remote access to file store

I have a client who is working with clinical data, and it will be my job to provide statistical analysis of that data as it is generated. We are talking potentially 300GB of data to be analyzed. The issue is that the institution’s legal department prefer the data never leave the premises. Obviously that makes things difficult, and I propose to put local storage in place at their site with secure remote access. I would need to be able to NFS or similar mount this to my server. Ideally data is transmitted encrypted. Any idea how to solve this problem at a REASONABLE cost?