DES 算法的具体原理
首先我们需要知道 DES 加密解密算法的具体原理以及流程，我们才能在 Python 中将其实现。DES 加密解密其实就是一种分组密码的实现，并且通过多轮代换以及异或操作最终完成加密，每次加密都有 8 个 S 合将其进行分组加密，详细可参见清华大学出版社的《现代密码学》第五版。
Python 代码实现
我们不妨先来导入一些基本的数据以及矩阵（这里用的 numpy，但其实不用也可以）：
pc1 = np.array([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])
pc2 = np.array([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])
sd = np.array([1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1])
ip = np.array([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])
ipReverse = np.array([40,8,48,16,56,24,64,32,
39,7,47,15,55,23,63,31,
38,6,46,14,54,22,62,30,
37,5,45,13,53,21,61,29,
36,4,44,12,52,20,60,28,
35,3,43,11,51,19,59,27,
34,2,42,10,50,18,58,26,
33,1,41,9,49,17,57,25])
E = np.array([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])
P = np.array([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])
s = np.array([[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,
13,8,10,1,3,15,4,2,11,6,7,12,10,5,14,9,],
[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]])
subKeys = [];然后我们首先来实现我们的字符与二进制的转换函数：
def str2bin(s):
res = []
for c in s:
k = str(bin(ord(c))[2:])
while len(k) < 8:
k = '0' + k
for i in k:
res.append(i)
return res
def bin2str(seq):
k = 0b0
s = ""
for i in range(len(seq)):
if i % 8 == 0:
s = s + chr(k)
k = 0b0
k = k << 1
k += int(seq[i])
if k != 0:
s = s + chr(k)
return s这里考虑到如果加密的数据太长，会导致溢出，所以使用矩阵代替单纯的数字，不过既然我们要用数组的话，那我们的异或也需要一个函数来实现：
def binListXOR(a, b):
res = []
for i in range(len(a)):
res.append(str(int(a[i]) ^ int(b[i])))
return res实现完异或的函数之后，我们接下来实现循环左移以及矩阵代换的函数，这里因为用了矩阵的关系，反而变得更好实现了，如果用整数类型的话就得搞一堆位运算了：
def permuBinList(seq, per):
res = []
for i in range(len(per)):
res.append(seq[per[i] - 1])
return res
def leftRecurrentShift(seq, n):
seq = list(seq)
for i in range(n):
seq.append(seq[0])
del seq[0]
return seq之后我们来实现我们的子密钥生成，主要用到了两个函数，这里需要注意的是我们 DES 加密中每一轮加密所使用的子密钥都是不一样的，所以 DES 中有 16 轮加密，我们就需要生成 16 个子密钥，我们会把这些子密钥放到 subKeys 数组里面保存：
def permuKey(ci, di):
k = []
k.extend(ci)
k.extend(di)
return permuBinList(k, pc2)
def genSubKeys(key):
# init Ci and Di
k = str2bin(key)
new_k = permuBinList(k, pc1)
ci, di = new_k[:28], new_k[28:]
# generate subKeys
for i in range(16):
ci, di = leftRecurrentShift(ci, sd[i]), leftRecurrentShift(di, sd[i])
subKeys.append(permuKey(ci, di))
return之后就是实现我们每一轮加密的函数以及 S 盒的函数啦：
def sBox(ri):
res = []
for i in range(8):
tmp = ri[i * 6: (i + 1) * 6]
row = int(ri[0]) * 2 + int(ri[5]);
col = int(ri[1]) * 8 + int(ri[2]) * 4 + int(ri[3]) * 2 + int(ri[4])
res.extend(str2bin(chr(s[i][row * 15 + col])))
return res
def fFunc(li, ri, k):
new_ri = permuBinList(ri, E)
new_ri = binListXOR(new_ri, k)
new_ri = sBox(new_ri)
new_ri = permuBinList(new_ri, P)
return binListXOR(new_ri, li)从这里基本上我们就能看出 DES 中单轮加密的流程了，那现在我们不妨定义一下我们要加密的内容以及我们的密钥：
key = "kabg3s$f"
message = "MiCh12#$"然后我们开始我们的 DES 加密：
# DES Encryption
binMessage = str2bin(message)
print("binMessage (Original):", "".join(binMessage))
binMessage = permuBinList(binMessage, ip)
li, ri = binMessage[:32], binMessage[32:]
for i in range(16):
li, ri = ri, fFunc(li, ri, subKeys[i])
li, ri = ri, li
binMessage = []
binMessage.extend(li)
binMessage.extend(ri)
binMessage = permuBinList(binMessage, ipReverse)
print("binMessage (Encrypted):", "".join(binMessage))
print("Message (Encrypted):", bin2str(binMessage))这里需要注意的是，有时候我们加密后的信息不一定能打印出来，因为可能出来的数字没办法在 ASCII 表里面找到，所以一般我们要用于传输或者展示的时候，最好还是弄一个 base64。之后我们不妨来看一下我们的解密流程，我们知道 DES 解密就是 DES 加密的逆流程，也就是所我们只需要重复加密时候的流程就可以了。不过需要注意的是，这里解密的子密钥就是从后往前用了：
# DES Decryption
binMessage = permuBinList(binMessage, ip)
li, ri = binMessage[:32], binMessage[32:]
for i in range(16):
li, ri = ri, fFunc(li, ri, subKeys[15 - i])
li, ri = ri, li
binMessage = []
binMessage.extend(li)
binMessage.extend(ri)
binMessage = permuBinList(binMessage, ipReverse)
print("binMessage (Decrypted): ", "".join(binMessage))
print("Message (Decrypted): ", bin2str(binMessage))至此，我们就实现完了我们的 DES 加密以及解密的全部算法流程了。完整代码如下：
import numpy as np
pc1 = np.array([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])
pc2 = np.array([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])
sd = np.array([1, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1])
ip = np.array([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])
ipReverse = np.array([40,8,48,16,56,24,64,32,
39,7,47,15,55,23,63,31,
38,6,46,14,54,22,62,30,
37,5,45,13,53,21,61,29,
36,4,44,12,52,20,60,28,
35,3,43,11,51,19,59,27,
34,2,42,10,50,18,58,26,
33,1,41,9,49,17,57,25])
E = np.array([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])
P = np.array([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])
s = np.array([[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,
13,8,10,1,3,15,4,2,11,6,7,12,10,5,14,9,],
[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]])
subKeys = [];
def str2bin(s):
res = []
for c in s:
k = str(bin(ord(c))[2:])
while len(k) < 8:
k = '0' + k
for i in k:
res.append(i)
return res
def bin2str(seq):
k = 0b0
s = ""
for i in range(len(seq)):
if i % 8 == 0:
s = s + chr(k)
k = 0b0
k = k << 1
k += int(seq[i])
if k != 0:
s = s + chr(k)
return s
def binListXOR(a, b):
res = []
for i in range(len(a)):
res.append(str(int(a[i]) ^ int(b[i])))
return res
def permuBinList(seq, per):
res = []
for i in range(len(per)):
res.append(seq[per[i] - 1])
return res
def leftRecurrentShift(seq, n):
seq = list(seq)
for i in range(n):
seq.append(seq[0])
del seq[0]
return seq
def permuKey(ci, di):
k = []
k.extend(ci)
k.extend(di)
return permuBinList(k, pc2)
def genSubKeys(key):
# init Ci and Di
k = str2bin(key)
new_k = permuBinList(k, pc1)
ci, di = new_k[:28], new_k[28:]
# generate subKeys
for i in range(16):
ci, di = leftRecurrentShift(ci, sd[i]), leftRecurrentShift(di, sd[i])
subKeys.append(permuKey(ci, di))
return
def sBox(ri):
res = []
for i in range(8):
tmp = ri[i * 6: (i + 1) * 6]
row = int(ri[0]) * 2 + int(ri[5]);
col = int(ri[1]) * 8 + int(ri[2]) * 4 + int(ri[3]) * 2 + int(ri[4])
res.extend(str2bin(chr(s[i][row * 15 + col])))
return res
def fFunc(li, ri, k):
new_ri = permuBinList(ri, E)
new_ri = binListXOR(new_ri, k)
new_ri = sBox(new_ri)
new_ri = permuBinList(new_ri, P)
return binListXOR(new_ri, li)
key = "kabg3s$f"
print("Key:", key)
message = "MiCh12#$"
print("Message (Original):", message)
genSubKeys(key)
# DES Encryption
binMessage = str2bin(message)
print("binMessage (Original):", "".join(binMessage))
binMessage = permuBinList(binMessage, ip)
li, ri = binMessage[:32], binMessage[32:]
for i in range(16):
li, ri = ri, fFunc(li, ri, subKeys[i])
li, ri = ri, li
binMessage = []
binMessage.extend(li)
binMessage.extend(ri)
binMessage = permuBinList(binMessage, ipReverse)
print("binMessage (Encrypted):", "".join(binMessage))
print("Message (Encrypted):", bin2str(binMessage))
# DES Decryption
binMessage = permuBinList(binMessage, ip)
li, ri = binMessage[:32], binMessage[32:]
for i in range(16):
li, ri = ri, fFunc(li, ri, subKeys[15 - i])
li, ri = ri, li
binMessage = []
binMessage.extend(li)
binMessage.extend(ri)
binMessage = permuBinList(binMessage, ipReverse)
print("binMessage (Decrypted): ", "".join(binMessage))
print("Message (Decrypted): ", bin2str(binMessage))
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