RSA Algorithm in C and C++ (Encryption and Decryption)

Here you will learn about RSA algorithm in C and C++.

RSA Algorithm is used to encrypt and decrypt data in modern computer systems and other electronic devices. RSA algorithm is an asymmetric cryptographic algorithm as it creates 2 different keys for the purpose of encryption and decryption. It is public key cryptography as one of the keys involved is made public. RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman who first publicly described it in 1978.

RSA makes use of prime numbers (arbitrary large numbers) to function. The public key is made available publicly (means to everyone) and only the person having the private key with them can decrypt the original message.

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Working of RSA Algorithm

RSA involves use of public and private key for its operation. The keys are generated using the following steps:-

1. Two prime numbers are selected as p and q
2. n = pq which is the modulus of both the keys.
3. Calculate totient = (p-1)(q-1)
4. Choose e such that e > 1 and coprime to totient which means gcd (e, totient) must be equal to 1, e is the public key
5. Choose d such that it satisfies the equation de = 1 + k (totient), d is the private key not known to everyone.
6. Cipher text is calculated using the equation c = m^e mod n where m is the message.
7. With the help of c and d we decrypt message using equation m = c^d mod n where d is the private key.

Note: If we take the two prime numbers very large it enhances security but requires implementation of Exponentiation by squaring algorithm and square and multiply algorithm for effective encryption and decryption. For simplicity the program is designed with relatively small prime numbers.

Below is the implementation of this algorithm in C and C++.

Program for RSA Algorithm in C

//Program for RSA asymmetric cryptographic algorithm
//for demonstration values are relatively small compared to practical application

#include<stdio.h>
#include<math.h>

//to find gcd
int gcd(int a, int h)
{
    int temp;
    while(1)
    {
        temp = a%h;
        if(temp==0)
        return h;
        a = h;
        h = temp;
    }
}

int main()
{
    //2 random prime numbers
    double p = 3;
    double q = 7;
    double n=p*q;
    double count;
    double totient = (p-1)*(q-1);

    //public key
    //e stands for encrypt
    double e=2;

    //for checking co-prime which satisfies e>1
    while(e<totient){
    count = gcd(e,totient);
    if(count==1)
        break;
    else
        e++;
    }

    //private key
    //d stands for decrypt
    double d;

    //k can be any arbitrary value
    double k = 2;

    //choosing d such that it satisfies d*e = 1 + k * totient
    d = (1 + (k*totient))/e;
    double msg = 12;
    double c = pow(msg,e);
    double m = pow(c,d);
    c=fmod(c,n);
    m=fmod(m,n);

    printf("Message data = %lf",msg);
    printf("\np = %lf",p);
    printf("\nq = %lf",q);
    printf("\nn = pq = %lf",n);
    printf("\ntotient = %lf",totient);
    printf("\ne = %lf",e);
    printf("\nd = %lf",d);
    printf("\nEncrypted data = %lf",c);
    printf("\nOriginal Message Sent = %lf",m);

    return 0;
}

Program for RSA Algorithm in C++

//Program for RSA asymmetric cryptographic algorithm
//for demonstration values are relatively small compared to practical application

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

using namespace std;

//to find gcd
int gcd(int a, int h)
{
    int temp;
    while(1)
    {
        temp = a%h;
        if(temp==0)
        return h;
        a = h;
        h = temp;
    }
}

int main()
{
    //2 random prime numbers
    double p = 3;
    double q = 7;
    double n=p*q;
    double count;
    double totient = (p-1)*(q-1);

    //public key
    //e stands for encrypt
    double e=2;

    //for checking co-prime which satisfies e>1
    while(e<totient){
    count = gcd(e,totient);
    if(count==1)
        break;
    else
        e++;
    }

    //private key
    //d stands for decrypt
    double d;

    //k can be any arbitrary value
    double k = 2;

    //choosing d such that it satisfies d*e = 1 + k * totient
    d = (1 + (k*totient))/e;
    double msg = 12;
    double c = pow(msg,e);
    double m = pow(c,d);
    c=fmod(c,n);
    m=fmod(m,n);

    cout<<"Message data = "<<msg;
    cout<<"\n"<<"p = "<<p;
    cout<<"\n"<<"q = "<<q;
    cout<<"\n"<<"n = pq = "<<n;
    cout<<"\n"<<"totient = "<<totient;
    cout<<"\n"<<"e = "<<e;
    cout<<"\n"<<"d = "<<d;
    cout<<"\n"<<"Encrypted data = "<<c;
    cout<<"\n"<<"Original Message sent = "<<m;

    return 0;
}

Output

This article is submitted by Rahul Maheshwari. You can connect with him on facebook.

Comment below if you have any queries related to above program for rsa algorithm in C and C++.

The post RSA Algorithm in C and C++ (Encryption and Decryption) appeared first on The Crazy Programmer.