> 1\]\[(h\_temp >> j) & 3\];

returnl\_temp;

//四位乘法

unsigned short find\_result4(unsigned char left,unsigned char right)

//“溢出位”替换码字

unsignedchar shift\[2\]\[16\] = \{ \{0x0, 0x1d, 0x3a, 0x27, 0x74, 0x69, 0x4e, 0x53,

0xe8, 0xf5, 0xd2, 0xcf, 0x9c, 0x81, 0xa6,0xbb\},

\{0x0, 0xcd, 0x87, 0x4a, 0x13, 0xde, 0x94,0x59,

0x26, 0xeb, 0xa1, 0x6c, 0x35, 0xf8, 0xb2,0x7f\}\};

//乘法表

unsignedchar list\[16\]\[16\] =\{

\{0x0,0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0\},

\{0x0,0x1, 0x2, 0x3, 0x4, 0x5, 0x6, 0x7, 0x8, 0x9, 0xA, 0xB, 0xC, 0xD, 0xE, 0xF\},

\{0x0,0x2, 0x4, 0x6, 0x8, 0xA, 0xC, 0xE, 0x10, 0x12, 0x14, 0x16, 0x18, 0x1A, 0x1C,0x1E\},

\{0x0,0x3, 0x6, 0x5, 0xC, 0xF, 0xA, 0x9, 0x18, 0x1B, 0x1E, 0x1D, 0x14, 0x17, 0x12,0x11\},

\{0x0,0x4, 0x8, 0xC, 0x10, 0x14, 0x18, 0x1C, 0x20, 0x24, 0x28, 0x2C, 0x30, 0x34,0x38, 0x3C\},

\{0x0,0x5, 0xA, 0xF, 0x14, 0x11, 0x1E, 0x1B, 0x28, 0x2D, 0x22, 0x27, 0x3C, 0x39,0x36, 0x33\},

\{0x0,0x6, 0xC, 0xA, 0x18, 0x1E, 0x14, 0x12, 0x30, 0x36, 0x3C, 0x3A, 0x28, 0x2E,0x24, 0x22\},

\{0x0,0x7, 0xE, 0x9, 0x1C, 0x1B, 0x12, 0x15, 0x38, 0x3F, 0x36, 0x31, 0x24, 0x23, 0x2A,0x2D\},

\{0x0,0x8, 0x10, 0x18, 0x20, 0x28, 0x30, 0x38, 0x40, 0x48, 0x50, 0x58, 0x60, 0x68,0x70, 0x78\},

\{0x0,0x9, 0x12, 0x1B, 0x24, 0x2D, 0x36, 0x3F, 0x48, 0x41, 0x5A, 0x53, 0x6C, 0x65,0x7E, 0x77\},

\{0x0,0xA, 0x14, 0x1E, 0x28, 0x22, 0x3C, 0x36, 0x50, 0x5A, 0x44, 0x4E, 0x78, 0x72,0x6C, 0x66\},

\{0x0,0xB, 0x16, 0x1D, 0x2C, 0x27, 0x3A, 0x31, 0x58, 0x53, 0x4E, 0x45, 0x74, 0x7F,0x62, 0x69\},

\{0x0,0xC, 0x18, 0x14, 0x30, 0x3C, 0x28, 0x24, 0x60, 0x6C, 0x78, 0x74, 0x50, 0x5C,0x48, 0x44\},

\{0x0,0xD, 0x1A, 0x17, 0x34, 0x39, 0x2E, 0x23, 0x68, 0x65, 0x72, 0x7F, 0x5C, 0x51,0x46, 0x4B\},

\{0x0,0xE, 0x1C, 0x12, 0x38, 0x36, 0x24, 0x2A, 0x70, 0x7E, 0x6C, 0x62, 0x48, 0x46,0x54, 0x5A\},

\{0x0,0xF, 0x1E, 0x11, 0x3C, 0x33, 0x22, 0x2D, 0x78, 0x77, 0x66, 0x69, 0x44, 0x4B,0x5A, 0x55\}\};

unsignedchar l\_shift = left, r\_shift = right;

unsignedchar i, j;

unsignedshort temp = 0;

unsignedchar h\_temp, l\_temp;

for(i =0; i < 8; i += 4)

for(j= 0; j < 8; j += 4)

temp^= (list\[(l\_shift >> j) & 0xf\]\[(r\_shift >> i) & 0xf\]<< (i + j));

h\_temp =(temp & 0xff00) >> 8;

l\_temp =temp & 0x00ff;

for(j =0; j < 8; j += 4)

l\_temp^= shift\[j >> 2\]\[(h\_temp >> j) & 0xf\];

returnl\_temp;

[Center]: https://img-blog.csdn.net/20130624205103984?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvbXlfbGl2ZV8xMjM=/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center
[Center 1]: https://img-blog.csdn.net/20130624205111375?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvbXlfbGl2ZV8xMjM=/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center
[Center 2]: https://img-blog.csdn.net/20130624205114718?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvbXlfbGl2ZV8xMjM=/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center
[Center 3]: /images/20220117/f7a923416e954eb2bc5b047217208622.png