# 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. Image Source

### 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++

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

Category: Algorithm A crazy computer and programming lover. He spend most of his time in programming, blogging and helping other programming geeks.

## 16 thoughts on “RSA Algorithm in C and C++ (Encryption and Decryption)”

1. Nicolás

Thanks for this tutorial!
I’m a bit confused, the code for encryption and decryption is all together. I think the “double m” is the variable where the decrypted message is stored, but it needs “pow(c,d)” and the variable “c” needs the message “msg” because of “c= pow(msg,e)”. If I am right, how can this be possible?

2. ARISTIDES TONDOLO

In fact, the code works correctly with current values of ‘p’ e ‘q’, but if assign other values decrypt is wrong.
I’m not understand a utility of ‘k’, too.

1. Shibli Qureshi

It is because if you use large values in p, q and e then the values you will get from them will be very large which cannot be stored in even long long int datatype.

3. An Idiot

This code does not work. Anything other than “12” will return false decryptions.

1. Neeraj Mishra Post author

You have to choose value of e and d in such a may that satisfies conditions mentioned in above article. Read the conditions properly.

4. RobbieTheK

I confirm that anything other than “12” will return false decryptions.

5. Akhilesh Pandey

The code is fine but here e is incremented in every iteration until the while condition is satisfied which to me doesn’t look appealing. I suggest you to randomly choose e such that ( e <(p-q)(q-1) ) and check for the condition and then increment e.

6. Mike

Very clear and concise! Thanks!

7. Vick

Hey really appreciate the tutorial you have set for RSA encryption. It is very useful for people like me who is just getting started in the field. However I have a small doubt, what happens when I want to increase key length to 1024 bits (pq = 128 bytes). How would i store the key and implement mathematical functions on it since the there is not a single self sufficient variable that would be able to store this long key. I am sure I will have to take it to binary operations and use arrays, but I am not experienced as much and would really help me if you could just show me a place to start 🙂

8. Manzar Ala,

Thanks for this beautiful piece of code.
I am trying to implement RSA and Blum Blum Shub algorithm to generate cryptographically secure pseuderandom bit stream.
Can you please explain me how to handle lagre primes in C.
I need to choose p,q such large that it will be 128 bits.

Thanking You!

9. dinisdineshkumar

Thanks for this tutorial!

10. DarlyB

Not ran the code but how can you decrypt (7) before it has been fully encrypted (6)?

Change:
double c = pow(msg,e);
double m = pow(c,d);
c=fmod(c,n);
m=fmod(m,n);

To:
double c = pow(msg,e);
c=fmod(c,n);
double m = pow(c,d);
m=fmod(m,n);

11. Salil Apte

It does not work for random primes assigned to p and q. Only works for current values of p and q.

12. sherif

i think the issue lies in k because it’s fixed 2 to find k you need to satisfy that d and k both integers
in the relation (d*e-1)mod(tontient)=0 .. d*e+k*tontient=1 where both d and k integers solve this by doing gcd(d,tontient) and using the equations to manipulate to reach linear equation x*e+y*tontient=1 then you can use those x,y values for k and d

13. tauseef

amazing code good job i like it

14. MarcDieter

To be fair, your code is quite simple and easy to understand. It is nice to play and fiddle around with and to test how RSA works. But you can’t use it for an actual implementation of RSA since you wouldn’t be able to store numbers in the range of typical RSA public keys (n is somewhere between 2000 and 3000 bits).
And there are a few minor flaws in your code. First of all, I wouldn’t use the type double for values which are supposed to be integers, since integers are more precise than doubles when dealing with integers.
The next thing is that your way of computing the private key d is wrong. The formula e*d = 1 + k * totient is correct but I think you misunderstood what it implies. k is arbitrary and should not be set to a fixed number like you did. What this formula actually means is
e*d = 1 + k * totient = 1 mod(totient).
Thus d is the modular multiplicative inverse of e mod(totient) an can be calculated with the extended euclidian algorithm.
The last flaw I spotted is your way of choosing e. e is supposed to be a random integer between 1 and n where n is p*q, but you are in fact not choosing it randomly but with a clear system. e will always be the smallest number which is coprime to (p-1)*(q-1). If your implementation of RSA gets public , everyone could derive some of the factors of (p-1)*(q-1) from e which would make RSA immediately less secure.
My last point: The totient doesn’t need to be (p-1)*(q-1) but only the lowest common multiple of (p-1) and (q-1). However, thats not too crucial.