RSA algorithm (Rivest-Shamir-Adleman)

This code implements the RSA encryption and decryption algorithm. It generates random prime numbers, calculates the public and private keys, encrypts and decrypts messages using these keys.

Functionality

The code performs the following steps:

1. Generates two random prime numbers, p and q, of the specified number of bits.

2. Calculates the modulus n as the product of p and q.

3. Calculates the Euler's totient function phi as (p-1) * (q-1).

4. Finds the optimal value of e that is relatively prime to phi.

5. Displays the generated prime numbers (p and q), modulus (n), Euler's totient function (phi), and the public key (e, n).

6. Encrypts the input plain text message using the public key to obtain the ciphertext.

7. Displays the encrypted ciphertext.

8. Calculates the private key d as the modular multiplicative inverse of e modulo phi.

9. Decrypts the ciphertext using the private key to obtain the original plain text message.

10. Displays the decrypted plain text message.

Go Implementation

Run The main.go file Using Command:

go run main.go

Output

C++ Implementation

Run The RSA.cpp file Using Command:

g++ RSA.cpp -o rsa

Once the compilation process is successful, you can execute the compiled program. To run the program, use the following command:

./rsa

Output

Customization

• You can modify the number of bits for the generated prime numbers by changing the numBits variable in the solve() function.

Acknowledgments

• The code is based on the RSA algorithm for encryption and decryption.
• The Miller-Rabin primality test is used to generate random prime numbers.
• The modular exponentiation and extended Euclidean algorithm functions are adapted from standard algorithms.