DES对称密码算法实验-CFANZ编程社区

一、实验目的

通过对DES算法进行分析，并使用DES算法对数据进行加密和解密，进一步理解DES的实现和加解密原理。

二、实验的软硬件环境要求

运行Windows操作系统的计算机，具有VC等C语言编译环境。

三、知识准备

1. 密钥处理

从用户处获得64位密钥，其中每第8位为校验位，为使密钥有正确的奇偶校验，每个密钥要有奇数个“1”位。具体过程如下:

（1）舍弃64位密钥中的奇偶校验位，根据下表（PC-1）进行密钥变换得到56位的密钥，在变换中，奇偶校验位已被舍弃。

Permuted Choice 1 (PC-1)

57	49	41	33	25	17	9
1	58	50	42	34	26	18
10	2	59	51	43	35	27
19	11	3	60	52	44	36
63	55	47	39	31	23	15
7	62	54	46	38	30	22
14	6	61	53	45	37	29
21	13	5	28	20	12	4

（2）把变换后的密钥等分成两部分,前28位记为C[0], 后28位记为D[0]。

（3）计算子密钥(共16个)，从i=1开始。

分别对C[i-1],D[i-1]作循环左移来生成C[i],D[i]。(共16次)。每次循环

（a）左移位数如下表所示：

循环次数	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
左移位数	1	1	2	2	2	2	2	2	1	2	2	2	2	2	2	1

（b）串联C[i],D[i]，得到一个56位数，然后对此数按下表（PC-2）作如下变换以产生48位子密钥K[i]。

Permuted Choice 2 (PC-2)

14	17	11	24	1	5
3	28	15	6	21	10
23	19	12	4	26	8
16	7	27	20	13	2
41	52	31	37	47	55
30	40	51	45	33	48
44	49	39	56	34	53
46	42	50	36	29	32

（c）从1.2.3.1处循环执行，计算出16个子密钥。

2．对64位数据块的处理

（1）把数据分成64位的数据块，不够64位的以补零方式填补。

（2）对数据块按下表（IP）变换。

Initial Permutation (IP)

58	50	42	34	26	18	10	2
60	52	44	36	28	20	12	4
62	54	46	38	30	22	14	6
64	56	48	40	32	24	16	8
57	49	41	33	25	17	9	1
59	51	43	35	27	19	11	3
61	53	45	37	29	21	13	5
63	55	47	39	31	23	15	7

（3）将变换后的数据块等分成前后两部分，前32位记为L[0],后32位记为R[0]。

（4）用16个子密钥对数据加密，初始I=1。

（a）根据下面的扩冲函数E，扩展32位的成48位

Expansion (E)

32	1	2	3	4	5
4	5	6	7	8	9
8	9	10	11	12	13
12	13	14	15	16	17
16	17	18	19	20	21
20	21	22	23	24	25
24	25	26	27	28	29
28	29	30	31	32	1

（b）用E{R[i-1]}与K[i]作异或运算。

（c）把所得的48位数分成8个6位数。1-6位为B[1]，7-12位为B[2],……43-48位为B[8]。

（d）按S表变换所有的B[J]，初始J=1。所有在S表的值都被当作4位长度处理。

i.将B[J]的第1位和第6位组合为一个2位长度的变量M，M作为在S[J]中的行号。

ii.将B[J]的第2位到第5位组合，作为一个4位长度的变量N，N作为在S[J]中的列号。

iii.用S[J][M][N]来取代B[J]。

Substitution Box 1 (S[1])

14	4	13	1	2	15	11	8	3	10	6	12	5	9	0	7
0	15	7	4	14	2	13	1	10	6	12	11	9	5	3	8
4	1	14	8	13	6	2	11	15	12	9	7	3	10	5	0
15	12	8	2	4	9	1	7	5	11	3	14	10	0	6	13

S[2]

15	1	8	14	6	11	3	4	9	7	2	13	12	0	5	10
3	13	4	7	15	2	8	14	12	0	1	10	6	9	11	5
0	14	7	11	10	4	13	1	5	8	12	6	9	3	2	15
13	8	10	1	3	15	4	2	11	6	7	12	0	5	14	9

S[3]

10	0	9	14	6	3	15	5	1	13	12	7	11	4	2	8
13	7	0	9	3	4	6	10	2	8	5	14	12	11	15	1
13	6	4	9	8	15	3	0	11	1	2	12	5	10	14	7
1	10	13	0	6	9	8	7	4	15	14	3	11	5	2	12

S[4]

7	13	14	3	0	6	9	10	1	2	8	5	11	12	4	15
13	8	11	5	6	15	0	3	4	7	2	12	1	10	14	9
10	6	9	0	12	11	7	13	15	1	3	14	5	2	8	4
3	15	0	6	10	1	13	8	9	4	5	11	12	7	2	14

S[5]

2	12	4	1	7	10	11	6	8	5	3	15	13	0	14	9
14	11	2	12	4	7	13	1	5	0	15	10	3	9	8	6
4	2	1	11	10	13	7	8	15	9	12	5	6	3	0	14
11	8	12	7	1	14	2	13	6	15	0	9	10	4	5	3

S[6]

12	1	10	15	9	2	6	8	0	13	3	4	14	7	5	11
10	15	4	2	7	12	9	5	6	1	13	14	0	11	3	8
9	14	15	5	2	8	12	3	7	0	4	10	1	13	11	6
4	3	2	12	9	5	15	10	11	14	1	7	6	0	8	13

S[7]

4	11	2	14	15	0	8	13	3	12	9	7	5	10	6	1
13	0	11	7	4	9	1	10	14	3	5	12	2	15	8	6
1	4	11	13	12	3	7	14	10	15	6	8	0	5	9	2
6	11	13	8	1	4	10	7	9	5	0	15	14	2	3	12

S[8]

13	2	8	4	6	15	11	1	10	9	3	14	5	0	12	7
1	15	13	8	10	3	7	4	12	5	6	11	0	14	9	2
7	11	4	1	9	12	14	2	0	6	10	13	15	3	5	8
2	1	14	7	4	10	8	13	15	12	9	0	3	5	6	11

iv.从i处循环执行，直到B[8]被替代完成。

v.将B[1]到B[8]组合，按下表（P）变换，得到P。

Permutation P

16	7	20	21
29	12	28	17
1	15	23	26
5	18	31	10
2	8	24	14
32	27	3	9
19	13	30	6
22	11	4	25

（e）异或P和L[I-1]结果放在R[I]，即R[I]=P XOR L[I-1]。

（f）L[I]=R[I-1]

（g）从a)处开始循环执行，直到K[16]被变换完成。

（h）组合变换后的R[16]L[16]（注意：R作为开始的32位），按下表（IP-1）变换得到最后的结果。

四、实验内容

分析实例代码，并对程序进行编译运行，实际演示和体验DES算法的实现过程。

五、实验代码

#include <iostream>
#include <fstream>
using namespace std;
const static char ip[] = {                   //IP置换
    58, 50, 42, 34, 26, 18, 10,  2,
    60, 52, 44, 36, 28, 20, 12,  4,
    62, 54, 46, 38, 30, 22, 14,  6,
    64, 56, 48, 40, 32, 24, 16,  8,
    57, 49, 41, 33, 25, 17,  9,  1,
    59, 51, 43, 35, 27, 19, 11,  3,
    61, 53, 45, 37, 29, 21, 13,  5,
    63, 55, 47, 39, 31, 23, 15,  7
};
const static char fp[] = {     //zuizhongzhihuan 
    40,  8, 48, 16, 56, 24, 64, 32,
    39,  7, 47, 15, 55, 23, 63, 31,
    38,  6, 46, 14, 54, 22, 62, 30,
    37,  5, 45, 13, 53, 21, 61, 29,
    36,  4, 44, 12, 52, 20, 60, 28,
    35,  3, 43, 11, 51, 19, 59, 27,
    34,  2, 42, 10, 50, 18, 58, 26,
    33,  1, 41,  9, 49, 17, 57, 25
};
const static char sbox[8][64] = {    //s_box
    /* S1 */
    14, 4,  13, 1,  2,  15, 11, 8,  3,  10, 6,  12, 5,  9,  0,  7,
    0,  15, 7,  4,  14, 2,  13, 1,  10, 6,  12, 11, 9,  5,  3,  8,
    4,  1,  14, 8,  13, 6,  2,  11, 15, 12, 9,  7,  3,  10, 5,  0,
    15, 12, 8,  2,  4,  9,  1,  7,  5,  11, 3, 14,  10, 0,  6,  13,


    /* S2 */
    15, 1,  8,  14, 6,  11, 3,  4,  9,  7,  2,  13, 12, 0,  5,  10,
    3,  13, 4,  7,  15, 2,  8,  14, 12, 0,  1,  10, 6,  9,  11, 5,
    0,  14, 7,  11, 10, 4,  13, 1,  5,  8,  12, 6,  9,  3,  2,  15,
    13, 8,  10, 1,  3,  15, 4,  2,  11, 6,  7,  12, 0,  5,  14, 9,


    /* S3 */
    10, 0,  9,  14, 6,  3,  15, 5,  1,  13, 12, 7,  11, 4,  2,  8,
    13, 7,  0,  9,  3,  4,  6,  10, 2,  8,  5,  14, 12, 11, 15, 1,
    13, 6,  4,  9,  8,  15, 3,  0,  11, 1,  2,  12, 5,  10, 14, 7,
    1,  10, 13, 0,  6,  9,  8,  7,  4,  15, 14, 3,  11, 5,  2,  12,


    /* S4 */
    7,  13, 14, 3,  0,  6,  9,  10, 1,  2,  8,  5,  11, 12, 4,  15,
    13, 8,  11, 5,  6,  15, 0,  3,  4,  7,  2,  12, 1,  10, 14, 9,
    10, 6,  9,  0,  12, 11, 7,  13, 15, 1,  3,  14, 5,  2,  8,  4,
    3,  15, 0,  6,  10, 1,  13, 8,  9,  4,  5,  11, 12, 7,  2,  14,


    /* S5 */
    2,  12, 4,  1,  7,  10, 11, 6,  8,  5,  3,  15, 13, 0,  14, 9,
    14, 11, 2,  12, 4,  7,  13, 1,  5,  0,  15, 10, 3,  9,  8,  6,
    4,  2,  1,  11, 10, 13, 7,  8,  15, 9,  12, 5,  6,  3,  0,  14,
    11, 8,  12, 7,  1,  14, 2,  13, 6,  15, 0,  9,  10, 4,  5,  3,


    /* S6 */
    12, 1,  10, 15, 9,  2,  6,  8,  0,  13, 3,  4,  14, 7,  5,  11,
    10, 15, 4,  2,  7,  12, 9,  5,  6,  1,  13, 14, 0,  11, 3,  8,
    9,  14, 15, 5,  2,  8,  12, 3,  7,  0,  4,  10, 1,  13, 11, 6,
    4,  3,  2,  12, 9,  5,  15, 10, 11, 14, 1,  7,  6,  0,  8,  13,


    /* S7 */
    4,  11, 2,  14, 15, 0,  8,  13, 3,  12, 9,  7,  5,  10, 6,  1,
    13, 0,  11, 7,  4,  9,  1,  10, 14, 3,  5,  12, 2,  15, 8,  6,
    1,  4,  11, 13, 12, 3,  7,  14, 10, 15, 6,  8,  0,  5,  9,  2,
    6,  11, 13, 8,  1,  4,  10, 7,  9,  5,  0,  15, 14, 2,  3,  12,


    /* S8 */
    13, 2,  8,  4,  6,  15, 11, 1,  10, 9,  3,  14, 5,  0,  12, 7,
    1,  15, 13, 8,  10, 3,  7,  4,  12, 5,  6,  11, 0,  14, 9,  2,
    7,  11, 4,  1,  9,  12, 14, 2,  0,  6,  10, 13, 15, 3,  5,  8,
    2,  1,  14, 7,  4,  10, 8,  13, 15, 12, 9,  0,  3,  5,  6,  11
};
const static char rar[] = {    //ya suo zhi huan
    14, 17, 11, 24, 1,  5,
    3,  28, 15, 6,  21, 10,
    23, 19, 12, 4,  26, 8,
    16, 7,  27, 20, 13, 2,
    41, 52, 31, 37, 47, 55,
    30, 40, 51, 45, 33, 48,
    44, 49, 39, 56, 34, 53,
    46, 42, 50, 36, 29, 32
};
const static char ei[] = {    //kuo zhan zhi huan
    32, 1,  2,  3,  4,  5,
    4,  5,  6,  7,  8,  9,
    8,  9,  10, 11, 12, 13,
    12, 13, 14, 15, 16, 17,
    16, 17, 18, 19, 20, 21,
    20, 21, 22, 23, 24, 25,
    24, 25, 26, 27, 28, 29,
    28, 29, 30, 31, 32, 1
};
const static char Pzh[] = {     //P置换
    16, 7,  20, 21,
    29, 12, 28, 17,
    1,  15, 23, 26,
    5,  18, 31, 10,
    2,  8,  24, 14,
    32, 27, 3,  9,
    19, 13, 30, 6,
    22, 11, 4,  25
};
const static char Keyrar[] = {
    57, 49, 41, 33, 25, 17, 9,
    1,  58, 50, 42, 34, 26, 18,
    10, 2,  59, 51, 43, 35, 27,
    19, 11, 3,  60, 52, 44, 36,


    63, 55, 47, 39, 31, 23, 15,
    7,  62, 54, 46, 38, 30, 22,
    14, 6,  61, 53, 45, 37, 29,
    21, 13, 5,  28, 20, 12, 4
};
bool key[16][48] = { 0 };/*rekey[16][48],*/
char key_in[8];
void ByteToBit(bool* Out, char* In, int bits)  //字节到位的转换
{
    int i;
    for (i = 0; i < bits; i++)
        Out[i] = (In[i / 8] >> (i % 8)) & 1;
}
void BitToByte(char* Out, bool* In, int bits)   //位到字节转换
{
    for (int i = 0; i < bits / 8; i++)
        Out[i] = 0;
    for (int i = 0; i < bits; i++)
        Out[i / 8] |= In[i] << (i % 8);   //"|="组合了位操作符和赋值操作符的功能
}
void Xor(bool* InA, const bool* InB, int len)    //按位异或
{
    for (int i = 0; i < len; i++)
        InA[i] ^= InB[i];
}
void keyfc(char* In)              //获取密钥函数
{
    int i, j = 0, mov, k;
    bool key0[56], temp, keyin[64];
    ByteToBit(keyin, In, 64);           //字节到位的转换
    for (i = 0; i < 56; i++)                      //密钥压缩为56位
        key0[i] = keyin[Keyrar[i] - 1];
    for (i = 0; i < 16; i++)       //16轮密钥产生
    {
        if (i == 0 || i == 1 || i == 8 || i == 15)
            mov = 1;
        else
            mov = 2;
        for (k = 0; k < mov; k++)    //分左右两块循环左移
        {
            //   for(int m=0;m<8;m++)
            //   {
            //    temp=key0[m*7];
            //    for(j=m*7;j<m*7+7;j++)
            //     key0[j]=key0[j+1];
            //    key0[m*7+6]=temp;
            //   }
            temp = key0[0];
            for (int m = 0; m < 27; m++)
                key0[m] = key0[m + 1];
            key0[27] = temp;
            temp = key0[28];
            for (int m = 28; m < 55; m++)
                key0[m] = key0[m + 1];
            key0[55] = temp;
        }


        for (j = 0; j < 48; j++)         //压缩置换并储存
            key[i][j] = key0[rar[j] - 1];
    }
}


void DES(char Out[8], char In[8], bool MS)//加密核心程序,ms=0时加密，反之解密
{
    bool MW[64], tmp[32], PMW[64]; //注意指针
    bool kzmw[48], keytem[48], ss[32];
    int hang, lie;
    ByteToBit(PMW, In, 64);
    for (int j = 0; j < 64; j++)
    {
        MW[j] = PMW[ip[j] - 1];          //初始置换
    }
    bool* Li = &MW[0], * Ri = &MW[32];
    for (int i = 0; i < 48; i++)       //右明文扩展置换
        kzmw[i] = Ri[ei[i] - 1];       //注意指针 


    if (MS == 0)          //DES加密过程
    {
        for (int lun = 0; lun < 16; lun++)
        {
            for (int i = 0; i < 32; i++)
                ss[i] = Ri[i];
            for (int i = 0; i < 48; i++)       //右明文扩展置换
                kzmw[i] = Ri[ei[i] - 1];       //注意指针
            for (int i = 0; i < 48; i++)
                keytem[i] = key[lun][i];      //轮密钥
            Xor(kzmw, keytem, 48);
            /*S盒置换*/
            for (int i = 0; i < 8; i++)
            {
                hang = kzmw[i * 6] * 2 + kzmw[i * 6 + 5];
                lie = kzmw[i * 6 + 1] * 8 + kzmw[i * 6 + 2] * 4 + kzmw[i * 6 + 3] * 2 + kzmw[i * 6 + 4];
                tmp[i * 4 + 3] = sbox[i][(hang + 1) * 16 + lie] % 2;
                tmp[i * 4 + 2] = (sbox[i][(hang + 1) * 16 + lie] / 2) % 2;
                tmp[i * 4 + 1] = (sbox[i][(hang + 1) * 16 + lie] / 4) % 2;
                tmp[i * 4] = (sbox[i][(hang + 1) * 16 + lie] / 8) % 2;
            }




            for (int i = 0; i < 32; i++)  //P置换  
                Ri[i] = tmp[Pzh[i] - 1];
            Xor(Ri, Li, 32);    //异或
            for (int i = 0; i < 32; i++)  //交换左右明文
            {
                Li[i] = ss[i];
            }
        }
        for (int i = 0; i < 32; i++)
        {
            tmp[i] = Li[i];
            Li[i] = Ri[i];
            Ri[i] = tmp[i];
        }
        for (int i = 0; i < 64; i++)
            PMW[i] = MW[fp[i] - 1];
        BitToByte(Out, PMW, 64);  //位到字节的转换 
    }
    else          //DES解密过程
    {

        for (int lun = 15; lun >= 0; lun--)
        {
            for (int i = 0; i < 32; i++)
                ss[i] = Ri[i];
            for (int i = 0; i < 48; i++)       //右明文扩展置换
                kzmw[i] = Ri[ei[i] - 1];       //注意指针
            for (int i = 0; i < 48; i++)
                keytem[i] = key[lun][i];      //轮密钥
            Xor(kzmw, keytem, 48);
            /*S盒置换*/
            for (int i = 0; i < 8; i++)
            {
                hang = kzmw[i * 6] * 2 + kzmw[i * 6 + 5];
                lie = kzmw[i * 6 + 1] * 8 + kzmw[i * 6 + 2] * 4 + kzmw[i * 6 + 3] * 2 + kzmw[i * 6 + 4];
                tmp[i * 4 + 3] = sbox[i][(hang + 1) * 16 + lie] % 2;
                tmp[i * 4 + 2] = (sbox[i][(hang + 1) * 16 + lie] / 2) % 2;
                tmp[i * 4 + 1] = (sbox[i][(hang + 1) * 16 + lie] / 4) % 2;
                tmp[i * 4] = (sbox[i][(hang + 1) * 16 + lie] / 8) % 2;
            }




            for (int i = 0; i < 32; i++)  //P置换  
                Ri[i] = tmp[Pzh[i] - 1];
            Xor(Ri, Li, 32);    //异或
            for (int i = 0; i < 32; i++)  //交换左右明文
            {
                Li[i] = ss[i];
            }

        }
        for (int i = 0; i < 32; i++)
        {
            tmp[i] = Li[i];
            Li[i] = Ri[i];
            Ri[i] = tmp[i];
        }
        for (int i = 0; i < 64; i++)
            PMW[i] = MW[fp[i] - 1];
        BitToByte(Out, PMW, 64);  //位到字节的转换
    }
}
int main()
{
    char Ki[8], jm[8], final[8];
    int i0;
    cout << "请输入密钥（8字节）：" << endl;
    for (i0 = 0; i0 < 8; i0++)
        cin >> Ki[i0];
    // if(i0<8)
    //  for(i0=0;i0<8;i0++)
    //  cin//[i0];
    keyfc(Ki);
    cout << "请输入明文：" << endl;
    for (i0 = 0; i0 < 8; i0++)
        cin >> jm[i0];
    DES(final, jm, 0);   //加密
    for (i0 = 0; i0 < 8; i0++)
        cout << final[i0];
    cout << endl;
    DES(jm, final, 1);   //解密
    for (i0 = 0; i0 < 8; i0++)
        cout << jm[i0];
    cout << endl;
}

57	49	41	33	25	17	9
1	58	50	42	34	26	18
10	2	59	51	43	35	27
19	11	3	60	52	44	36
63	55	47	39	31	23	15
7	62	54	46	38	30	22
14	6	61	53	45	37	29
21	13	5	28	20	12	4

14	17	11	24	1	5
3	28	15	6	21	10
23	19	12	4	26	8
16	7	27	20	13	2
41	52	31	37	47	55
30	40	51	45	33	48
44	49	39	56	34	53
46	42	50	36	29	32

58	50	42	34	26	18	10	2
60	52	44	36	28	20	12	4
62	54	46	38	30	22	14	6
64	56	48	40	32	24	16	8
57	49	41	33	25	17	9	1
59	51	43	35	27	19	11	3
61	53	45	37	29	21	13	5
63	55	47	39	31	23	15	7

32	1	2	3	4	5
4	5	6	7	8	9
8	9	10	11	12	13
12	13	14	15	16	17
16	17	18	19	20	21
20	21	22	23	24	25
24	25	26	27	28	29
28	29	30	31	32	1

14	4	13	1	2	15	11	8	3	10	6	12	5	9	0	7
0	15	7	4	14	2	13	1	10	6	12	11	9	5	3	8
4	1	14	8	13	6	2	11	15	12	9	7	3	10	5	0
15	12	8	2	4	9	1	7	5	11	3	14	10	0	6	13

15	1	8	14	6	11	3	4	9	7	2	13	12	0	5	10
3	13	4	7	15	2	8	14	12	0	1	10	6	9	11	5
0	14	7	11	10	4	13	1	5	8	12	6	9	3	2	15
13	8	10	1	3	15	4	2	11	6	7	12	0	5	14	9

10	0	9	14	6	3	15	5	1	13	12	7	11	4	2	8
13	7	0	9	3	4	6	10	2	8	5	14	12	11	15	1
13	6	4	9	8	15	3	0	11	1	2	12	5	10	14	7
1	10	13	0	6	9	8	7	4	15	14	3	11	5	2	12

7	13	14	3	0	6	9	10	1	2	8	5	11	12	4	15
13	8	11	5	6	15	0	3	4	7	2	12	1	10	14	9
10	6	9	0	12	11	7	13	15	1	3	14	5	2	8	4
3	15	0	6	10	1	13	8	9	4	5	11	12	7	2	14

2	12	4	1	7	10	11	6	8	5	3	15	13	0	14	9
14	11	2	12	4	7	13	1	5	0	15	10	3	9	8	6
4	2	1	11	10	13	7	8	15	9	12	5	6	3	0	14
11	8	12	7	1	14	2	13	6	15	0	9	10	4	5	3

12	1	10	15	9	2	6	8	0	13	3	4	14	7	5	11
10	15	4	2	7	12	9	5	6	1	13	14	0	11	3	8
9	14	15	5	2	8	12	3	7	0	4	10	1	13	11	6
4	3	2	12	9	5	15	10	11	14	1	7	6	0	8	13

57	49	41	33	25	17	9
1	58	50	42	34	26	18
10	2	59	51	43	35	27
19	11	3	60	52	44	36
63	55	47	39	31	23	15
7	62	54	46	38	30	22
14	6	61	53	45	37	29
21	13	5	28	20	12	4

14	17	11	24	1	5
3	28	15	6	21	10
23	19	12	4	26	8
16	7	27	20	13	2
41	52	31	37	47	55
30	40	51	45	33	48
44	49	39	56	34	53
46	42	50	36	29	32

58	50	42	34	26	18	10	2
60	52	44	36	28	20	12	4
62	54	46	38	30	22	14	6
64	56	48	40	32	24	16	8
57	49	41	33	25	17	9	1
59	51	43	35	27	19	11	3
61	53	45	37	29	21	13	5
63	55	47	39	31	23	15	7

32	1	2	3	4	5
4	5	6	7	8	9
8	9	10	11	12	13
12	13	14	15	16	17
16	17	18	19	20	21
20	21	22	23	24	25
24	25	26	27	28	29
28	29	30	31	32	1

14	4	13	1	2	15	11	8	3	10	6	12	5	9	0	7
0	15	7	4	14	2	13	1	10	6	12	11	9	5	3	8
4	1	14	8	13	6	2	11	15	12	9	7	3	10	5	0
15	12	8	2	4	9	1	7	5	11	3	14	10	0	6	13

15	1	8	14	6	11	3	4	9	7	2	13	12	0	5	10
3	13	4	7	15	2	8	14	12	0	1	10	6	9	11	5
0	14	7	11	10	4	13	1	5	8	12	6	9	3	2	15
13	8	10	1	3	15	4	2	11	6	7	12	0	5	14	9

10	0	9	14	6	3	15	5	1	13	12	7	11	4	2	8
13	7	0	9	3	4	6	10	2	8	5	14	12	11	15	1
13	6	4	9	8	15	3	0	11	1	2	12	5	10	14	7
1	10	13	0	6	9	8	7	4	15	14	3	11	5	2	12

7	13	14	3	0	6	9	10	1	2	8	5	11	12	4	15
13	8	11	5	6	15	0	3	4	7	2	12	1	10	14	9
10	6	9	0	12	11	7	13	15	1	3	14	5	2	8	4
3	15	0	6	10	1	13	8	9	4	5	11	12	7	2	14

2	12	4	1	7	10	11	6	8	5	3	15	13	0	14	9
14	11	2	12	4	7	13	1	5	0	15	10	3	9	8	6
4	2	1	11	10	13	7	8	15	9	12	5	6	3	0	14
11	8	12	7	1	14	2	13	6	15	0	9	10	4	5	3

12	1	10	15	9	2	6	8	0	13	3	4	14	7	5	11
10	15	4	2	7	12	9	5	6	1	13	14	0	11	3	8
9	14	15	5	2	8	12	3	7	0	4	10	1	13	11	6
4	3	2	12	9	5	15	10	11	14	1	7	6	0	8	13

57	49	41	33	25	17	9
1	58	50	42	34	26	18
10	2	59	51	43	35	27
19	11	3	60	52	44	36
63	55	47	39	31	23	15
7	62	54	46	38	30	22
14	6	61	53	45	37	29
21	13	5	28	20	12	4

14	17	11	24	1	5
3	28	15	6	21	10
23	19	12	4	26	8
16	7	27	20	13	2
41	52	31	37	47	55
30	40	51	45	33	48
44	49	39	56	34	53
46	42	50	36	29	32

58	50	42	34	26	18	10	2
60	52	44	36	28	20	12	4
62	54	46	38	30	22	14	6
64	56	48	40	32	24	16	8
57	49	41	33	25	17	9	1
59	51	43	35	27	19	11	3
61	53	45	37	29	21	13	5
63	55	47	39	31	23	15	7

32	1	2	3	4	5
4	5	6	7	8	9
8	9	10	11	12	13
12	13	14	15	16	17
16	17	18	19	20	21
20	21	22	23	24	25
24	25	26	27	28	29
28	29	30	31	32	1

14	4	13	1	2	15	11	8	3	10	6	12	5	9	0	7
0	15	7	4	14	2	13	1	10	6	12	11	9	5	3	8
4	1	14	8	13	6	2	11	15	12	9	7	3	10	5	0
15	12	8	2	4	9	1	7	5	11	3	14	10	0	6	13

15	1	8	14	6	11	3	4	9	7	2	13	12	0	5	10
3	13	4	7	15	2	8	14	12	0	1	10	6	9	11	5
0	14	7	11	10	4	13	1	5	8	12	6	9	3	2	15
13	8	10	1	3	15	4	2	11	6	7	12	0	5	14	9

10	0	9	14	6	3	15	5	1	13	12	7	11	4	2	8
13	7	0	9	3	4	6	10	2	8	5	14	12	11	15	1
13	6	4	9	8	15	3	0	11	1	2	12	5	10	14	7
1	10	13	0	6	9	8	7	4	15	14	3	11	5	2	12

7	13	14	3	0	6	9	10	1	2	8	5	11	12	4	15
13	8	11	5	6	15	0	3	4	7	2	12	1	10	14	9
10	6	9	0	12	11	7	13	15	1	3	14	5	2	8	4
3	15	0	6	10	1	13	8	9	4	5	11	12	7	2	14

2	12	4	1	7	10	11	6	8	5	3	15	13	0	14	9
14	11	2	12	4	7	13	1	5	0	15	10	3	9	8	6
4	2	1	11	10	13	7	8	15	9	12	5	6	3	0	14
11	8	12	7	1	14	2	13	6	15	0	9	10	4	5	3

12	1	10	15	9	2	6	8	0	13	3	4	14	7	5	11
10	15	4	2	7	12	9	5	6	1	13	14	0	11	3	8
9	14	15	5	2	8	12	3	7	0	4	10	1	13	11	6
4	3	2	12	9	5	15	10	11	14	1	7	6	0	8	13