One way to achieve encrypted remote file storage is to combine Linux's EncFS² with some other type of remote storage protocol such as CIFS. The basic idea is to mount a CIFS volume from a server you don't trust with your unencrypted files, then you mount that directory again with EncFS to get to the unencrypted files.

The main drawbacks are that EncFS will not hide your directory structure and file sizes and also that not all of the EncFS vulnerabilities that were discovered in 2014 have been addressed with an EncFS 2.0 release.

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² or one of its similar alternatives of course