AKA, what type of encryption would you trust to store ultra-private information in a public location?

One of my limitations to using a password manager has been the centralization of the DB file. I use several machines with varying OS's. I need to create/change passwords frequently but then have to worry about sync'ing the DB file.

If we put the DB in "the cloud" somewhere we could solve the sync problem. Sure, we could have a user/pass protected service, but I place no trust in the service provided actually keeping this file hidden. So let's treat this information as essentially publically accessible.

Given that it's a central file to all my other accounts, what type of encryption would be suitable to protect it?