I would say assured in this case. When you assure something, you confirm that it is going to happen. Assuring someone’s privacy is a guarantee of privacy
The word insure means to take out a policy against losses with an underwriter. That is not the meaning that you want here. I think perhaps you have confused insure with ensure.
When you ensure something, you guarantee to make it happen. The difference in pronunciation is subtle but significant. Ensuring someone’s privacy is taking action to make something private.
Take this sentence for example:
“Our system uses secure password management to ensure that your privacy is assured at all times. However, just in case, you should be insured for any loss of data by taking out a Public Liability Policy before using our service.”