Your iMessage may or may not be safe from the prying eyes of the overprotective institutes, but the people you are contacting are not. Every time you write an iMessage, Apple stores the data on people you’re contacting with. Every time you start a message, iMessage contacts Apple in order to determine whether the message will be an SMS or iMessage. When that happens, Apple logs data about every one of your contacts, even those you haven’t contacted yet. The log even includes the exact date and time of when you entered the number. These logs’re being kept by Apple for 30 days, after which they’re removed.
It feels a bit strange to know that, while your own messages are relatively safe, the people you contact with aren’t.