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gpg supports using public / private keypairs to encrypt any amount of data you like. I use it for uni-directional backups from machines where trust is an issue.

Or is the reality of this that it's just encrypting a symmetric key with the asymmetric cipher, and then encrypting data using that key?

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Everything is encrypted with a symmetric key. It is just that sometimes there is an asymmetrically encrypted symmetric key packet included in the message so that GPG (or whatever) does not have to ask you for the symmetric key. This is all fairly generic, if you actually have the symmetric key you can use it directly even if a key packet exists. This means that you can give some entity a key to decrypt a particular message/file without revealing your asymmetric secret key associated with your identity.

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