学步园

密钥生成：

公钥e,n放在publicKey.txt中，私钥d,p,q放在private.txt中

因为要按字符（0-255）处理，所以素数表从17开始，以确保n大于256

#include <iostream>
#include <fstream>
#include <time.h>
#include <cstdlib>
using namespace std;
//素筛法得出的大素数表
long long int primeTable[162]={17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127
                               ,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233
                               ,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353
                               ,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467
                               ,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607
                               ,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739
                               ,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877
                               ,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997
                              };

int gcd(int a,int b)
{
    int temp;
    if(a<b)
    {
        temp=a;
        a=b;
        b=temp;
    }

    int r=1;
    while(r)
    {
        r=a%b;
        a=b;
        b=r;
    }
    return a;
}

long long int ExtendedEuclid( long long int f,long long int d ,long long int *result)
{
    long long int x1,x2,x3,y1,y2,y3,t1,t2,t3,q;
    x1 = y2 = 1;
    x2 = y1 = 0;
    x3 = ( f>=d )?f:d;
    y3 = ( f>=d )?d:f;

    while( 1 )
    {
        if ( y3 == 0 )
        {
            *result = x3; /* 两个数不互素则result为两个数的最大公约数，此时返回值为零 */
            //if(*result<0)*result=*result+x3;
            return 0;
        }
        if ( y3 == 1 )
        {
            *result = y2; /* 两个数互素则resutl为其乘法逆元，此时返回值为1 */
            //if(*result<0)*result=*result+y2;
            return 1;
        }

        q = x3/y3;
        t1 = x1 - q*y1;
        t2 = x2 - q*y2;
        t3 = x3 - q*y3;
        x1 = y1;
        x2 = y2;
        x3 = y3;
        y1 = t1;
        y2 = t2;
        y3 = t3;
    }
}

int main()
{
    ofstream out1("publicKey.txt");
    ofstream out2("private.txt");

    long long int p,q,d,e,n;

    srand(time(NULL));
    int index1,index2;
    index1=rand()%162;
    p=primeTable[index1];
    //确保p,q互异
    index2=rand()%162;
    while(index2==index1)
    {
        index2=rand()%162;
    }
    q=primeTable[index2];
    n=p*q;
    long long int fai_n=(p-1)*(q-1);
    long long int temp;
    while(!(temp>0 && temp<fai_n && gcd(fai_n,temp)==1))
    {
        temp=rand()%fai_n;
    }
    e=temp;
    long long int _e;
    ExtendedEuclid(e,fai_n,&_e);
    d=_e%fai_n;
    if(d<0)d=d+fai_n;

    out1<<e<<" "<<n;
    out2<<d<<" "<<p<<" "<<q;

    out1.close();
    out2.close();

    return 0;
}

加密解密算法：

因为是按字节处理，所以可以加密解密任何格式文件，默认的是明文为p.txt，加密结果放在encode.txt中，解密结果放在decode.txt中

//RSA
#include <iostream>
#include <fstream>
#include <cstdlib>
using namespace std;

long long int modexp(long long int a,long long int b,long long int n)
{
    long long  int ret=1;
    long long  int tmp=a;
    while(b)
    {
        if(b&0x1) ret=ret*tmp%n;
        tmp=tmp*tmp%n;
        b>>=1;
    }
    return ret;
}

int main()
{

    long long int p,q,n,e,d;
    ifstream in1("publicKey.txt");
    ifstream in2("private.txt");
    in1>>e>>n;
    in2>>d>>p>>q;
    in1.close();
    in2.close();

    //cout<<e<<" "<<n<<" "<<d<<" "<<p<<" "<<q<<endl;
//encode
    ifstream pinput("p.txt",ios::binary);
    ofstream outc("encode.txt");
    unsigned char temp;
    while(pinput.read((char*)&temp,1))
    {
        outc<<modexp(temp,e,n)<<" ";
    }
    pinput.close();
    outc.close();
//decode
    long long int c;
    ifstream cinput("encode.txt");
    ofstream outr("decode.txt",ios::binary);
    long long int result;
    while(cinput>>c)
    {
        result=modexp(c,d,n);
        outr.write((char*)&result,1);
    }
    cinput.close();
    outr.close();
    return 0;
}