1.前言
AES（ Advanced Encryption Standard ）高级加密标准，又称 Rijndael加密法。它是由 美国国家标准与技术研究院 （NIST）于2001年11月26日发布于FIPS PUB 197，并在2002年5月26日成为有效的标准 。 该算法由比利时密码学家Joan Daemen和Vincent Rijmen所设计，结合两位作者的名字 而命名。AES标准支持固定分组128位，密钥长度可以是128位、192位、256位。
2.工作模式
我们知道，对明文进行加密的过程中，如果明文超过了分组大小，那么就需要进行切割处理，而AES提供给我们多种工作模式，分别是：ECB(电子密码本)、CBC(密文分组链接)、CFB（密文反馈）、OFB（输出反馈）、CTR（计数器），而我们今天只针对128位的明文进行加密解密处理，分组工作模式不在我们今天讨论的范畴。
3.介绍
3.1 状态矩阵
AES算法中的状态矩阵是垂直排列的，如下图所示。
明文第一步需要转换成状态矩阵，而初始密钥在进行扩展密钥之前也需要转化成状态矩阵。在对密文进行解密时，最后需要将状态矩阵还原为明文矩阵。
3.2 密钥扩展
密钥扩展会生成44组4个字节的轮密钥，每16个字节为1轮密钥，在进行轮密钥加的时候，需要将处理过的明文状态矩阵根据每轮的密钥进行加密处理。下面我们来看一个例子，假如初始密钥16位为： abcdefghijklmnop ,那么它的初始轮密钥如下所示：
接下来还需要生成40组W，计算公式如下：
W[n] = W[n-4] xor W[n-1] (if n%4 !== 0)
W[n] = W[n-4] xor 字节替换(循环左移1位(W[n-1])) xor 轮常量[(n/4) – 1] (if n%4 === 0)
循环左移：如0x12345678 => 0x34567812
轮常量是固定的数组如下所示:
3.3 字节替换
字节替换，是利用AES提供的S盒来进行替换的，其中高4位代表行数，而低4位则代表列数。在解密时，也用相同的规则在S逆盒中进行替换还原。
3.4 行移位
行移位第0行无需移动，第i行则向左循环移动i次，解密时则向右循环移动i次。下面时一个例子：
3.5列混合
列混合的操作是基于有限域伽罗华域的计算，详情请参考：https://www.cnblogs.com/pitmanhuang/p/16175550.html
在进行列混合操作时，将状态矩阵与固定的常量矩阵进行有限域的乘积，将结果异或得出列混合后的值。其中加密和解密的常量值数组是不同的，它们分别为:
4.代码示例
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/** *伽罗华域乘积 *@param$a *@paramint$b *@returnint|mixed */ functionaes_multi($a,$b=0) { if($a>=2**8||2**8<=$b){ exit('只支持GF(2^8)域的计算'); } $binMulti=[]; $result=0; for($i=0;$i<8;$i++){ $a=($a&0x100)?(($a&0xFF)^0x1B):$a; $binMulti[]=$a; $a=$a<<1; } $binString=str_pad(base_convert($b,10,2),8,0,STR_PAD_LEFT); for($i=0;$i<8;$i++){ if($binString{$i}==='1'){ $pos=strlen(substr($binString,$i))-1; $result^=$binMulti[$pos]; } } return$result; } $rcon=[ 0x01000000,0x02000000,0x04000000,0x08000000,0x10000000, 0x20000000,0x40000000,0x80000000,0x1B000000,0x36000000]; $constArray=[0x02,0x03,0x01,0x01,0x01,0x02,0x03,0x01,0x01,0x01,0x02,0x03,0x03,0x01,0x01,0x02]; $constArrayReverse=[0x0E,0x0B,0x0D,0x09,0x09,0x0E,0x0B,0x0D,0x0D,0x09,0x0E,0x0B,0x0B,0x0D,0x09,0x0E]; //S盒 $s=[ 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, 0x53,0xD1,0x00,0xED,0x20,0xFC,0xB1,0x5B,0x6A,0xCB,0xBE,0x39,0x4A,0x4C,0x58,0xCF, 0xD0,0xEF,0xAA,0xFB,0x43,0x4D,0x33,0x85,0x45,0xF9,0x02,0x7F,0x50,0x3C,0x9F,0xA8, 0x51,0xA3,0x40,0x8F,0x92,0x9D,0x38,0xF5,0xBC,0xB6,0xDA,0x21,0x10,0xFF,0xF3,0xD2, 0xCD,0x0C,0x13,0xEC,0x5F,0x97,0x44,0x17,0xC4,0xA7,0x7E,0x3D,0x64,0x5D,0x19,0x73, 0x60,0x81,0x4F,0xDC,0x22,0x2A,0x90,0x88,0x46,0xEE,0xB8,0x14,0xDE,0x5E,0x0B,0xDB, 0xE0,0x32,0x3A,0x0A,0x49,0x06,0x24,0x5C,0xC2,0xD3,0xAC,0x62,0x91,0x95,0xE4,0x79, 0xE7,0xC8,0x37,0x6D,0x8D,0xD5,0x4E,0xA9,0x6C,0x56,0xF4,0xEA,0x65,0x7A,0xAE,0x08, 0xBA,0x78,0x25,0x2E,0x1C,0xA6,0xB4,0xC6,0xE8,0xDD,0x74,0x1F,0x4B,0xBD,0x8B,0x8A, 0x70,0x3E,0xB5,0x66,0x48,0x03,0xF6,0x0E,0x61,0x35,0x57,0xB9,0x86,0xC1,0x1D,0x9E, 0xE1,0xF8,0x98,0x11,0x69,0xD9,0x8E,0x94,0x9B,0x1E,0x87,0xE9,0xCE,0x55,0x28,0xDF, 0x8C,0xA1,0x89,0x0D,0xBF,0xE6,0x42,0x68,0x41,0x99,0x2D,0x0F,0xB0,0x54,0xBB,0x16]; //逆S盒 $ss=[ 0x52,0x09,0x6A,0xD5,0x30,0x36,0xA5,0x38,0xBF,0x40,0xA3,0x9E,0x81,0xF3,0xD7,0xFB, 0x7C,0xE3,0x39,0x82,0x9B,0x2F,0xFF,0x87,0x34,0x8E,0x43,0x44,0xC4,0xDE,0xE9,0xCB, 0x54,0x7B,0x94,0x32,0xA6,0xC2,0x23,0x3D,0xEE,0x4C,0x95,0x0B,0x42,0xFA,0xC3,0x4E, 0x08,0x2E,0xA1,0x66,0x28,0xD9,0x24,0xB2,0x76,0x5B,0xA2,0x49,0x6D,0x8B,0xD1,0x25, 0x72,0xF8,0xF6,0x64,0x86,0x68,0x98,0x16,0xD4,0xA4,0x5C,0xCC,0x5D,0x65,0xB6,0x92, 0x6C,0x70,0x48,0x50,0xFD,0xED,0xB9,0xDA,0x5E,0x15,0x46,0x57,0xA7,0x8D,0x9D,0x84, 0x90,0xD8,0xAB,0x00,0x8C,0xBC,0xD3,0x0A,0xF7,0xE4,0x58,0x05,0xB8,0xB3,0x45,0x06, 0xD0,0x2C,0x1E,0x8F,0xCA,0x3F,0x0F,0x02,0xC1,0xAF,0xBD,0x03,0x01,0x13,0x8A,0x6B, 0x3A,0x91,0x11,0x41,0x4F,0x67,0xDC,0xEA,0x97,0xF2,0xCF,0xCE,0xF0,0xB4,0xE6,0x73, 0x96,0xAC,0x74,0x22,0xE7,0xAD,0x35,0x85,0xE2,0xF9,0x37,0xE8,0x1C,0x75,0xDF,0x6E, 0x47,0xF1,0x1A,0x71,0x1D,0x29,0xC5,0x89,0x6F,0xB7,0x62,0x0E,0xAA,0x18,0xBE,0x1B, 0xFC,0x56,0x3E,0x4B,0xC6,0xD2,0x79,0x20,0x9A,0xDB,0xC0,0xFE,0x78,0xCD,0x5A,0xF4, 0x1F,0xDD,0xA8,0x33,0x88,0x07,0xC7,0x31,0xB1,0x12,0x10,0x59,0x27,0x80,0xEC,0x5F, 0x60,0x51,0x7F,0xA9,0x19,0xB5,0x4A,0x0D,0x2D,0xE5,0x7A,0x9F,0x93,0xC9,0x9C,0xEF, 0xA0,0xE0,0x3B,0x4D,0xAE,0x2A,0xF5,0xB0,0xC8,0xEB,0xBB,0x3C,0x83,0x53,0x99,0x61, 0x17,0x2B,0x04,0x7E,0xBA,0x77,0xD6,0x26,0xE1,0x69,0x14,0x63,0x55,0x21,0x0C,0x7D]; /** *密钥扩展 *@param$keys */ functionaes_key_extend($keys) { $w=[]; global$rcon; for($i=0;$i<strlen($keys);$i+=4){ $first=ord($keys{$i})<<24; $second=ord($keys{$i+1})<<16; $third=ord($keys{$i+2})<<8; $fourth=ord($keys{$i+3}); $w[]=($first|$second|$third|$fourth); } for($n=4;$n<=43;$n++){ if($n%4!==0){ $w[$n]=$w[$n-4]^$w[$n-1]; }else{ $mix=(($w[$n-1]&0xFF000000)>>24)|(($w[$n-1]&0x00FFFFFF)<<8); $mix=subBytes($mix); $w[$n]=(($w[$n-4]^$mix^$rcon[($n/4)-1])); } } return$w; } /** *字节替换，将32位key按照S盒替换，高4位为行数，低4位为列数 *@param$keys *@returnint */ functionsubBytes($keys) { $first=getSValue(((((0xFF000000&$keys)>>24)&0xF0)>>4)*16+(((0xFF000000&$keys)>>24)&0xF))<<24; $second=getSValue(((((0x00FF0000&$keys)>>16)&0xF0)>>4)*16+(((0x00FF0000&$keys)>>16)&0xF))<<16; $third=getSValue(((((0x0000FF00&$keys)>>8)&0xF0)>>4)*16+(((0x0000FF00&$keys)>>8)&0xF))<<8; $fourth=getSValue((((0x000000FF&$keys)&0xF0)>>4)*16+((0x000000FF&$keys)&0xF)); return$first|$second|$third|$fourth; } /** *将8位字节按S盒规则替换 *@param$key *@param$type */ functionsubByte($key,$type=1) { $row=($key&0xF0)>>4; $col=($key&0xF); returngetSValue($row*16+$col,$type); } /** *将16个字节转成4*4的矩阵，并用S盒替换 *@param$plainText *@returnarray */ functionto4x4Array($plainText) { $states=[]; for($i=0;$i<4;$i++){ for($j=0;$j<4;$j++){ $states[]=ord($plainText{($j===0?$i:4*$j+$i)}); } } return$states; } functiongetSValue($key,$type=1) { global$s,$ss; return$type===1?$s[$key]:$ss[$key]; } /** *行移位 *第0行不变，第i行左移i位i>0 *@param&$arr *@param$type */ functionshiftRows(&$arr,$type=1) { for($i=1;$i<4;$i++){ $index=4*$i; $temp=$arr; for($j=0;$j<4;$j++){ $key=($index+$i+$j)>(4*$i+3)?4*$i-1+($index+$i+$j-4*$i-3):$index+$j+$i; if($type===2){ $key=($index+$j-$i<4*$i)?4*($i+1)-(4*$i-($index+$j-$i)):$index+$j-$i; } $arr[$index+$j]=$temp[$key]; } } } /** *列混合 *@param$arr *@param$type */ functionmixColumns(&$arr,$type=1) { global$constArray,$constArrayReverse; $mixStates=[]; for($i=0;$i<16;$i++){ $result=0; for($j=0;$j<4;$j++){ $result^=aes_multi($arr[4*$j+$i%4],$type===1?$constArray[4*(floor($i/4))+$j]:$constArrayReverse[4*(floor($i/4))+$j]); } $mixStates[$i]=$result; } $arr=$mixStates; } functionroundAddKey($states,$keys,$round=0) { static$result=[]; $tempStates=$states; if($round>10){ returnimplode('',array_map(function($n){ returnsprintf("%02X",$n); },$tempStates)); } if($round!==0){ $tempStates=[]; foreach($statesas$k=>$val){ $tempStates[]=subByte($val); } shiftRows($tempStates); if($round!==10){//最后一轮无需列混合 mixColumns($tempStates); } } foreach($tempStatesas$k2=>$val2){ $result[$round][]=$val2^$keys[$round][$k2]; } returnroundAddKey($result[$round],$keys,++$round); } functionroundReverseAddKey($states,$keys,$round=10) { static$result=[]; $tempStates=[]; foreach($statesas$k=>$val){ $tempStates[]=$val^$keys[$round][$k]; } if($round===0){ $result[$round]=$tempStates; $newest=[]; for($i=0;$i<4;$i++){ for($j=0;$j<4;$j++){ $newest[]=$tempStates[4*$j+$i]; } } returnimplode('',array_map(function($n){ returnchr($n); },$newest)); }elseif($round!==10){ mixColumns($tempStates,2); } shiftRows($tempStates,2); foreach($tempStatesas$k=>$state){ $result[$round][]=subByte($state,2); } returnroundReverseAddKey($result[$round],$keys,--$round); } functionaddRoundKey($states,$extendKeys,$type=1) { $new4x4Keys=[]; $cloneStates=$states; $roundKeys=array_chunk($extendKeys,4); foreach($roundKeysas$k=>$keys){ foreach($keysas$index=>$key){ $temp=[]; $temp[]=($key&0xFF000000)>>24; $temp[]=($key&0x00FF0000)>>16; $temp[]=($key&0x0000FF00)>>8; $temp[]=($key&0xFF); for($row=0;$row<4;$row++){ $new4x4Keys[$k][$row*4+$index]=$temp[$row]; } ksort($new4x4Keys[$k]); } } return$type===1? roundAddKey($cloneStates,$new4x4Keys,0): roundReverseAddKey($cloneStates,$new4x4Keys,10); } functionphp_aes_encrypt($key,$plain) { returnaddRoundKey(to4x4Array($plain),aes_key_extend($key)); } functionphp_aes_decrypt($key,$plain) { $states=[]; for($i=0;$i<32;$i+=2){ $states[]=hexdec($plain{$i}.$plain{$i+1}); } returnaddRoundKey($states,aes_key_extend($key),2); } $p='abcdefghijklmnop'; $k='1234567890abcdef'; $plain=php_aes_encrypt($k,$p); var_dump($plain); var_dump(php_aes_decrypt($k,$plain)); |
