密码学原理精解【5】

移位密码

概述

$$\begin{gathered} 以z_{26}运算为例,k为密钥 \\ 加密：e_k(x)=(x+k)mod26 \\ 解密：d_k(x)=(x-k)mod26 \end{gathered}$$
实际中，我们使用$Z_{256}$运算（群的加法运算）

代码

#include <iostream>
#include <fstream>
#include<cstring>using namespace std;int main(){//加密写入ofstream fileOut;char helloTxt[]{"&9*&((@#$)((%#^^hello,world!\n123456789"};int txtLen{strlen(helloTxt)};fileOut.open("hello.data",ios::binary);int k=77;for(int i=0;i<txtLen;i++){fileOut<<char((helloTxt[i]+k) %256);}fileOut.close();//解密读出ifstream fileIn;char helloChar;fileIn.open("hello.data",ios::binary);while (fileIn.get(helloChar)){cout<<char((helloChar-k) %256);}fileIn.close();}

&9*&((@#$)((%#^^hello,world!
123456789
Process returned 0 (0x0)   execution time : 0.120 s
Press any key to continue.

希尔密码($Z_{256}$)

待加密长度被3整除

#include <iostream>
#include <fstream>
#include<cstring>
#include "e:/eigen/Eigen/Dense"using namespace std;
using namespace Eigen;int main(){//加密写入ofstream fileOut;char helloTxt[]{"123456789$#%(&Yoiu9"};int txtLen{strlen(helloTxt)};fileOut.open("hello.data",ios::binary);for(int i=0;i<txtLen;i+=3){Matrix<int,1,3> x{helloTxt[i],helloTxt[i+1],helloTxt[i+2]};Matrix<int,3,3> k{{16,91,215}, {171,253,50}, {8,186,121}};Matrix<int,1,3>  e_data=x*k;for (int j=0;j<3;j++){fileOut<<char(int(e_data[j]) % 256);}}fileOut.close();//解密读出ifstream fileIn;char helloChar;fileIn.open("hello.data",ios::binary);char txtBuffer[4];for(int i=0;i<txtLen;i+=3){fileIn.read(txtBuffer,3);Matrix<int,1,3> y{txtBuffer[0],txtBuffer[1],txtBuffer[2]};Matrix<int,3,3> k_ni{{9,11, 227},{101 ,152 ,37},{134 ,248 ,127}};Matrix<int,1,3> e_data=y*k_ni;for (int j=0;j<3;j++){cout<<char(int(e_data[j]) % 256);}}fileIn.close();}

待加密长度不一定被3整除

继续完善程序，针对加密长度不一定是3的倍数。

#include <iostream>
#include <fstream>
#include<cstring>
#include "e:/eigen/Eigen/Dense"using namespace std;
using namespace Eigen;int main(){//加密写入ofstream fileOut;char helloTxt[]{"123456789p"};int txtLen{strlen(helloTxt)};fileOut.open("hello.data",ios::binary);for(int i=0;i<txtLen;i+=3){if ((txtLen-i)==1){Matrix<int,1,3> x{helloTxt[i],0,0};Matrix<int,3,3> k{{16,91,215}, {171,253,50}, {8,186,121}};Matrix<int,1,3>  e_data=x*k;for (int j=0;j<3;j++){fileOut<<char(int(e_data[j]) % 256);}}else if ((txtLen-i)==2){Matrix<int,1,3> x{helloTxt[i],helloTxt[i+1],0};Matrix<int,3,3> k{{16,91,215}, {171,253,50}, {8,186,121}};Matrix<int,1,3>  e_data=x*k;for (int j=0;j<3;j++){fileOut<<char(int(e_data[j]) % 256);}}else{Matrix<int,1,3> x{helloTxt[i],helloTxt[i+1],helloTxt[i+2]};Matrix<int,3,3> k{{16,91,215}, {171,253,50}, {8,186,121}};Matrix<int,1,3>  e_data=x*k;for (int j=0;j<3;j++){fileOut<<char(int(e_data[j]) % 256);}}}fileOut.close();//解密读出ifstream fileIn;char helloChar;fileIn.open("hello.data",ios::binary);char txtBuffer[4];for(int i=0;i<txtLen;i+=3){fileIn.read(txtBuffer,3);Matrix<int,1,3> y{txtBuffer[0],txtBuffer[1],txtBuffer[2]};Matrix<int,3,3> k_ni{{9,11, 227},{101 ,152 ,37},{134 ,248 ,127}};Matrix<int,1,3> e_data=y*k_ni;char d_data[3];for (int j=0;j<3;j++){d_data[j]=char(int(e_data[j]) % 256);}if ((txtLen-i)==2 ){cout<<d_data[0]<<d_data[1];}else if((txtLen-i)==1 ){cout<<d_data[0];}else{for (int j=0;j<3;j++){cout<<d_data[j];}}}fileIn.close();}

123456789p
Process returned 0 (0x0)   execution time : 0.376 s
Press any key to continue.

加解密文件

#include <iostream>
#include <fstream>
#include<cstring>
#include "e:/eigen/Eigen/Dense"using namespace std;
using namespace Eigen;int main(){//加密写入ifstream  picfs("test.png", ios::ate|ios::binary);// 获取文件大小std::streampos picSize = picfs.tellg();picfs.close(); // 关闭文件std::cout << "文件长度: " << picSize << " 字节" << std::endl;ifstream  ifs("test.png", ios::in|ios::binary);char *picData=new char[picSize+1];for (int i=0;i<picSize;i++){ifs.get(picData[i]);}ifs.close();int txtLen{picSize};ofstream  fileOut;fileOut.open("pic.dat",ios::binary);for(int i=0;i<txtLen;i+=3){if ((txtLen-i)==1){Matrix<int,1,3> x{picData[i],0,0};Matrix<int,3,3> k{{16,91,215}, {171,253,50}, {8,186,121}};Matrix<int,1,3>  e_data=x*k;for (int j=0;j<3;j++){fileOut<<char(int(e_data[j]) % 256);}}else if ((txtLen-i)==2){Matrix<int,1,3> x{picData[i],picData[i+1],0};Matrix<int,3,3> k{{16,91,215}, {171,253,50}, {8,186,121}};Matrix<int,1,3>  e_data=x*k;for (int j=0;j<3;j++){fileOut<<char(int(e_data[j]) % 256);}}else{Matrix<int,1,3> x{picData[i],picData[i+1],picData[i+2]};Matrix<int,3,3> k{{16,91,215}, {171,253,50}, {8,186,121}};Matrix<int,1,3>  e_data=x*k;for (int j=0;j<3;j++){fileOut<<char(int(e_data[j]) % 256);}}}fileOut.close();//解密读出ofstream deFileOut;deFileOut.open("test_d.png",ios::binary);ifstream fileIn;char helloChar;fileIn.open("pic.dat",ios::binary);char txtBuffer[4];for(int i=0;i<txtLen;i+=3){fileIn.read(txtBuffer,3);Matrix<int,1,3> y{txtBuffer[0],txtBuffer[1],txtBuffer[2]};Matrix<int,3,3> k_ni{{9,11, 227},{101 ,152 ,37},{134 ,248 ,127}};Matrix<int,1,3> e_data=y*k_ni;char d_data[3];for (int j=0;j<3;j++){d_data[j]=char(int(e_data[j]) % 256);}if ((txtLen-i)==2 ){deFileOut<<d_data[0]<<d_data[1];}else if((txtLen-i)==1 ){deFileOut<<d_data[0];}else{for (int j=0;j<3;j++){deFileOut<<d_data[j];}}}deFileOut.close();fileIn.close();delete[] picData;}