算法原理:
DES算法是一種對稱加密算法,以64位爲分組對數據加密,加密和解密用的是同一個算法。它的密鑰長度是56位(因爲每個第8 位都用作奇偶校驗),密鑰可以是任意的56位的數,而且可以任意時候改變。其中有極少數被認爲是易破解的弱密鑰,但是很容易避開它們不用。所以保密性依賴於密鑰。
其基本流程如下:
首先要生成一套加密密鑰,從用戶處取得一個64位長的密碼口令,然後通過等分、移位、選取和迭代形成一套16個加密密鑰,分別供每一輪運算中使用。
DES對64位(bit)的明文分組M進行操作,M經過一個初始置換IP,置換成m0。將m0明文分成左半部分和右半部分m0 = (L0,R0),各32位長。然後進行16輪完全相同的運算(迭代),這些運算被稱爲函數f,在每一輪運算過程中數據與相應的密鑰結合。
在每一輪中,密鑰位移位,然後再從密鑰的56位中選出48位。通過一個擴展置換將數據的右半部分擴展成48位,並通過一個異或操作替代成新的48位數據,再將其壓縮置換成32位。這四步運算構成了函數f。然後,通過另一個異或運算,函數f的輸出與左半部分結合,其結果成爲新的右半部分,原來的右半部分成爲新的左半部分。將該操作重複16次。
經過16輪迭代後,左,右半部分合在一起經過一個末置換(數據整理),這樣就完成了加密過程。
DES的解密和加密唯一的不同是密鑰的次序相反。如果各輪加密密鑰分別是K1,K2,K3…K16,那麼解密密鑰就是K16,K15,K14…K1。
總體結構:
Feistel結構:
模塊分解:
由給定的密鑰獲取16個子密鑰:
- 對K 的56個非校驗位實行置換PC-1,得到C0D0,其中C0 和D0 分別由PC-1 置換後的前28位和後28位組成。
//密鑰置換表
const int PC_1[56] = {
57, 49, 41, 33, 25, 17, 9,
1, 58, 50, 42, 34, 26, 18,
10, 2, 59, 51, 43, 35, 27,
19, 11, 3, 60, 52, 44, 36,
63, 55, 47, 39, 31, 23, 15,
7, 62, 54, 46, 38, 30, 22,
14, 6, 61, 53, 45, 37, 29,
21, 13, 5, 28, 20, 12, 4
};
- 計算Ci = LSi(Ci-1) 和Di = LSi(Di-1)
//密鑰置換時每輪移動的位數
const int shift[16] = {1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1};
//將密鑰的前後部分分別左移
void leftShift(unsigned char K[28], int shift) {
unsigned char ar[28];
memcpy(ar, K, 28);
int i = 0;
for(i = 27; i >= 0; i--)
{
if(i-shift < 0)
K[i] = ar[i-shift+28];
else
K[i] = ar[i-shift];
}
}
- 對56位的CiDi 實行PC-2 壓縮置換,得到48位的Ki 。i= i+1。
//壓縮置換表
const int PC_2[48] = {
14, 17, 11, 24, 1, 5,
3, 28, 15, 6, 21, 10,
23, 19, 12, 4, 26, 8,
16, 7, 27, 20, 13, 2,
41, 52, 31, 37, 47, 55,
30, 40, 51, 45, 33, 48,
44, 49, 39, 56, 34, 53,
46, 42, 50, 36, 29, 32
};
- 之後的16輪按照以上步驟重複得到16個子密鑰
- 總的算法實現:
void getMyKey(unsigned char key[64], unsigned char subKey[16][48]) {
//去掉奇偶檢驗位的key
unsigned char key_f[56];
//左半部分
unsigned char L[28];
//右半部分
unsigned char R[28];
int i = 0, j = 0;
unsigned char C_key[48];
for (i = 0; i < 56; i++) {
key_f[55-i] = key[64-PC_1[i]];
}
//生成左右子密鑰
for (i = 0; i < 16; i++) {
for (j = 0; j < 28; j++) {
L[j] = key_f[j+28];
}
for (j = 0; j < 28; j++) {
R[j] = key_f[j];
}
//左移
leftShift(L, shift[i]);
leftShift(R, shift[i]);
//壓縮置換
for (j = 0; j < 28; j++) {
key_f[j+28] = L[j];
}
for (j = 0; j < 28; j++) {
key_f[j] = R[j];
}
for (j = 0; j < 48; j++) {
C_key[47-j] = key_f[56-PC_2[j]];
}
memcpy(subKey[i], C_key, 48);
}
}
初始IP置換:
給定64位明文塊M,通過一個固定的初始置換IP來重排M中的二進制位,得到二進制串M0 = IP(M) = L0 R0,這裏L0 和R0分別是M0 的前32位和後32位。
//IP置換表
const int IP[64] = {
58, 50, 42, 34, 26, 18, 10, 2,
60, 52, 44, 36, 28, 20, 12, 4,
62, 54, 46, 38, 30, 22, 14, 6,
64, 56, 48, 40, 32, 24, 16, 8,
57, 49, 41, 33, 25, 17, 9, 1,
59, 51, 43, 35, 27, 19, 11, 3,
61, 53, 45, 37, 29, 21, 13, 5,
63, 55, 47, 39, 31, 23, 15, 7
};
//初始置換IP
int i = 0;
unsigned char FirstKey[64];
for (i = 0; i < 64; i++) {
FirstKey[63-i] = word[64-IP[i]];
}
迭代T
- 根據L0R0 按下述規則進行16次迭代,即
- 這裏 (XOR) 是32位二進制串按位異或運算,f 是輸出32位的Feistel 輪函數;
- 16個長度爲48位的子密鑰Ki(i= 1 … 16) 由密鑰K生成;
- 16次迭代後得到L16R16 ;
- 左右交換輸出R16L16 。
//16輪迭代
unsigned char L[32];
unsigned char R[32];
for(i = 0; i < 32; i++) {
L[i] = FirstKey[i+32];
}
for(i = 0; i < 32; i++) {
R[i] = FirstKey[i];
}
for (i = 0; i < 16; i++) {
unsigned char tmp_R[32];
unsigned char R1[32];
memcpy(tmp_R, R, 32);
f(R, subKey[i], R1);
XOR_32(L, R1);
memcpy(R, L, 32);
memcpy(L, tmp_R, 32);
}
輪詢函數Feistel:
- 將長度爲32位的串Ri-1作E-擴展,成爲48位的串E(Ri-1);
//擴展置換表
const int E[48] = {
32, 1, 2, 3, 4, 5,
4, 5, 6, 7, 8, 9,
8, 9, 10, 11, 12, 13,
12, 13, 14, 15, 16, 17,
16, 17, 18, 19, 20, 21,
20, 21, 22, 23, 24, 25,
24, 25, 26, 27, 28, 29,
28, 29, 30, 31, 32, 1
};
- 將E(Ri-1) 和長度爲48位的子密鑰Ki作48位二進制串按位異或運算,Ki 由密鑰K生成;
void XOR_48(unsigned char ER[48], unsigned char K[48]) {
int i = 0;
for (i = 0; i < 48; i++) {
ER[i] ^= K[i];
}
}
- 將上面得到的結果平均分成8個分組(每個分組長度6位),各個分 組分別經過8個不同的S-盒進行6-4 轉換,得到8個長度分別爲4 位的分組;
// S盒置換表,每個S盒是4x16的置換表
const int S_BOX[8][4][16] = {
{
{14,4,13,1,2,15,11,8,3,10,6,12,5,9,0,7},
{0,15,7,4,14,2,13,1,10,6,12,11,9,5,3,8},
{4,1,14,8,13,6,2,11,15,12,9,7,3,10,5,0},
{15,12,8,2,4,9,1,7,5,11,3,14,10,0,6,13}
},
{
{15,1,8,14,6,11,3,4,9,7,2,13,12,0,5,10},
{3,13,4,7,15,2,8,14,12,0,1,10,6,9,11,5},
{0,14,7,11,10,4,13,1,5,8,12,6,9,3,2,15},
{13,8,10,1,3,15,4,2,11,6,7,12,0,5,14,9}
},
{
{10,0,9,14,6,3,15,5,1,13,12,7,11,4,2,8},
{13,7,0,9,3,4,6,10,2,8,5,14,12,11,15,1},
{13,6,4,9,8,15,3,0,11,1,2,12,5,10,14,7},
{1,10,13,0,6,9,8,7,4,15,14,3,11,5,2,12}
},
{
{7,13,14,3,0,6,9,10,1,2,8,5,11,12,4,15},
{13,8,11,5,6,15,0,3,4,7,2,12,1,10,14,9},
{10,6,9,0,12,11,7,13,15,1,3,14,5,2,8,4},
{3,15,0,6,10,1,13,8,9,4,5,11,12,7,2,14}
},
{
{2,12,4,1,7,10,11,6,8,5,3,15,13,0,14,9},
{14,11,2,12,4,7,13,1,5,0,15,10,3,9,8,6},
{4,2,1,11,10,13,7,8,15,9,12,5,6,3,0,14},
{11,8,12,7,1,14,2,13,6,15,0,9,10,4,5,3}
},
{
{12,1,10,15,9,2,6,8,0,13,3,4,14,7,5,11},
{10,15,4,2,7,12,9,5,6,1,13,14,0,11,3,8},
{9,14,15,5,2,8,12,3,7,0,4,10,1,13,11,6},
{4,3,2,12,9,5,15,10,11,14,1,7,6,0,8,13}
},
{
{4,11,2,14,15,0,8,13,3,12,9,7,5,10,6,1},
{13,0,11,7,4,9,1,10,14,3,5,12,2,15,8,6},
{1,4,11,13,12,3,7,14,10,15,6,8,0,5,9,2},
{6,11,13,8,1,4,10,7,9,5,0,15,14,2,3,12}
},
{
{13,2,8,4,6,15,11,1,10,9,3,14,5,0,12,7},
{1,15,13,8,10,3,7,4,12,5,6,11,0,14,9,2},
{7,11,4,1,9,12,14,2,0,6,10,13,15,3,5,8},
{2,1,14,7,4,10,8,13,15,12,9,0,3,5,6,11}
}
};
- 將上面得到的分組結果順序連接得到長度爲32位的串;
- 再將上面的32位串經過P-置換,得到的結果作爲輪函數f(Ri-1, Ki) 的最終32位輸出。
//P盒置換表
const int P[32] = {
16, 7, 20, 21,
29, 12, 28, 17,
1, 15, 23, 26,
5, 18, 31, 10,
2, 8, 24, 14,
32, 27, 3, 9,
19, 13, 30, 6,
22, 11, 4, 25
};
- 整個函數的實現過程:
//輪詢函數Feistel
void f(unsigned char R[32], unsigned char K[48], unsigned char R1[32]) {
//將32位進行擴展成48位
unsigned char ER[48];
int i = 0, j = 0;
for (i = 0; i < 48; i++) {
ER[47-i] = R[32-E[i]];
}
//擴展後的R和K異或
XOR_48(ER, K);
//輪詢S_Box,將6->4
for (i = 0; i < 48; i+=6, j+=4) {
int m = (ER[47-i]<<1) +ER[47-i-5];
int n = (ER[47-i-1]<<3) + (ER[47-i-2]<<2) + (ER[47-i-3]<<1) + ER[47-i-4];
int num = S_BOX[i/6][m][n];
//printf("%d %d", m, n);
R1[31-j] = (num&0x08) >> 3;
R1[31-j-1] = (num&0x04) >> 2;
R1[31-j-2] = (num&0x02) >> 1;
R1[31-j-3] = num&0x01;
}
//P置換, 32->32
unsigned char ar[32];
memcpy(ar, R1, 32);
for (i = 0; i < 32; i++) {
R1[31-i] = ar[32-P[i]];
}
}
加密:
void EnCode(unsigned char word[64], unsigned char cipher[64], unsigned char subKey[16][48]) {
//初始置換IP
int i = 0;
unsigned char FirstKey[64];
for (i = 0; i < 64; i++) {
FirstKey[63-i] = word[64-IP[i]];
}
//16輪迭代
unsigned char L[32];
unsigned char R[32];
for(i = 0; i < 32; i++) {
L[i] = FirstKey[i+32];
}
for(i = 0; i < 32; i++) {
R[i] = FirstKey[i];
}
for (i = 0; i < 16; i++) {
unsigned char tmp_R[32];
unsigned char R1[32];
memcpy(tmp_R, R, 32);
f(R, subKey[i], R1);
XOR_32(L, R1);
memcpy(R, L, 32);
memcpy(L, tmp_R, 32);
}
//合併迭代後的L和R,並進行IP-1的置換
unsigned char LR[64];
for (i = 0; i < 32; i++) {
LR[i] = L[i];
}
for (i = 0; i < 32; i++) {
LR[i+32] = R[i];
}
unsigned char tmp_LR[64];
memcpy(tmp_LR, LR, 64);
for (i = 0; i < 64; i++) {
cipher[63-i] = tmp_LR[64-IP_1[i]];
}
}
解密:
- 分析所有的代替、置換、異或和循環移動過程,獲得一個非常 有用的性質:DES 的加密和解密可使用相同的算法和密鑰。
- DES 的過程設計使得用相同的函數來加密或解密每個分組成爲 可能。加解密過程中使用由同一個密鑰K 經過相同的子密鑰生 成算法得到的子密鑰序列,唯一不同之處是加解密過程中子密 鑰的調度次序恰好相反。
- 加密過程的子密鑰按(K1 K2 … K15 K16) 次序調度
- 解密過程的子密鑰按(K16 K15 … K2 K1) 次序調度
代碼實現:
void DeCode(unsigned char cipher[64], unsigned char word[64], unsigned char subKey[16][48]) {
//初始置換IP
int i = 0;
unsigned char FirstKey[64];
for (i = 0; i < 64; i++) {
FirstKey[63-i] = cipher[64-IP[i]];
}
//16輪迭代
unsigned char L[32];
unsigned char R[32];
for(i = 0; i < 32; i++) {
L[i] = FirstKey[i+32];
}
for(i = 0; i < 32; i++) {
R[i] = FirstKey[i];
}
for (i = 0; i < 16; i++) {
unsigned char tmp_R[32];
unsigned char R1[32];
memcpy(tmp_R, R, 32);
f(R, subKey[15-i], R1);
XOR_32(L, R1);
memcpy(R, L, 32);
memcpy(L, tmp_R, 32);
}
//合併迭代後的L和R,並進行IP-1的置換
unsigned char LR[64];
for (i = 0; i < 32; i++) {
LR[i] = L[i];
}
for (i = 0; i < 32; i++) {
LR[i+32] = R[i];
}
unsigned char tmp_LR[64];
memcpy(tmp_LR, LR, 64);
for (i = 0; i < 64; i++) {
word[63-i] = tmp_LR[64-IP_1[i]];
}
}
數據結構:
使用unsigned char數組來存儲二進制位串
通過c語言的移位操作符實現二進制位串的邏輯運算。
通過以下代碼實現字符串與二進制位串的轉換:
//字符轉換成二進制符號
void CharToBit(unsigned char c, unsigned char bit[8]){
int i;
for(i = 0; i < 8; i++){
*(bit+i) = (c>>i) & 1;
}
}
//將長度爲8的字符串轉爲64位二進制
void StringToBits(unsigned char c[8], unsigned char bit[64]){
int i;
for(i = 0; i < 8; i++){
CharToBit(*(c + i), bit + (i<<3));
}
}
//二進制轉換成字節
void BitToChar(unsigned char bit[8], unsigned char *c){
int i;
for(i = 0; i < 8; i++){
*c |= *(bit + i) << i;
}
}
//將二進制字節轉爲長度爲8的字符串
void BitsToString(unsigned char bit[64], unsigned char c[8]){
int i;
memset(c,0,8);
for(i = 0; i < 8; i++){
BitToChar(bit + (i<<3), c + i);
}
}
二進制位串的一些邏輯運算如下:
void XOR_32(unsigned char ER[32], unsigned char K[32]) {
int i = 0;
for (i = 0; i < 32; i++) {
ER[i] ^= K[i];
}
}
int m = (ER[47-i]<<1) +ER[47-i-5];
int n = (ER[47-i-1]<<3) + (ER[47-i-2]<<2) + (ER[47-i-3]<<1) + ER[47-i-4];
int num = S_BOX[i/6][m][n];
//printf("%d %d", m, n);
R1[31-j] = (num&0x08) >> 3;
R1[31-j-1] = (num&0x04) >> 2;
R1[31-j-2] = (num&0x02) >> 1;
R1[31-j-3] = num&0x01;
編譯運行結果:
用於測試的main文件:
- 將加密的文字存到一個記事本里,解密過程讀取記事本中的位串進行解碼。
#include <stdio.h>
#include <stdlib.h>
#include "desCode.h"
#include <time.h>
int main () {
printf("please input the words you want to encode: \n\n");
//加密的文字
unsigned char word[8];
memset(word, 0, 8);
unsigned char *s_word = (unsigned char*)malloc(8*sizeof(unsigned char));
gets(s_word);
strcpy(word, s_word);
free(s_word);
unsigned char words[64];
StringToBits(word, words);
//密鑰
unsigned char c_key[8];
//取1~9的隨機數作爲密鑰
srand(time(0));
for (int i = 0; i < 8; i++) {
int key_1 = rand() % 10;
c_key[i] = key_1 + '0';
}
printf("\nthe key help us to encode is: \n");
for (int i = 0; i < 8; i++) {
printf("%c", c_key[i]);
}
printf("\n\n");
//unsigned char *c_key = "12342a78";
unsigned char key[64];
StringToBits(c_key, key);
//根據提供的密鑰生成16個子密鑰
unsigned char subKey[16][48];
getMyKey(key, subKey);
//加密過程
unsigned char cipher[64];
EnCode(words, cipher, subKey);
printf("After encode, your cipher is: \n");
for (int i = 0; i < 64; i++) {
printf("%c", cipher[i]);
}
printf("\n\n");
//將密碼寫到密碼本里面
FILE *fp;
fp = fopen("code.txt","w+t");
fwrite(cipher, sizeof(char), 64, fp);
fclose(fp);
//將密碼本的密碼讀取出
unsigned char cipher_read[64];
fp = fopen("code.txt","r+t");
fread(cipher_read, sizeof(char), 64, fp);
//fscanf(fp, "%s", cipher_read);
fclose(fp);
//解密過程
unsigned char decode[64];
unsigned char answer[8];
DeCode(cipher_read, decode, subKey);
BitsToString(decode, answer);
printf("After decode, your answer is: \n");
for (int i = 0; i < 8; i++) {
printf("%c", answer[i]);
}
printf("\n");
return 0;
}
運行結果: