How can I reassure users that feedback they provide will be anonymous?

I'm a huge proponent of privacy, so within any application, I want to ensure users that they'll be protected. I'm in the early stages of creating an application that will allow patrons of a business / restaurant to submit a review within an iPad/iPhone application as a small piece of a larger system. While I don't plan to have any personal information attached to the feedback, people still seem to be skeptical of providing information on a device that isn't their own, irrespective of the fact that I am not asking for names, phone numbers, etc.

Is there a good way of putting users at ease with regards to anonymity either within the application or via some other means? The system will only work if users feel they can be completely honest. At the same time, I want to keep the experience as minimal as possible, so I'd rather not paste pages of guarantees.