本文概述

• C ++
• Java
• Python3
• C#

希尔密码是一种基于线性代数的测谎替换密码。每个字母都由数字模26表示。通常使用简单方案A = 0, B = 1, …, Z = 25, 但这并不是密码。为了加密消息, 将n个字母的每个块(被视为n分量矢量)乘以可逆n×n矩阵(模数为26)。要解密消息, 将每个块乘以用于矩阵的逆。加密。
用于加密的矩阵是密码密钥, 应从一组可逆的n×n矩阵(模数为26)中随机选择。
例子：

Input: Plaintext: ACTKey: GYBNQKURPOutput : Ciphertext: POH

Input: Plaintext: GFGKey: HILLMAGIC Output : Ciphertext: SWK

加密
我们必须对消息" ACT"(n = 3)进行加密。密钥为" GYBNQKURP", 可以将其写为nxn矩阵：

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消息" ACT"被写为矢量：

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加密的向量为：

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对应于" POH"的密文
解密
为了解密消息, 我们将密文转换回向量, 然后简单地乘以密钥矩阵的逆矩阵(字母为IFKVIVVMI)。上例中使用的矩阵的逆为：

文章图片
对于先前的密文" POH"：

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这使我们返回" ACT"。
假定所有字母均大写。
以下是n = 3时上述想法的实现。
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 CipherkeyMatrix = [[ 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] % 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 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

输出如下：

Ciphertext: POH

以类似的方式, 你可以按照上述步骤编写用于解密加密消息的代码。
【希尔密码指南和代码实现详解】参考：
https://en.wikipedia.org/wiki/Hill_cipher

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