k is arbitrary and should not be set to a fixed number like you did. The formula e*d = 1 + k * totient is correct but I think you misunderstood what it implies. The next thing is that your way of computing the private key d is wrong. 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. 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 20 bits).Īnd there are a few minor flaws in your code. It is nice to play and fiddle around with and to test how RSA works. To be fair, your code is quite simple and easy to understand. Printf(' Original Message Sent = %lf',m) Ĭout<<' '<<'Original Message sent = '<1 for demonstration values are relatively small compared to practical application Program for RSA asymmetric cryptographic algorithm For simplicity the program is designed with relatively small prime numbers.īelow is the implementation of this algorithm in C and C++. 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.

With the help of c and d we decrypt message using equation m = c^d mod n where d is the private key.

Cipher text is calculated using the equation c = m^e mod n where m is the message.

Choose d such that it satisfies the equation de = 1 + k (totient), d is the private key not known to everyone.

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.

n = pq which is the modulus of both the keys.

Two prime numbers are selected as p and q.The keys are generated using the following steps:.

RSA involves use of public and private key for its operation. 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. RSA makes use of prime numbers (arbitrary large numbers) to function. RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman who first publicly described it in 1978. It is public key cryptography as one of the keys involved is made public. RSA algorithm is an asymmetric cryptographic algorithm as it creates 2 different keys for the purpose of encryption and decryption. RSA Algorithm is used to encrypt and decrypt data in modern computer systems and other electronic devices. Here you will learn about RSA algorithm in C and C++.

Python decrypt rsa with c d and n