Is there a strategy for answering security questions via telephone modestly securely while in an insecure environment? For example: I am at a coffee shop and am locked out of my account, I call the helpdesk to unlock and they ask for my userID, DOB, and last4 of social. I would like to protect all of that information so that no one listening could catch it.
For instance, I imagine a system where the technician says, is the month Jan, I say no, then ask, is it Feb, I say no, then is it Mar, I say yes... and so forth until we confirm all the secrets. This is really the only method I can think of short of a situation where the technician plays a game of 'is this your card'. There are drawbacks to both of these methods and so I'm wondering if there are better ones?
Also is this threat even real and/or is it worth securing against?