Sure LUKS will do what you tell it. Bitlocker will do what it wants and just use the TPM unless you jump through a bunch of group policy edits and such. But you are correct, I had forgotten it does give you the option to backup the key to a txt file during the installation or initial encryption process :)
Nope. As soon as you move the disk to your second system/TPM, you lose any ability to decrypt it at all.
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The key is inside the TPM.
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Sure LUKS will do what you tell it. Bitlocker will do what it wants and just use the TPM unless you jump through a bunch of group policy edits and such. But you are correct, I had forgotten it does give you the option to backup the key to a txt file during the installation or initial encryption process :)