the main question is, after the encrypted message that was encrypted using Alice's public key earlier 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 (e.g., Lecture 17: Re-encryption, the most gentle material I found but still cannot understand...). Could anyone introduce it in a layman perspective, maybe via a working example? Introductions like these would be of great help.

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

Here is the use case: A uses B's public key to encrypt a message and sent it to B. In later stages, a new member C joins and B would like to let C be able to see this encrypted message (i.e., give the decryption ability to C) without sharing his/her private key or letting A encrypt the message again using C's public key. It is in this question. A useful solution in that question is proxy re-encryption. In that case, B will generate a re-encryption key using B's private key and C's public key and send it to a proxy. The proxy will re-encrypt the encrypted message using the re-encryption key and send it to C. Then C can use his/her private key to decrypt the re-encrypted message to get the original one.

The main question is, after the encrypted message that was encrypted using B's public key earlier is re-encrypted using the re-encryption key generated from B's private key and C's public key, how can C use his/her 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 (e.g., Lecture 17: Re-encryption, the most gentle material I found but still cannot understand...). Could anyone introduce it in a layman perspective, maybe via a working example? Introductions like these would be of great help.

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

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 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!

the main question is, after the encrypted message that was encrypted using Alice's public key earlier 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 (e.g., Lecture 17: Re-encryption, the most gentle material I found but still cannot understand...). Could anyone introduce it in a layman perspective, maybe via a working example? Introductions like these would be of great help.

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