For coding in cryptography you are free to use openssl direct commands or any C or C++ program a) Write a C/C++ program to implement RSA trapdoor permutation. Your program should do the following 1. Implement a routine/function to generate RSA key pair (public key and secret key). You are free to use any method for generating the keys 2. Implement the functionality for RSA and RSA inverse operations 3. For a given plain text input, your program should execute the RSA operation with public key and output the result 4. Given the output of RSA operation (from step-c above), your program should execute the RSA inverse operation with the secret key and output the original plain text b). Enhance the C/C++ program above to add RSA signature capabilities. Your program should also do the following 1. Derive a new set of public and secret keys (you can use the key generation routine from problem 1 above to generate new set of public and secret keys for signature operations) 2. Use the functionality of RSA and RSA inverse operations (developed for problem-1 above) to perform signing and verification algorithms