I read several papers about user revocation in IBE recently. A common point is that when a user is revoked, some other valid users should also update their private keys. Does this mean that one identity is actually associated with many users? If not, why do other valid users still need to update the keys?
I am also thinking whether the PKG can keep a list of revoked IDs. Then before sending out the message, the sender will check the list. If the ID is revoked, the sender can modify the public key as ID+ a random number. Then the receiver can update the private key according to the new public key. What's the problem with this idea? Does it violate the design philosophy of IBE?