Based on linear algebra Hill cipher is a polygraphic substitution cipher in cryptography.
To encrypt a message: The key string and message string are represented as a matrix form. They are multiplied then, against modulo 26. The key matrix should have an inverse to decrypt the message.
To decrypt a message: The encrypted message is multiplied by inverse key matrix used for encryption against modulo 26 to get decrypt the message.
#include "stdc++.h"
#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();
}