I believe Julian Assange worked on a system that would make it impossible for an external entity to determine if there is any useful information on a data partition. Basically you would have a hard drive full of random numbers and it would be unfeasible to determine if there is any actual information on it, without the right keys and tools.
Its trivial to make a system where the content of the messages can only be read by the recipient. PGP and GPG email is an example of this end-to-end encryption.
The weakness in these schemes is two-fold: the update mechanism for the software (e.g. if its web-based, do you trust the server that serves the page?) and authentication: how do you know that the credentials you have for the recipient are accurate?
Its less trivial to make a system where who-is-corresponding-with-whom is obscured. Onion Routing (e.g. TOR) is in this direction, but there are laborious ways to peel the onion.