You can cheat a little, but it will require assistance from a sysadmin.
Under your home directory, create a new directory owned by root with these permissions:
drwx--x--x 3 root sys 512 Oct 25 07:19 archive
Within that "archive" sub-directory, create the directory you wish to have exclusive access to. Name it something hard to guess (just like a password would be).
# cd archive
# mkdir hicknild
# chown u11111 hicknild
# chmod 755 hicknild
Now there is a directory named /home/u11111/archive/hicknild, but only you (and everybody reading this post) are aware of its existence.
Log in as you normally would and set a variable:
$ SAFE=/home/u11111/archive/hicknild
When you wish to go to that directory, just do this:
$ cd $SAFE
Due to the permissions of the parent directory, only a superuser would be able to even see that subdirectory name.