Ye cannot defeat root !
The root user can have complete control of the machine. The best that you can hope for is encryption: use GnuPG to encrypt the data with a sufficiently strong random password, that, of course, you won't reveal to the root user.
However, as soon as you decrypt the file on the machine, wherever you put it, root will be able to see it. Similarly, root has all the required power to plant a keylogger (and thus grab your password) or modify the
gpg binary so as to recover a copy of your precious data as soon as you encrypt or decrypt it. The best you can hope for is the following:
You may hope to "fly under the radar" by making your file inconspicuous, not to be detected through some massive scans that the administrator runs regularly. This requires that you delete the decrypted file as soon as possible; this assumes that root activity is indeed a nightly scan or something like that.
On a general basis, this concept is known as steganography.
You could encrypt and decrypt the file elsewhere, e.g. on your own laptop computer, using the machine-with-hostile-root only as storage space. That way, the root will only ever see the encrypted data, and not know the contents.