Greg Kumparak, writing for TechCrunch:
So if Apple never has your private key, how do messages arrive at all of your devices in a readable form? How do your private key(s) get from one device to the other? Simple answer: they don’t. You’ve actually got one set of keys for each device you add to iCloud, and each iMessage is encrypted independently for each device. So if you have two devices — say, an iPad and an iPhone — each message sent to you is actually encrypted (AES-128) and stored on Apple’s servers twice. Once for each device. When you pull down a message, it’s specifically encrypted for the device you’re on.