C++ Program to Implement the RSA Algorithm

RSA is an asymmetric cryptography algorithm which works on two keys-public key and private key.

Algorithms

Begin
1. Choose two prime numbers p and q.
2. Compute n = p*q.
3. Calculate phi = (p-1) * (q-1).
4. Choose an integer e such that 1 < e < phi(n) and gcd(e, phi(n)) = 1; i.e., e and phi(n) are coprime.
5. Calculate d as d ≡ e−1 (mod phi(n)); here, d is the modular multiplicative inverse of e modulo phi(n).
6. For encryption, c = me mod n, where m = original message.
7. For decryption, m = c d mod n.
End

Example

Live Demo

#include<iostream>
#include<math.h>
using namespace std;
// find gcd
int gcd(int a, int b) {
int t;
while(1) {
t= a%b;
if(t==0)
return b;
a = b;
b= t;
}
}
int main() {
//2 random prime numbers
double p = 13;
double q = 11;
double n=p*q;//calculate n
double track;
double phi= (p-1)*(q-1);//calculate phi
//public key
//e stands for encrypt
double e=7;
//for checking that 1 < e < phi(n) and gcd(e, phi(n)) = 1; i.e., e and phi(n) are coprime.
while(e<phi) {
track = gcd(e,phi);
if(track==1)
break;
else
e++;
}
//private key
//d stands for decrypt
//choosing d such that it satisfies d*e = 1 mod phi
double d1=1/e;
double d=fmod(d1,phi);
double message = 9;
double c = pow(message,e); //encrypt the message
double m = pow(c,d);
c=fmod(c,n);
m=fmod(m,n);
cout<<"Original Message = "<<message;
cout<<"\n"<<"p = "<<p;
cout<<"\n"<<"q = "<<q;
cout<<"\n"<<"n = pq = "<<n;
cout<<"\n"<<"phi = "<<phi;
cout<<"\n"<<"e = "<<e;
cout<<"\n"<<"d = "<<d;
cout<<"\n"<<"Encrypted message = "<<c;
cout<<"\n"<<"Decrypted message = "<<m;
return 0;
}

Output

p = 13
q = 11
n = pq = 143
phi = 120
e = 7
d = 0.142857
Original Message = 9

Encrypted message = 48
Decrypted message = 9