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法学实现希尔密码的 C++ 程序
基于线性代数，希尔密码是一种密码学中的多音替换密码。
加密信息：密钥字符串和信息字符串以矩阵形式表示。然后对它们进行乘法，然后对 26 求模。用于加密信息的关键矩阵应该有逆矩阵。
解密信息：用用于加密的逆密钥矩阵乘以加密信息，并对 26 求模，即可获得解密信息。
例如
密钥矩阵
1 0 1 2 4 0 3 5 6
矩阵形式的信息字符串“ABC”−
0 1 2
加密
乘以上述两个矩阵后，我们得到，
2 4 17
这将是加密信息“CER”
解密
密钥矩阵的逆矩阵为−
1.09091 0.227273 -0.181818 -0.545455 0.136364 0.0909091 -0.0909091 -0.227273 0.181818
现在将密钥矩阵的逆矩阵与加密信息矩阵相乘为−
0 1 2
这便是原始信息字符串“ABC”。
下面是一个实现上述示例的 C++ 程序。
算法
Begin Function getKeyMatrix() For i = 0 to 2 For j = 0 to 3 Take the elements of matrix a[i][j] as input. m[i][j] = a[i][j] done done Take the message string as user input. For i = 0 to 2 msg[i][0] = mes[i] - 65 done End Begin Function encrypt() For i = 0 to 2 For j = 0 to 0 For k = 0 to 2 en[i][j] = en[i][j] + a[i][k] * msg[k][j] Take modulo 26 for each element of the matrix obtained by multiplication and print the encrypted message. End Begin Function decrypt() Call function inversematrix() For i = 0 to 2 For j = 0 to 0 For k = 0 to 2 de[i][j] = de[i][j] + b[i][k] * en[k][j] Take modulo 26 of the multiplication to get the original message.
示例
#include<iostream>
#include<math.h>
using namespace std;
float en[3][1], de[3][1], a[3][3], b[3][3], msg[3][1], m[3][3];
void getKeyMatrix() { //get key and message from user
int i, j;
char mes[3];
cout<<"Enter 3x3 matrix for key (should have inverse):\n";
for(i = 0; i < 3; i++)
for(j = 0; j < 3; j++) {
cin>>a[i][j];
m[i][j] = a[i][j];
}
cout<<"\nEnter a string of 3 letter(use A through Z): ";
cin>>mes;
for(i = 0; i < 3; i++)
msg[i][0] = mes[i] - 65;
}
void encrypt() { //encrypts the message
int i, j, k;
for(i = 0; i < 3; i++)
for(j = 0; j < 1; j++)
for(k = 0; k < 3; k++)
en[i][j] = en[i][j] + a[i][k] * msg[k][j];
cout<<"\nEncrypted string is: ";
for(i = 0; i < 3; i++)
cout<<(char)(fmod(en[i][0], 26) + 65); //modulo 26 is taken for each element of the matrix obtained by multiplication
}
void inversematrix() { //find inverse of key matrix
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 = m[i][k];
q = m[k][k];
for(j = 0; j < 3; j++) {
if(i != k) {
m[i][j] = m[i][j]*q - p*m[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] / m[i][i];
cout<<"\n\nInverse Matrix is:\n";
for(i = 0; i < 3; i++) {
for(j = 0; j < 3; j++)
cout<<b[i][j]<<" ";
cout<<"\n";
}
}
void decrypt() { //decrypt the message
int i, j, k;
inversematrix();
for(i = 0; i < 3; i++)
for(j = 0; j < 1; j++)
for(k = 0; k < 3; k++)
de[i][j] = de[i][j] + b[i][k] * en[k][j];
cout<<"\nDecrypted string is: ";
for(i = 0; i < 3; i++)
cout<<(char)(fmod(de[i][0], 26) + 65); //modulo 26 is taken to get the original message
cout<<"\n";
}
int main() {
getKeyMatrix();
encrypt();
decrypt();
}输出
Enter 3x3 matrix for key (should have inverse): 1 0 1 2 4 0 3 5 6 Enter a string of 3 letter(use A through Z): ABC Encrypted string is: CER Inverse Matrix is: 1.09091 0.227273 -0.181818 -0.545455 0.136364 0.0909091 -0.0909091 -0.227273 0.181818 Decrypted string is: ABC
更新于： 30-Jul-2019
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