a little bit tangential, but is it known how received imessages are able to be decrypted on multiple devices?

if the sender's message encryption key is encrypted with my iphone's public key, then my iphone's private key is the only key that can recover the the key used for the message.

so then how can desktop imessage also recover the key and decrypt the message? it seems like either: * private keys are shared between devices (doesn't seem good) * imessages are encrypted multiple times based on the number of registered devices the recipient has (plausible?)