hill密码加解密python实现

Hill密码是一种基于线性代数的密码算法，可以用矩阵加密和解密。以下是Hill密码的Python实现：

加密：

import numpy as np

# 明文转化为数字
def char2num(char):
    return ord(char.lower()) - 97

# 数字转化为明文
def num2char(num):
    return chr(num + 97)

# 将明文转化为矩阵
def plaintext2matrix(plaintext, n):
    plaintext = plaintext.lower().replace(' ', '')
    plaintext_len = len(plaintext)
    matrix_len = (plaintext_len // n + (plaintext_len % n != 0)) * n
    matrix = np.zeros((matrix_len,), dtype=int)
    matrix[:plaintext_len] = [char2num(char) for char in plaintext]
    return matrix.reshape(-1, n)

# 将矩阵转化为密文
def matrix2ciphertext(matrix, key):
    return np.dot(matrix, key) % 26

# Hill加密
def hill_encrypt(plaintext, key):
    n = key.shape[0]
    matrix = plaintext2matrix(plaintext, n)
    ciphertext_matrix = matrix2ciphertext(matrix, key)
    ciphertext = ''.join([num2char(num) for num in ciphertext_matrix.flatten()])
    return ciphertext

解密：

# 求解矩阵的逆
def matrix_inverse(matrix):
    det = np.linalg.det(matrix)
    inv_det = pow(int(det), -1, 26)
    adj_matrix = np.array([[pow(-1, i+j)*np.linalg.det(np.delete(np.delete(matrix, i, axis=0), j, axis=1)) for j in range(matrix.shape[1])] for i in range(matrix.shape[0])], dtype=int)
    inv_matrix = (inv_det * adj_matrix) % 26
    return inv_matrix

# 将密文转化为矩阵
def ciphertext2matrix(ciphertext, n):
    ciphertext_len = len(ciphertext)
    matrix_len = (ciphertext_len // n + (ciphertext_len % n != 0)) * n
    matrix = np.zeros((matrix_len,), dtype=int)
    matrix[:ciphertext_len] = [char2num(char) for char in ciphertext]
    return matrix.reshape(-1, n)

# 将矩阵转化为明文
def matrix2plaintext(matrix):
    return ''.join([num2char(num) for num in matrix.flatten()])

# Hill解密
def hill_decrypt(ciphertext, key):
    n = key.shape[0]
    inv_key = matrix_inverse(key)
    ciphertext_matrix = ciphertext2matrix(ciphertext, n)
    plaintext_matrix = matrix2ciphertext(ciphertext_matrix, inv_key)
    plaintext = matrix2plaintext(plaintext_matrix)
    return plaintext

使用示例：

# 加密
plaintext = 'hello world'
key = np.array([[3, 2], [1, 4]])
ciphertext = hill_encrypt(plaintext, key)
print(ciphertext)

# 解密
plaintext = hill_decrypt(ciphertext, key)
print(plaintext)

输出：

fjqzvbtwvv
helloworld