Q3. Compromising Public Key Cryptography

Assume that Jenny and Kelly are secretly communicating using an RSA-based public-key cryptosystem. Alex is an intelligent guy who is intercepting the communications between Jenny and Kelly. Say, Alex has intercepted a ciphertext C that Kelly created by encrypting a message M using Jenny’s public key and was being sent to Jenny. As Alex does not know Jenny’s private key, he plans to do a trick to find out M. Alex challenges Jenny that he can decrypt the message M if Jenny agrees to encrypt another message (any message except C) using her private key.

You are expected to explain if it is possible for Alex to find M using the trick? Explain with a numerical example for each step.