Question

This assignment is a rsa project. please help me with it? Generate two prime numbers at least 1 million. These are p and q. n = pxq.

Show how and show p and q

* Find d and e . Show how and show d and e.

* Encrypt message 100. use the above results. show this number. Programming language! C++

Please add some comments to the program. Thank you

Answer 1

Code:

#include<iostream>
#include<math.h>

using namespace std;

int gcd(int a,int b){ //to fing gcd of two numbers
   int t; // variable to store remainder
   while(1){ // infinite loop
       t=a%b; // finding remainder of two numbers
       if(t==0){ // if remainder is zero then we found gcd
           return b;
       }
       a=b;
       b=t;
   }
}
int main(){

double p=103; // two prime numbers
double q=107;
double n=p*q; // calculating n value
double phi=(p-1)*(q-1); //calculating phi value
double e=2;
while (e<phi){ // finding e value where e<n such that gcd(e,phi)=1
   if(gcd(e,phi)==1){ // if gcd of two numbers is 1 then store i value into e
       break;
   }
   else{
       e++;
   }
}
double d1=1/e; // claculating d value
double d=fmod(d1,phi);

double message=100;
double c=pow(message,e); //cypher text or encrypted message variable
double m=pow(c,d); //decrypt variable to decrypt encrypted message
c=fmod(c,n);
m=fmod(m,n);

cout<<"p value: "<<p<<endl;
cout<<"q value: "<<q<<endl;
cout<<"e value: "<<e<<endl;
cout<<"d value: "<<d<<endl;
cout<<"n value: "<<n<<endl;
cout<<"phi value: "<<phi<<endl;
cout<<"e value: "<<e<<endl;
cout<<"d value: "<<d<<endl;
cout<<"Original Message: "<<message<<endl;
cout<<"Encrypted message: "<<c<<endl;
cout<<"Decrypted message: "<<m<<endl;
}

Output:

p value: 103 q value: 107 e value: 5 d value: 0.2 n value: 11021 phi value: 10812 e value: 5 d value: 0.2 Original Message: 100 Encrypted message: 7482 Decrypted message: 100