El cifrado de Hill es un cifrado de sustitución poligráfico basado en álgebra lineal. Cada letra está representada por un número módulo 26. A menudo se usa el esquema simple A = 0, B = 1, …, Z = 25, pero esta no es una característica esencial de el cifrado Para cifrar un mensaje, cada bloque de n letras (considerado como un vector de n componentes) se multiplica por una array invertible n × n, contra módulo 26. Para descifrar el mensaje, cada bloque se multiplica por la inversa de la array utilizada para encriptación
La array utilizada para el cifrado es la clave de cifrado, y debe elegirse aleatoriamente del conjunto de arrays invertibles n × n (módulo 26).
Ejemplos:
Input : Plaintext: ACT
Key: GYBNQKURP
Output : Ciphertext: POH
Input : Plaintext: GFG
Key: HILLMAGIC
Output : Ciphertext: SWK
Cifrado
Tenemos que cifrar el mensaje ‘ACT’ (n=3). La clave es ‘GYBNQKURP’, que se puede escribir como la array nxn:
El mensaje ‘ACT’ se escribe como vector:
El vector cifrado se da como:
que corresponde al texto cifrado de ‘POH’
Descifrado
Para descifrar el mensaje, volvemos a convertir el texto cifrado en un vector, luego simplemente multiplicamos por la array inversa de la array clave (IFKVIVVMI en letras). La inversa de la array utilizada en el ejemplo anterior es:
Para el texto cifrado anterior ‘POH’:
lo que nos devuelve ‘ACT’.
Suponga que todos los alfabetos están en mayúsculas.
A continuación se muestra la implementación de la idea anterior para 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>
Producción:
Ciphertext: POH
De manera similar, puede escribir el código para descifrar el mensaje cifrado siguiendo los pasos explicados anteriormente.
Referencia: https://en.wikipedia.org/wiki/Hill_cipher
Publicación traducida automáticamente
Artículo escrito por DamanAnand y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA