As a layman, I'd intuitively want to try to solve this problem with an adversarial approach, i.e. train an adversary network to predict the info we want hidden better than chance given oracle access to the system we're trying to secure. But as I understand it GANs are currently regarded as flaky because training them requires the two component networks' learning be fairly matched. I wish I had a better understanding of the "competitors"/"successors" to GANs and how they would work on this sort of problem.