Are iphone conversations secure and private? I was recently asked to verify my ID over the phone.

I do believe that imessage is private...unless you are setting it up for the first time you do not have to give any additional info...so DONT DO IT.

CDMA cellular transmissions are encrypted. I believe the same is true of GSM. While it is certainly within the realm of possibility that someone with enough technology, enough time and enough interest in you and your activiities could conceivably get access to your conversation, they cannot be casually intercepted. I would be far more concerned about information sent over an unsecured WiFi network or by people standing near you and listening or watching you while you were providing sensitive information.

Glad it helped!