希尔密码指南和代码实现详解

2021年3月12日14:37:14 发表评论 1,271 次浏览

本文概述

希尔密码是一种基于线性代数的测谎替换密码。每个字母都由数字模26表示。通常使用简单方案A = 0, B = 1, …, Z = 25, 但这并不是密码。为了加密消息, 将n个字母的每个块(被视为n分量矢量)乘以可逆n×n矩阵(模数为26)。要解密消息, 将每个块乘以用于矩阵的逆。加密。

用于加密的矩阵是密码密钥, 应从一组可逆的n×n矩阵(模数为26)中随机选择。

例子：

Input  : Plaintext: ACT
         Key: GYBNQKURP
Output : Ciphertext: POH
Input  : Plaintext: GFG
         Key: HILLMAGIC 
Output : Ciphertext: SWK

加密

我们必须对消息" ACT"(n = 3)进行加密。密钥为" GYBNQKURP", 可以将其写为nxn矩阵：

密码钥匙

消息" ACT"被写为矢量：

消息向量

加密的向量为：

加密向量

对应于" POH"的密文

解密

为了解密消息, 我们将密文转换回向量, 然后简单地乘以密钥矩阵的逆矩阵(字母为IFKVIVVMI)。上例中使用的矩阵的逆为：

逆矩阵

对于先前的密文" POH"：

解密

这使我们返回" ACT"。

假定所有字母均大写。

以下是n = 3时上述想法的实现。

C ++

// C++ code to implement Hill Cipher
#include <iostream>
using namespace std;
  
// Following function generates the
//  key matrix for the key string
void getKeyMatrix(string key, int keyMatrix[][3])
{
     int k = 0;
     for ( int i = 0; i < 3; i++) 
     {
         for ( int j = 0; j < 3; j++) 
         {
             keyMatrix[i][j] = (key[k]) % 65;
             k++;
         }
     }
}
  
// Following function encrypts the message
void encrypt( int cipherMatrix[][1], int keyMatrix[][3], int messageVector[][1])
{
     int x, i, j;
     for (i = 0; i < 3; i++) 
     {
         for (j = 0; j < 1; j++)
         {
             cipherMatrix[i][j] = 0;
           
              for (x = 0; x < 3; x++)
             {
                 cipherMatrix[i][j] += 
                      keyMatrix[i][x] * messageVector[x][j];
             }
          
             cipherMatrix[i][j] = cipherMatrix[i][j] % 26;
         }
     }
}
  
// Function to implement Hill Cipher
void HillCipher(string message, string key)
{
     // Get key matrix from the key string
     int keyMatrix[3][3];
     getKeyMatrix(key, keyMatrix);
  
     int messageVector[3][1];
  
     // Generate vector for the message
     for ( int i = 0; i < 3; i++)
         messageVector[i][0] = (message[i]) % 65;
  
     int cipherMatrix[3][1];
  
     // Following function generates
     // the encrypted vector
     encrypt(cipherMatrix, keyMatrix, messageVector);
  
     string CipherText;
  
     // Generate the encrypted text from 
     // the encrypted vector
     for ( int i = 0; i < 3; i++)
         CipherText += cipherMatrix[i][0] + 65;
  
     // Finally print the ciphertext
     cout << " Ciphertext:" << CipherText;
}
  
// Driver function for above code
int main()
{
     // Get the message to be encrypted
     string message = "ACT" ;
  
     // Get the key
     string key = "GYBNQKURP" ;
  
     HillCipher(message, key);
  
     return 0;
}

Java

// Java code to implement Hill Cipher
class GFG 
{
  
// Following function generates the
// key matrix for the key string
static void getKeyMatrix(String key, int keyMatrix[][])
{
     int k = 0 ;
     for ( int i = 0 ; i < 3 ; i++) 
     {
         for ( int j = 0 ; j < 3 ; j++) 
         {
             keyMatrix[i][j] = (key.charAt(k)) % 65 ;
             k++;
         }
     }
}
  
// Following function encrypts the message
static void encrypt( int cipherMatrix[][], int keyMatrix[][], int messageVector[][])
{
     int x, i, j;
     for (i = 0 ; i < 3 ; i++) 
     {
         for (j = 0 ; j < 1 ; j++)
         {
             cipherMatrix[i][j] = 0 ;
          
             for (x = 0 ; x < 3 ; x++)
             {
                 cipherMatrix[i][j] += 
                     keyMatrix[i][x] * messageVector[x][j];
             }
          
             cipherMatrix[i][j] = cipherMatrix[i][j] % 26 ;
         }
     }
}
  
// Function to implement Hill Cipher
static void HillCipher(String message, String key)
{
     // Get key matrix from the key string
     int [][]keyMatrix = new int [ 3 ][ 3 ];
     getKeyMatrix(key, keyMatrix);
  
     int [][]messageVector = new int [ 3 ][ 1 ];
  
     // Generate vector for the message
     for ( int i = 0 ; i < 3 ; i++)
         messageVector[i][ 0 ] = (message.charAt(i)) % 65 ;
  
     int [][]cipherMatrix = new int [ 3 ][ 1 ];
  
     // Following function generates
     // the encrypted vector
     encrypt(cipherMatrix, keyMatrix, messageVector);
  
     String CipherText= "" ;
  
     // Generate the encrypted text from 
     // the encrypted vector
     for ( int i = 0 ; i < 3 ; i++)
         CipherText += ( char )(cipherMatrix[i][ 0 ] + 65 );
  
     // Finally print the ciphertext
     System.out.print( " Ciphertext:" + CipherText);
}
  
// Driver code
public static void main(String[] args) 
{
     // Get the message to be encrypted
     String message = "ACT" ;
  
     // Get the key
     String key = "GYBNQKURP" ;
  
     HillCipher(message, key);
     }
}
  
// This code has been contributed by 29AjayKumar

Python3

# Python3 code to implement Hill Cipher
  
keyMatrix = [[ 0 ] * 3 for i in range ( 3 )]
  
# Generate vector for the message
messageVector = [[ 0 ] for i in range ( 3 )]
  
# Generate vector for the cipher
cipherMatrix = [[ 0 ] for i in range ( 3 )]
  
# Following function generates the
# key matrix for the key string
def getKeyMatrix(key):
     k = 0
     for i in range ( 3 ):
         for j in range ( 3 ):
             keyMatrix[i][j] = ord (key[k]) % 65
             k + = 1
  
# Following function encrypts the message
def encrypt(messageVector):
     for i in range ( 3 ):
         for j in range ( 1 ):
             cipherMatrix[i][j] = 0
             for x in range ( 3 ):
                 cipherMatrix[i][j] + = (keyMatrix[i][x] * 
                                        messageVector[x][j])
             cipherMatrix[i][j] = cipherMatrix[i][j] % 26
  
def HillCipher(message, key):
  
     # Get key matrix from the key string
     getKeyMatrix(key)
  
     # Generate vector for the message
     for i in range ( 3 ):
         messageVector[i][ 0 ] = ord (message[i]) % 65
  
     # Following function generates
     # the encrypted vector
     encrypt(messageVector)
  
     # Generate the encrypted text 
     # from the encrypted vector
     CipherText = []
     for i in range ( 3 ):
         CipherText.append( chr (cipherMatrix[i][ 0 ] + 65 ))
  
     # Finally print the ciphertext
     print ( "Ciphertext: " , "".join(CipherText))
  
# Driver Code
def main():
  
     # Get the message to 
     # be encrypted
     message = "ACT"
  
     # Get the key
     key = "GYBNQKURP"
  
     HillCipher(message, key)
  
if __name__ = = "__main__" :
     main()
  
# This code is contributed 
# by Pratik Somwanshi

C#

// C# code to implement Hill Cipher
using System;
  
class GFG 
{ 
  
// Following function generates the 
// key matrix for the key string 
static void getKeyMatrix(String key, int [, ]keyMatrix) 
{ 
     int k = 0; 
     for ( int i = 0; i < 3; i++) 
     { 
         for ( int j = 0; j < 3; j++) 
         { 
             keyMatrix[i, j] = (key[k]) % 65; 
             k++; 
         } 
     } 
} 
  
// Following function encrypts the message 
static void encrypt( int [, ]cipherMatrix, int [, ]keyMatrix, int [, ]messageVector) 
{ 
     int x, i, j; 
     for (i = 0; i < 3; i++) 
     { 
         for (j = 0; j < 1; j++) 
         { 
             cipherMatrix[i, j] = 0; 
          
             for (x = 0; x < 3; x++) 
             { 
                 cipherMatrix[i, j] += keyMatrix[i, x] * 
                                       messageVector[x, j]; 
             } 
          
             cipherMatrix[i, j] = cipherMatrix[i, j] % 26; 
         } 
     } 
} 
  
// Function to implement Hill Cipher 
static void HillCipher(String message, String key) 
{ 
      
     // Get key matrix from the key string 
     int [, ]keyMatrix = new int [3, 3]; 
     getKeyMatrix(key, keyMatrix); 
  
     int [, ]messageVector = new int [3, 1]; 
  
     // Generate vector for the message 
     for ( int i = 0; i < 3; i++) 
         messageVector[i, 0] = (message[i]) % 65; 
  
     int [, ]cipherMatrix = new int [3, 1]; 
  
     // Following function generates 
     // the encrypted vector 
     encrypt(cipherMatrix, keyMatrix, messageVector); 
  
     String CipherText = "" ; 
  
     // Generate the encrypted text from 
     // the encrypted vector 
     for ( int i = 0; i < 3; i++) 
         CipherText += ( char )(cipherMatrix[i, 0] + 65); 
  
     // Finally print the ciphertext 
     Console.Write( "Ciphertext: " + CipherText); 
} 
  
// Driver code 
public static void Main(String[] args) 
{ 
     // Get the message to be encrypted 
     String message = "ACT" ; 
  
     // Get the key 
     String key = "GYBNQKURP" ; 
  
     HillCipher(message, key); 
} 
} 
  
// This code is contributed by Rajput-Ji

输出如下：

Ciphertext: POH

以类似的方式, 你可以按照上述步骤编写用于解密加密消息的代码。

参考：

https://en.wikipedia.org/wiki/Hill_cipher

木子山

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