1.3 希爾密碼python實現 - 三階

引例： 1.3 三階矩陣希爾加密

1.3. 計算定義在Zg上矩陣K=((1 11 12),(4 23 2),(17 15 9))的逆K-1，並用K作為希爾密碼體制的密鑰完成對
明文串： looking forward to our national day 的加密和相應密文串的解密.

1.3 答案說明：逆矩陣是對的，但是密文串與答案不符。原因是輸入矩陣時，按行輸入和按列輸入的差異。如下提供兩種python求解方式
代碼結果：按行輸入舉證，密文串密文：VEDUQRVLRZCVSTLSCEEDQPCXPWIFIH
代碼結果：按列輸入舉證，密文串密文：TDADVTEBABROOVRUWMRSWDFGSWVVDS -- 這是答案中的

代碼一：自定義階數求解

import numpy as np
import math
from sympy import Matrix


# decryption function
def decrypt(key_matrix_inv, cipher_text,dimensions):
    """
    Arguments: key matrix inverse, cipher text
    Returns: plain text
    """
    print("Matrix Inverse is: \n", key_matrix_inv)
    cipher_len = len(cipher_text)
    
    # create cipher text matrix (ASCII Values - 65 to get from 0 to X)

    cipher_text_matrix = []
    addLen=0
    plain_text=""
    
    #print("cipher_text",cipher_text)

    if cipher_len % dimensions != 0:
        addLen = dimensions - cipher_len % dimensions
        
    for i in range(int((cipher_len+addLen)/dimensions)):
        result = []
        cipher_text_matrix=[]
        for j in range(dimensions):
            # print(i," ",j)
            cipher_text_matrix.append(cipher_text[i*dimensions+j]-65)
        cipher_text_matrix = np.array(cipher_text_matrix)
        #print("Cipher Key Matrix",i,":\n", cipher_text_matrix)
        # multiply inverse with cipher text matrix
        result = np.array(np.dot(key_matrix_inv, cipher_text_matrix))
        #print("Decrypted Matrix\n", result)
        # convert result matrix to plain text by using chr()
        for t in range(dimensions):
            plain_text += chr(result[t] % 26 + 65)

    return plain_text
'''
    # multiply inverse with cipher text matrix
    result = np.array(np.dot(key_matrix_inv, cipher_text_matrix))

    # BUG
    # print(result[0][1], int(result[0][1]))
    print("Decrypted Matrix\n", result) 

    # create empty string for plain text
    plain_text = ""
    # convert result matrix to plain text by using chr()
    for i in range(dimensions):
        plain_text += chr(int(round(result[0][i], 0) % 26 + 65))

    # return the decrypted plain text
    return plain_text
'''
if __name__ == "__main__":
    # take input from the user
    plain_text = str(input("Plain Text: ")).upper()

    # dimensions of the matrix = length(plain text) x length(plain text)
    dimensions = int(input("Dimensions:"))
    cipher_len = len(plain_text.lower())
    
    # plain text matrix
    plain_text_matrix = []
    
    # creating a column matrix for plain text characters
    for i in range(cipher_len):
        plain_text_matrix.append(ord(plain_text[i]))
    plain_text_matrix = np.array(plain_text_matrix)
    
    print("Plain Text Matrix\n", plain_text_matrix)

    print("Enter values for the key: ")

    # take values for the key matrix
    key_matrix = []
    for i in range(dimensions):
        row_ = []
        for j in range(dimensions):
            value = int(input(str(i) + ", " + str(j) + " value: "))                         
            row_.append(value)
        key_matrix.append(row_)

    print("Key Matrix: \n")
        
    # for encryption
    key_matrix = np.array(key_matrix)
    # for decryption
    #key_matrix_inv = (np.linalg.inv(np.matrix(key_matrix)) % 26)
    #key_matrix_inv = multi_inverse(np.linalg.det(key_matrix), 26) * \
    #       np.matrix(key_matrix).getH()
    #print(np.matrix(key_matrix).getH())
    
    # calculate key matrix inverse using modulo multiplicative inverse
    #5-=21
    #17=23
    key_matrix=Matrix(key_matrix)
    key_matrix_inv = key_matrix.inv_mod(26)
    print("key_matrix_inv",key_matrix_inv)
    key_matrix_inv= np.array(key_matrix_inv)


    matrix_result = np.matmul(key_matrix_inv,key_matrix) %  26
    #print("Result Matrix: \n", matrix_result)
    
    #print("Inverse Key Matrix: \n", key_matrix_inv)

    cipher_text=decrypt(key_matrix,plain_text_matrix,dimensions)

    print("cipher_text: \n", cipher_text.upper())
    print("cipher_len:",cipher_len)
    cipher_text_matrix=[]
    for i in range(cipher_len):
        cipher_text_matrix.append(ord(cipher_text[i]))
    cipher_text_matrix = np.array(cipher_text_matrix)
    
    decrypted_plain_text=decrypt(key_matrix_inv,cipher_text_matrix,dimensions)
    print("decrypted_plain_text: \n", decrypted_plain_text.lower())


## 注意輸入文本不含空格
# Plain Text: lookingforwardtoournationalday      
# Dimensions:3
# Plain Text Matrix
#  [76 79 79 75 73 78 71 70 79 82 87 65 82 68 84 79 79 85 82 78 65 84 73 79
#  78 65 76 68 65 89]
# Enter values for the key: 
# 0, 0 value: 1
# 0, 1 value: 11
# 0, 2 value: 12
# 1, 0 value: 4
# 1, 1 value: 23
# 1, 2 value: 2
# 2, 0 value: 17
# 2, 1 value: 15
# 2, 2 value: 9
# Key Matrix:

# key_matrix_inv Matrix([[25, 11, 22], [10, 13, 4], [17, 24, 1]])
# Matrix Inverse is:
#  Matrix([[1, 11, 12], [4, 23, 2], [17, 15, 9]])
# cipher_text:
#  VEDUQRVLRZCVSTLSCEEDQPCXPWIFIH
# cipher_len: 30
# Matrix Inverse is:
#  [[25 11 22]
#  [10 13 4]
#  [17 24 1]]
# decrypted_plain_text:
#  lookingforwardtoournationalday

代碼二：指定階數求解

import numpy as np


def encode(string, size):
    # 轉換小寫字母
    if not string.islower():
        string = string.lower()
    # 分成 size個 字的分段
    blocks = [string[i:i+size] for i in range(0, len(string), size)]
    # 明文字串與密鑰矩陣階數不整除。。字串補a
    if len(blocks[-1]) != size:
        blocks[-1] = blocks[-1].ljust(size,'a')
    # 將 a-z 編碼為 0-25
    temp = np.array([list(map(ord, block)) for block in blocks]) - ord('a')
#     print(temp)
    return temp


def analysis(crypter, code):
    return ((crypter @ code.T) % 26).T + ord('a')


# 要加密的信息
encode_msg = 'lookingforwardtoournationalday'.lower()
print('待加密的信息：'+encode_msg)

# 密鑰
encryption_matrix = np.array([[1,11,12], [4, 23,2],[17, 15,9]])
print('密鑰：')
print(encryption_matrix)

# 加密代碼
encrypted_code = analysis(encryption_matrix, encode(encode_msg, 3))

# 密文
Decryption_matrixtext = ''.join(map(chr, encrypted_code.ravel()))
print("密文：" + Decryption_matrixtext[:len(encode_msg)].upper())


# 待加密的信息：lookingforwardtoournationalday
# 密鑰：
# [[ 1 11 12]
#  [ 4 23  2]
#  [17 15  9]]
# 密文：VEDUQRVLRZCVSTLSCEEDQPCXPWIFIH