Duplicity backs directories by producing encrypted tar-format volumes and uploading them to a remote or local file server. Because duplicity uses librsync, the incremental archives are space efficient and only record the parts of files that have changed since the last backup. Because duplicity uses GnuPG to encrypt and/or sign these archives, they will be safe from spying and/or modification by the server.
If you have a low-spec'ed computer (64 to 128 MB of RAM, less than 1 GHz processor), you may have difficulty with a regular Ubuntu installation. You may, even if you have a higher-spec'ed computer want to create a minimal installation for other reasons.