Multiparty encryption and decryption Is it possible to send a single encrypted data message to multiple users so that the users receiving the message can only decrypt certain parts of the message, depending on their rights.

For example, I send a message "Hello World", User A could decrypt and receive the whole message(hello world), but user B could only decrypt a certain part and receive the message as "hello" only.
This is - in a way - Functional Encryption. 

From Wikipedia: 


  Functional encryption is a type of public-key encryption in which
  possessing a secret key allows one to learn a function of what the
  ciphertext is encrypting.


So, YES, it is possible. 

For more information this paper might prove useful.