AES加密演算法的詳細介紹與實現
阿新 • • 發佈：2018-12-10
#include <stdio.h> #include <stdlib.h> #include <string.h> #include "aes.h" /** * S盒 */ static const int S[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, 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 */ static const int S2[16][16] = { 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 }; /** * 獲取整形資料的低8位的左4個位 */ static int getLeft4Bit(int num) { int left = num & 0x000000f0; return left >> 4; } /** * 獲取整形資料的低8位的右4個位 */ static int getRight4Bit(int num) { return num & 0x0000000f; } /** * 根據索引，從S盒中獲得元素 */ static int getNumFromSBox(int index) { int row = getLeft4Bit(index); int col = getRight4Bit(index); return S[row][col]; } /** * 把一個字元轉變成整型 */ static int getIntFromChar(char c) { int result = (int) c; return result & 0x000000ff; } /** * 把16個字元轉變成4X4的陣列， * 該矩陣中位元組的排列順序為從上到下， * 從左到右依次排列。 */ static void convertToIntArray(char *str, int pa[4][4]) { int k = 0; for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++) { pa[j][i] = getIntFromChar(str[k]); k++; } } /** * 列印4X4的陣列 */ static void printArray(int a[4][4]) { for(int i = 0; i < 4; i++){ for(int j = 0; j < 4; j++) printf("a[%d][%d] = 0x%x ", i, j, a[i][j]); printf("\n"); } printf("\n"); } /** * 列印字串的ASSCI， * 以十六進位制顯示。 */ static void printASSCI(char *str, int len) { for(int i = 0; i < len; i++) printf("0x%x ", getIntFromChar(str[i])); printf("\n"); } /** * 把連續的4個字符合併成一個4位元組的整型 */ static int getWordFromStr(char *str) { int one = getIntFromChar(str[0]); one = one << 24; int two = getIntFromChar(str[1]); two = two << 16; int three = getIntFromChar(str[2]); three = three << 8; int four = getIntFromChar(str[3]); return one | two | three | four; } /** * 把一個4位元組的數的第一、二、三、四個位元組取出， * 入進一個4個元素的整型數組裡面。 */ static void splitIntToArray(int num, int array[4]) { int one = num >> 24; array[0] = one & 0x000000ff; int two = num >> 16; array[1] = two & 0x000000ff; int three = num >> 8; array[2] = three & 0x000000ff; array[3] = num & 0x000000ff; } /** * 將陣列中的元素迴圈左移step位 */ static void leftLoop4int(int array[4], int step) { int temp[4]; for(int i = 0; i < 4; i++) temp[i] = array[i]; int index = step % 4 == 0 ? 0 : step % 4; for(int i = 0; i < 4; i++){ array[i] = temp[index]; index++; index = index % 4; } } /** * 把陣列中的第一、二、三和四元素分別作為 * 4位元組整型的第一、二、三和四位元組，合併成一個4位元組整型 */ static int mergeArrayToInt(int array[4]) { int one = array[0] << 24; int two = array[1] << 16; int three = array[2] << 8; int four = array[3]; return one | two | three | four; } /** * 常量輪值表 */ static const int Rcon[10] = { 0x01000000, 0x02000000, 0x04000000, 0x08000000, 0x10000000, 0x20000000, 0x40000000, 0x80000000, 0x1b000000, 0x36000000 }; /** * 金鑰擴充套件中的T函式 */ static int T(int num, int round) { int numArray[4]; splitIntToArray(num, numArray); leftLoop4int(numArray, 1);//字迴圈 //位元組代換 for(int i = 0; i < 4; i++) numArray[i] = getNumFromSBox(numArray[i]); int result = mergeArrayToInt(numArray); return result ^ Rcon[round]; } //金鑰對應的擴充套件陣列 static int w[44]; /** * 擴充套件金鑰，結果是把w[44]中的每個元素初始化 */ static void extendKey(char *key) { for(int i = 0; i < 4; i++) w[i] = getWordFromStr(key + i * 4); for(int i = 4, j = 0; i < 44; i++) { if( i % 4 == 0) { w[i] = w[i - 4] ^ T(w[i - 1], j); j++;//下一輪 }else { w[i] = w[i - 4] ^ w[i - 1]; } } } /** * 輪金鑰加 */ static void addRoundKey(int array[4][4], int round) { int warray[4]; for(int i = 0; i < 4; i++) { splitIntToArray(w[ round * 4 + i], warray); for(int j = 0; j < 4; j++) { array[j][i] = array[j][i] ^ warray[j]; } } } /** * 位元組代換 */ static void subBytes(int array[4][4]){ for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++) array[i][j] = getNumFromSBox(array[i][j]); } /** * 行移位 */ static void shiftRows(int array[4][4]) { int rowTwo[4], rowThree[4], rowFour[4]; //複製狀態矩陣的第2,3,4行 for(int i = 0; i < 4; i++) { rowTwo[i] = array[1][i]; rowThree[i] = array[2][i]; rowFour[i] = array[3][i]; } //迴圈左移相應的位數 leftLoop4int(rowTwo, 1); leftLoop4int(rowThree, 2); leftLoop4int(rowFour, 3); //把左移後的行復制回狀態矩陣中 for(int i = 0; i < 4; i++) { array[1][i] = rowTwo[i]; array[2][i] = rowThree[i]; array[3][i] = rowFour[i]; } } /** * 列混合要用到的矩陣 */ static const int colM[4][4] = { 2, 3, 1, 1, 1, 2, 3, 1, 1, 1, 2, 3, 3, 1, 1, 2 }; static int GFMul2(int s) { int result = s << 1; int a7 = result & 0x00000100; if(a7 != 0) { result = result & 0x000000ff; result = result ^ 0x1b; } return result; } static int GFMul3(int s) { return GFMul2(s) ^ s; } static int GFMul4(int s) { return GFMul2(GFMul2(s)); } static int GFMul8(int s) { return GFMul2(GFMul4(s)); } static int GFMul9(int s) { return GFMul8(s) ^ s; } static int GFMul11(int s) { return GFMul9(s) ^ GFMul2(s); } static int GFMul12(int s) { return GFMul8(s) ^ GFMul4(s); } static int GFMul13(int s) { return GFMul12(s) ^ s; } static int GFMul14(int s) { return GFMul12(s) ^ GFMul2(s); } /** * GF上的二元運算 */ static int GFMul(int n, int s) { int result; if(n == 1) result = s; else if(n == 2) result = GFMul2(s); else if(n == 3) result = GFMul3(s); else if(n == 0x9) result = GFMul9(s); else if(n == 0xb)//11 result = GFMul11(s); else if(n == 0xd)//13 result = GFMul13(s); else if(n == 0xe)//14 result = GFMul14(s); return result; } /** * 列混合 */ static void mixColumns(int array[4][4]) { int tempArray[4][4]; for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++) tempArray[i][j] = array[i][j]; for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++){ array[i][j] = GFMul(colM[i][0],tempArray[0][j]) ^ GFMul(colM[i][1],tempArray[1][j]) ^ GFMul(colM[i][2],tempArray[2][j]) ^ GFMul(colM[i][3], tempArray[3][j]); } } /** * 把4X4陣列轉回字串 */ static void convertArrayToStr(int array[4][4], char *str) { for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++) *str++ = (char)array[j][i]; } /** * 檢查金鑰長度 */ static int checkKeyLen(int len) { if(len == 16) return 1; else return 0; } /** * 引數 p: 明文的字串陣列。 * 引數 plen: 明文的長度。 * 引數 key: 金鑰的字串陣列。 */ void aes(char *p, int plen, char *key){ int keylen = strlen(key); if(plen == 0 || plen % 16 != 0) { printf("明文字元長度必須為16的倍數！\n"); exit(0); } if(!checkKeyLen(keylen)) { printf("金鑰字元長度錯誤！長度必須為16、24和32。當前長度為%d\n",keylen); exit(0); } extendKey(key);//擴充套件金鑰 int pArray[4][4]; for(int k = 0; k < plen; k += 16) { convertToIntArray(p + k, pArray); addRoundKey(pArray, 0);//一開始的輪金鑰加 for(int i = 1; i < 10; i++){//前9輪 subBytes(pArray);//位元組代換 shiftRows(pArray);//行移位 mixColumns(pArray);//列混合 addRoundKey(pArray, i); } //第10輪 subBytes(pArray);//位元組代換 shiftRows(pArray);//行移位 addRoundKey(pArray, 10); convertArrayToStr(pArray, p + k); } } /** * 根據索引從逆S盒中獲取值 */ static int getNumFromS1Box(int index) { int row = getLeft4Bit(index); int col = getRight4Bit(index); return S2[row][col]; } /** * 逆位元組變換 */ static void deSubBytes(int array[4][4]) { for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++) array[i][j] = getNumFromS1Box(array[i][j]); } /** * 把4個元素的陣列迴圈右移step位 */ static void rightLoop4int(int array[4], int step) { int temp[4]; for(int i = 0; i < 4; i++) temp[i] = array[i]; int index = step % 4 == 0 ? 0 : step % 4; index = 3 - index; for(int i = 3; i >= 0; i--) { array[i] = temp[index]; index--; index = index == -1 ? 3 : index; } } /** * 逆行移位 */ static void deShiftRows(int array[4][4]) { int rowTwo[4], rowThree[4], rowFour[4]; for(int i = 0; i < 4; i++) { rowTwo[i] = array[1][i]; rowThree[i] = array[2][i]; rowFour[i] = array[3][i]; } rightLoop4int(rowTwo, 1); rightLoop4int(rowThree, 2); rightLoop4int(rowFour, 3); for(int i = 0; i < 4; i++) { array[1][i] = rowTwo[i]; array[2][i] = rowThree[i]; array[3][i] = rowFour[i]; } } /** * 逆列混合用到的矩陣 */ static const int deColM[4][4] = { 0xe, 0xb, 0xd, 0x9, 0x9, 0xe, 0xb, 0xd, 0xd, 0x9, 0xe, 0xb, 0xb, 0xd, 0x9, 0xe }; /** * 逆列混合 */ static void deMixColumns(int array[4][4]) { int tempArray[4][4]; for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++) tempArray[i][j] = array[i][j]; for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++){ array[i][j] = GFMul(deColM[i][0],tempArray[0][j]) ^ GFMul(deColM[i][1],tempArray[1][j]) ^ GFMul(deColM[i][2],tempArray[2][j]) ^ GFMul(deColM[i][3], tempArray[3][j]); } } /** * 把兩個4X4陣列進行異或 */ static void addRoundTowArray(int aArray[4][4],int bArray[4][4]) { for(int i = 0; i < 4; i++) for(int j = 0; j < 4; j++) aArray[i][j] = aArray[i][j] ^ bArray[i][j]; } /** * 從4個32位的金鑰字中獲得4X4陣列， * 用於進行逆列混合 */ static void getArrayFrom4W(int i, int array[4][4]) { int index = i * 4; int colOne[4], colTwo[4], colThree[4], colFour[4]; splitIntToArray(w[index], colOne); splitIntToArray(w[index + 1], colTwo); splitIntToArray(w[index + 2], colThree); splitIntToArray(w[index + 3], colFour); for(int i = 0; i < 4; i++) { array[i][0] = colOne[i]; array[i][1] = colTwo[i]; array[i][2] = colThree[i]; array[i][3] = colFour[i]; } } /** * 引數 c: 密文的字串陣列。 * 引數 clen: 密文的長度。 * 引數 key: 金鑰的字串陣列。 */ void deAes(char *c, int clen, char *key) { int keylen = strlen(key); if(clen == 0 || clen % 16 != 0) { printf("密文字元長度必須為16的倍數！現在的長度為%d\n",clen); exit(0); } if(!checkKeyLen(keylen)) { printf("金鑰字元長度錯誤！長度必須為16、24和32。當前長度為%d\n",keylen); exit(0); } extendKey(key);//擴充套件金鑰 int cArray[4][4]; for(int k = 0; k < clen; k += 16) { convertToIntArray(c + k, cArray); addRoundKey(cArray, 10); int wArray[4][4]; for(int i = 9; i >= 1; i--) { deSubBytes(cArray); deShiftRows(cArray); deMixColumns(cArray); getArrayFrom4W(i, wArray); deMixColumns(wArray); addRoundTowArray(cArray, wArray); } deSubBytes(cArray); deShiftRows(cArray); addRoundKey(cArray, 0); convertArrayToStr(cArray, c + k); } } --------------------- 作者：TimeShatter 來源：CSDN 原文：https://blog.csdn.net/qq_28205153/article/details/55798628 版權宣告：本文為博主原創文章，轉載請附上博文連結！
#include <stdio.h> #include <unistd.h> #include <string.h> #include <stdlib.h> #include "aes.h" #define MAXLEN 1024 void getString(char *str, int len){ int slen = read(0, str, len); for(int i = 0; i < slen; i++,str++){ if(*str == '\n'){ *str = '\0'; break; } } } void printASCCI(char *str, int len) { int c; for(int i = 0; i < len; i++) { c = (int)*str++; c = c & 0x000000ff; printf("0x%x ", c); } printf("\n"); } /** * 從標準輸入中讀取使用者輸入的字串 */ void readPlainText(char *str, int *len) { int plen; while(1) { getString(str, MAXLEN); plen = strlen(str); if(plen != 0 && plen % 16 == 0) { printf("你輸入的明文為：%s\n", str); break; }else{ printf("明文字元長度必須為16的倍數,現在的長度為%d\n", plen); } } *len = plen; } /** * 把字串寫進檔案 */ void writeStrToFile(char *str, int len, char *fileName) { FILE *fp; fp = fopen(fileName, "wb"); for(int i = 0; i < len; i++) putc(str[i], fp); fclose(fp); } void aesStrToFile(char *key) { char p[MAXLEN]; int plen; printf("請輸入你的明文，明文字元長度必須為16的倍數\n"); readPlainText(p,&plen); printf("進行AES加密..................\n"); aes(p, plen, key);//AES加密 printf("加密完後的明文的ASCCI為：\n"); printASCCI(p, plen); char fileName[64]; printf("請輸入你想要寫進的檔名，比如'test.txt':\n"); if(scanf("%s", fileName) == 1) { writeStrToFile(p, plen, fileName); printf("已經將密文寫進%s中了,可以在執行該程式的當前目錄中找到它。\n", fileName); } } /** * 從檔案中讀取字串 */ int readStrFromFile(char *fileName, char *str) { FILE *fp = fopen(fileName, "rb"); if(fp == NULL) { printf("開啟檔案出錯，請確認檔案存在當前目錄下！\n"); exit(0); } int i; for(i = 0; i < MAXLEN && (str[i] = getc(fp)) != EOF; i++); if(i >= MAXLEN) { printf("解密檔案過大！\n"); exit(0); } str[i] = '\0'; fclose(fp); return i; } void deAesFile(char *key) { char fileName[64]; char c[MAXLEN];//密文字串 printf("請輸入要解密的檔名，該檔案必須和本程式在同一個目錄\n"); if(scanf("%s", fileName) == 1) { int clen = readStrFromFile(fileName, c); printf("開始解密.........\n"); deAes(c, clen, key); printf("解密後的明文ASCII為：\n"); printASCCI(c, clen); printf("明文為：%s\n", c); writeStrToFile(c,clen,fileName); printf("現在可以開啟%s來檢視解密後的密文了！\n",fileName); } } void aesFile(char *key) { char fileName[64]; char fileP[MAXLEN]; printf("請輸入要加密的檔名，該檔案必須和本程式在同一個目錄\n"); if(scanf("%s", fileName) == 1) { readStrFromFile(fileName, fileP); int plen = strlen(fileP); printf("開始加密.........\n"); printf("加密前檔案中字元的ASCII為：\n"); printASCCI(fileP, plen); aes(fileP, plen, key);//開始加密 printf("加密後的密文ASCII為：\n"); printASCCI(fileP, plen); writeStrToFile(fileP,plen,fileName); printf("已經將加密後的密文寫進%s中了\n",fileName); } } int main(int argc, char const *argv[]) { char key[17]; printf("請輸入16個字元的金鑰：\n"); int klen; while(1){ getString(key,17); klen = strlen(key); if(klen != 16){ printf("請輸入16個字元的金鑰,當前金鑰的長度為%d\n",klen); }else{ printf("你輸入的金鑰為：%s\n",key); break; } } printf("輸入's'表示要加密輸入的字串,並將加密後的內容寫入到檔案\n"); printf("請輸入要功能選項並按回車，輸入'f'表示要加密檔案\n"); printf("輸入'p'表示要解密檔案\n"); char c; if(scanf("%s",&c) == 1) { if(c == 's') aesStrToFile(key);//用AES加密字串，並將字串寫進檔案中 else if(c == 'p') deAesFile(key);//把檔案中的密文解密，並寫回檔案中 else if(c == 'f')//用AES加密檔案 aesFile(key); } return 0; } --------------------- 作者：TimeShatter 來源：CSDN 原文：https://blog.csdn.net/qq_28205153/article/details/55798628 版權宣告：本文為博主原創文章，轉載請附上博文連結！
#ifndef AES_H #define AES_H /** * 引數 p: 明文的字串陣列。 * 引數 plen: 明文的長度,長度必須為16的倍數。 * 引數 key: 金鑰的字串陣列。 */ void aes(char *p, int plen, char *key); /** * 引數 c: 密文的字串陣列。 * 引數 clen: 密文的長度,長度必須為16的倍數。 * 引數 key: 金鑰的字串陣列。 */ void deAes(char *c, int clen, char *key); #endif --------------------- 作者：TimeShatter 來源：CSDN 原文：https://blog.csdn.net/qq_28205153/article/details/55798628 版權宣告：本文為博主原創文章，轉載請附上博文連結！