NIST 800-57 compatible unattended encryption?

[gnupg at raf.org]

Hi,

Apologies in advance for my profound ignorance on
matters cryptological.

I use an RSA 2048 keypair for encrypting and decrypting
files, not to send to anyone, just for backups.

I'd like to manage my keys according to the
recommendations of NIST SP 800-57. Luckily, I don't
actually have to fully comply with it but I'd like to
get as close as I can (without spending lots of money).

Unfortunately, it seems that NIST SP 800-57 only likes
symmetric algorithms for data encryption and it only
likes asymmetric algorithms for signing and
key-agreement. I think they're expecting quantum computing
armageddon making asymmetric algorithms useless.

For some dumb reason I think I was hoping that the RSA
algorithm wasn't really used to encrypt all the data. I
thought it was probably used to encrypt a per-file
randomly-generated symmetric key which was then used to
encrypt the file (and was encrypted along with the
file) because it could be faster. But I think I'm
confusing it with network protocols like TLS.

Is that what happens with RSA in gpg? [Probably not] If
so, how can I tell which symmetric algorithm is used to
actually encrypt the data or choose that algorithm?

If not, is there a way to make that kind of behaviour
happen with gpg? Apparently, NIST SP 800-56B describes
an approved method of using RSA for key-agreement but
it looks hideous (to the untrained brain) and I'm sure
that it's of no use to me. And key-agreement shouldn't
be necessary, just a cryptographically random per-file
key would probably do as long as the file itself were
encrypted using a symmetric algorithm. Mind you, NIST
800-57 only likes symmetric keys for encrypting other
keys as well so that probably wouldn't be approved
either.

Symmetric encryption isn't really an option for
automated backups as cron can't be expected to enter
a passphrase. The passphrase should only be required
to decrypt the files.

Thanks in advance for any answers or advice, even if
the advice is to give up. :-) I'm not going to stop
doing automatic backups just to satisfy NIST's
recommendations.

cheers,
raf