本文主要介绍了AES的四种加密算法的c源代码,边肖觉得挺不错的。现在分享给大家,给大家一个参考。
作为新一代加密标准,AES旨在取代DES(参见《DES加密算法的C++实现》)以满足当今分布式开放网络对数据加密安全的要求。在分析AES加密原理的基础上,重点介绍了算法实现的具体步骤,并使用C对文件进行加密和解密。
一、AES 介绍
AES (Advanced Encryption Standard)又称密码学中的Rijndael加密,是美国联邦政府采用的分组加密标准。该标准用于取代最初的DES,已在世界范围内广泛使用,成为最流行的对称密钥算法之一。
在AES出现之前,最常用的对称密钥算法是DES加密算法,1977年作为美国政府的商业加密标准发布。DES的主要问题是密钥长度短,逐渐不适应分布式开放网络对数据加密安全的要求。因此,1998年,美国政府决定不再继续使用DES作为联邦加密标准,并发起了收集AES候选算法的运动。征集活动中对AES的基本要求是:比三重DES快,至少和三重DES一样安全,数据包长度128位,密钥长度128/192/256位。
经过三年多的评选,由比利时密码学家设计的Rijndael算法最终脱颖而出,成为新一代高级加密标准,由NIST于2001年在FIPS PUB 197上发表。
二、AES 算法原理
AES算法(Rijndael算法)是一种对称分组密码算法。数据包长度必须为128位,使用的密钥长度为128、192或256位。三种密钥长度不同的AES算法分别称为AES-128、AES-192和AES-256。(Rijndael的设计也可以处理其他的包长度和密钥长度,但是在AES标准中没有采用)
下图是AES加密和解密的整体流程图:
这里我们需要知道三个符号:Nb—— State包含的列数(32位字),即NB=4;Nk——密钥中包含的32位字的个数,即Nk=4、6或8;对于不同的密钥长度,Nr——加密的轮数不同,如下图所示:
下面分为三个部分:密钥扩展、分组加密和分组解密。我会尽量做到简明扼要。如果还是不明白,请自己谷歌一下。
1)密钥扩展
AES算法通过密钥扩展程序对用户输入的密钥K进行扩展,生成Nb(Nr 1)个字,存储在线性数组w[Nb*(Nr 1)]中。如下所示:
位置转换函数RotWord()接受一个字[a0,a1,a2,a3]作为输入,将其循环左移一个字节并输出[a1,a2,a3,a0]。
s盒转换函数SubWord(),它接受一个单词[a0,a1,a2,a3]作为输入。S-box是一个16x16的表,其中每个元素是一个字节。对于每个输入字节,前四位组成十六进制数X作为行号,后四位组成十六进制数Y作为列号,以便在表中查找对应的值。最后,该函数输出一个由四个新字节组成的32位字。
圆整常数Rcon[],怎么算,就不说了。就当是常量数组吧。
扩展密钥数组w[]的前Nk个元素为外密钥K,后续元素w[i]等于其前一个元素w[i-1]与第一个Nk元素w[i-Nk]的异或,即W[I]=W[I-1]XOR W[I-Nk];但如果I是Nk的倍数,那么W [I]=W [I-NK] XOR子字(rot word(W[I-1]))XOR rcon[I/Nk-1]。
注意,上面的第四步适用于AES-128和AES-192,详细伪码如下:
密钥扩展程序(AES-128)的c代码:
#包括iostream
#包含位集
使用命名空间std
typedef位集8字节;
typedef位集32字;
const int Nr=10//AES-128需要10轮加密
const int Nk=4;//Nk表示输入键的字数。
字节S_Box[16][16]={
{0x 63.0 x7c,0x 77.0 x7b,0x 2.0 x 6b,0x6F,0x 5.0 x 30.0x 01,0x 67.0 x 2b,0x e,0x 7.0 xab,0x76},
{0x 82.0 xc 9.0 x7d . 0 xfa .0x 59.0 x 47.0 x 47.0 x xad .0x 4.0 xa 2.0 xaf .0x 9c .0x 4.0 x 72.0 x xc0 },
{0x 7.0 x 93.0 x 26.0 x 36.0 x 3 f .0x 7.0 x 34.0 x 5.0 x 1.0 x 71.0 x 8.0 x 31.0 x 15 },
{0x 04.0 xc 7.0 x 23.0 xc 3.0 x 18.0 x 96.0 x 05.0 x 9a.0 x 07.0 x 12.0 x 80.0 x 2.0 xeb . 0 x 27.0 XB 2.0 x 75 },
{0x 09.0 x 83.0 x 2c.0 x 1a.0 x 1b.0 x 6e.0 x 5a.0 xa 0.0 x 52.0 x 3b.0 xd 6.0 XB 3.0 x 29.0 xe 3.0 x 2 f.0 x 84 },
{0x 53.0 xd 1.0 x 00.0 xed,0x 20.0 xfc,0x 1.0 x 5b,0x6A,0xB,0x b,0x 39.0 x 4a,0x4C,0x 58.0 xcf },
{ 0 xd 0.0 xef,0xAA,0xFB,0 x 43.0 x4 d,0 x 33.0 x 85.0 x 45.0 xf9.0 x 02.0 x 7f,0 x 50.0 x 3c,0x9F,0xA8},
{0x 51.0 xa 3.0 x 40.0 x 8f . 0 x 92.0 x 9d . 0 x 38.0 xf 5.0 xbc . 0 XB 6.0 xda . 0 x 21.0 x 10.0 xff . 0 xff 3.0 xd 2 },
{0x 0 c,0x 13.0 exec,0x5F,0x 97.0 x 44.0 x 17.0 xc 4.0 xa 7.0 x 7e,0x 3 3d,0x 64.0 x 5d,0x 19.0 x 73 },
{0x 60.0 x 81.0 x 4f,0x 22.0 x 2a,0x 90.0 x 88.0 x 46.0 xee,0x 8.0 x 14.0 xd,0x5E,0x0B,0xDB},
{0x 0.0x 32.0 x3a .0x 49.0 x 06.0 x 24.0 x 5c .0x xc 2.0 x xd 3.0 xac .0x 62.0 x 91.0 x 95.0 x 4.0 x 79 },
{0x 7.0 xc 8.0 x 37.0 x 6d.0 x 8d.0 xd 5.0 x 4e.0 xa 9.0 x 6c.0 x 56.0 xf 4.0 xea .0x 65.0 x 7a.0 xae .0x 08 },
{0xBA,0x78,0x25,0x2E,0x1C,0x 6,0x 6,0x 6,0x 8,0x 8,0x74,0x1F,0x4B,0x8B,0x8A},
{0x 70.0 x 3e .0x 5.0 x 66.0 x 48.0 x 03.0 x 6.0 x 61.0 x 35.0 x 57.0 x 9.0 x 86.0 x 1.0 x 1d .0x 9e },
{0x 1.0x 8.0x 98.0 x 11.0 x 69.0 x 9.0 x 8 e.0 x 94.0 x 9 b.0 x 1e.0 x 87.0 x 9.0 x 55.0 x 28.0 xdf },
{0x8C,0 xa 1.0 x 89.0 x 0d,0xBF,0 xe 6.0 x 42.0 x 68.0 x 41.0 x 99.0 x 2d,0x0F,0 XB 0.0 x 54.0 xbb,0x16}
}:
//轮常数,密钥扩展中用到。(AES-128只需要10轮)
S7-1200可编程控制器,
0x 20000000.0 x 40000000.0 x 80000000.0 x 1b 000000.0 x 36000000 };
/**
*将四个字节数转换为一个单词(字)
*/
单词(字节k1,字节k2,字节k3,字节k4)
{
字结果(0x 00000000);
临时字;
临时=kto _ ulong();//K1
临时=24;
结果|=温度
临时=kto _ ulong();//K2
临时=16;
结果|=温度
临时=kto _ ulong();//k3b
临时=8;
结果|=温度
临时=kto _ ulong();//K4
结果|=温度
返回结果;
}
/**
*按字节循环左移一位
*即把[a0、a1、a2、a3]变成[a1、a2、a3、a0]
*/
word RotWord(word rw)
{
字高=rw 8;
字低=rw 24
返回高|低;
}
/**
*对输入单词(字)中的每一个字节进行表示“上帝的”: 'sblood盒变换
*/
word子词(word sw)
{
临时字;
for(int I=0);i3 32i=8)
{
int row=SW[i7]* 8 SW[i6]* 4 SW[i5]* 2 SW[i4];
int col=SW[i3]* 8 SW[I2]* 4 SW[i1]* 2 SW[I];
字节val=s _ box[行][col];
for(int j=0);j8型;(j)
临时[I j]=val[j];
}
返回临时雇员
}
/**
*密钥扩展函数-对128位密钥进行扩展得到w[4*(第一号)]
*/
请参阅密钥扩展(位元组金钥[4*Nk]、单词w[4 *(NR 1])
{
临时字;
int I=0;
//w[]的前四个就是输入的关键点
而(我Nk)
{
w[i]=Word(key[4*i]、key[4*i 1]、key[4*i 2]、key[4 * i3]);
(i);
}
我=nk
while(i1 *(NR 1))
{
临时=w[I-1];//记录前一个单词(字)
if(i % Nk==0)
w[I]=w[I-NK]子字(腐字(temp));rcon[I/NK-1];
其他语句
w[I]=w[I-NK]temp;
(i);
}
}
int main()
{
字节键[16]={0x2b,0x7e,0x15,0x16,
0x 28.0 xae,0x 2.0 xa 6,
0xab,0 xf7.0 x 15.0 x 88,
0x 09.0 xcf,0x4f,0x 3c };
字w[4*(第一号)];
“cout”键是:“;
for(int I=0);i16(一)
通道十六进制密钥[I]to _ ulong()';
端盖;端盖;
关键点扩展(关键点,w);
//测试
for(int I=0);i4*(第一号);(一)
cout ' w[' dec I ']=' hex w[I]to _ ulong()结束;
返回0;
}
测试输出结果:
2)加密美元
根据-AES加密的整体流程图(本文开头),伪代码如下:
从伪代码描述中可以看出,AES加密涉及的子程序有SubBytes()、ShiftRows()、MixColumns()和AddRoundKey()。让我们逐一介绍:
S盒变换-亚字节()
如密钥扩展部分所述,S盒是一个16行16列的表,表中的每个元素都是一个字节。s盒转换非常简单:函数SubBytes()接受一个4x4字节的矩阵作为输入。对于每个字节,前四个数字组成十六进制数X作为行号,后四个数字组成十六进制数Y作为列号。查找表中的相应值将替换原始位置的字节。
行变换-ShiftRows()
行转换也很简单。它只是以字节为单位循环移位矩阵的每一行:第一行不变,第二行左移一位,第三行左移两位,第四行左移三位。如下图所示:
列转换-MixColumns()
MixColumns()函数也接受一个4x4字节的矩阵作为输入,并按以下方式逐列转换矩阵:
请注意,公式中使用的乘法是伽罗瓦域(GF,有限域)上的乘法,这在fips-197中有所描述。如果还是不明白,请自己谷歌一下。
与扩展密钥-AddRoundKey()进行异或运算
扩展键只参与这一步。根据当前加密的轮数,w[]中的四个扩展密钥用于与矩阵的四列进行按位异或。如下图:
好了,这就是AES加密的所有部分。算法的C源代码在文章后面的第三部分。
3)解密
根据AES解密的整体流程图(本文开头),伪代码如下:
从伪代码中可以看出,我们需要分别实现S盒变换、行变换、列变换的逆变换InvShiftRows()、InvSubBytes()和InvMixColumns()。我们来简单说一下这三个逆变换:
逆向转换-InvShiftRows()
如上所述,ShiftRows()循环左移矩阵的每一行,因此InvShiftRows()循环右移矩阵的每一行。
逆S盒变换-InvSubBytes()
和S-Box变换一样,也是查表,查表的方式也是一样的,只不过是另一个置换表(S盒的逆表)。
逆列变换-InvMixColumns()
与列变换方式相同,只是计算公式的系数矩阵发生了变化。如下图:
好了,AES解密到此结束。只要写出三个逆变换函数,那么AES解密算法就可以根据伪代码轻松实现。
三、C++实现
下面,我用C实现AES的加解密算法,实现文件的加解密。这里我用C STL的bitset来定义两种类型:字节和字。应该提到的是,对于有限域上的乘法,我们可以查找表(6个结果表)或编写函数。当然查表会更有效率,但是考虑到贴代码,这里我用一个函数来实现。
以下是AES-128加密和解密128位数据的源代码:
/*************************************************************************
文件名:AEScpp
作者:宋丽
电子邮箱:lisongshine@qqcom
创建时间:2014年12月12日星期五20: 15: 50
个人博客:http://songleegithubcom
************************************************************************/
#包括iostream
#包含位集
#包含字符串
使用命名空间std
typedef位集8字节;
typedef位集32字;
const int Nr=10//AES-128需要10轮加密
const int Nk=4;//Nk表示输入键的字数。
字节S_Box[16][16]={
{0x63,0x7C,0x77,0x7B,0xF2,0x6B,0x6F,0xC5,0x30,0x01,0x67,0x2B,0xFE,0xD7,0xAB,0x76},
{0xCA,0x82,0xC9,0x7D,0xFA,0x59,0x47,0xF0,0xAD,0xD4,0xA2,0xAF,0x9C,0xA4,0x72,0xC0},
{0xB7,0xFD,0x93,0x26,0x36,0x3F,0xF7,0xCC,0x34,0xA5,0xE5,0xF1,0x71,0xD8,0x31,0x15},
{0x04,0xC7,0x23,0xC3,0x18,0x96,0x05,0x9A,0x07,0x12,0x80,0xE2,0xEB,0x27,0xB2,0x75},
{0x09,0x83,0x2C,0x1A,0x1B,0x6E,0x5A,0xA0,0x52,0x3B,0xD6,0xB3,0x29,0xE3,0x2F,0x84},
{0x 53.0 xd 1.0 x 00.0 xed,0x 20.0 xfc,0x 1.0 x 5b,0x6A,0xB,0x b,0x 39.0 x 4a,0x4C,0x 58.0 xcf },
{ 0 xd 0.0 xef,0xAA,0xFB,0 x 43.0 x4 d,0 x 33.0 x 85.0 x 45.0 xf9.0 x 02.0 x 7f,0 x 50.0 x 3c,0x9F,0xA8},
{0x 51.0 xa 3.0 x 40.0 x 8f . 0 x 92.0 x 9d . 0 x 38.0 xf 5.0 xbc . 0 XB 6.0 xda . 0 x 21.0 x 10.0 xff . 0 xff 3.0 xd 2 },
{0x 0 c,0x 13.0 exec,0x5F,0x 97.0 x 44.0 x 17.0 xc 4.0 xa 7.0 x 7e,0x 3 3d,0x 64.0 x 5d,0x 19.0 x 73 },
{0x 60.0 x 81.0 x 4f,0x 22.0 x 2a,0x 90.0 x 88.0 x 46.0 xee,0x 8.0 x 14.0 xd,0x5E,0x0B,0xDB},
{0x 0.0 x 32.0 x 3a .0x 49.0 x 06.0 x 24.0 x 5c .0x xc 2.0 x 3.0 x 62.0 x 91.0 x 95.0 x 4.0 x 79 },
{0x 7.0 xc 8.0 x 37.0 x 6d.0 x 8d.0 xd 5.0 x 4e.0 xa 9.0 x 6c.0 x 56.0 xf 4.0 xea .0x 65.0 x 7a.0 xae .0x 08 },
{0xBA,0x78,0x25,0x2E,0x1C,0x 6,0x 6,0x 6,0x 8,0x 8,0x74,0x1F,0x4B,0x8B,0x8A},
{0x 70.0 x 3e .0x 5.0 x 66.0 x 48.0 x 03.0 x 6.0 x 61.0 x 35.0 x 57.0 x 9.0 x 86.0 x 1.0 x 1d .0x 9e },
{0x 1.0x 8.0x 98.0 x 11.0 x 69.0 x 9.0 x 8 e.0 x 94.0 x 9 b.0 x 1e.0 x 87.0 x 9.0 x 55.0 x 28.0 xdf },
{0x8C,0 xa 1.0 x 89.0 x 0d,0xBF,0 xe 6.0 x 42.0 x 68.0 x 41.0 x 99.0 x 2d,0x0F,0 XB 0.0 x 54.0 xbb,0x16}
}:
S7-1200可编程控制器
{0x 52.0x 09.0x 6 a,0x 5.0x 30.0x 36.0x 5.0x 38.0x ff,0x 40.0x 3.0x 9 e,0x 81.0x 3.0x 7.0x b },
{0x7C,0x 3.0x 39.0x 82.0x 9 b,0x2F,0x 87.0x 34.0x 8 e,0x 43.0x 44.0x 4.0x 9.0x 9.0x b },
{0x 54.0 x7b .0x 94.0 x 32.0 xa 6.0 x 2.0 x 23.0 x 3.0 x e、0x4C、0x 95.0x 42.0x a、0x 3.0x 4 e },
{0x 08.0 x2 e . 0 xa 1.0 x 66.0 x 28.0 xd 9.0 x 24.0 XB 2.0 x 76.0 x 5b.0 xa 2.0 x 49.0 x 6d.0 x 8b.0 xd 1.0 x 25 },
{0x 72.0 xf 8.0 xf 6.0 x 64.0 x 86.0 x 68.0 x 98.0 x 16.0 xd 4.0 xa 4.0 x 5c.0 xcc . 0 x 5d.0 x 65.0 XB 6.0 x 92 },
{0x6C,0x 70.0 x 48.0 x 50.0 xfd,0xED,0x 9.0 xda,0x5E,0x 15.0 x 46.0 x 57.0 xa 7.0 x 8d,0x9D,0x84},
{0x90,0x 8.0 xab,0x00,0x8C,0x c,0x 3.0x 0 a,0x 7.0x 4.0x 58.0 x 05.0 x 8.0 x 3.0 x 45.0 x 06 },
{0x 2 c,0x1E,0x8F,0x 2,0x3F,0x02,0x1,0x 1,0xD,0x03,0x01,0x13,0x8A,0x6B},
{0x3A,0x91,0x11,0x41,0x4F,0x67,0x67,0x97,0x 97,0x 2,0x xcf,0x xce,0x4,0x6,0x73},
{0x 96.0 xac,0x 74.0 x 22.0 xe 7.0 xad,0x 35.0 x 85.0 xe 2.0 xf 9.0 x 37.0 xe 8.0 x 1c.0 x 75.0 xdf,0x6E},
{0x 47.0 xf 1.0 x1 a,0x 71.0 x1 d,0x 29.0 xc 5.0 x 89.0 x 6f,0x 7.0 x 62.0 x 0e,0x xaa,0x 18.0 xbe,0x1B},
{0x 56.0x 3 e,0x4B,0x 6.0x 79.0x 20.0x 9 a,0x xdb,0x 0.0 x3e,0x 78.0x xcd,0x5A,0x 4 },
{0x1F,0xDD,0xa 8.0 x 33.0 x 88.0 x 07.0 x xc 7.0 x 31.0 XB 1.0 x 12.0 x 10.0 x 59.0 x 27.0 x 80.0 exec,0x5F},
{0x 60.0x 51.0x 7 f,0x 9.0x 19.0x 5.0x 4 a,0x0D,0x 2,0x 5.0x 7 a,0x9F,0x 93.0x 9.0x 9 c,0x 9.0 xef },
{ 0 xa 0.0 xe 0.0 x3 b . 0 x4 d . 0 xae . 0 x2 a . 0 xf 5.0 XB 0.0 xc 8.0 xeb . 0 xbb . 0 x3c . 0 x 83.0 x 53.0 x 99.0 x 61 }
{0x 17.0 x2 b .0x 04.0 x7e .0x a .0x 77.0 x 6.0 x 26.0 x 1.0 x 69.0 x 14.0 x 63.0 x 55.0 x 21.0 x 0 c .0x 7d }
}:
//轮常数,密钥扩展中用到。(AES-128只需要10轮)
S7-1200可编程控制器,
0x 20000000.0 x 40000000.0 x 80000000.0 x 1b 000000.0 x 36000000 };
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/*/
/* AES算法实现*/
/*/
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我的天啊下面是加密的变换函数-好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧,好吧。
/**
* S盒变换-前四位为行号,后四位为列号
*/
请参见子字节(字节氨甲喋呤[4*4])
{
for(int I=0);i16(一)
{
int row=MTX[I][7]* 8 MTX[I][6]* 4 MTX[I][5]* 2 MTX[I][4];
int col=MTX[I][3]* 8 MTX[I][2]* 4 MTX[I][1]* 2 MTX[I][0];
MTX=s _ box行][col];
}
}
/**
*行变换-按字节循环移位
*/
参见移动电话(字节氨甲喋呤[4*4])
{
//第二行循环左移一位
字节temp=MTX[4];
for(int I=0);i3;和:(一)
MTX[i4]=MTX[i5];
S7-1200可编程控制器:
//第三行循环左移两位
for(int I=0);i2个;(一)
{
temp=MTX[8i];
MTX[i18]=MTX[i10];
MTX[i10]=temp;
}
//第四行循环左移三位
temp=MTX[15];
for(int I=3;i0;-我)
MTX[i12]=MTX[i11];
MTX[12]=temp;
}
/**
* 有限域上的乘法GF(2^8)
*/
字节GFMul(字节一,字节b) {
字节p=0;
字节hi _ bit _ set
for(int counter=0;8号柜台;计数器){
如果((b字节(1))!=0) {
p ^=a;
}
hi_bit_set=(字节)(一个字节(0x 80));
a=1;
if (hi_bit_set!=0) {
一个^=0x1b;/* x^8 x^4 x^3 x 1 */
}
b=1;
}
返回p;
}
/**
* 列变换
*/
空的混合列(字节氨甲喋呤[4*4])
{
字节arr[4];
for(int I=0;i4;我)
{
for(int j=0;j4;j)
arr[j]=MTX[I j * 4];
mtx[i]=GFMul(0x02,arr[0])^ gfmul(0x03,arr[1])^ arr[2]^ arr[3];
mtx[i 4]=arr[0] ^ GFMul(0x02,arr[1])^ gfmul(0x03,arr[2])^ arr[3];
MTX[I 8]=arr[0]^ arr[1]^ gf mul(0x 02,arr[2]) ^ GFMul(0x03,arr[3]);
MTX[I 12]=gfmul(0x03,arr[0])^ arr[1]^ arr[2]^ gf mul(0x 02,arr[3]);
}
}
/**
* 轮密钥加变换-将每一列与扩展密钥进行异或
*/
void AddRoundKey(字节mtx[4*4],字k[4])
{
for(int I=0;i4;我)
{
字k1=k[I]24;
word k2=(k[I]8)24;
字k3=(k[I]16)24;
字k4=(k[I]24)24;
mtx[i]=mtx[i] ^字节(kto _ ulong());
氨甲喋呤[i 4]=氨甲喋呤^字节(kto _ ulong());
甲氨蝶呤[i 8]=甲氨蝶呤[i 8] ^字节(kto _ ulong());
甲氨蝶呤[i 12]=甲氨蝶呤[i 12] ^字节(kto _ ulong());
}
}
/**************************下面是解密的逆变换函数***********************/
/**
* 逆S盒变换
*/
void子字节(字节氨甲喋呤[4*4])
{
for(int I=0;i16我)
{
int row=MTX[I][7]* 8 MTX[I][6]* 4 MTX[I][5]* 2 MTX[I][4];
int col=MTX[I][3]* 8 MTX[I][2]* 4 MTX[I][1]* 2 MTX[I][0];
MTX[I]=Inv _ S _ Box[row][col];
}
}
/**
* 逆行变换-以字节为单位循环右移
*/
void InvShiftRows(字节氨甲喋呤[4*4])
{
//第二行循环右移一位
字节温度=MTX[7];
for(int I=3;i0;-我)
MTX[i4]=MTX[i3];
MTX[4]=temp;
//第三行循环右移两位
for(int I=0;I2;我)
{
temp=MTX[I 8];
MTX[I 8]=MTX[I 10];
MTX[i10]=temp;
}
//第四行循环右移三位
temp=MTX[12];
for(int I=0;i3;我)
MTX[i12]=MTX[i13];
MTX[15]=temp;
}
void InvMixColumns(字节氨甲喋呤[4*4])
{
字节arr[4];
for(int I=0;i4;我)
{
for(int j=0;j4;j)
arr[j]=MTX[I j * 4];
mtx[i]=GFMul(0x0e,arr[0]) ^ GFMul(0x0b,arr[1]) ^ GFMul(0x0d,arr[2]) ^ GFMul(0x09,arr[3]);
mtx[i 4]=GFMul(0x09,arr[0]) ^ GFMul(0x0e,arr[1]) ^ GFMul(0x0b,arr[2]) ^ GFMul(0x0d,arr[3]);
mtx[i 8]=GFMul(0x0d,arr[0]) ^ GFMul(0x09,arr[1]) ^ GFMul(0x0e,arr[2]) ^ GFMul(0x0b,arr[3]);
mtx[i 12]=GFMul(0x0b,arr[0]) ^ GFMul(0x0d,arr[1]) ^ GFMul(0x09,arr[2]) ^ GFMul(0x0e,arr[3]);
}
}
/******************************下面是密钥扩展部分***********************/
/**
* 将四个字节转换为一个单词
*/
单词单词(字节k1、字节k2、字节k3、字节k4)
{
字结果(0x 00000000);
word temp
temp=kto _ ulong();//K1
温度=24
结果|=温度
temp=kto _ ulong();//K2
温度=16
结果|=温度
temp=kto _ ulong();//K3
temp=8;
结果|=温度
temp=kto _ ulong();//K4
结果|=温度
返回结果;
}
/**
* 按字节循环左移一位
* 即把[a0,a1,a2,a3]变成[a1,a2,a3,a0]
*/
word RotWord(word rw)
{
字高=rw 8;
字低=rw 24
返高|低;
}
/**
* 对输入单词中的每一个字节进行表示"上帝的":' sblood盒变换
*/
单词子词(word软件)
{
word temp
for(int I=0;i32i=8)
{
int row=SW[i7]* 8 SW[i6]* 4 SW[i5]* 2 SW[i4];
int col=SW[I 3]* 8 SW[I 2]* 4 SW[I 1]* 2 SW[I];
byte val=S _ Box[row][col];
for(int j=0;j8;j)
temp[I j]=val[j];
}
返回温度;
}
/**
* 密钥扩展函数-对128位密钥进行扩展得到w[4*(Nr 1)]
*/
void密钥扩展(字节键[4*Nk],字w[4*(Nr 1)])
{
word temp
int I=0;
//w[]的前四个就是输入的键
当(我认为)
{
w[i]=Word(key[4*i],key[4*i 1],key[4*i 2],key[4 * I 3]);
我;
}
我=Nk
while(i 4*(Nr 1))
{
temp=w[I-1];//记录前一个单词
if(i % Nk==0)
^子字(罗特word(temp))^ rcon[I/NK-1];
其他
^温度;
我;
}
}
/******************************下面是加密和解密函数**************************/
/**
* 加密
*/
void加密(字节在[4*4]中,字w[4*(Nr 1)])
{
字键[4];
for(int I=0;i4;我)
key[I]=w[I];
AddRoundKey(in,key);
for(int round=1;圆形Nr圆形)
{
亚字节(英寸);
移位行(进);
混合列(英寸);
for(int I=0;i4;我)
key[I]=w[4 * round I];
AddRoundKey(in,key);
}
亚字节(英寸);
移位行(进);
for(int I=0;i4;我)
key[I]=w[4 * Nr I];
AddRoundKey(in,key);
}
/**
* 解密
*/
无效解密(字节在[4*4],字w[4*(Nr 1)])
{
字键[4];
for(int I=0;i4;我)
key[I]=w[4 * Nr I];
AddRoundKey(in,key);
for(int round=Nr-1;round0-圆形)
{
invshift行(in);
inv子字节(in);
for(int I=0;i4;我)
key[I]=w[4 * round I];
AddRoundKey(in,key);
InvMixColumns(in);
}
invshift行(in);
inv子字节(in);
for(int I=0;i4;我)
key[I]=w[I];
AddRoundKey(in,key);
}
/**********************************************************************/
/* */
/* 测试*/
/* */
/**********************************************************************/
int main()
{
字节键[16]={0x2b,0x7e,0x15,0x16,
0x28、0xae、0xd2、0xa6、
0xab、0xf7、0x15、0x88、
0x09,0xcf,0x4f,0x3c };
byte plain[16]={0x32,0x88,0x31,0xe0,
0x43、0x5a、0x31、0x37、
0xf6、0x30、0x98、0x07、
0xa8,0x8d,0xa2,0x 34 };
//输出密钥
cout '密钥是:';
for(int I=0;i16我)
标准输出十六进制密钥[I]to _ ulong()" ";
cout结束
word w[4 *(Nr 1)];
KeyExpansion(key,w);
//输出待加密的明文
cout endl '待加密的明文:' endl
for(int I=0;i16我)
{
cout hex plain[I]to _ ulong()" ";
如果((^ 1)% 4==0)
cout结束
}
cout结束
//加密,输出密文
加密(平原,w);
cout '加密后的密文:' endl
for(int I=0;i16我)
{
cout hex plain[I]to _ ulong()" ";
如果((^ 1)% 4==0)
cout结束
}
cout结束
//解密,输出明文
解密(平原,w);
cout '解密后的明文:' endl
for(int I=0;i16我)
{
cout hex plain[I]to _ ulong()" ";
如果((^ 1)% 4==0)
cout结束
}
cout结束
返回0;
}
测试用例如下图:
测试结果截图:
可见,测试结果和预期输出相同,表明对数据的加密和解密成功!
下面我们来写俄歇电子能谱对文件的加密和解密,在对128 位的数据加解密成功以后,对文件的加解密就很简单了!只需要每次读128 位,加密以后,将128 位的密文写入另外一个文件…如此循环,直到文件尾。下面是对一张图片进行俄歇电子能谱加密和解密的测试代码(效率先不管了,有时间我再优化):
//#包含fstream
typedef位集8字节;
typedef位集32字;
/**
* 将一个茶字符数组转化为二进制
* 存到一个字节数组中
*/
空图表字节(字节输出[16],常量字符s[16])
{
for(int I=0;i16我)
for(int j=0;j8;j)
out[I][j]=((s[I]j)1);
}
/**
* 将连续的128位分成16组,存到一个字节数组中
*/
void divideToByte(字节输出[16],位集128数据)
{
位集128温度
f
or(int i=0; i<16; ++i) { temp = (data << 8*i) >> 120; out[i] = tempto_ulong(); } } /** * 将16个 byte 合并成连续的128位 */ bitset<128> mergeByte(byte in[16]) { bitset<128> res; resreset(); // 置0 bitset<128> temp; for(int i=0; i<16; ++i) { temp = in[i]to_ulong(); temp <<= 8*(15-i); res |= temp; } return res; } int main() { string keyStr = "abcdefghijklmnop"; byte key[16]; charToByte(key, keyStrc_str()); // 密钥扩展 word w[4*(Nr+1)]; KeyExpansion(key, w); bitset<128> data; byte plain[16]; // 将文件 flowerjpg 加密到 ciphertxt 中 ifstream in; ofstream out; inopen("D://flowerjpg", ios::binary); outopen("D://ciphertxt", ios::binary); while(inread((char*)&data, sizeof(data))) { divideToByte(plain, data); encrypt(plain, w); data = mergeByte(plain); outwrite((char*)&data, sizeof(data)); datareset(); // 置0 } inclose(); outclose(); // 解密 ciphertxt,并写入图片 flowerjpg inopen("D://ciphertxt", ios::binary); outopen("D://flowerjpg", ios::binary); while(inread((char*)&data, sizeof(data))) { divideToByte(plain, data); decrypt(plain, w); data = mergeByte(plain); outwrite((char*)&data, sizeof(data)); datareset(); // 置0 } inclose(); outclose(); return 0; }有限域 GF(28) 上的乘法改用查表的方式实现,AES的加密速度马上提升 80% 以上,所以建议最好使用查表的方式。下面是 AES 算法中用到的 6 个乘法结果表:
byte Mul_02[256] = { 0x00,0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,0x10,0x12,0x14,0x16,0x18,0x1a,0x1c,0x1e, 0x20,0x22,0x24,0x26,0x28,0x2a,0x2c,0x2e,0x30,0x32,0x34,0x36,0x38,0x3a,0x3c,0x3e, 0x40,0x42,0x44,0x46,0x48,0x4a,0x4c,0x4e,0x50,0x52,0x54,0x56,0x58,0x5a,0x5c,0x5e, 0x60,0x62,0x64,0x66,0x68,0x6a,0x6c,0x6e,0x70,0x72,0x74,0x76,0x78,0x7a,0x7c,0x7e, 0x80,0x82,0x84,0x86,0x88,0x8a,0x8c,0x8e,0x90,0x92,0x94,0x96,0x98,0x9a,0x9c,0x9e, 0xa0,0xa2,0xa4,0xa6,0xa8,0xaa,0xac,0xae,0xb0,0xb2,0xb4,0xb6,0xb8,0xba,0xbc,0xbe, 0xc0,0xc2,0xc4,0xc6,0xc8,0xca,0xcc,0xce,0xd0,0xd2,0xd4,0xd6,0xd8,0xda,0xdc,0xde, 0xe0,0xe2,0xe4,0xe6,0xe8,0xea,0xec,0xee,0xf0,0xf2,0xf4,0xf6,0xf8,0xfa,0xfc,0xfe, 0x1b,0x19,0x1f,0x1d,0x13,0x11,0x17,0x15,0x0b,0x09,0x0f,0x0d,0x03,0x01,0x07,0x05, 0x3b,0x39,0x3f,0x3d,0x33,0x31,0x37,0x35,0x2b,0x29,0x2f,0x2d,0x23,0x21,0x27,0x25, 0x5b,0x59,0x5f,0x5d,0x53,0x51,0x57,0x55,0x4b,0x49,0x4f,0x4d,0x43,0x41,0x47,0x45, 0x7b,0x79,0x7f,0x7d,0x73,0x71,0x77,0x75,0x6b,0x69,0x6f,0x6d,0x63,0x61,0x67,0x65, 0x9b,0x99,0x9f,0x9d,0x93,0x91,0x97,0x95,0x8b,0x89,0x8f,0x8d,0x83,0x81,0x87,0x85, 0xbb,0xb9,0xbf,0xbd,0xb3,0xb1,0xb7,0xb5,0xab,0xa9,0xaf,0xad,0xa3,0xa1,0xa7,0xa5, 0xdb,0xd9,0xdf,0xdd,0xd3,0xd1,0xd7,0xd5,0xcb,0xc9,0xcf,0xcd,0xc3,0xc1,0xc7,0xc5, 0xfb,0xf9,0xff,0xfd,0xf3,0xf1,0xf7,0xf5,0xeb,0xe9,0xef,0xed,0xe3,0xe1,0xe7,0xe5 }; byte Mul_03[256] = { 0x00,0x03,0x06,0x05,0x0c,0x0f,0x0a,0x09,0x18,0x1b,0x1e,0x1d,0x14,0x17,0x12,0x11, 0x30,0x33,0x36,0x35,0x3c,0x3f,0x3a,0x39,0x28,0x2b,0x2e,0x2d,0x24,0x27,0x22,0x21, 0x60,0x63,0x66,0x65,0x6c,0x6f,0x6a,0x69,0x78,0x7b,0x7e,0x7d,0x74,0x77,0x72,0x71, 0x50,0x53,0x56,0x55,0x5c,0x5f,0x5a,0x59,0x48,0x4b,0x4e,0x4d,0x44,0x47,0x42,0x41, 0xc0,0xc3,0xc6,0xc5,0xcc,0xcf,0xca,0xc9,0xd8,0xdb,0xde,0xdd,0xd4,0xd7,0xd2,0xd1, 0xf0,0xf3,0xf6,0xf5,0xfc,0xff,0xfa,0xf9,0xe8,0xeb,0xee,0xed,0xe4,0xe7,0xe2,0xe1, 0xa0,0xa3,0xa6,0xa5,0xac,0xaf,0xaa,0xa9,0xb8,0xbb,0xbe,0xbd,0xb4,0xb7,0xb2,0xb1, 0x90,0x93,0x96,0x95,0x9c,0x9f,0x9a,0x99,0x88,0x8b,0x8e,0x8d,0x84,0x87,0x82,0x81, 0x9b,0x98,0x9d,0x9e,0x97,0x94,0x91,0x92,0x83,0x80,0x85,0x86,0x8f,0x8c,0x89,0x8a, 0xab,0xa8,0xad,0xae,0xa7,0xa4,0xa1,0xa2,0xb3,0xb0,0xb5,0xb6,0xbf,0xbc,0xb9,0xba, 0xfb,0xf8,0xfd,0xfe,0xf7,0xf4,0xf1,0xf2,0xe3,0xe0,0xe5,0xe6,0xef,0xec,0xe9,0xea, 0xcb,0xc8,0xcd,0xce,0xc7,0xc4,0xc1,0xc2,0xd3,0xd0,0xd5,0xd6,0xdf,0xdc,0xd9,0xda, 0x5b,0x58,0x5d,0x5e,0x57,0x54,0x51,0x52,0x43,0x40,0x45,0x46,0x4f,0x4c,0x49,0x4a, 0x6b,0x68,0x6d,0x6e,0x67,0x64,0x61,0x62,0x73,0x70,0x75,0x76,0x7f,0x7c,0x79,0x7a, 0x3b,0x38,0x3d,0x3e,0x37,0x34,0x31,0x32,0x23,0x20,0x25,0x26,0x2f,0x2c,0x29,0x2a, 0x0b,0x08,0x0d,0x0e,0x07,0x04,0x01,0x02,0x13,0x10,0x15,0x16,0x1f,0x1c,0x19,0x1a }; byte Mul_09[256] = { 0x00,0x09,0x12,0x1b,0x24,0x2d,0x36,0x3f,0x48,0x41,0x5a,0x53,0x6c,0x65,0x7e,0x77, 0x90,0x99,0x82,0x8b,0xb4,0xbd,0xa6,0xaf,0xd8,0xd1,0xca,0xc3,0xfc,0xf5,0xee,0xe7, 0x3b,0x32,0x29,0x20,0x1f,0x16,0x0d,0x04,0x73,0x7a,0x61,0x68,0x57,0x5e,0x45,0x4c, 0xab,0xa2,0xb9,0xb0,0x8f,0x86,0x9d,0x94,0xe3,0xea,0xf1,0xf8,0xc7,0xce,0xd5,0xdc, 0x76,0x7f,0x64,0x6d,0x52,0x5b,0x40,0x49,0x3e,0x37,0x2c,0x25,0x1a,0x13,0x08,0x01, 0xe6,0xef,0xf4,0xfd,0xc2,0xcb,0xd0,0xd9,0xae,0xa7,0xbc,0xb5,0x8a,0x83,0x98,0x91, 0x4d,0x44,0x5f,0x56,0x69,0x60,0x7b,0x72,0x05,0x0c,0x17,0x1e,0x21,0x28,0x33,0x3a, 0xdd,0xd4,0xcf,0xc6,0xf9,0xf0,0xeb,0xe2,0x95,0x9c,0x87,0x8e,0xb1,0xb8,0xa3,0xaa, 0xec,0xe5,0xfe,0xf7,0xc8,0xc1,0xda,0xd3,0xa4,0xad,0xb6,0xbf,0x80,0x89,0x92,0x9b, 0x7c,0x75,0x6e,0x67,0x58,0x51,0x4a,0x43,0x34,0x3d,0x26,0x2f,0x10,0x19,0x02,0x0b, 0xd7,0xde,0xc5,0xcc,0xf3,0xfa,0xe1,0xe8,0x9f,0x96,0x8d,0x84,0xbb,0xb2,0xa9,0xa0, 0x47,0x4e,0x55,0x5c,0x63,0x6a,0x71,0x78,0x0f,0x06,0x1d,0x14,0x2b,0x22,0x39,0x30, 0x9a,0x93,0x88,0x81,0xbe,0xb7,0xac,0xa5,0xd2,0xdb,0xc0,0xc9,0xf6,0xff,0xe4,0xed, 0x0a,0x03,0x18,0x11,0x2e,0x27,0x3c,0x35,0x42,0x4b,0x50,0x59,0x66,0x6f,0x74,0x7d, 0xa1,0xa8,0xb3,0xba,0x85,0x8c,0x97,0x9e,0xe9,0xe0,0xfb,0xf2,0xcd,0xc4,0xdf,0xd6, 0x31,0x38,0x23,0x2a,0x15,0x1c,0x07,0x0e,0x79,0x70,0x6b,0x62,0x5d,0x54,0x4f,0x46 }; byte Mul_0b[256] = { 0x00,0x0b,0x16,0x1d,0x2c,0x27,0x3a,0x31,0x58,0x53,0x4e,0x45,0x74,0x7f,0x62,0x69, 0xb0,0xbb,0xa6,0xad,0x9c,0x97,0x8a,0x81,0xe8,0xe3,0xfe,0xf5,0xc4,0xcf,0xd2,0xd9, 0x7b,0x70,0x6d,0x66,0x57,0x5c,0x41,0x4a,0x23,0x28,0x35,0x3e,0x0f,0x04,0x19,0x12, 0xcb,0xc0,0xdd,0xd6,0xe7,0xec,0xf1,0xfa,0x93,0x98,0x85,0x8e,0xbf,0xb4,0xa9,0xa2, 0xf6,0xfd,0xe0,0xeb,0xda,0xd1,0xcc,0xc7,0xae,0xa5,0xb8,0xb3,0x82,0x89,0x94,0x9f, 0x46,0x4d,0x50,0x5b,0x6a,0x61,0x7c,0x77,0x1e,0x15,0x08,0x03,0x32,0x39,0x24,0x2f, 0x8d,0x86,0x9b,0x90,0xa1,0xaa,0xb7,0xbc,0xd5,0xde,0xc3,0xc8,0xf9,0xf2,0xef,0xe4, 0x3d,0x36,0x2b,0x20,0x11,0x1a,0x07,0x0c,0x65,0x6e,0x73,0x78,0x49,0x42,0x5f,0x54, 0xf7,0xfc,0xe1,0xea,0xdb,0xd0,0xcd,0xc6,0xaf,0xa4,0xb9,0xb2,0x83,0x88,0x95,0x9e, 0x47,0x4c,0x51,0x5a,0x6b,0x60,0x7d,0x76,0x1f,0x14,0x09,0x02,0x33,0x38,0x25,0x2e, 0x8c,0x87,0x9a,0x91,0xa0,0xab,0xb6,0xbd,0xd4,0xdf,0xc2,0xc9,0xf8,0xf3,0xee,0xe5, 0x3c,0x37,0x2a,0x21,0x10,0x1b,0x06,0x0d,0x64,0x6f,0x72,0x79,0x48,0x43,0x5e,0x55, 0x01,0x0a,0x17,0x1c,0x2d,0x26,0x3b,0x30,0x59,0x52,0x4f,0x44,0x75,0x7e,0x63,0x68, 0xb1,0xba,0xa7,0xac,0x9d,0x96,0x8b,0x80,0xe9,0xe2,0xff,0xf4,0xc5,0xce,0xd3,0xd8, 0x7a,0x71,0x6c,0x67,0x56,0x5d,0x40,0x4b,0x22,0x29,0x34,0x3f,0x0e,0x05,0x18,0x13, 0xca,0xc1,0xdc,0xd7,0xe6,0xed,0xf0,0xfb,0x92,0x99,0x84,0x8f,0xbe,0xb5,0xa8,0xa3 }; byte Mul_0d[256] = { 0x00,0x0d,0x1a,0x17,0x34,0x39,0x2e,0x23,0x68,0x65,0x72,0x7f,0x5c,0x51,0x46,0x4b, 0xd0,0xdd,0xca,0xc7,0xe4,0xe9,0xfe,0xf3,0xb8,0xb5,0xa2,0xaf,0x8c,0x81,0x96,0x9b, 0xbb,0xb6,0xa1,0xac,0x8f,0x82,0x95,0x98,0xd3,0xde,0xc9,0xc4,0xe7,0xea,0xfd,0xf0, 0x6b,0x66,0x71,0x7c,0x5f,0x52,0x45,0x48,0x03,0x0e,0x19,0x14,0x37,0x3a,0x2d,0x20, 0x6d,0x60,0x77,0x7a,0x59,0x54,0x43,0x4e,0x05,0x08,0x1f,0x12,0x31,0x3c,0x2b,0x26, 0xbd,0xb0,0xa7,0xaa,0x89,0x84,0x93,0x9e,0xd5,0xd8,0xcf,0xc2,0xe1,0xec,0xfb,0xf6, 0xd6,0xdb,0xcc,0xc1,0xe2,0xef,0xf8,0xf5,0xbe,0xb3,0xa4,0xa9,0x8a,0x87,0x90,0x9d, 0x06,0x0b,0x1c,0x11,0x32,0x3f,0x28,0x25,0x6e,0x63,0x74,0x79,0x5a,0x57,0x40,0x4d, 0xda,0xd7,0xc0,0xcd,0xee,0xe3,0xf4,0xf9,0xb2,0xbf,0xa8,0xa5,0x86,0x8b,0x9c,0x91, 0x0a,0x07,0x10,0x1d,0x3e,0x33,0x24,0x29,0x62,0x6f,0x78,0x75,0x56,0x5b,0x4c,0x41, 0x61,0x6c,0x7b,0x76,0x55,0x58,0x4f,0x42,0x09,0x04,0x13,0x1e,0x3d,0x30,0x27,0x2a, 0xb1,0xbc,0xab,0xa6,0x85,0x88,0x9f,0x92,0xd9,0xd4,0xc3,0xce,0xed,0xe0,0xf7,0xfa, 0xb7,0xba,0xad,0xa0,0x83,0x8e,0x99,0x94,0xdf,0xd2,0xc5,0xc8,0xeb,0xe6,0xf1,0xfc, 0x67,0x6a,0x7d,0x70,0x53,0x5e,0x49,0x44,0x0f,0x02,0x15,0x18,0x3b,0x36,0x21,0x2c, 0x0c,0x01,0x16,0x1b,0x38,0x35,0x22,0x2f,0x64,0x69,0x7e,0x73,0x50,0x5d,0x4a,0x47, 0xdc,0xd1,0xc6,0xcb,0xe8,0xe5,0xf2,0xff,0xb4,0xb9,0xae,0xa3,0x80,0x8d,0x9a,0x97 }; byte Mul_0e[256] = { 0x00,0x0e,0x1c,0x12,0x38,0x36,0x24,0x2a,0x70,0x7e,0x6c,0x62,0x48,0x46,0x54,0x5a, 0xe0,0xee,0xfc,0xf2,0xd8,0xd6,0xc4,0xca,0x90,0x9e,0x8c,0x82,0xa8,0xa6,0xb4,0xba, 0xdb,0xd5,0xc7,0xc9,0xe3,0xed,0xff,0xf1,0xab,0xa5,0xb7,0xb9,0x93,0x9d,0x8f,0x81, 0x3b,0x35,0x27,0x29,0x03,0x0d,0x1f,0x11,0x4b,0x45,0x57,0x59,0x73,0x7d,0x6f,0x61, 0xad,0xa3,0xb1,0xbf,0x95,0x9b,0x89,0x87,0xdd,0xd3,0xc1,0xcf,0xe5,0xeb,0xf9,0xf7, 0x4d,0x43,0x51,0x5f,0x75,0x7b,0x69,0x67,0x3d,0x33,0x21,0x2f,0x05,0x0b,0x19,0x17, 0x76,0x78,0x6a,0x64,0x4e,0x40,0x52,0x5c,0x06,0x08,0x1a,0x14,0x3e,0x30,0x22,0x2c, 0x96,0x98,0x8a,0x84,0xae,0xa0,0xb2,0xbc,0xe6,0xe8,0xfa,0xf4,0xde,0xd0,0xc2,0xcc, 0x41,0x4f,0x5d,0x53,0x79,0x77,0x65,0x6b,0x31,0x3f,0x2d,0x23,0x09,0x07,0x15,0x1b, 0xa1,0xaf,0xbd,0xb3,0x99,0x97,0x85,0x8b,0xd1,0xdf,0xcd,0xc3,0xe9,0xe7,0xf5,0xfb, 0x9a,0x94,0x86,0x88,0xa2,0xac,0xbe,0xb0,0xea,0xe4,0xf6,0xf8,0xd2,0xdc,0xce,0xc0, 0x7a,0x74,0x66,0x68,0x42,0x4c,0x5e,0x50,0x0a,0x04,0x16,0x18,0x32,0x3c,0x2e,0x20, 0xec,0xe2,0xf0,0xfe,0xd4,0xda,0xc8,0xc6,0x9c,0x92,0x80,0x8e,0xa4,0xaa,0xb8,0xb6, 0x0c,0x02,0x10,0x1e,0x34,0x3a,0x28,0x26,0x7c,0x72,0x60,0x6e,0x44,0x4a,0x58,0x56, 0x37,0x39,0x2b,0x25,0x0f,0x01,0x13,0x1d,0x47,0x49,0x5b,0x55,0x7f,0x71,0x63,0x6d, 0xd7,0xd9,0xcb,0xc5,0xef,0xe1,0xf3,0xfd,0xa7,0xa9,0xbb,0xb5,0x9f,0x91,0x83,0x8d };以上就是本文的全部内容,希望对大家的学习有所帮助,也希望大家多多支持我们。
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