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1) If I am using public key cryptography (like openpgp) and I encrypt a message for a recipient using their public key, can I decrypt that message using my private key in the future?

2) Does a method of asymmetric cryptography exist that allows one to generate public and private key pairs based on a "master" key such that the "master" can always decrypt anything encrypted with the keys generated/computed from it?

The reason I ask these questions is that I am wondering if there exists a cryptographic method whererby a hierarchy of keys can be created such that any private key can be used to generate any number of public/private key pairs and any message encrypted using these keys derived from the "master" can not only be decrypted by the recipient (of course), but also by the "master" keys from which it was derived.

Does something like this currently exist? Any info is appreciated.