2021SC@SDUSC 山东大学软件学院软件工程应用与实践

一、mraes.c结构

mraec.c的总体结构如下，具有fbsub、ftable1等数组，主要实现了aes_decrypt 、aes_encrypt、aes_end、aes_getreg、aes_init、aes_reset几个在miracl开源库中比较重要的函数，这一次的博客就是读一下这函数的功能。

二、头文件

】

stdlib 头文件即standard library标准库头文件。stdlib.h里面定义了五种类型、一些宏和通用工具函数。类型例如size_t、wchar_t、div_t、ldiv_t和lldiv_t；宏例如EXIT_FAILURE、EXIT_SUCCESS、RAND_MAX和MB_CUR_MAX等等；常用的函数如malloc()、calloc()、realloc()、free()、system()、atoi()、atol()、rand()、srand()、exit()等等。具体的内容可以打开编译器的include目录里面的stdlib.h头文件查看。

miracl.h则是miracl库自己设计的头文件，定义了诸多标识符来表示常量，还定义了很多函数，结构体以及自定义数据类型。

二、主体代码

2.1 宏定义

在mirdef.h中mr_unsign32被定义为unsigned int，即无符号的整型数据，如下图：

在mraec.c中MR_WORD也是自定义数据类型，指的是无符号整型数据。

ROTL(x)是一个带参数的宏定义，主要作用就是将二进制字符串左移动1字节，ROTL8(x)、ROTL16(x)、ROTL24(x)的作用分别是将32位字向左移动1、2或3字节。

2.2 数据

static const MR_BYTE InCo[4]={0xB,0xD,0x9,0xE};  /* Inverse Coefficients */static const MR_BYTE ptab[]=
{1,3,5,15,17,51,85,255,26,46,114,150,161,248,19,53,
95,225,56,72,216,115,149,164,247,2,6,10,30,34,102,170,
229,52,92,228,55,89,235,38,106,190,217,112,144,171,230,49,
83,245,4,12,20,60,68,204,79,209,104,184,211,110,178,205,
76,212,103,169,224,59,77,215,98,166,241,8,24,40,120,136,
131,158,185,208,107,189,220,127,129,152,179,206,73,219,118,154,
181,196,87,249,16,48,80,240,11,29,39,105,187,214,97,163,
254,25,43,125,135,146,173,236,47,113,147,174,233,32,96,160,
251,22,58,78,210,109,183,194,93,231,50,86,250,21,63,65,
195,94,226,61,71,201,64,192,91,237,44,116,156,191,218,117,
159,186,213,100,172,239,42,126,130,157,188,223,122,142,137,128,
155,182,193,88,232,35,101,175,234,37,111,177,200,67,197,84,
252,31,33,99,165,244,7,9,27,45,119,153,176,203,70,202,
69,207,74,222,121,139,134,145,168,227,62,66,198,81,243,14,
18,54,90,238,41,123,141,140,143,138,133,148,167,242,13,23,
57,75,221,124,132,151,162,253,28,36,108,180,199,82,246,1};static const MR_BYTE ltab[]=
{0,255,25,1,50,2,26,198,75,199,27,104,51,238,223,3,
100,4,224,14,52,141,129,239,76,113,8,200,248,105,28,193,
125,194,29,181,249,185,39,106,77,228,166,114,154,201,9,120,
101,47,138,5,33,15,225,36,18,240,130,69,53,147,218,142,
150,143,219,189,54,208,206,148,19,92,210,241,64,70,131,56,
102,221,253,48,191,6,139,98,179,37,226,152,34,136,145,16,
126,110,72,195,163,182,30,66,58,107,40,84,250,133,61,186,
43,121,10,21,155,159,94,202,78,212,172,229,243,115,167,87,
175,88,168,80,244,234,214,116,79,174,233,213,231,230,173,232,
44,215,117,122,235,22,11,245,89,203,95,176,156,169,81,160,
127,12,246,111,23,196,73,236,216,67,31,45,164,118,123,183,
204,187,62,90,251,96,177,134,59,82,161,108,170,85,41,157,
151,178,135,144,97,190,220,252,188,149,207,205,55,63,91,209,
83,57,132,60,65,162,109,71,20,42,158,93,86,242,211,171,
68,17,146,217,35,32,46,137,180,124,184,38,119,153,227,165,
103,74,237,222,197,49,254,24,13,99,140,128,192,247,112,7};static const MR_BYTE fbsub[]=
{99,124,119,123,242,107,111,197,48,1,103,43,254,215,171,118,
202,130,201,125,250,89,71,240,173,212,162,175,156,164,114,192,
183,253,147,38,54,63,247,204,52,165,229,241,113,216,49,21,
4,199,35,195,24,150,5,154,7,18,128,226,235,39,178,117,
9,131,44,26,27,110,90,160,82,59,214,179,41,227,47,132,
83,209,0,237,32,252,177,91,106,203,190,57,74,76,88,207,
208,239,170,251,67,77,51,133,69,249,2,127,80,60,159,168,
81,163,64,143,146,157,56,245,188,182,218,33,16,255,243,210,
205,12,19,236,95,151,68,23,196,167,126,61,100,93,25,115,
96,129,79,220,34,42,144,136,70,238,184,20,222,94,11,219,
224,50,58,10,73,6,36,92,194,211,172,98,145,149,228,121,
231,200,55,109,141,213,78,169,108,86,244,234,101,122,174,8,
186,120,37,46,28,166,180,198,232,221,116,31,75,189,139,138,
112,62,181,102,72,3,246,14,97,53,87,185,134,193,29,158,
225,248,152,17,105,217,142,148,155,30,135,233,206,85,40,223,
140,161,137,13,191,230,66,104,65,153,45,15,176,84,187,22};static const MR_BYTE rbsub[]=
{82,9,106,213,48,54,165,56,191,64,163,158,129,243,215,251,
124,227,57,130,155,47,255,135,52,142,67,68,196,222,233,203,
84,123,148,50,166,194,35,61,238,76,149,11,66,250,195,78,
8,46,161,102,40,217,36,178,118,91,162,73,109,139,209,37,
114,248,246,100,134,104,152,22,212,164,92,204,93,101,182,146,
108,112,72,80,253,237,185,218,94,21,70,87,167,141,157,132,
144,216,171,0,140,188,211,10,247,228,88,5,184,179,69,6,
208,44,30,143,202,63,15,2,193,175,189,3,1,19,138,107,
58,145,17,65,79,103,220,234,151,242,207,206,240,180,230,115,
150,172,116,34,231,173,53,133,226,249,55,232,28,117,223,110,
71,241,26,113,29,41,197,137,111,183,98,14,170,24,190,27,
252,86,62,75,198,210,121,32,154,219,192,254,120,205,90,244,
31,221,168,51,136,7,199,49,177,18,16,89,39,128,236,95,
96,81,127,169,25,181,74,13,45,229,122,159,147,201,156,239,
160,224,59,77,174,42,245,176,200,235,187,60,131,83,153,97,
23,43,4,126,186,119,214,38,225,105,20,99,85,33,12,125};static const MR_WORD rco[]=
{1,2,4,8,16,32,64,128,27,54,108,216,171,77,154,47};static const MR_WORD ftable[]=
{0xa56363c6,0x847c7cf8,0x997777ee,0x8d7b7bf6,0xdf2f2ff,0xbd6b6bd6,
0xb16f6fde,0x54c5c591,0x50303060,0x3010102,0xa96767ce,0x7d2b2b56,
0x19fefee7,0x62d7d7b5,0xe6abab4d,0x9a7676ec,0x45caca8f,0x9d82821f,
0x40c9c989,0x877d7dfa,0x15fafaef,0xeb5959b2,0xc947478e,0xbf0f0fb,
0xecadad41,0x67d4d4b3,0xfda2a25f,0xeaafaf45,0xbf9c9c23,0xf7a4a453,
0x967272e4,0x5bc0c09b,0xc2b7b775,0x1cfdfde1,0xae93933d,0x6a26264c,
0x5a36366c,0x413f3f7e,0x2f7f7f5,0x4fcccc83,0x5c343468,0xf4a5a551,
0x34e5e5d1,0x8f1f1f9,0x937171e2,0x73d8d8ab,0x53313162,0x3f15152a,
0xc040408,0x52c7c795,0x65232346,0x5ec3c39d,0x28181830,0xa1969637,
0xf05050a,0xb59a9a2f,0x907070e,0x36121224,0x9b80801b,0x3de2e2df,
0x26ebebcd,0x6927274e,0xcdb2b27f,0x9f7575ea,0x1b090912,0x9e83831d,
0x742c2c58,0x2e1a1a34,0x2d1b1b36,0xb26e6edc,0xee5a5ab4,0xfba0a05b,
0xf65252a4,0x4d3b3b76,0x61d6d6b7,0xceb3b37d,0x7b292952,0x3ee3e3dd,
0x712f2f5e,0x97848413,0xf55353a6,0x68d1d1b9,0x0,0x2cededc1,
0x60202040,0x1ffcfce3,0xc8b1b179,0xed5b5bb6,0xbe6a6ad4,0x46cbcb8d,
0xd9bebe67,0x4b393972,0xde4a4a94,0xd44c4c98,0xe85858b0,0x4acfcf85,
0x6bd0d0bb,0x2aefefc5,0xe5aaaa4f,0x16fbfbed,0xc5434386,0xd74d4d9a,
0x55333366,0x94858511,0xcf45458a,0x10f9f9e9,0x6020204,0x817f7ffe,
0xf05050a0,0x443c3c78,0xba9f9f25,0xe3a8a84b,0xf35151a2,0xfea3a35d,
0xc0404080,0x8a8f8f05,0xad92923f,0xbc9d9d21,0x48383870,0x4f5f5f1,
0xdfbcbc63,0xc1b6b677,0x75dadaaf,0x63212142,0x30101020,0x1affffe5,
0xef3f3fd,0x6dd2d2bf,0x4ccdcd81,0x140c0c18,0x35131326,0x2fececc3,
0xe15f5fbe,0xa2979735,0xcc444488,0x3917172e,0x57c4c493,0xf2a7a755,
0x827e7efc,0x473d3d7a,0xac6464c8,0xe75d5dba,0x2b191932,0x957373e6,
0xa06060c0,0x98818119,0xd14f4f9e,0x7fdcdca3,0x66222244,0x7e2a2a54,
0xab90903b,0x8388880b,0xca46468c,0x29eeeec7,0xd3b8b86b,0x3c141428,
0x79dedea7,0xe25e5ebc,0x1d0b0b16,0x76dbdbad,0x3be0e0db,0x56323264,
0x4e3a3a74,0x1e0a0a14,0xdb494992,0xa06060c,0x6c242448,0xe45c5cb8,
0x5dc2c29f,0x6ed3d3bd,0xefacac43,0xa66262c4,0xa8919139,0xa4959531,
0x37e4e4d3,0x8b7979f2,0x32e7e7d5,0x43c8c88b,0x5937376e,0xb76d6dda,
0x8c8d8d01,0x64d5d5b1,0xd24e4e9c,0xe0a9a949,0xb46c6cd8,0xfa5656ac,
0x7f4f4f3,0x25eaeacf,0xaf6565ca,0x8e7a7af4,0xe9aeae47,0x18080810,
0xd5baba6f,0x887878f0,0x6f25254a,0x722e2e5c,0x241c1c38,0xf1a6a657,
0xc7b4b473,0x51c6c697,0x23e8e8cb,0x7cdddda1,0x9c7474e8,0x211f1f3e,
0xdd4b4b96,0xdcbdbd61,0x868b8b0d,0x858a8a0f,0x907070e0,0x423e3e7c,
0xc4b5b571,0xaa6666cc,0xd8484890,0x5030306,0x1f6f6f7,0x120e0e1c,
0xa36161c2,0x5f35356a,0xf95757ae,0xd0b9b969,0x91868617,0x58c1c199,
0x271d1d3a,0xb99e9e27,0x38e1e1d9,0x13f8f8eb,0xb398982b,0x33111122,
0xbb6969d2,0x70d9d9a9,0x898e8e07,0xa7949433,0xb69b9b2d,0x221e1e3c,
0x92878715,0x20e9e9c9,0x49cece87,0xff5555aa,0x78282850,0x7adfdfa5,
0x8f8c8c03,0xf8a1a159,0x80898909,0x170d0d1a,0xdabfbf65,0x31e6e6d7,
0xc6424284,0xb86868d0,0xc3414182,0xb0999929,0x772d2d5a,0x110f0f1e,
0xcbb0b07b,0xfc5454a8,0xd6bbbb6d,0x3a16162c};static const MR_WORD rtable[]=
{0x50a7f451,0x5365417e,0xc3a4171a,0x965e273a,0xcb6bab3b,0xf1459d1f,
0xab58faac,0x9303e34b,0x55fa3020,0xf66d76ad,0x9176cc88,0x254c02f5,
0xfcd7e54f,0xd7cb2ac5,0x80443526,0x8fa362b5,0x495ab1de,0x671bba25,
0x980eea45,0xe1c0fe5d,0x2752fc3,0x12f04c81,0xa397468d,0xc6f9d36b,
0xe75f8f03,0x959c9215,0xeb7a6dbf,0xda595295,0x2d83bed4,0xd3217458,
0x2969e049,0x44c8c98e,0x6a89c275,0x78798ef4,0x6b3e5899,0xdd71b927,
0xb64fe1be,0x17ad88f0,0x66ac20c9,0xb43ace7d,0x184adf63,0x82311ae5,
0x60335197,0x457f5362,0xe07764b1,0x84ae6bbb,0x1ca081fe,0x942b08f9,
0x58684870,0x19fd458f,0x876cde94,0xb7f87b52,0x23d373ab,0xe2024b72,
0x578f1fe3,0x2aab5566,0x728ebb2,0x3c2b52f,0x9a7bc586,0xa50837d3,
0xf2872830,0xb2a5bf23,0xba6a0302,0x5c8216ed,0x2b1ccf8a,0x92b479a7,
0xf0f207f3,0xa1e2694e,0xcdf4da65,0xd5be0506,0x1f6234d1,0x8afea6c4,
0x9d532e34,0xa055f3a2,0x32e18a05,0x75ebf6a4,0x39ec830b,0xaaef6040,
0x69f715e,0x51106ebd,0xf98a213e,0x3d06dd96,0xae053edd,0x46bde64d,
0xb58d5491,0x55dc471,0x6fd40604,0xff155060,0x24fb9819,0x97e9bdd6,
0xcc434089,0x779ed967,0xbd42e8b0,0x888b8907,0x385b19e7,0xdbeec879,
0x470a7ca1,0xe90f427c,0xc91e84f8,0x0,0x83868009,0x48ed2b32,
0xac70111e,0x4e725a6c,0xfbff0efd,0x5638850f,0x1ed5ae3d,0x27392d36,
0x64d90f0a,0x21a65c68,0xd1545b9b,0x3a2e3624,0xb1670a0c,0xfe75793,
0xd296eeb4,0x9e919b1b,0x4fc5c080,0xa220dc61,0x694b775a,0x161a121c,
0xaba93e2,0xe52aa0c0,0x43e0223c,0x1d171b12,0xb0d090e,0xadc78bf2,
0xb9a8b62d,0xc8a91e14,0x8519f157,0x4c0775af,0xbbdd99ee,0xfd607fa3,
0x9f2601f7,0xbcf5725c,0xc53b6644,0x347efb5b,0x7629438b,0xdcc623cb,
0x68fcedb6,0x63f1e4b8,0xcadc31d7,0x10856342,0x40229713,0x2011c684,
0x7d244a85,0xf83dbbd2,0x1132f9ae,0x6da129c7,0x4b2f9e1d,0xf330b2dc,
0xec52860d,0xd0e3c177,0x6c16b32b,0x99b970a9,0xfa489411,0x2264e947,
0xc48cfca8,0x1a3ff0a0,0xd82c7d56,0xef903322,0xc74e4987,0xc1d138d9,
0xfea2ca8c,0x360bd498,0xcf81f5a6,0x28de7aa5,0x268eb7da,0xa4bfad3f,
0xe49d3a2c,0xd927850,0x9bcc5f6a,0x62467e54,0xc2138df6,0xe8b8d890,
0x5ef7392e,0xf5afc382,0xbe805d9f,0x7c93d069,0xa92dd56f,0xb31225cf,
0x3b99acc8,0xa77d1810,0x6e639ce8,0x7bbb3bdb,0x97826cd,0xf418596e,
0x1b79aec,0xa89a4f83,0x656e95e6,0x7ee6ffaa,0x8cfbc21,0xe6e815ef,
0xd99be7ba,0xce366f4a,0xd4099fea,0xd67cb029,0xafb2a431,0x31233f2a,
0x3094a5c6,0xc066a235,0x37bc4e74,0xa6ca82fc,0xb0d090e0,0x15d8a733,
0x4a9804f1,0xf7daec41,0xe50cd7f,0x2ff69117,0x8dd64d76,0x4db0ef43,
0x544daacc,0xdf0496e4,0xe3b5d19e,0x1b886a4c,0xb81f2cc1,0x7f516546,
0x4ea5e9d,0x5d358c01,0x737487fa,0x2e410bfb,0x5a1d67b3,0x52d2db92,
0x335610e9,0x1347d66d,0x8c61d79a,0x7a0ca137,0x8e14f859,0x893c13eb,
0xee27a9ce,0x35c961b7,0xede51ce1,0x3cb1477a,0x59dfd29c,0x3f73f255,
0x79ce1418,0xbf37c773,0xeacdf753,0x5baafd5f,0x146f3ddf,0x86db4478,
0x81f3afca,0x3ec468b9,0x2c342438,0x5f40a3c2,0x72c31d16,0xc25e2bc,
0x8b493c28,0x41950dff,0x7101a839,0xdeb30c08,0x9ce4b4d8,0x90c15664,
0x6184cb7b,0x70b632d5,0x745c6c48,0x4257b8d0};#ifndef MR_SMALL_AESstatic const MR_WORD ftable1[]=
{0x6363c6a5,0x7c7cf884,0x7777ee99,0x7b7bf68d,0xf2f2ff0d,0x6b6bd6bd,
0x6f6fdeb1,0xc5c59154,0x30306050,0x1010203,0x6767cea9,0x2b2b567d,
0xfefee719,0xd7d7b562,0xabab4de6,0x7676ec9a,0xcaca8f45,0x82821f9d,
0xc9c98940,0x7d7dfa87,0xfafaef15,0x5959b2eb,0x47478ec9,0xf0f0fb0b,
0xadad41ec,0xd4d4b367,0xa2a25ffd,0xafaf45ea,0x9c9c23bf,0xa4a453f7,
0x7272e496,0xc0c09b5b,0xb7b775c2,0xfdfde11c,0x93933dae,0x26264c6a,
0x36366c5a,0x3f3f7e41,0xf7f7f502,0xcccc834f,0x3434685c,0xa5a551f4,
0xe5e5d134,0xf1f1f908,0x7171e293,0xd8d8ab73,0x31316253,0x15152a3f,
0x404080c,0xc7c79552,0x23234665,0xc3c39d5e,0x18183028,0x969637a1,
0x5050a0f,0x9a9a2fb5,0x7070e09,0x12122436,0x80801b9b,0xe2e2df3d,
0xebebcd26,0x27274e69,0xb2b27fcd,0x7575ea9f,0x909121b,0x83831d9e,
0x2c2c5874,0x1a1a342e,0x1b1b362d,0x6e6edcb2,0x5a5ab4ee,0xa0a05bfb,
0x5252a4f6,0x3b3b764d,0xd6d6b761,0xb3b37dce,0x2929527b,0xe3e3dd3e,
0x2f2f5e71,0x84841397,0x5353a6f5,0xd1d1b968,0x0,0xededc12c,
0x20204060,0xfcfce31f,0xb1b179c8,0x5b5bb6ed,0x6a6ad4be,0xcbcb8d46,
0xbebe67d9,0x3939724b,0x4a4a94de,0x4c4c98d4,0x5858b0e8,0xcfcf854a,
0xd0d0bb6b,0xefefc52a,0xaaaa4fe5,0xfbfbed16,0x434386c5,0x4d4d9ad7,
0x33336655,0x85851194,0x45458acf,0xf9f9e910,0x2020406,0x7f7ffe81,
0x5050a0f0,0x3c3c7844,0x9f9f25ba,0xa8a84be3,0x5151a2f3,0xa3a35dfe,
0x404080c0,0x8f8f058a,0x92923fad,0x9d9d21bc,0x38387048,0xf5f5f104,
0xbcbc63df,0xb6b677c1,0xdadaaf75,0x21214263,0x10102030,0xffffe51a,
0xf3f3fd0e,0xd2d2bf6d,0xcdcd814c,0xc0c1814,0x13132635,0xececc32f,
0x5f5fbee1,0x979735a2,0x444488cc,0x17172e39,0xc4c49357,0xa7a755f2,
0x7e7efc82,0x3d3d7a47,0x6464c8ac,0x5d5dbae7,0x1919322b,0x7373e695,
0x6060c0a0,0x81811998,0x4f4f9ed1,0xdcdca37f,0x22224466,0x2a2a547e,
0x90903bab,0x88880b83,0x46468cca,0xeeeec729,0xb8b86bd3,0x1414283c,
0xdedea779,0x5e5ebce2,0xb0b161d,0xdbdbad76,0xe0e0db3b,0x32326456,
0x3a3a744e,0xa0a141e,0x494992db,0x6060c0a,0x2424486c,0x5c5cb8e4,
0xc2c29f5d,0xd3d3bd6e,0xacac43ef,0x6262c4a6,0x919139a8,0x959531a4,
0xe4e4d337,0x7979f28b,0xe7e7d532,0xc8c88b43,0x37376e59,0x6d6ddab7,
0x8d8d018c,0xd5d5b164,0x4e4e9cd2,0xa9a949e0,0x6c6cd8b4,0x5656acfa,
0xf4f4f307,0xeaeacf25,0x6565caaf,0x7a7af48e,0xaeae47e9,0x8081018,
0xbaba6fd5,0x7878f088,0x25254a6f,0x2e2e5c72,0x1c1c3824,0xa6a657f1,
0xb4b473c7,0xc6c69751,0xe8e8cb23,0xdddda17c,0x7474e89c,0x1f1f3e21,
0x4b4b96dd,0xbdbd61dc,0x8b8b0d86,0x8a8a0f85,0x7070e090,0x3e3e7c42,
0xb5b571c4,0x6666ccaa,0x484890d8,0x3030605,0xf6f6f701,0xe0e1c12,
0x6161c2a3,0x35356a5f,0x5757aef9,0xb9b969d0,0x86861791,0xc1c19958,
0x1d1d3a27,0x9e9e27b9,0xe1e1d938,0xf8f8eb13,0x98982bb3,0x11112233,
0x6969d2bb,0xd9d9a970,0x8e8e0789,0x949433a7,0x9b9b2db6,0x1e1e3c22,
0x87871592,0xe9e9c920,0xcece8749,0x5555aaff,0x28285078,0xdfdfa57a,
0x8c8c038f,0xa1a159f8,0x89890980,0xd0d1a17,0xbfbf65da,0xe6e6d731,
0x424284c6,0x6868d0b8,0x414182c3,0x999929b0,0x2d2d5a77,0xf0f1e11,
0xb0b07bcb,0x5454a8fc,0xbbbb6dd6,0x16162c3a};static const MR_WORD rtable1[]=
{0xa7f45150,0x65417e53,0xa4171ac3,0x5e273a96,0x6bab3bcb,0x459d1ff1,
0x58faacab,0x3e34b93,0xfa302055,0x6d76adf6,0x76cc8891,0x4c02f525,
0xd7e54ffc,0xcb2ac5d7,0x44352680,0xa362b58f,0x5ab1de49,0x1bba2567,
0xeea4598,0xc0fe5de1,0x752fc302,0xf04c8112,0x97468da3,0xf9d36bc6,
0x5f8f03e7,0x9c921595,0x7a6dbfeb,0x595295da,0x83bed42d,0x217458d3,
0x69e04929,0xc8c98e44,0x89c2756a,0x798ef478,0x3e58996b,0x71b927dd,
0x4fe1beb6,0xad88f017,0xac20c966,0x3ace7db4,0x4adf6318,0x311ae582,
0x33519760,0x7f536245,0x7764b1e0,0xae6bbb84,0xa081fe1c,0x2b08f994,
0x68487058,0xfd458f19,0x6cde9487,0xf87b52b7,0xd373ab23,0x24b72e2,
0x8f1fe357,0xab55662a,0x28ebb207,0xc2b52f03,0x7bc5869a,0x837d3a5,
0x872830f2,0xa5bf23b2,0x6a0302ba,0x8216ed5c,0x1ccf8a2b,0xb479a792,
0xf207f3f0,0xe2694ea1,0xf4da65cd,0xbe0506d5,0x6234d11f,0xfea6c48a,
0x532e349d,0x55f3a2a0,0xe18a0532,0xebf6a475,0xec830b39,0xef6040aa,
0x9f715e06,0x106ebd51,0x8a213ef9,0x6dd963d,0x53eddae,0xbde64d46,
0x8d5491b5,0x5dc47105,0xd406046f,0x155060ff,0xfb981924,0xe9bdd697,
0x434089cc,0x9ed96777,0x42e8b0bd,0x8b890788,0x5b19e738,0xeec879db,
0xa7ca147,0xf427ce9,0x1e84f8c9,0x0,0x86800983,0xed2b3248,
0x70111eac,0x725a6c4e,0xff0efdfb,0x38850f56,0xd5ae3d1e,0x392d3627,
0xd90f0a64,0xa65c6821,0x545b9bd1,0x2e36243a,0x670a0cb1,0xe757930f,
0x96eeb4d2,0x919b1b9e,0xc5c0804f,0x20dc61a2,0x4b775a69,0x1a121c16,
0xba93e20a,0x2aa0c0e5,0xe0223c43,0x171b121d,0xd090e0b,0xc78bf2ad,
0xa8b62db9,0xa91e14c8,0x19f15785,0x775af4c,0xdd99eebb,0x607fa3fd,
0x2601f79f,0xf5725cbc,0x3b6644c5,0x7efb5b34,0x29438b76,0xc623cbdc,
0xfcedb668,0xf1e4b863,0xdc31d7ca,0x85634210,0x22971340,0x11c68420,
0x244a857d,0x3dbbd2f8,0x32f9ae11,0xa129c76d,0x2f9e1d4b,0x30b2dcf3,
0x52860dec,0xe3c177d0,0x16b32b6c,0xb970a999,0x489411fa,0x64e94722,
0x8cfca8c4,0x3ff0a01a,0x2c7d56d8,0x903322ef,0x4e4987c7,0xd138d9c1,
0xa2ca8cfe,0xbd49836,0x81f5a6cf,0xde7aa528,0x8eb7da26,0xbfad3fa4,
0x9d3a2ce4,0x9278500d,0xcc5f6a9b,0x467e5462,0x138df6c2,0xb8d890e8,
0xf7392e5e,0xafc382f5,0x805d9fbe,0x93d0697c,0x2dd56fa9,0x1225cfb3,
0x99acc83b,0x7d1810a7,0x639ce86e,0xbb3bdb7b,0x7826cd09,0x18596ef4,
0xb79aec01,0x9a4f83a8,0x6e95e665,0xe6ffaa7e,0xcfbc2108,0xe815efe6,
0x9be7bad9,0x366f4ace,0x99fead4,0x7cb029d6,0xb2a431af,0x233f2a31,
0x94a5c630,0x66a235c0,0xbc4e7437,0xca82fca6,0xd090e0b0,0xd8a73315,
0x9804f14a,0xdaec41f7,0x50cd7f0e,0xf691172f,0xd64d768d,0xb0ef434d,
0x4daacc54,0x496e4df,0xb5d19ee3,0x886a4c1b,0x1f2cc1b8,0x5165467f,
0xea5e9d04,0x358c015d,0x7487fa73,0x410bfb2e,0x1d67b35a,0xd2db9252,
0x5610e933,0x47d66d13,0x61d79a8c,0xca1377a,0x14f8598e,0x3c13eb89,
0x27a9ceee,0xc961b735,0xe51ce1ed,0xb1477a3c,0xdfd29c59,0x73f2553f,
0xce141879,0x37c773bf,0xcdf753ea,0xaafd5f5b,0x6f3ddf14,0xdb447886,
0xf3afca81,0xc468b93e,0x3424382c,0x40a3c25f,0xc31d1672,0x25e2bc0c,
0x493c288b,0x950dff41,0x1a83971,0xb30c08de,0xe4b4d89c,0xc1566490,
0x84cb7b61,0xb632d570,0x5c6c4874,0x57b8d042};static const MR_WORD ftable2[]=
{0x63c6a563,0x7cf8847c,0x77ee9977,0x7bf68d7b,0xf2ff0df2,0x6bd6bd6b,
0x6fdeb16f,0xc59154c5,0x30605030,0x1020301,0x67cea967,0x2b567d2b,
0xfee719fe,0xd7b562d7,0xab4de6ab,0x76ec9a76,0xca8f45ca,0x821f9d82,
0xc98940c9,0x7dfa877d,0xfaef15fa,0x59b2eb59,0x478ec947,0xf0fb0bf0,
0xad41ecad,0xd4b367d4,0xa25ffda2,0xaf45eaaf,0x9c23bf9c,0xa453f7a4,
0x72e49672,0xc09b5bc0,0xb775c2b7,0xfde11cfd,0x933dae93,0x264c6a26,
0x366c5a36,0x3f7e413f,0xf7f502f7,0xcc834fcc,0x34685c34,0xa551f4a5,
0xe5d134e5,0xf1f908f1,0x71e29371,0xd8ab73d8,0x31625331,0x152a3f15,
0x4080c04,0xc79552c7,0x23466523,0xc39d5ec3,0x18302818,0x9637a196,
0x50a0f05,0x9a2fb59a,0x70e0907,0x12243612,0x801b9b80,0xe2df3de2,
0xebcd26eb,0x274e6927,0xb27fcdb2,0x75ea9f75,0x9121b09,0x831d9e83,
0x2c58742c,0x1a342e1a,0x1b362d1b,0x6edcb26e,0x5ab4ee5a,0xa05bfba0,
0x52a4f652,0x3b764d3b,0xd6b761d6,0xb37dceb3,0x29527b29,0xe3dd3ee3,
0x2f5e712f,0x84139784,0x53a6f553,0xd1b968d1,0x0,0xedc12ced,
0x20406020,0xfce31ffc,0xb179c8b1,0x5bb6ed5b,0x6ad4be6a,0xcb8d46cb,
0xbe67d9be,0x39724b39,0x4a94de4a,0x4c98d44c,0x58b0e858,0xcf854acf,
0xd0bb6bd0,0xefc52aef,0xaa4fe5aa,0xfbed16fb,0x4386c543,0x4d9ad74d,
0x33665533,0x85119485,0x458acf45,0xf9e910f9,0x2040602,0x7ffe817f,
0x50a0f050,0x3c78443c,0x9f25ba9f,0xa84be3a8,0x51a2f351,0xa35dfea3,
0x4080c040,0x8f058a8f,0x923fad92,0x9d21bc9d,0x38704838,0xf5f104f5,
0xbc63dfbc,0xb677c1b6,0xdaaf75da,0x21426321,0x10203010,0xffe51aff,
0xf3fd0ef3,0xd2bf6dd2,0xcd814ccd,0xc18140c,0x13263513,0xecc32fec,
0x5fbee15f,0x9735a297,0x4488cc44,0x172e3917,0xc49357c4,0xa755f2a7,
0x7efc827e,0x3d7a473d,0x64c8ac64,0x5dbae75d,0x19322b19,0x73e69573,
0x60c0a060,0x81199881,0x4f9ed14f,0xdca37fdc,0x22446622,0x2a547e2a,
0x903bab90,0x880b8388,0x468cca46,0xeec729ee,0xb86bd3b8,0x14283c14,
0xdea779de,0x5ebce25e,0xb161d0b,0xdbad76db,0xe0db3be0,0x32645632,
0x3a744e3a,0xa141e0a,0x4992db49,0x60c0a06,0x24486c24,0x5cb8e45c,
0xc29f5dc2,0xd3bd6ed3,0xac43efac,0x62c4a662,0x9139a891,0x9531a495,
0xe4d337e4,0x79f28b79,0xe7d532e7,0xc88b43c8,0x376e5937,0x6ddab76d,
0x8d018c8d,0xd5b164d5,0x4e9cd24e,0xa949e0a9,0x6cd8b46c,0x56acfa56,
0xf4f307f4,0xeacf25ea,0x65caaf65,0x7af48e7a,0xae47e9ae,0x8101808,
0xba6fd5ba,0x78f08878,0x254a6f25,0x2e5c722e,0x1c38241c,0xa657f1a6,
0xb473c7b4,0xc69751c6,0xe8cb23e8,0xdda17cdd,0x74e89c74,0x1f3e211f,
0x4b96dd4b,0xbd61dcbd,0x8b0d868b,0x8a0f858a,0x70e09070,0x3e7c423e,
0xb571c4b5,0x66ccaa66,0x4890d848,0x3060503,0xf6f701f6,0xe1c120e,
0x61c2a361,0x356a5f35,0x57aef957,0xb969d0b9,0x86179186,0xc19958c1,
0x1d3a271d,0x9e27b99e,0xe1d938e1,0xf8eb13f8,0x982bb398,0x11223311,
0x69d2bb69,0xd9a970d9,0x8e07898e,0x9433a794,0x9b2db69b,0x1e3c221e,
0x87159287,0xe9c920e9,0xce8749ce,0x55aaff55,0x28507828,0xdfa57adf,
0x8c038f8c,0xa159f8a1,0x89098089,0xd1a170d,0xbf65dabf,0xe6d731e6,
0x4284c642,0x68d0b868,0x4182c341,0x9929b099,0x2d5a772d,0xf1e110f,
0xb07bcbb0,0x54a8fc54,0xbb6dd6bb,0x162c3a16};static const MR_WORD rtable2[]=
{0xf45150a7,0x417e5365,0x171ac3a4,0x273a965e,0xab3bcb6b,0x9d1ff145,
0xfaacab58,0xe34b9303,0x302055fa,0x76adf66d,0xcc889176,0x2f5254c,
0xe54ffcd7,0x2ac5d7cb,0x35268044,0x62b58fa3,0xb1de495a,0xba25671b,
0xea45980e,0xfe5de1c0,0x2fc30275,0x4c8112f0,0x468da397,0xd36bc6f9,
0x8f03e75f,0x9215959c,0x6dbfeb7a,0x5295da59,0xbed42d83,0x7458d321,
0xe0492969,0xc98e44c8,0xc2756a89,0x8ef47879,0x58996b3e,0xb927dd71,
0xe1beb64f,0x88f017ad,0x20c966ac,0xce7db43a,0xdf63184a,0x1ae58231,
0x51976033,0x5362457f,0x64b1e077,0x6bbb84ae,0x81fe1ca0,0x8f9942b,
0x48705868,0x458f19fd,0xde94876c,0x7b52b7f8,0x73ab23d3,0x4b72e202,
0x1fe3578f,0x55662aab,0xebb20728,0xb52f03c2,0xc5869a7b,0x37d3a508,
0x2830f287,0xbf23b2a5,0x302ba6a,0x16ed5c82,0xcf8a2b1c,0x79a792b4,
0x7f3f0f2,0x694ea1e2,0xda65cdf4,0x506d5be,0x34d11f62,0xa6c48afe,
0x2e349d53,0xf3a2a055,0x8a0532e1,0xf6a475eb,0x830b39ec,0x6040aaef,
0x715e069f,0x6ebd5110,0x213ef98a,0xdd963d06,0x3eddae05,0xe64d46bd,
0x5491b58d,0xc471055d,0x6046fd4,0x5060ff15,0x981924fb,0xbdd697e9,
0x4089cc43,0xd967779e,0xe8b0bd42,0x8907888b,0x19e7385b,0xc879dbee,
0x7ca1470a,0x427ce90f,0x84f8c91e,0x0,0x80098386,0x2b3248ed,
0x111eac70,0x5a6c4e72,0xefdfbff,0x850f5638,0xae3d1ed5,0x2d362739,
0xf0a64d9,0x5c6821a6,0x5b9bd154,0x36243a2e,0xa0cb167,0x57930fe7,
0xeeb4d296,0x9b1b9e91,0xc0804fc5,0xdc61a220,0x775a694b,0x121c161a,
0x93e20aba,0xa0c0e52a,0x223c43e0,0x1b121d17,0x90e0b0d,0x8bf2adc7,
0xb62db9a8,0x1e14c8a9,0xf1578519,0x75af4c07,0x99eebbdd,0x7fa3fd60,
0x1f79f26,0x725cbcf5,0x6644c53b,0xfb5b347e,0x438b7629,0x23cbdcc6,
0xedb668fc,0xe4b863f1,0x31d7cadc,0x63421085,0x97134022,0xc6842011,
0x4a857d24,0xbbd2f83d,0xf9ae1132,0x29c76da1,0x9e1d4b2f,0xb2dcf330,
0x860dec52,0xc177d0e3,0xb32b6c16,0x70a999b9,0x9411fa48,0xe9472264,
0xfca8c48c,0xf0a01a3f,0x7d56d82c,0x3322ef90,0x4987c74e,0x38d9c1d1,
0xca8cfea2,0xd498360b,0xf5a6cf81,0x7aa528de,0xb7da268e,0xad3fa4bf,
0x3a2ce49d,0x78500d92,0x5f6a9bcc,0x7e546246,0x8df6c213,0xd890e8b8,
0x392e5ef7,0xc382f5af,0x5d9fbe80,0xd0697c93,0xd56fa92d,0x25cfb312,
0xacc83b99,0x1810a77d,0x9ce86e63,0x3bdb7bbb,0x26cd0978,0x596ef418,
0x9aec01b7,0x4f83a89a,0x95e6656e,0xffaa7ee6,0xbc2108cf,0x15efe6e8,
0xe7bad99b,0x6f4ace36,0x9fead409,0xb029d67c,0xa431afb2,0x3f2a3123,
0xa5c63094,0xa235c066,0x4e7437bc,0x82fca6ca,0x90e0b0d0,0xa73315d8,
0x4f14a98,0xec41f7da,0xcd7f0e50,0x91172ff6,0x4d768dd6,0xef434db0,
0xaacc544d,0x96e4df04,0xd19ee3b5,0x6a4c1b88,0x2cc1b81f,0x65467f51,
0x5e9d04ea,0x8c015d35,0x87fa7374,0xbfb2e41,0x67b35a1d,0xdb9252d2,
0x10e93356,0xd66d1347,0xd79a8c61,0xa1377a0c,0xf8598e14,0x13eb893c,
0xa9ceee27,0x61b735c9,0x1ce1ede5,0x477a3cb1,0xd29c59df,0xf2553f73,
0x141879ce,0xc773bf37,0xf753eacd,0xfd5f5baa,0x3ddf146f,0x447886db,
0xafca81f3,0x68b93ec4,0x24382c34,0xa3c25f40,0x1d1672c3,0xe2bc0c25,
0x3c288b49,0xdff4195,0xa8397101,0xc08deb3,0xb4d89ce4,0x566490c1,
0xcb7b6184,0x32d570b6,0x6c48745c,0xb8d04257};static const MR_WORD ftable3[]=
{0xc6a56363,0xf8847c7c,0xee997777,0xf68d7b7b,0xff0df2f2,0xd6bd6b6b,
0xdeb16f6f,0x9154c5c5,0x60503030,0x2030101,0xcea96767,0x567d2b2b,
0xe719fefe,0xb562d7d7,0x4de6abab,0xec9a7676,0x8f45caca,0x1f9d8282,
0x8940c9c9,0xfa877d7d,0xef15fafa,0xb2eb5959,0x8ec94747,0xfb0bf0f0,
0x41ecadad,0xb367d4d4,0x5ffda2a2,0x45eaafaf,0x23bf9c9c,0x53f7a4a4,
0xe4967272,0x9b5bc0c0,0x75c2b7b7,0xe11cfdfd,0x3dae9393,0x4c6a2626,
0x6c5a3636,0x7e413f3f,0xf502f7f7,0x834fcccc,0x685c3434,0x51f4a5a5,
0xd134e5e5,0xf908f1f1,0xe2937171,0xab73d8d8,0x62533131,0x2a3f1515,
0x80c0404,0x9552c7c7,0x46652323,0x9d5ec3c3,0x30281818,0x37a19696,
0xa0f0505,0x2fb59a9a,0xe090707,0x24361212,0x1b9b8080,0xdf3de2e2,
0xcd26ebeb,0x4e692727,0x7fcdb2b2,0xea9f7575,0x121b0909,0x1d9e8383,
0x58742c2c,0x342e1a1a,0x362d1b1b,0xdcb26e6e,0xb4ee5a5a,0x5bfba0a0,
0xa4f65252,0x764d3b3b,0xb761d6d6,0x7dceb3b3,0x527b2929,0xdd3ee3e3,
0x5e712f2f,0x13978484,0xa6f55353,0xb968d1d1,0x0,0xc12ceded,
0x40602020,0xe31ffcfc,0x79c8b1b1,0xb6ed5b5b,0xd4be6a6a,0x8d46cbcb,
0x67d9bebe,0x724b3939,0x94de4a4a,0x98d44c4c,0xb0e85858,0x854acfcf,
0xbb6bd0d0,0xc52aefef,0x4fe5aaaa,0xed16fbfb,0x86c54343,0x9ad74d4d,
0x66553333,0x11948585,0x8acf4545,0xe910f9f9,0x4060202,0xfe817f7f,
0xa0f05050,0x78443c3c,0x25ba9f9f,0x4be3a8a8,0xa2f35151,0x5dfea3a3,
0x80c04040,0x58a8f8f,0x3fad9292,0x21bc9d9d,0x70483838,0xf104f5f5,
0x63dfbcbc,0x77c1b6b6,0xaf75dada,0x42632121,0x20301010,0xe51affff,
0xfd0ef3f3,0xbf6dd2d2,0x814ccdcd,0x18140c0c,0x26351313,0xc32fecec,
0xbee15f5f,0x35a29797,0x88cc4444,0x2e391717,0x9357c4c4,0x55f2a7a7,
0xfc827e7e,0x7a473d3d,0xc8ac6464,0xbae75d5d,0x322b1919,0xe6957373,
0xc0a06060,0x19988181,0x9ed14f4f,0xa37fdcdc,0x44662222,0x547e2a2a,
0x3bab9090,0xb838888,0x8cca4646,0xc729eeee,0x6bd3b8b8,0x283c1414,
0xa779dede,0xbce25e5e,0x161d0b0b,0xad76dbdb,0xdb3be0e0,0x64563232,
0x744e3a3a,0x141e0a0a,0x92db4949,0xc0a0606,0x486c2424,0xb8e45c5c,
0x9f5dc2c2,0xbd6ed3d3,0x43efacac,0xc4a66262,0x39a89191,0x31a49595,
0xd337e4e4,0xf28b7979,0xd532e7e7,0x8b43c8c8,0x6e593737,0xdab76d6d,
0x18c8d8d,0xb164d5d5,0x9cd24e4e,0x49e0a9a9,0xd8b46c6c,0xacfa5656,
0xf307f4f4,0xcf25eaea,0xcaaf6565,0xf48e7a7a,0x47e9aeae,0x10180808,
0x6fd5baba,0xf0887878,0x4a6f2525,0x5c722e2e,0x38241c1c,0x57f1a6a6,
0x73c7b4b4,0x9751c6c6,0xcb23e8e8,0xa17cdddd,0xe89c7474,0x3e211f1f,
0x96dd4b4b,0x61dcbdbd,0xd868b8b,0xf858a8a,0xe0907070,0x7c423e3e,
0x71c4b5b5,0xccaa6666,0x90d84848,0x6050303,0xf701f6f6,0x1c120e0e,
0xc2a36161,0x6a5f3535,0xaef95757,0x69d0b9b9,0x17918686,0x9958c1c1,
0x3a271d1d,0x27b99e9e,0xd938e1e1,0xeb13f8f8,0x2bb39898,0x22331111,
0xd2bb6969,0xa970d9d9,0x7898e8e,0x33a79494,0x2db69b9b,0x3c221e1e,
0x15928787,0xc920e9e9,0x8749cece,0xaaff5555,0x50782828,0xa57adfdf,
0x38f8c8c,0x59f8a1a1,0x9808989,0x1a170d0d,0x65dabfbf,0xd731e6e6,
0x84c64242,0xd0b86868,0x82c34141,0x29b09999,0x5a772d2d,0x1e110f0f,
0x7bcbb0b0,0xa8fc5454,0x6dd6bbbb,0x2c3a1616};static const MR_WORD rtable3[]=
{0x5150a7f4,0x7e536541,0x1ac3a417,0x3a965e27,0x3bcb6bab,0x1ff1459d,
0xacab58fa,0x4b9303e3,0x2055fa30,0xadf66d76,0x889176cc,0xf5254c02,
0x4ffcd7e5,0xc5d7cb2a,0x26804435,0xb58fa362,0xde495ab1,0x25671bba,
0x45980eea,0x5de1c0fe,0xc302752f,0x8112f04c,0x8da39746,0x6bc6f9d3,
0x3e75f8f,0x15959c92,0xbfeb7a6d,0x95da5952,0xd42d83be,0x58d32174,
0x492969e0,0x8e44c8c9,0x756a89c2,0xf478798e,0x996b3e58,0x27dd71b9,
0xbeb64fe1,0xf017ad88,0xc966ac20,0x7db43ace,0x63184adf,0xe582311a,
0x97603351,0x62457f53,0xb1e07764,0xbb84ae6b,0xfe1ca081,0xf9942b08,
0x70586848,0x8f19fd45,0x94876cde,0x52b7f87b,0xab23d373,0x72e2024b,
0xe3578f1f,0x662aab55,0xb20728eb,0x2f03c2b5,0x869a7bc5,0xd3a50837,
0x30f28728,0x23b2a5bf,0x2ba6a03,0xed5c8216,0x8a2b1ccf,0xa792b479,
0xf3f0f207,0x4ea1e269,0x65cdf4da,0x6d5be05,0xd11f6234,0xc48afea6,
0x349d532e,0xa2a055f3,0x532e18a,0xa475ebf6,0xb39ec83,0x40aaef60,
0x5e069f71,0xbd51106e,0x3ef98a21,0x963d06dd,0xddae053e,0x4d46bde6,
0x91b58d54,0x71055dc4,0x46fd406,0x60ff1550,0x1924fb98,0xd697e9bd,
0x89cc4340,0x67779ed9,0xb0bd42e8,0x7888b89,0xe7385b19,0x79dbeec8,
0xa1470a7c,0x7ce90f42,0xf8c91e84,0x0,0x9838680,0x3248ed2b,
0x1eac7011,0x6c4e725a,0xfdfbff0e,0xf563885,0x3d1ed5ae,0x3627392d,
0xa64d90f,0x6821a65c,0x9bd1545b,0x243a2e36,0xcb1670a,0x930fe757,
0xb4d296ee,0x1b9e919b,0x804fc5c0,0x61a220dc,0x5a694b77,0x1c161a12,
0xe20aba93,0xc0e52aa0,0x3c43e022,0x121d171b,0xe0b0d09,0xf2adc78b,
0x2db9a8b6,0x14c8a91e,0x578519f1,0xaf4c0775,0xeebbdd99,0xa3fd607f,
0xf79f2601,0x5cbcf572,0x44c53b66,0x5b347efb,0x8b762943,0xcbdcc623,
0xb668fced,0xb863f1e4,0xd7cadc31,0x42108563,0x13402297,0x842011c6,
0x857d244a,0xd2f83dbb,0xae1132f9,0xc76da129,0x1d4b2f9e,0xdcf330b2,
0xdec5286,0x77d0e3c1,0x2b6c16b3,0xa999b970,0x11fa4894,0x472264e9,
0xa8c48cfc,0xa01a3ff0,0x56d82c7d,0x22ef9033,0x87c74e49,0xd9c1d138,
0x8cfea2ca,0x98360bd4,0xa6cf81f5,0xa528de7a,0xda268eb7,0x3fa4bfad,
0x2ce49d3a,0x500d9278,0x6a9bcc5f,0x5462467e,0xf6c2138d,0x90e8b8d8,
0x2e5ef739,0x82f5afc3,0x9fbe805d,0x697c93d0,0x6fa92dd5,0xcfb31225,
0xc83b99ac,0x10a77d18,0xe86e639c,0xdb7bbb3b,0xcd097826,0x6ef41859,
0xec01b79a,0x83a89a4f,0xe6656e95,0xaa7ee6ff,0x2108cfbc,0xefe6e815,
0xbad99be7,0x4ace366f,0xead4099f,0x29d67cb0,0x31afb2a4,0x2a31233f,
0xc63094a5,0x35c066a2,0x7437bc4e,0xfca6ca82,0xe0b0d090,0x3315d8a7,
0xf14a9804,0x41f7daec,0x7f0e50cd,0x172ff691,0x768dd64d,0x434db0ef,
0xcc544daa,0xe4df0496,0x9ee3b5d1,0x4c1b886a,0xc1b81f2c,0x467f5165,
0x9d04ea5e,0x15d358c,0xfa737487,0xfb2e410b,0xb35a1d67,0x9252d2db,
0xe9335610,0x6d1347d6,0x9a8c61d7,0x377a0ca1,0x598e14f8,0xeb893c13,
0xceee27a9,0xb735c961,0xe1ede51c,0x7a3cb147,0x9c59dfd2,0x553f73f2,
0x1879ce14,0x73bf37c7,0x53eacdf7,0x5f5baafd,0xdf146f3d,0x7886db44,
0xca81f3af,0xb93ec468,0x382c3424,0xc25f40a3,0x1672c31d,0xbc0c25e2,
0x288b493c,0xff41950d,0x397101a8,0x8deb30c,0xd89ce4b4,0x6490c156,
0x7b6184cb,0xd570b632,0x48745c6c,0xd04257b8};

miracl开源库在mraes.c中创建的随机数数组，用于数据的加密和解密。

2.3 函数

static MR_WORD pack(const MR_BYTE *b)
{ return ((MR_WORD)b[3]<<24)|((MR_WORD)b[2]<<16)|((MR_WORD)b[1]<<8)|(MR_WORD)b[0];
}

pack方法的作用就是把输入的指针指向的无符号字节型数据按顺序左移0、1、2、3个字节再强转为无符号整型数据，意即把字节打包为32位字。

static void unpack(MR_WORD a,MR_BYTE *b)
{ b[0]=MR_TOBYTE(a);b[1]=MR_TOBYTE(a>>8);b[2]=MR_TOBYTE(a>>16);b[3]=MR_TOBYTE(a>>24);
}

unpack方法的作用和pack相反，是把整型数据分别右移0、1、2、3个字节再强制为无符号字节型数据，意即从字中解压字节。

static MR_BYTE bmul(MR_BYTE x,MR_BYTE y)
{ if (x && y) return ptab[(ltab[x]+ltab[y])%255];else return 0;
}

bmul方法是按如上方法把x、y转化为ptab数组中的一个数据，想要求（Log(x) + Log(y)）的反对数。

static MR_WORD SubByte(MR_WORD a)
{MR_BYTE b[4];unpack(a,b);b[0]=fbsub[b[0]];b[1]=fbsub[b[1]];b[2]=fbsub[b[2]];b[3]=fbsub[b[3]];return pack(b);
}

SubByte方法首先使用unpack方法把输入的数据解压，再用fbsub数组中的相应数据替换掉这些数据，最后把这些数据打包。

static MR_BYTE product(MR_WORD x,MR_WORD y)
{ MR_BYTE xb[4],yb[4];unpack(x,xb);unpack(y,yb); return bmul(xb[0],yb[0])^bmul(xb[1],yb[1])^bmul(xb[2],yb[2])^bmul(xb[3],yb[3]);
}

product方法首先把输入数据解压，再求这两个4字节数组的点积。

static MR_WORD InvMixCol(MR_WORD x)
{ MR_WORD y,m;MR_BYTE b[4];m=pack(InCo);b[3]=product(m,x);m=ROTL24(m);b[2]=product(m,x);m=ROTL24(m);b[1]=product(m,x);m=ROTL24(m);b[0]=product(m,x);y=pack(b);return y;
}

InvMixCol方法通过复用product方法求两个4字节数组的点积实现了矩阵乘法。

void aes_reset(aes *a,int mode,char *iv)
{ int i;a->mode=mode;for (i=0;i<4*NB;i++)a->f[i]=0;if (mode!=MR_ECB && iv!=NULL) {for (i=0;i<4*NB;i++)a->f[i]=iv[i];}
}

aes_reset方法首先把aes结构体中的mode重置，如果mode不等于0以及iv不为空的话，把结构体中的f数组重置为iv。

void aes_getreg(aes *a,char *ir)
{int i;for (i=0;i<4*NB;i++) ir[i]=a->f[i];
}

aes_getreg方法的额作用是获取aes结构体中f的值。

BOOL aes_init(aes* a,int mode,int nk,char *key,char *iv)
{ int i,j,k,N,nr;MR_WORD CipherKey[8];nk/=4;if (nk!=4 && nk!=6 && nk!=8) return FALSE;nr=6+nk;a->Nk=nk; a->Nr=nr;aes_reset(a,mode,iv);N=NB*(nr+1);for (i=j=0;i<nk;i++,j+=4){CipherKey[i]=pack((MR_BYTE *)&key[j]);}for (i=0;i<nk;i++) a->fkey[i]=CipherKey[i];for (j=nk,k=0;j<N;j+=nk,k++){a->fkey[j]=a->fkey[j-nk]^SubByte(ROTL24(a->fkey[j-1]))^rco[k];if (nk<=6){for (i=1;i<nk && (i+j)<N;i++)a->fkey[i+j]=a->fkey[i+j-nk]^a->fkey[i+j-1];}else{for (i=1;i<4 && (i+j)<N;i++)a->fkey[i+j]=a->fkey[i+j-nk]^a->fkey[i+j-1];if ((j+4)<N) a->fkey[j+4]=a->fkey[j+4-nk]^SubByte(a->fkey[j+3]);for (i=5;i<nk && (i+j)<N;i++)a->fkey[i+j]=a->fkey[i+j-nk]^a->fkey[i+j-1];}}for (j=0;j<NB;j++) a->rkey[j+N-NB]=a->fkey[j]; for (i=NB;i<N-NB;i+=NB){k=N-NB-i;for (j=0;j<NB;j++) a->rkey[k+j]=InvMixCol(a->fkey[i+j]);}for (j=N-NB;j<N;j++) a->rkey[j-N+NB]=a->fkey[j];return TRUE;
}

aes-init方法使用高级加密标准（AES）初始化加密/解密会话。这是一个块密码系统，使用 128 位、192 位或 256 位的密钥在 128 位块中加密数据。首先利用输入数据初始化aes结构体中的基本数据，然后通过pack()、异或、数组移位等复杂方法求出aes结构体中的加密密钥，最后通过矩阵乘法等复杂方法按相反顺序查看扩展的解密密钥。

void aes_ecb_encrypt(aes *a,MR_BYTE *buff)
{int i,j,k;MR_WORD p[4],q[4],*x,*y,*t;#ifdef AES_NI_SUPPORT__m128i ky,m = _mm_loadu_si128((__m128i *) buff);ky = _mm_loadu_si128((__m128i *) &a->fkey[0]);m = _mm_xor_si128       (m, ky); k=NB;for (i=1;i<a->Nr;i++){ky=_mm_loadu_si128((__m128i *) &a->fkey[k]);m =_mm_aesenc_si128(m, ky); k+=4;}ky=_mm_loadu_si128((__m128i *) &a->fkey[k]);m=_mm_aesenclast_si128(m, ky);_mm_storeu_si128((__m128i *)buff, m);
#elsefor (i=j=0;i<NB;i++,j+=4){p[i]=pack((MR_BYTE *)&buff[j]);p[i]^=a->fkey[i];}k=NB;x=p; y=q;/* State alternates between x and y */for (i=1;i<a->Nr;i++){ /* Nr is number of rounds. May be odd. */
#ifndef MR_SMALL_AESy[0]=a->fkey[k]^ftable[MR_TOBYTE(x[0])]^ftable1[MR_TOBYTE(x[1]>>8)]^ftable2[MR_TOBYTE(x[2]>>16)]^ftable3[x[3]>>24];y[1]=a->fkey[k+1]^ftable[MR_TOBYTE(x[1])]^ftable1[MR_TOBYTE(x[2]>>8)]^ftable2[MR_TOBYTE(x[3]>>16)]^ftable3[x[0]>>24];y[2]=a->fkey[k+2]^ftable[MR_TOBYTE(x[2])]^ftable1[MR_TOBYTE(x[3]>>8)]^ftable2[MR_TOBYTE(x[0]>>16)]^ftable3[x[1]>>24];y[3]=a->fkey[k+3]^ftable[MR_TOBYTE(x[3])]^ftable1[MR_TOBYTE(x[0]>>8)]^ftable2[MR_TOBYTE(x[1]>>16)]^ftable3[x[2]>>24];
#elsey[0]=a->fkey[k]^ftable[MR_TOBYTE(x[0])]^ROTL8(ftable[MR_TOBYTE(x[1]>>8)])^ROTL16(ftable[MR_TOBYTE(x[2]>>16)])^ROTL24(ftable[x[3]>>24]);y[1]=a->fkey[k+1]^ftable[MR_TOBYTE(x[1])]^ROTL8(ftable[MR_TOBYTE(x[2]>>8)])^ROTL16(ftable[MR_TOBYTE(x[3]>>16)])^ROTL24(ftable[x[0]>>24]);y[2]=a->fkey[k+2]^ftable[MR_TOBYTE(x[2])]^ROTL8(ftable[MR_TOBYTE(x[3]>>8)])^ROTL16(ftable[MR_TOBYTE(x[0]>>16)])^ROTL24(ftable[x[1]>>24]);y[3]=a->fkey[k+3]^ftable[MR_TOBYTE(x[3])]^ROTL8(ftable[MR_TOBYTE(x[0]>>8)])^ROTL16(ftable[MR_TOBYTE(x[1]>>16)])^ROTL24(ftable[x[2]>>24]);
#endifk+=4;t=x; x=y; y=t;      /* swap pointers */}/* Last Round */ y[0]=a->fkey[k]^(MR_WORD)fbsub[MR_TOBYTE(x[0])]^ROTL8((MR_WORD)fbsub[MR_TOBYTE(x[1]>>8)])^ROTL16((MR_WORD)fbsub[MR_TOBYTE(x[2]>>16)])^ROTL24((MR_WORD)fbsub[x[3]>>24]);y[1]=a->fkey[k+1]^(MR_WORD)fbsub[MR_TOBYTE(x[1])]^ROTL8((MR_WORD)fbsub[MR_TOBYTE(x[2]>>8)])^ROTL16((MR_WORD)fbsub[MR_TOBYTE(x[3]>>16)])^ROTL24((MR_WORD)fbsub[x[0]>>24]);y[2]=a->fkey[k+2]^(MR_WORD)fbsub[MR_TOBYTE(x[2])]^ROTL8((MR_WORD)fbsub[MR_TOBYTE(x[3]>>8)])^ROTL16((MR_WORD)fbsub[MR_TOBYTE(x[0]>>16)])^ROTL24((MR_WORD)fbsub[x[1]>>24]);y[3]=a->fkey[k+3]^(MR_WORD)fbsub[MR_TOBYTE(x[3])]^ROTL8((MR_WORD)fbsub[MR_TOBYTE(x[0]>>8)])^ROTL16((MR_WORD)fbsub[MR_TOBYTE(x[1]>>16)])^ROTL24((MR_WORD)fbsub[x[2]>>24]);for (i=j=0;i<NB;i++,j+=4){unpack(y[i],(MR_BYTE *)&buff[j]);x[i]=y[i]=0;   /* clean up stack */}
#endif
}

aes_ecb_encrypt方法对输入数据进行加密。首先通过打包buff获得的数据和aes结构体中的加密密钥（fkey）做异或运算，再对得到的数据进行复杂的加密操作，最后解压赋值给buff。

void aes_ecb_decrypt(aes *a,MR_BYTE *buff)
{int i,j,k;MR_WORD p[4],q[4],*x,*y,*t;#ifdef AES_NI_SUPPORT__m128i ky,m = _mm_loadu_si128((__m128i *) buff);ky = _mm_loadu_si128((__m128i *) &a->rkey[0]);m = _mm_xor_si128       (m, ky); k=NB;for (i=1;i<a->Nr;i++){ky=_mm_loadu_si128((__m128i *) &a->rkey[k]);m =_mm_aesdec_si128    (m, ky); k+=4;}ky=_mm_loadu_si128((__m128i *) &a->rkey[k]);m=_mm_aesdeclast_si128(m, ky);_mm_storeu_si128((__m128i *)buff, m);
#elsefor (i=j=0;i<NB;i++,j+=4){p[i]=pack((MR_BYTE *)&buff[j]);p[i]^=a->rkey[i];}k=NB;x=p; y=q;/* State alternates between x and y */for (i=1;i<a->Nr;i++){ /* Nr is number of rounds. May be odd. */
#ifndef MR_SMALL_AESy[0]=a->rkey[k]^rtable[MR_TOBYTE(x[0])]^rtable1[MR_TOBYTE(x[3]>>8)]^rtable2[MR_TOBYTE(x[2]>>16)]^rtable3[x[1]>>24];y[1]=a->rkey[k+1]^rtable[MR_TOBYTE(x[1])]^rtable1[MR_TOBYTE(x[0]>>8)]^rtable2[MR_TOBYTE(x[3]>>16)]^rtable3[x[2]>>24];y[2]=a->rkey[k+2]^rtable[MR_TOBYTE(x[2])]^rtable1[MR_TOBYTE(x[1]>>8)]^rtable2[MR_TOBYTE(x[0]>>16)]^rtable3[x[3]>>24];y[3]=a->rkey[k+3]^rtable[MR_TOBYTE(x[3])]^rtable1[MR_TOBYTE(x[2]>>8)]^rtable2[MR_TOBYTE(x[1]>>16)]^rtable3[x[0]>>24];
#elsey[0]=a->rkey[k]^rtable[MR_TOBYTE(x[0])]^ROTL8(rtable[MR_TOBYTE(x[3]>>8)])^ROTL16(rtable[MR_TOBYTE(x[2]>>16)])^ROTL24(rtable[x[1]>>24]);y[1]=a->rkey[k+1]^rtable[MR_TOBYTE(x[1])]^ROTL8(rtable[MR_TOBYTE(x[0]>>8)])^ROTL16(rtable[MR_TOBYTE(x[3]>>16)])^ROTL24(rtable[x[2]>>24]);y[2]=a->rkey[k+2]^rtable[MR_TOBYTE(x[2])]^ROTL8(rtable[MR_TOBYTE(x[1]>>8)])^ROTL16(rtable[MR_TOBYTE(x[0]>>16)])^ROTL24(rtable[x[3]>>24]);y[3]=a->rkey[k+3]^rtable[MR_TOBYTE(x[3])]^ROTL8(rtable[MR_TOBYTE(x[2]>>8)])^ROTL16(rtable[MR_TOBYTE(x[1]>>16)])^ROTL24(rtable[x[0]>>24]);
#endifk+=4;t=x; x=y; y=t;      /* swap pointers */}/* Last Round */ y[0]=a->rkey[k]^(MR_WORD)rbsub[MR_TOBYTE(x[0])]^ROTL8((MR_WORD)rbsub[MR_TOBYTE(x[3]>>8)])^ROTL16((MR_WORD)rbsub[MR_TOBYTE(x[2]>>16)])^ROTL24((MR_WORD)rbsub[x[1]>>24]);y[1]=a->rkey[k+1]^(MR_WORD)rbsub[MR_TOBYTE(x[1])]^ROTL8((MR_WORD)rbsub[MR_TOBYTE(x[0]>>8)])^ROTL16((MR_WORD)rbsub[MR_TOBYTE(x[3]>>16)])^ROTL24((MR_WORD)rbsub[x[2]>>24]);y[2]=a->rkey[k+2]^(MR_WORD)rbsub[MR_TOBYTE(x[2])]^ROTL8((MR_WORD)rbsub[MR_TOBYTE(x[1]>>8)])^ROTL16((MR_WORD)rbsub[MR_TOBYTE(x[0]>>16)])^ROTL24((MR_WORD)rbsub[x[3]>>24]);y[3]=a->rkey[k+3]^(MR_WORD)rbsub[MR_TOBYTE(x[3])]^ROTL8((MR_WORD)rbsub[MR_TOBYTE(x[2]>>8)])^ROTL16((MR_WORD)rbsub[MR_TOBYTE(x[1]>>16)])^ROTL24((MR_WORD)rbsub[x[0]>>24]);for (i=j=0;i<NB;i++,j+=4){unpack(y[i],(MR_BYTE *)&buff[j]);x[i]=y[i]=0;   /* clean up stack */}
#endif
}

aes_ecb_decrypt方法对输入数据进行解。首先通过打包buff获得的数据和aes结构体中的解密密钥（rkey）做异或运算，再对得到的数据进行复杂的解密操作，最后解压赋值给buff。

mr_unsign32 aes_encrypt(aes* a,char *buff)
{int j,bytes;char st[16];mr_unsign32 fell_off;/* Supported Modes of Operation */fell_off=0;switch (a->mode){case MR_ECB: aes_ecb_encrypt(a,(MR_BYTE *)buff);return 0;case MR_CBC:for (j=0;j<4*NB;j++) buff[j]^=a->f[j];aes_ecb_encrypt(a,(MR_BYTE *)buff);for (j=0;j<4*NB;j++) a->f[j]=buff[j];return 0;case MR_CFB1:case MR_CFB2:case MR_CFB4:bytes=a->mode-MR_CFB1+1;for (j=0;j<bytes;j++) fell_off=(fell_off<<8)|a->f[j];for (j=0;j<4*NB;j++) st[j]=a->f[j];for (j=bytes;j<4*NB;j++) a->f[j-bytes]=a->f[j];aes_ecb_encrypt(a,(MR_BYTE *)st);for (j=0;j<bytes;j++) {buff[j]^=st[j];a->f[16-bytes+j]=buff[j];}return fell_off;case MR_OFB1:case MR_OFB2:case MR_OFB4:case MR_OFB8:case MR_OFB16:bytes=a->mode-MR_OFB1+1;aes_ecb_encrypt(a,(MR_BYTE *)(a->f));for (j=0;j<bytes;j++) buff[j]^=a->f[j];return 0;case MR_PCFB1:   /* error propagating CFB */case MR_PCFB2:case MR_PCFB4:   bytes=a->mode-MR_PCFB1+1;for (j=0;j<bytes;j++) fell_off=(fell_off<<8)|a->f[j];for (j=0;j<4*NB;j++) st[j]=a->f[j];for (j=bytes;j<4*NB;j++) a->f[j-bytes]=a->f[j];aes_ecb_encrypt(a,(MR_BYTE *)st);for (j=0;j<bytes;j++) {buff[j]^=st[j];a->f[16-bytes+j]=buff[j]^st[16-bytes+j];}return fell_off;default:return 0;}
}

aes_encrypt方法按照aes结构体中mode的不同数值采用不同的数据当作buff参数，调用aes_ecb_encrypt方法进行加密，再更新aes结构体中的f数组。

mr_unsign32 aes_decrypt(aes *a,char *buff)
{int j,bytes;char st[16];mr_unsign32 fell_off;/* Supported modes of operation */fell_off=0;switch (a->mode){case MR_ECB:aes_ecb_decrypt(a,(MR_BYTE *)buff);return 0;case MR_CBC:for (j=0;j<4*NB;j++) {st[j]=a->f[j];a->f[j]=buff[j];}aes_ecb_decrypt(a,(MR_BYTE *)buff);for (j=0;j<4*NB;j++){ buff[j]^=st[j];st[j]=0;}return 0;case MR_CFB1:case MR_CFB2:case MR_CFB4:bytes=a->mode-MR_CFB1+1;for (j=0;j<bytes;j++) fell_off=(fell_off<<8)|a->f[j];for (j=0;j<4*NB;j++) st[j]=a->f[j];for (j=bytes;j<4*NB;j++) a->f[j-bytes]=a->f[j];aes_ecb_encrypt(a,(MR_BYTE *)st);for (j=0;j<bytes;j++){a->f[16-bytes+j]=buff[j];buff[j]^=st[j];}return fell_off;case MR_OFB1:case MR_OFB2:case MR_OFB4:case MR_OFB8:case MR_OFB16:bytes=a->mode-MR_OFB1+1;aes_ecb_encrypt(a,(MR_BYTE *)(a->f));for (j=0;j<bytes;j++) buff[j]^=a->f[j];return 0;case MR_PCFB1:   /* error propagating CFB */case MR_PCFB2:case MR_PCFB4:bytes=a->mode-MR_PCFB1+1;for (j=0;j<bytes;j++) fell_off=(fell_off<<8)|a->f[j];for (j=0;j<4*NB;j++) st[j]=a->f[j];for (j=bytes;j<4*NB;j++) a->f[j-bytes]=a->f[j];aes_ecb_encrypt(a,(MR_BYTE *)st);for (j=0;j<bytes;j++){a->f[16-bytes+j]=buff[j]^st[16-bytes+j];buff[j]^=st[j];}return fell_off;default:return 0;}
}

aes_decrypt方法按照aes结构体中mode的不同数值采用不同的数据当作buff参数，调用aes_ecb_decrypt方法进行解密，再更新aes结构体中的f数组。

void aes_end(aes *a)
{ /* clean up */int i;for (i=0;i<NB*(a->Nr+1);i++)a->fkey[i]=a->rkey[i]=0;for (i=0;i<4*NB;i++)a->f[i]=0;
}

aes-end方法将aes结构体中的有数据清零。

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Miracle密码算法开源库（一）源码分析 :mraes.c

一、mraes.c结构

二、头文件

二、主体代码

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