Encrypted cloud storage for backup

I'm looking to use some free cloud storage service to keep backup copies of stuff from my Android tablet. I'm much less interested in sharing documents across devices or Android-to-Windows than I am in simply making sure that I have copies of things.

I also want data to be encrypted before I transmit it, and remain encrypted on the provider's servers. For one thing, I'm paranoid and believe that if I put stuff on Microsoft or Google servers, it will be read and used for targeted advertising.

Any suggestions? Especially from someone who's done something similar? I'm sniffing at Boxcryptor, but it's a paid solution.

Thanks.