# Write a C Program to Implement the Hill Fair Substitution Technique

#### Aim:

To write a C Program to Implement the Simple Substitution Technique Named Hill Fair.

#### Algorithm:

1. Hill cipher is a polygraphic substitution cipher based on linear algebra.Each letter is represented by a number modulo 26.
2. Often the simple scheme A = 0, B = 1, â€¦, Z = 25 is used, but this is not an essential feature of the cipher.
3. To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n Ã— n matrix, against modulus 26.
4. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
5. The matrix used for encryption is the cipher key, and it should be chosen randomly from the set of invertible n Ã— n matrices
6. End.

#### Program:

```#include<stdio.h>
#include<math.h>
float encrypt[3][1], decrypt[3][1], a[3][3], b[3][3], mes[3][1], c[3][3];
void encryption();
void decryption();
void getKeyMessage();
void inverse();
void main() {
getKeyMessage();
encryption();
decryption();
}
void encryption() {
int i, j, k;
for(i = 0; i < 3; i++)
for(j = 0; j < 1; j++)
for(k = 0; k < 3; k++)
encrypt[i][j] = encrypt[i][j] + a[i][k] * mes[k][j];
printf("\nEncrypted string is: ");
for(i = 0; i < 3; i++)
printf("%c", (char)(fmod(encrypt[i][0], 26) + 97));
}
void decryption() {
int i, j, k;
inverse();
for(i = 0; i < 3; i++)
for(j = 0; j < 1; j++)
for(k = 0; k < 3; k++)
decrypt[i][j] = decrypt[i][j] + b[i][k] * encrypt[k][j];
printf("\nDecrypted string is: ");
for(i = 0; i < 3; i++)
printf("%c", (char)(fmod(decrypt[i][0], 26) + 97));
printf("\n");
}
void getKeyMessage() {
int i, j;
char msg[3];
printf("Enter 3x3 matrix for key :\n");
for(i = 0; i < 3; i++)
for(j = 0; j < 3; j++) {
scanf("%f", &a[i][j]);
c[i][j] = a[i][j];
}
printf("\nEnter a 3 letter string: ");
scanf("%s", msg);
for(i = 0; i < 3; i++)
mes[i][0] = msg[i] - 97;
}
void inverse() {
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 = c[i][k];
q = c[k][k];
for(j = 0; j < 3; j++) {
if(i != k) {
c[i][j] = c[i][j]*q - p*c[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] / c[i][i];
printf("\n\nInverse Matrix is:\n");
for(i = 0; i < 3; i++) {
for(j = 0; j < 3; j++)
printf("%d ", b[i][j]);
printf("\n");
}
}```

#### Execution:

```Input:
6 24 1 13 16 10 20 17 15 act

Output:

Enter 3x3 matrix for key :

Enter a 3 letter string:
Encrypted string is: poh

Inverse Matrix is:
4197934 2147483640 2147483637
-2144388608 2147483636 2147483637
-2144388608 2147483636 2147483637

Decrypted string is: act```

#### Result:

Thus implementation of the Hill Fair program was executed Successfully.