AES加密算法

先搞定AES算法，基本变换包括SubBytes（字节替代）、ShiftRows（行移位）、MixColumns（列混淆）、AddRoundKey(轮密钥加）

其算法一般描述为

明文及密钥的组织排列方式

 

ByteSubstitution（字节替代）

非线性的字节替代，单独处理每个字节：

求该字节在有限域GF(2⁸)上的乘法逆，"0"被映射为自身，即对于α∈GF(2⁸)，求β∈GF(2⁸)，

使得α·β=β·α=1mod(x⁸+x⁴+x²+x+1)。

对上一步求得的乘法逆作仿射变换

y_i=x_i + x_(i+4)mod8 + x_(i+6)mod8 + x_(i+7)mod8 + c_i

(其中c_i是63₁₀即01100011₂的第i位），用矩阵表示为

本来打算把求乘法逆和仿射变换算法敲上去，最后还是放弃了...直接打置换表

 

unsigned char sBox[] =
{ /*  0    1    2    3    4    5    6    7    8    9    a    b    c    d    e    f */
    0x63,0x7c,0x77,0x7b,0xf2,0x6b,0x6f,0xc5,0x30,0x01,0x67,0x2b,0xfe,0xd7,0xab,0x76, /*0*/
    0xca,0x82,0xc9,0x7d,0xfa,0x59,0x47,0xf0,0xad,0xd4,0xa2,0xaf,0x9c,0xa4,0x72,0xc0, /*1*/
    0xb7,0xfd,0x93,0x26,0x36,0x3f,0xf7,0xcc,0x34,0xa5,0xe5,0xf1,0x71,0xd8,0x31,0x15, /*2*/
    0x04,0xc7,0x23,0xc3,0x18,0x96,0x05,0x9a,0x07,0x12,0x80,0xe2,0xeb,0x27,0xb2,0x75, /*3*/
    0x09,0x83,0x2c,0x1a,0x1b,0x6e,0x5a,0xa0,0x52,0x3b,0xd6,0xb3,0x29,0xe3,0x2f,0x84, /*4*/
    0x53,0xd1,0x00,0xed,0x20,0xfc,0xb1,0x5b,0x6a,0xcb,0xbe,0x39,0x4a,0x4c,0x58,0xcf, /*5*/
    0xd0,0xef,0xaa,0xfb,0x43,0x4d,0x33,0x85,0x45,0xf9,0x02,0x7f,0x50,0x3c,0x9f,0xa8, /*6*/
    0x51,0xa3,0x40,0x8f,0x92,0x9d,0x38,0xf5,0xbc,0xb6,0xda,0x21,0x10,0xff,0xf3,0xd2, /*7*/
    0xcd,0x0c,0x13,0xec,0x5f,0x97,0x44,0x17,0xc4,0xa7,0x7e,0x3d,0x64,0x5d,0x19,0x73, /*8*/
    0x60,0x81,0x4f,0xdc,0x22,0x2a,0x90,0x88,0x46,0xee,0xb8,0x14,0xde,0x5e,0x0b,0xdb, /*9*/
    0xe0,0x32,0x3a,0x0a,0x49,0x06,0x24,0x5c,0xc2,0xd3,0xac,0x62,0x91,0x95,0xe4,0x79, /*a*/
    0xe7,0xc8,0x37,0x6d,0x8d,0xd5,0x4e,0xa9,0x6c,0x56,0xf4,0xea,0x65,0x7a,0xae,0x08, /*b*/
    0xba,0x78,0x25,0x2e,0x1c,0xa6,0xb4,0xc6,0xe8,0xdd,0x74,0x1f,0x4b,0xbd,0x8b,0x8a, /*c*/
    0x70,0x3e,0xb5,0x66,0x48,0x03,0xf6,0x0e,0x61,0x35,0x57,0xb9,0x86,0xc1,0x1d,0x9e, /*d*/
    0xe1,0xf8,0x98,0x11,0x69,0xd9,0x8e,0x94,0x9b,0x1e,0x87,0xe9,0xce,0x55,0x28,0xdf, /*e*/
    0x8c,0xa1,0x89,0x0d,0xbf,0xe6,0x42,0x68,0x41,0x99,0x2d,0x0f,0xb0,0x54,0xbb,0x16  /*f*/
};

 

 下面是逆置换表，解密时使用

 

unsigned char invsBox[256] =
{ /*  0    1    2    3    4    5    6    7    8    9    a    b    c    d    e    f  */
    0x52,0x09,0x6a,0xd5,0x30,0x36,0xa5,0x38,0xbf,0x40,0xa3,0x9e,0x81,0xf3,0xd7,0xfb, /*0*/
    0x7c,0xe3,0x39,0x82,0x9b,0x2f,0xff,0x87,0x34,0x8e,0x43,0x44,0xc4,0xde,0xe9,0xcb, /*1*/
    0x54,0x7b,0x94,0x32,0xa6,0xc2,0x23,0x3d,0xee,0x4c,0x95,0x0b,0x42,0xfa,0xc3,0x4e, /*2*/
    0x08,0x2e,0xa1,0x66,0x28,0xd9,0x24,0xb2,0x76,0x5b,0xa2,0x49,0x6d,0x8b,0xd1,0x25, /*3*/
    0x72,0xf8,0xf6,0x64,0x86,0x68,0x98,0x16,0xd4,0xa4,0x5c,0xcc,0x5d,0x65,0xb6,0x92, /*4*/
    0x6c,0x70,0x48,0x50,0xfd,0xed,0xb9,0xda,0x5e,0x15,0x46,0x57,0xa7,0x8d,0x9d,0x84, /*5*/
    0x90,0xd8,0xab,0x00,0x8c,0xbc,0xd3,0x0a,0xf7,0xe4,0x58,0x05,0xb8,0xb3,0x45,0x06, /*6*/
    0xd0,0x2c,0x1e,0x8f,0xca,0x3f,0x0f,0x02,0xc1,0xaf,0xbd,0x03,0x01,0x13,0x8a,0x6b, /*7*/
    0x3a,0x91,0x11,0x41,0x4f,0x67,0xdc,0xea,0x97,0xf2,0xcf,0xce,0xf0,0xb4,0xe6,0x73, /*8*/
    0x96,0xac,0x74,0x22,0xe7,0xad,0x35,0x85,0xe2,0xf9,0x37,0xe8,0x1c,0x75,0xdf,0x6e, /*9*/
    0x47,0xf1,0x1a,0x71,0x1d,0x29,0xc5,0x89,0x6f,0xb7,0x62,0x0e,0xaa,0x18,0xbe,0x1b, /*a*/
    0xfc,0x56,0x3e,0x4b,0xc6,0xd2,0x79,0x20,0x9a,0xdb,0xc0,0xfe,0x78,0xcd,0x5a,0xf4, /*b*/
    0x1f,0xdd,0xa8,0x33,0x88,0x07,0xc7,0x31,0xb1,0x12,0x10,0x59,0x27,0x80,0xec,0x5f, /*c*/
    0x60,0x51,0x7f,0xa9,0x19,0xb5,0x4a,0x0d,0x2d,0xe5,0x7a,0x9f,0x93,0xc9,0x9c,0xef, /*d*/
    0xa0,0xe0,0x3b,0x4d,0xae,0x2a,0xf5,0xb0,0xc8,0xeb,0xbb,0x3c,0x83,0x53,0x99,0x61, /*e*/
    0x17,0x2b,0x04,0x7e,0xba,0x77,0xd6,0x26,0xe1,0x69,0x14,0x63,0x55,0x21,0x0c,0x7d  /*f*/
};

 

这里遇到问题了，本来用纯c初始化数组很正常，封装成类以后发现不能初始化，不管是声明、构造函数都无法初始化，百歌谷度了一通后没有任何答案，无奈只能在构造函数中声明一个局部变量数组并初始化，然后用memcpy，（成员变量名为Sbox/InvSbox，局部变量名sBox/invsBox）

void AES::SubBytes(unsigned char state[][4])
{
    int r,c;
    for (r=0; r<4; r++)
    {
        for (c=0; c<4; c++)
        {
            state[r][c] = Sbox[state[r][c]];
        }
    }
}

 ShiftRows（行移位变换）

行移位变换完成基于行的循环位移操作，变换方法： 

即行移位变换作用于行上，第0行不变，第1行循环左移1个字节，第2行循环左移2个字节，第3行循环左移3个字节。

 

void AES::ShiftRows(unsigned char state[][4])
{
    unsigned char t[4];
    int r,c;
    for (r=1; r<4; r++)
    {
        for (c=0; c<4; c++)
        {
            t[c] = state[r][(c+r)%4];
        }
        for (c=0; c<4; c++)
        {
            state[r][c] = t[c];
        }
    }
}

MixColumns（列混淆变换） 

 逐列混合，方法：

b(x) = (03·x³ + 01·x² + 01·x + 02) · a(x) mod(x⁴ + 1)

矩阵表示形式：

 

void AES::MixColumns(unsigned char state[][4])
{
    unsigned char t[4];
    int r,c;
    for (c=0; c< 4; c++)
    {
        for (r=0; r<4; r++)
        {
            t[r] = state[r][c];
        }
        for (r=0; r<4; r++)
        {
            state[r][c] = FFmul(0x02, t[r])
                        ^ FFmul(0x03, t[(r+1)%4])
                        ^ FFmul(0x01, t[(r+2)%4])
                        ^ FFmul(0x01, t[(r+3)%4]);
        }
    }
}

unsigned char AES::FFmul(unsigned char a, unsigned char b)
{
    unsigned char bw[4];
    unsigned char res=0;
    int i;
    bw[0] = b;
    for (i=1; i<4; i++)
    {
        bw[i] = bw[i-1]<<1;
        if (bw[i-1]&0x80)
        {
            bw[i]^=0x1b;
        }
    }
    for (i=0; i<4; i++)
    {
        if ((a>>i)&0x01)
        {
            res ^= bw[i];
        }
    }
    return res;
}

 

其中FFmul为有限域GF(2⁸)上的乘法，标准算法应该是循环8次（b与a的每一位相乘，结果相加），但这里只用到最低2位，解密时用到的逆列混淆也只用了低4位，所以在这里高4位的运算是多余的，只计算低4位。

 

AddRoundKey（轮密钥加变换） 

 简单来说就是逐字节相加，有限域GF(2⁸)上的加法是模2加法，即异或

 

void AES::AddRoundKey(unsigned char state[][4], unsigned char k[][4])
{
    int r,c;
    for (c=0; c<4; c++)
    {
        for (r=0; r<4; r++)
        {
            state[r][c] ^= k[r][c];
        }
    }
}

 

 KeyExpansion（密钥扩展）

 将输入的密钥扩展为11组128位密钥组，其中第0组为输入密钥本身 

 其后第n组第i列 为 第n-1组第i列 与 第n组第i-1列之和（模2加法，1<= i <=3）

对于每一组 第一列即i=0，有特殊的处理

将前一列即第n-1组第3列的4个字节循环左移1个字节，

并对每个字节进行字节替代变换SubBytes

将第一行（即第一个字节）与轮常量rc[n]相加 

最后再与前一组该列相加 

 

void AES::KeyExpansion(unsigned char * key, unsigned char w[][4][4])
{
    int i,j,r,c;
    unsigned char rc[] = {0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40, 0x80, 0x1b, 0x36};
    for (r=0; r<4; r++)
    {
        for (c=0; c<4; c++)
        {
            w[0][r][c] = key[r+c*4];
        }
    }
    for (i=1; i<=10; i++)
    {
        for (j=0; j<4; j++)
        {
            unsigned char t[4];
            for (r=0; r<4; r++)
            {
                t[r] = j ? w[i][r][j-1] : w[i-1][r][3];
            }
            if (j == 0)
            {
                unsigned char temp = t[0];
                for (r=0; r<3; r++)
                {
                    t[r] = Sbox[t[(r+1)%4]];
                }
                t[3] = Sbox[temp];
                t[0] ^= rc[i-1];
            }
            for (r=0; r<4; r++)
            {
                w[i][r][j] = w[i-1][r][j] ^ t[r];
            }
        }
    }
}

 

解密的基本运算

AES解密算法与加密不同，基本运算中除了AddRoundKey（轮密钥加）不变外，其余的都需要进行逆变换，即

InvSubBytes（逆字节替代）、InvShiftRows（逆行移位）、InvMixColumns（逆列混淆）

 

void AES::InvSubBytes(unsigned char state[][4])
{
    int r,c;
    for (r=0; r<4; r++)
    {
        for (c=0; c<4; c++)
        {
            state[r][c] = InvSbox[state[r][c]];
        }
    }
}

void AES::InvShiftRows(unsigned char state[][4])
{
    unsigned char t[4];
    int r,c;
    for (r=1; r<4; r++)
    {
        for (c=0; c<4; c++)
        {
            t[c] = state[r][(c-r+4)%4];
        }
        for (c=0; c<4; c++)
        {
            state[r][c] = t[c];
        }
    }
}

void AES::InvMixColumns(unsigned char state[][4])
{
    unsigned char t[4];
    int r,c;
    for (c=0; c< 4; c++)
    {
        for (r=0; r<4; r++)
        {
            t[r] = state[r][c];
        }
        for (r=0; r<4; r++)
        {
            state[r][c] = FFmul(0x0e, t[r])
                        ^ FFmul(0x0b, t[(r+1)%4])
                        ^ FFmul(0x0d, t[(r+2)%4])
                        ^ FFmul(0x09, t[(r+3)%4]);
        }
    }
}

 

加密过程

先将输入的明文按列序组合成4*4的矩阵，直接与第0组密钥（即输入的密钥）相加（异或），作为轮加密的输入

然后循环10次进行SubBytes、ShiftRows、MixColumns、AddRoundKey运算，最后恢复原序列

需要注意的是最后一轮并不进行MixColumns（列混淆变换）

 

unsigned char * AES::Cipher(unsigned char * input)
{
    unsigned char state[4][4];
    int i,r,c;

    for (r=0; r<4; r++)
    {
        for (c=0; c<4 ;c++)
        {
            state[r][c] = input[c*4+r];
        }
    }

    AddRoundKey(state,w[0]);

    for (i=1; i<=10; i++)
    {
        SubBytes(state);
        ShiftRows(state);
        if (i!=10)MixColumns(state);
        AddRoundKey(state,w[i]);
    }

    for (r=0; r<4; r++)
    {
        for (c=0; c<4 ;c++)
        {
            input[c*4+r] = state[r][c];
        }
    }

    return input;
}

 

解密过程

 

unsigned char * AES::InvCipher(unsigned char * input)
{
    unsigned char state[4][4];
    int i,r,c;

    for (r=0; r<4; r++)
    {
        for (c=0; c<4 ;c++)
        {
            state[r][c] = input[c*4+r];
        }
    }

    AddRoundKey(state, w[10]);
    for (i=9; i>=0; i--)
    {
        InvShiftRows(state);
        InvSubBytes(state);
        AddRoundKey(state, w[i]);
        if (i)InvMixColumns(state);
    }

    for (r=0; r<4; r++)
    {
        for (c=0; c<4 ;c++)
        {
            input[c*4+r] = state[r][c];
        }
    }

    return input;
}

 

对外部数据的加密/解密

至此已经实现了AES加密与解密的原型，在使用的时候一般处理的是字符串等，而不是直接传入128位的数据，所以要封装一下对外部数据的加解密处理

void * AES::Cipher( void * input, int length)
{
    unsigned char * in = (unsigned char *) input;
    int i;
    if (!length)
    {
        while (*(in+length++));
        in = (unsigned char *) input;
    }
    for (i=0; i
    {
        Cipher(in+i);
    }
    return input;
}

void * AES::InvCipher( void * input, int length)
{
    unsigned char * in = (unsigned char *) input;
    int i;
    for (i=0; i
    {
        InvCipher(in+i);
    }
    return input;
}

 

加密时默认参数length=0,为要加密的数据长度，如果使用默认值，则作为字符串处理，以'\0'为结尾计算长度

加密时传进的指针要预留够16整数倍字节的空间，因为加密操作直接修改原数据，不足128位可能造成内存溢出