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: GYBNQKURP
Output : 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 stringvoid 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 messagevoid 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 Ciphervoid 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 codeint 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 Cipherclass GFG {// Following function generates the// key matrix for the key stringstatic 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 messagestatic 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 Cipherstatic 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 codepublic 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 CipherkeyMatrix = [[0] * 3 for i in range(3)]# Generate vector for the messagemessageVector = [[0] for i in range(3)]# Generate vector for the ciphercipherMatrix = [[0] for i in range(3)]# Following function generates the# key matrix for the key stringdef 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 messagedef 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] % 26def 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 Codedef 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 Cipherusing 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 stringfunction 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 messagefunction 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 Cipherfunction 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 encryptedlet message = "ACT";// Get the keylet 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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