AES加密算法(C++实现,附源码)

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博客地址:http://mingcn.cnblogs.com/

本文地址:http://mingcn.cnblogs.com/archive/2010/10/31/aes_c.html

 

快毕业了,最后一个课程设计,《基于Windows Socket的安全通信》,内容就是基于AES加密的SOCKET通信,貌似挺简单,不过要用VC++6.0开发,C++我确实没有任何代码经验,虽然不是强制性,但由于机房里各种纠结,只能用它了(用Java没有挑战性,封装得太好了...也算熟悉下VC++吧)

 

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

yi=xi + x(i+4)mod8 + x(i+6)mod8 + x(i+7)mod8 + ci

(其中ci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<length; i+=16)
	{
		Cipher(in+i);
	}
	return input;
}

void* AES::InvCipher(void* input, int length)
{
	unsigned char* in = (unsigned char*) input;
	int i;
	for(i=0; i<length; i+=16)
	{
		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

 

 最后附上源代码  Source_AES_Cipher

posted @ 2010-10-31 02:58  xelz  阅读(109694)  评论(52编辑  收藏