Attacking unuauthenticated RSA
The attack is even more simple with RSA than with symmetric keys, because the asymmetric encryption key is assumed to be public.

Let me tell you a story involving Alice, Bob and Mallory :). Alice wants to send a message to Bob using RSA. 


Alice encrypts the message using Bob's public key and sends it
Mallory performs a Man-In-The-Middle attack, and encrypts another message using Bob's public key (as it's public)
Bob received the new message thinking it comes from Alice, as there's no origin authentication.