We know that at some point someone that has a shred(1)ed disk will be told to "decrypt" it or face indefinite detention...
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I wonder if it then makes sense to write 0s as part of a permanent deletion process. No ambiguity about remaining content or intent when you do that.
Quite the reverse - you should always overwrite with random data so you have plausible deniability.
I frequently, but DO NOT ALWAYS, do this when I am erasing hard drives.
When I do this it is more of a flag to remind my self that I have, in fact, finished scrubbing the device.
Using pseudorandom data is pointless. If overwriting with 0s isn't enough you should be physically shredding the drives.