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If a group planned ahead they could give out some secondary kind of key. Gmail gives out these really long codes I can use to login should I not have the authenticator app.

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Sorry, I might be missing something here, but would there be any tangible differences between the service provider having access to a secondary key vs them having access to the primary key if both can be used to access your data?

I'm honestly interested because I'm building a distributed system where only the user has the decryption key, and I've always just assumed that password recovery is a lost cause in such systems.

I would assume the recovery key is not stored in plain-text - it's likely hashed, similar to a password. If you need to use it, you enter the (hopefully safely stored) recovery key you have, they re-hash it and compare to the hashed one they keep.

OS X's whole-disk encryption (FileVault 2) similarly creates a recovery key at encrypt-time.

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