C++ Program to Implement the Hill Cypher

Based on linear algebra Hill cipher is a polygraphic substitution cipher in cryptography.

To encrypt message: The key string and message string are represented as matrix form. They are multiplied then, against modulo 26. The key matrix should have inverse to decrypt the message.

To decrypt message: The encrypted message is multiplied by inverse key matrix used for encryption against modulo 26 to get decrypt message.

For example

Key matrix

1 0 1
2 4 0
3 5 6

Message string ‘ABC’ in matrix form −

0
1
2

For encryption

After multiplying above two matrices we get,

2
4
17

Which will be the encrypted message ‘CER’

For decryption

Inverse of key matrix is −

1.09091 0.227273 -0.181818
-0.545455 0.136364 0.0909091
-0.0909091 -0.227273 0.181818

Now after multiplying the inverse matrix of key matrix with encrypted message matrix is −

0
1
2

Which is the original message string is ‘ABC’.

Here, is a C++ program to implement above example.

Algorithms

Begin
Function getKeyMatrix()
   For i = 0 to 2
      For j = 0 to 3
      Take the elements of matrix a[i][j] as input.
         m[i][j] = a[i][j]
      done
   done
   Take the message string as user input.
   For i = 0 to 2
      msg[i][0] = mes[i] - 65
   done
End
Begin
Function encrypt()
   For i = 0 to 2
      For j = 0 to 0
         For k = 0 to 2
            en[i][j] = en[i][j] + a[i][k] * msg[k][j]
   Take modulo 26 for each element of the matrix obtained by multiplication and print the encrypted message.
End
Begin
Function decrypt()
   Call function inversematrix()
   For i = 0 to 2
      For j = 0 to 0
         For k = 0 to 2
            de[i][j] = de[i][j] + b[i][k] * en[k][j]
Take modulo 26 of the multiplication to get the original message.

Example

#include<iostream>
#include<math.h>
using namespace std;
float en[3][1], de[3][1], a[3][3], b[3][3], msg[3][1], m[3][3];
void getKeyMatrix() { //get key and message from user
   int i, j;
   char mes[3];
   cout<<"Enter 3x3 matrix for key (should have inverse):\n";
   for(i = 0; i < 3; i++)
   for(j = 0; j < 3; j++) {
      cin>>a[i][j];
      m[i][j] = a[i][j];
   }
   cout<<"\nEnter a string of 3 letter(use A through Z): ";
   cin>>mes;
   for(i = 0; i < 3; i++)
   msg[i][0] = mes[i] - 65;
}
void encrypt() { //encrypts the message
   int i, j, k;
   for(i = 0; i < 3; i++)
   for(j = 0; j < 1; j++)
   for(k = 0; k < 3; k++)
   en[i][j] = en[i][j] + a[i][k] * msg[k][j];
   cout<<"\nEncrypted string is: ";
   for(i = 0; i < 3; i++)
   cout<<(char)(fmod(en[i][0], 26) + 65); //modulo 26 is taken for each element of the matrix obtained by multiplication
}
void inversematrix() { //find inverse of key matrix
   int i, j, k;
   float p, q;
   for(i = 0; i < 3; i++)
   for(j = 0; j < 3; j++) {
      if(i == j)
         b[i][j]=1;
      else
         b[i][j]=0;
   }
   for(k = 0; k < 3; k++) {
      for(i = 0; i < 3; i++) {
         p = m[i][k];
         q = m[k][k];
         for(j = 0; j < 3; j++) {
            if(i != k) {
               m[i][j] = m[i][j]*q - p*m[k][j];
               b[i][j] = b[i][j]*q - p*b[k][j];
            }
         }
      }
   }
   for(i = 0; i < 3; i++)
   for(j = 0; j < 3; j++)
   b[i][j] = b[i][j] / m[i][i];
   cout<<"\n\nInverse Matrix is:\n";
   for(i = 0; i < 3; i++) {
      for(j = 0; j < 3; j++)
      cout<<b[i][j]<<" ";
      cout<<"\n";
   }
}
void decrypt() { //decrypt the message
   int i, j, k;
   inversematrix();
   for(i = 0; i < 3; i++)
   for(j = 0; j < 1; j++)
   for(k = 0; k < 3; k++)
   de[i][j] = de[i][j] + b[i][k] * en[k][j];
   cout<<"\nDecrypted string is: ";
   for(i = 0; i < 3; i++)
   cout<<(char)(fmod(de[i][0], 26) + 65); //modulo 26 is taken to get the original message
   cout<<"\n";
}
int main() {
   getKeyMatrix();
   encrypt();
   decrypt();
}

Output

Enter 3x3 matrix for key (should have inverse):
1
0
1
2
4
0
3
5
6

Enter a string of 3 letter(use A through Z): ABC

Encrypted string is: CER

Inverse Matrix is:
1.09091 0.227273 -0.181818
-0.545455 0.136364 0.0909091
-0.0909091 -0.227273 0.181818

Decrypted string is: ABC