the main question is, after the enctyped message that was encrypted using Alice's public key eariler is re-encrypted using the re-encryption key generated from Alice's private key and Bob's public key, how can Bob use his private key to decrypt the re-encrypted message to get the original one? What makes this happen? 

Could anyone please give a gentle introduction on how this proxy re-encryption works? I know there are many papers about it and I have tried to understand them but still cannot make anything of them. Could anyone introduce it in a layman perspective, maybe via a working example? Introductions like [these][1] would be of great help. 

Sorry if this question is too shallow here, but I really need such introductions becasue I am not a cryptography guy while I need to use this concpet and need to understand basic principles of it. Thank you!





  [1]: https://www.khanacademy.org/computing/computer-science/cryptography/modern-crypt/v/diffie-hellman-key-exchange-part-2