SM4算法学习笔记

简介

SM4分组密码算法，于2012年3月21日发布，行标GM/T 0002-2012，已上升为国标GB/T 32907-2016。

简介

• 密钥长度：128 bits == 16 bytes
• 分组长度：128 bits == 16 bytes
• 加密算法与密钥扩展算法均采用非线性迭代结构
• 运算轮数32轮
• 强度与AES相当

轮函数F

static uint32_t F(uint32_t x0
	, uint32_t x1
	, uint32_t x2
	, uint32_t x3
	, uint32_t rk)
{
	return x0 ^ T(x1 ^ x2 ^ x3 ^ rk);
}

其中，rk参数是基于加密密钥扩展生成的轮密钥。

合成置换T，其实就是将输入先执行一遍AES的SubWord进行Sbox变换，再进行循环左移线性变换。

static uint32_t T(uint32_t a)
{
	uint32_t nRet = 0;

	// aes subword
	nRet += sbox[(a >> 4) & 0xF][a & 0xF];
	nRet += sbox[(a >> 12) & 0xF][(a >> 8) & 0xF] << 8;
	nRet += sbox[(a >> 20) & 0xF][(a >> 16) & 0xF] << 16;
	nRet += sbox[(a >> 28) & 0xF][(a >> 24) & 0xF] << 24;

	nRet = nRet
		^ ROTL32(nRet, 2)
		^ ROTL32(nRet, 10)
		^ ROTL32(nRet, 18)
		^ ROTL32(nRet, 24);


	return  nRet;
}

Sbox如下：

static const uint8_t sbox[16][16] =
{
	{0xd6, 0x90, 0xe9, 0xfe, 0xcc, 0xe1, 0x3d, 0xb7, 0x16, 0xb6, 0x14, 0xc2, 0x28, 0xfb, 0x2c, 0x05},
	{0x2b, 0x67, 0x9a, 0x76, 0x2a, 0xbe, 0x04, 0xc3, 0xaa, 0x44, 0x13, 0x26, 0x49, 0x86, 0x06, 0x99},
	{0x9c, 0x42, 0x50, 0xf4, 0x91, 0xef, 0x98, 0x7a, 0x33, 0x54, 0x0b, 0x43, 0xed, 0xcf, 0xac, 0x62},
	{0xe4, 0xb3, 0x1c, 0xa9, 0xc9, 0x08, 0xe8, 0x95, 0x80, 0xdf, 0x94, 0xfa, 0x75, 0x8f, 0x3f, 0xa6},
	{0x47, 0x07, 0xa7, 0xfc, 0xf3, 0x73, 0x17, 0xba, 0x83, 0x59, 0x3c, 0x19, 0xe6, 0x85, 0x4f, 0xa8},
	{0x68, 0x6b, 0x81, 0xb2, 0x71, 0x64, 0xda, 0x8b, 0xf8, 0xeb, 0x0f, 0x4b, 0x70, 0x56, 0x9d, 0x35},
	{0x1e, 0x24, 0x0e, 0x5e, 0x63, 0x58, 0xd1, 0xa2, 0x25, 0x22, 0x7c, 0x3b, 0x01, 0x21, 0x78, 0x87},
	{0xd4, 0x00, 0x46, 0x57, 0x9f, 0xd3, 0x27, 0x52, 0x4c, 0x36, 0x02, 0xe7, 0xa0, 0xc4, 0xc8, 0x9e},
	{0xea, 0xbf, 0x8a, 0xd2, 0x40, 0xc7, 0x38, 0xb5, 0xa3, 0xf7, 0xf2, 0xce, 0xf9, 0x61, 0x15, 0xa1},
	{0xe0, 0xae, 0x5d, 0xa4, 0x9b, 0x34, 0x1a, 0x55, 0xad, 0x93, 0x32, 0x30, 0xf5, 0x8c, 0xb1, 0xe3},
	{0x1d, 0xf6, 0xe2, 0x2e, 0x82, 0x66, 0xca, 0x60, 0xc0, 0x29, 0x23, 0xab, 0x0d, 0x53, 0x4e, 0x6f},
	{0xd5, 0xdb, 0x37, 0x45, 0xde, 0xfd, 0x8e, 0x2f, 0x03, 0xff, 0x6a, 0x72, 0x6d, 0x6c, 0x5b, 0x51},
	{0x8d, 0x1b, 0xaf, 0x92, 0xbb, 0xdd, 0xbc, 0x7f, 0x11, 0xd9, 0x5c, 0x41, 0x1f, 0x10, 0x5a, 0xd8},
	{0x0a, 0xc1, 0x31, 0x88, 0xa5, 0xcd, 0x7b, 0xbd, 0x2d, 0x74, 0xd0, 0x12, 0xb8, 0xe5, 0xb4, 0xb0},
	{0x89, 0x69, 0x97, 0x4a, 0x0c, 0x96, 0x77, 0x7e, 0x65, 0xb9, 0xf1, 0x09, 0xc5, 0x6e, 0xc6, 0x84},
	{0x18, 0xf0, 0x7d, 0xec, 0x3a, 0xdc, 0x4d, 0x20, 0x79, 0xee, 0x5f, 0x3e, 0xd7, 0xcb, 0x39, 0x48}
};

算法描述

流程很简单，但想要理解它的设计思想还是需要一些数学功力。。

密钥扩展

基于16字节密钥扩展出32个轮密钥。

static uint32_t InvT(uint32_t a)
{
	uint32_t nRet = 0;

	// aes subword
	nRet += sbox[(a >> 4) & 0xF][a & 0xF];
	nRet += sbox[(a >> 12) & 0xF][(a >> 8) & 0xF] << 8;
	nRet += sbox[(a >> 20) & 0xF][(a >> 16) & 0xF] << 16;
	nRet += sbox[(a >> 28) & 0xF][(a >> 24) & 0xF] << 24;

	nRet = nRet
		^ ROTL32(nRet, 13)
		^ ROTL32(nRet, 23);


	return  nRet;
}


static ErrCrypto KeyExpansion(sm4_ctx* pCtx, uint8_t key[SM4_KEY_SIZE])
{
	ErrCrypto errRet = ERR_OK;
	uint32_t MK[4] = { 0 };
	uint32_t K[36] = {0};
	uint32_t i = 0;

	static const uint32_t FK[4] = { 
		0xa3b1bac6, 0x56aa3350, 0x677d9197, 0xb27022dc 
	};
	static const uint32_t CK[32] =
	{
		0x00070e15, 0x1c232a31, 0x383f464d, 0x545b6269,
		0x70777e85, 0x8c939aa1, 0xa8afb6bd, 0xc4cbd2d9,
		0xe0e7eef5, 0xfc030a11, 0x181f262d, 0x343b4249,
		0x50575e65, 0x6c737a81, 0x888f969d, 0xa4abb2b9,
		0xc0c7ced5, 0xdce3eaf1, 0xf8ff060d, 0x141b2229,
		0x30373e45, 0x4c535a61, 0x686f767d, 0x848b9299,
		0xa0a7aeb5, 0xbcc3cad1, 0xd8dfe6ed, 0xf4fb0209,
		0x10171e25, 0x2c333a41, 0x484f565d, 0x646b7279
	};

	if (!pCtx || !key)
	{
		return ERR_NULL;
	}

	MK[0] = u8to32_big(key);
	MK[1] = u8to32_big(key + 4);
	MK[2] = u8to32_big(key + 8);
	MK[3] = u8to32_big(key + 12);

	K[0] = MK[0] ^ FK[0];
	K[1] = MK[1] ^ FK[1];
	K[2] = MK[2] ^ FK[2];
	K[3] = MK[3] ^ FK[3];

	for (i = 0; i < SM4_ROUNDS; ++i)
	{
		pCtx->rk[i] 
		= K[i + 4]
		= K[i]
			^ InvT(K[i+1]
				^ K[i + 2]
				^ K[i + 3]
				^ CK[i]);
	}
	
	return errRet;
}

其中，InvT相比T变换，仅仅是线性变换不同。

加密

设输入为x[0], x[1], x[2], x[3]，执行32轮F运算即可：

uint32_t x[36] = {0};
for (i = 0; i < SM4_ROUNDS; ++i)
{
    x[i+4] = F(x[i], x[i + 1], x[i + 2], x[i + 3], pCtx->rk[i]);
}

最后，密文为x[35], x[34], x[33], x[32]。

解密

和加密一样的流程，只不过轮密钥要反着用。

实现

https://github.com/C0deStarr/CryptoImp/tree/main/Cipher/BlockCipher

• sm4.h
• sm4.c

参考资料

我国SM4分组密码算法正式成为ISO/IEC国际标准_国家密码管理局 (sca.gov.cn)

国家标准|GB/T 32907-2016 (samr.gov.cn)

www.gmbz.org.cn/main/viewfile/20180108015408199368.html