Last Updated : 21 Jul, 2021
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Hill cipher is a polygraphic substitution cipher based on linear algebra.Each letter is represented by a number modulo 26. Often the simple scheme A = 0, B = 1, …, Z = 25 is used, but this is not an essential feature of the cipher. To encrypt a message, each block of n letters (considered as an n-component vector) is multiplied by an invertible n × n matrix, against modulus 26. To decrypt the message, each block is multiplied by the inverse of the matrix used for encryption.
The matrix used for encryption is the cipher key, and it should be chosen randomly from the set of invertible n × n matrices (modulo 26).
Examples:
Input : Plaintext: ACT Key: GYBNQKURPOutput : Ciphertext: POH
Input : Plaintext: GFG Key: HILLMAGIC Output : Ciphertext: SWK
Encryption
We have to encrypt the message ‘ACT’ (n=3).The key is ‘GYBNQKURP’ which can be written as the nxn matrix:
The message ‘ACT’ is written as vector:
The enciphered vector is given as:
which corresponds to ciphertext of ‘POH’
Decryption
To decrypt the message, we turn the ciphertext back into a vector, then simply multiply by the inverse matrix of the key matrix (IFKVIVVMI in letters).The inverse of the matrix used in the previous example is:
For the previous Ciphertext ‘POH’:
which gives us back ‘ACT’.
Assume that all the alphabets are in upper case.
Below is the implementation of the above idea for n=3.
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
Javascript
<script>
// Javascript code to implement Hill Cipher
// Following function generates the
// key matrix for the key string
function getKeyMatrix(key,keyMatrix)
{
let k = 0;
for (let i = 0; i < 3; i++)
{
for (let j = 0; j < 3; j++)
{
keyMatrix[i][j] = (key[k]).charCodeAt(0) % 65;
k++;
}
}
}
// Following function encrypts the message
function encrypt(cipherMatrix,keyMatrix,messageVector)
{
let 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
function HillCipher(message, key)
{
// Get key matrix from the key string
let keyMatrix = new Array(3);
for(let i=0;i<3;i++)
{
keyMatrix[i]=new Array(3);
for(let j=0;j<3;j++)
keyMatrix[i][j]=0;
}
getKeyMatrix(key, keyMatrix);
let messageVector = new Array(3);
for(let i=0;i<3;i++)
{
messageVector[i]=new Array(1);
messageVector[i][0]=0;
}
// Generate vector for the message
for (let i = 0; i < 3; i++)
messageVector[i][0] = (message[i]).charCodeAt(0) % 65;
let cipherMatrix = new Array(3);
for(let i=0;i<3;i++)
{
cipherMatrix[i]=new Array(1);
cipherMatrix[i][0]=0;
}
// Following function generates
// the encrypted vector
encrypt(cipherMatrix, keyMatrix, messageVector);
let CipherText="";
// Generate the encrypted text from
// the encrypted vector
for (let i = 0; i < 3; i++)
CipherText += String.fromCharCode(cipherMatrix[i][0] + 65);
// Finally print the ciphertext
document.write(" Ciphertext: " + CipherText);
}
// Driver code
// Get the message to be encrypted
let message = "ACT";
// Get the key
let key = "GYBNQKURP";
HillCipher(message, key);
// This code is contributed by rag2127
</script>
Output:
Ciphertext: POH
In a similar way you can write the code for decrypting the encrypted message by following the steps explained above.
Reference: https://en.wikipedia.org/wiki/Hill_cipher
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