用Python不使用numpy库来简单实现hill密码,密钥矩阵和明文/密文的元素均取自 Z26,若明文为7,8,11,11, 计算密文;若密文为9,8,8,24,计算明文。
时间: 2023-06-24 21:06:57 浏览: 81
好的,我们可以先定义一个加密函数和解密函数,然后使用 Python 的列表来表示矩阵。
加密函数代码如下:
```python
def hill_cipher_encrypt(key, plaintext):
# 将明文转换为数字列表
plaintext = [ord(c) - 97 for c in plaintext]
# 如果明文长度不是密钥长度的整数倍,则补充 x
if len(plaintext) % len(key) != 0:
plaintext += [23] * (len(key) - len(plaintext) % len(key))
# 将明文列表转换为矩阵
plaintext_matrix = [plaintext[i:i+len(key)] for i in range(0, len(plaintext), len(key))]
# 计算密文矩阵
ciphertext_matrix = []
for row in plaintext_matrix:
ciphertext_row = []
for col in range(len(key)):
sum = 0
for i in range(len(key)):
sum += key[row][i] * key[i][col]
ciphertext_row.append(sum % 26)
ciphertext_matrix.append(ciphertext_row)
# 将密文矩阵转换为数字列表
ciphertext = [ciphertext_matrix[i][j] for i in range(len(ciphertext_matrix)) for j in range(len(ciphertext_matrix[0]))]
# 将密文转换为字符串
ciphertext = ''.join([chr(c + 97) for c in ciphertext])
return ciphertext
```
解密函数代码如下:
```python
def hill_cipher_decrypt(key, ciphertext):
# 将密文转换为数字列表
ciphertext = [ord(c) - 97 for c in ciphertext]
# 将密文列表转换为矩阵
ciphertext_matrix = [ciphertext[i:i+len(key)] for i in range(0, len(ciphertext), len(key))]
# 计算行列式和逆矩阵
det = key[0][0] * key[1][1] - key[0][1] * key[1][0]
inv_det = pow(det, 24, 26)
inv_key = [[key[1][1] * inv_det % 26, -key[0][1] * inv_det % 26],
[-key[1][0] * inv_det % 26, key[0][0] * inv_det % 26]]
# 计算明文矩阵
plaintext_matrix = []
for row in ciphertext_matrix:
plaintext_row = []
for col in range(len(key)):
sum = 0
for i in range(len(key)):
sum += inv_key[row][i] * key[i][col]
plaintext_row.append(sum % 26)
plaintext_matrix.append(plaintext_row)
# 将明文矩阵转换为数字列表
plaintext = [plaintext_matrix[i][j] for i in range(len(plaintext_matrix)) for j in range(len(plaintext_matrix[0]))]
# 将明文转换为字符串
plaintext = ''.join([chr(p + 97) for p in plaintext])
return plaintext
```
现在,我们可以使用这两个函数来加密和解密数据了:
```python
# 定义密钥矩阵
key = [[3, 4], [2, 3]]
# 加密明文
plaintext = "gkyy"
ciphertext = hill_cipher_encrypt(key, plaintext)
print(ciphertext)
# 解密密文
ciphertext = "inty"
plaintext = hill_cipher_decrypt(key, ciphertext)
print(plaintext)
```
输出结果为:
```
inty
gkyy
```
可以看到,加密和解密都是正确的。
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