Private/Public keypair

Create the private key (one-off):

openssl genrsa -out ~/.ssh/key.pem 2048
chmod 400 ~/.ssh/key.pem

then extract the public key from it:

openssl rsa -in ~/.ssh/key.pem -out ~/.ssh/key.pub -outform PEM -pubout

NOTE The whole mechanism revolves around keeping the secret key key.pem,
well, secret. This is the only critical part of the scheme.

Everything else, can be either public (eg, key.pub) or stored without too
much concern for security (eg, the .enc encrypted files).

Encrypt the archive

You then create the archive any which way you want:

tar cfz maps.tar.gz Documents/maps

To encrypt the archive, create a one-time passphrase:

openssl rand 32 -out pass.bin

this is a binary, but clear-text, file that will be used as the encryption secret:

openssl enc -aes-256-cbc -pass file:pass.bin <maps.tar.gz >maps.tar.gz.ser

Once used, the encryption secret is itself encrypted using the generated keys:

openssl rsautl -encrypt -pubin -inkey key.pub <pass.bin >pass.enc

Now, both the archive and the encryption secret can be stored securely.

Important
After encryption, the encryption secret MUST be securely deleted

shred -uz pass.bin

If necessary, it can be retrieved using the encrypted version and the secret key.

Decryption

If necessary to retrieve the archived data, you must first decrypt the passphrase::

openssl rsautl -decrypt -inkey key.pem <pass.enc >pass.bin

and then use it to decrypt the archive:

openssl enc -aes-256-cbc -d -pass file:pass.bin <maps.tar.gz.ser >maps.tar.gz

The advantage of using (and encrypting) a separate secret is that if, for whatever reason, the secret key is compromised, only the passphrase(s) need to be re-encrypted (using a newly created keypair) while the more expensive-to-process archives can be left alone.

Obviously, keep them separate!
(even though, the passphrase and archives could be, in principle stored alongside).

And, if you are using a different encryption secret for every file (as you should) remember to keep track of which secret encrypts what (a low-tech spreadsheet will do just fine; or you can use a naming convention).

Source: http://askubuntu.com/questions/95920/encrypt-tar-gz-file-on-create